Time-resolved Kerr-effect and Spin Dynamics in
Itinerant Ferromagnets
Bert Koopmans
Eindhoven University of Technology, Eindhoven, The Netherlands
1
2
3
4
5
6
7
8
Introduction
Classification and Basics
Experimental Approaches
Pioneering Work on Laser-induced Dynamics
Population Dynamics
Experiments on Orbital Momentum Transfer
Demagnetization Dynamics
Anisotropy Dynamics and Laser-induced
Precession
9 Ultrafast Phasetransitions and Growth of
Magnetism
10 Concluding Remarks
References
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INTRODUCTION
The time-resolved optical exploration of the ultimate limits
of magnetization dynamics in itinerant ferromagnets (FMs)
is widely recognized as an intriguing field of research (for
reviews, see Zhang, Hübner and Bigot, 2002; Koopmans,
2003; Bennemann, 2004). Clearly, it has been driven by the
quest for fundamental understanding of magnetization processes in the strongly nonequilibrium regime – a particularly
nontrivial issue. How to understand the magnetism of materials, when by an almost instantaneous perturbation of the
Handbook of Magnetism and Advanced Magnetic Materials. Edited
by Helmut Kronmüller and Stuart Parkin. Volume 3: Novel Techniques for Characterizing and Preparing Samples.  2007 John
Wiley & Sons, Ltd. ISBN: 978-0-470-02217-7.
material different subsystems, such as electrons and lattice,
are no longer in thermal equilibrium? What are the limiting
timescales at which we can manipulate the magnetic order?
And what are the relevant processes that we need to understand and maybe even can control?
Apart from this fundamental interest, there are two other
obvious drivers that have led to an exciting, rapidly progressing field of research. First of all there is the availability
since the 1990s of commercial and easy-to-handle systems
for producing femtosecond laser pulses, and the development
of ultrasensitive magneto-optical (MO) pump-probe schemes
with unprecedented time resolution.
Secondly, there is the intimate relation of the field with
the booming area of spintronics, and related therewith all
applications that require ultrafast control of magnetic materials and devices. Exemplary is the extremely rapid progress
in magnetic hard disk recording, where the need for subnanosecond control over media and heads has emerged. A
similar driver is provided by the development of magnetic
random access memory (MRAM), for which new magnetic
switching schemes are being considered. More general, the
fundamental exploration of ultrafast magnetization dynamics provides generic insight in elementary spin-scattering
phenomena that are of profound interest for many novel spintronic devices.
Finally, technologies that combine the interaction of laser
light with magnetic materials within the application itself,
such as MO recording, have to be identified as an important
stimulus for laser-based studies of fast magnetic processes.
Of particular interest from this viewpoint are recent activities
striving for laser-based heat-assisted magnetic recording.
In general, pump-probe schemes have been most successful in search for the ultimate timescales. In such a
1590
Magneto-optical techniques
stroboscopic scheme, a first, pulsed perturbation is being
applied to the magnetic system under investigation after
which a second probe pulse, arriving at a preset delay time,
is being used to probe the magnetic state. By scanning the
delay time, the full temporal evolution of the magnet state
after its initial perturbation can be followed. It has to be
emphasized, however, that in general the probe only provides a limited access to the multidimensional character of
the strongly nonequilibrium magnetic state, which makes
interpretation of such experiments an art itself.
It should be stressed that any perturbation that changes
the magnetic ground state will do – although the physics
being probed may (and will) be strongly depending on the
type of excitation chosen. Also, probing the magnetization
dynamics can be achieved by different means; the choice
made again affecting the view on the magnetic system being
obtained. Although a number of approaches will be explained
throughout this chapter, our main focus will be on all-optical
approaches, in which femtosecond laser pulses are used both
as the perturbation and as the probe.
By now it is generally known that pulsed-laser excitation
triggers a rich spectrum of spin dynamical processes. The
field started with pioneering experiments by Beaurepaire,
Merle, Daunois and Bigot (1996), who addressed the truly
nonequlibrium regime of itinerant FMs for the first time. It
was found that laser heating of ferromagnetic thin films gives
rise to a loss of magnetic order within the first picosecond.
This exciting result became soon confirmed by several
groups. By now, a general consensus has been achieved on
a characteristic ‘demagnetization’ timescale of a hundred to
a few hundreds of femtoseconds.
Apart from the ultrafast loss of magnetic order, the experiments provided access to spin-dependent dynamics in the
population of electronic states that could be interpreted as
‘artifacts’ when striving for resolving the genuine magnetization dynamics, but could be seen as a highly challenging
spin-dependent phenomenon on itself as well.
Moreover, in many cases it turned out possible to trigger
precessional dynamics by perturbing the magnetic anisotropy
on a picosecond timescale by the laser heating. On the
one hand, this offered an alternative to pulsed field-induced
precessional experiments, on the other hand, it provided
a complementary view on the dynamics of the magnetic
anisotropy itself. In this respect, a particularly interesting
research topic that emerged is the ultrafast manipulation
of the interlayer exchange coupling between a FM and a
neighboring antiferromagnetic (AF) layer.
Despite the interest in laser-induced loss of magnetic order,
from technological point of view it would be of superior
interest not only to quench, but also being able to increase
or even fully create ferromagnetic order at a subpicosecond
timescale. Also this has been recently achieved in pioneering
experiments in FeRh thin films, by driving the metamagnetic
AF to FM phase transition by pulsed heating.
Today, we have reached the end of the first (extremely
successful) decade of laser-induced magnetization dynamics,
where the field went through a continuous discovery of new
phenomena and development of novel approaches. Theoretical understanding of the processes at a microscopic level
is lagging somewhat behind. However, there is a growing
awareness being witnessed that these issues should be considered among the major challenges of modern condensedmatter physics. It would be welcomed if this opinion would
lead to a significant increase of theoretical efforts.
The scope of this chapter is as follows. In Section 2
we start with a general overview, and introduce basic concepts. In Section 3, experimental approaches, mostly concentrating on all-optical ones, are described in detail. Particular emphasis is on the subtle and nontrivial way the
targeted physical parameters are being probed. Then, a
number of sections reviewing experimental progress over
the past decade can be found. After a brief review of
the pioneering, early days (Section 4), sections on population dynamics (Section 5), light-induced orbital momentum
transfer (Section 6), demagnetization dynamics (Section 7),
anisotropy dynamics induced precession (Section 8), and
growth of magnetic order by triggering phase transitions
(Section 9) will follow. Finally, concluding remarks will be
drawn in Section 10.
2
CLASSIFICATION AND BASICS
Within this section, first the dynamics of the average magnetization vector (orientational or precessional dynamics) and
the thermodynamics of spin systems (dealing with the magnitude of the magnetization) are discussed separately. Then,
after some considerations regarding conservation of angular
momentum, different scattering mechanisms are briefly introduced: electron–electron scattering, electron–phonon scattering, and different types of spin-flip scattering.
2.1
Precessional dynamics
The most elementary spin dynamics process is that of the
precession of a single spin in an applied magnetic field
H . The field introduces a splitting between spin-up and
spin-down states with an energy difference equal to γ µ0 H ,
where γ is the gyromagnetic ratio. As a consequence,
the dynamics of any electron that is in a superposition
of the two eigenstates corresponds to a precession of the
spin expectation value around the field-axis at the Larmor
frequency ωL = γ µ0 H /. The same frequency is found
Time-resolved Kerr-effect and spin dynamics in itinerant ferromagnets 1591
of a
for an ensemble of spins, or the magnetization M
homogeneous magnetic material. Characteristic frequencies
are in the gigahertz regime, as can be estimated from γ / =
176 ns−1 T−1 .
Including dissipation will lead to a damped precessional
motion, in which a gradual decay toward the lowest energy
with the
state is accompanied by the alignment of M
applied magnetic field. Accounting for dissipation in a
phenomenological way in the spirit of Gilbert, leads to
the well-known Landau–Lifshitz–Gilbert (LLG) equation of
motion (Miltat, Albuquerque and Thiaville, 2002)
α
d
M
dM
× Heff +
×
= γ µ0 M
M
(1)
dt
M
dt
where we replaced the applied (external) field H by the
effective field
Heff = H + Hanis = H −
1 ∇Eanis (M)
µ0 M
(2)
Herein, the anisotropy field (Hanis , related to the gradient of
the anisotropy energy Eanis ) may include contributions from
dipolar fields by the system itself (resulting in the ‘shape
anisotropy’), crystalline anisotropy (mediated by spin-orbit
interactions), and others. Note that this effective field depends
on the orientation of the magnetization vector itself, and
thereby becomes explicitly time-dependent even for a constant external field. Finally, equation (1) can be generalized
r , t), in
to a nonhomogeneous magnetization distribution M(
which the exchange interaction between noncollinear spins
has to be included as well.
It should be noted that the process of energy dissipation
is much more complicated than would have been expected
from the appearance of a single damping parameter in
equation (1). In fact, the value of α depends on almost all
details of the (micromagnetic) system; the ‘constant’ being
far more than a materials specific parameter. Exploration
of magnetic damping is an active field of research (see
e.g., Urban, Woltersdorf and Heinrich, 2001; Tserkovnyak,
Brataas and Bauer, 2002; Woltersdorf, Buess and Back, 2005;
Buess, Haug, Scheinfein and Back, 2005; Steiauf and Fähnle,
2005).
2.2
Thermodynamics–transfer of energy
After having treated the dynamics of the average magnetization vector, we consider the thermodynamic evolution
of spin fluctuations. In general, for an ordinary ferromagnetic system, the thermal equilibrium value of the magnetization (Meq ) displays a continuous decrease as a function
of increasing temperature. Above the Curie temperature and
in the absence of a magnetic field, any long-range magnetic
order vanishes. Without loss of generality, one can introduce
a spin temperature Ts , from the one-to-one relation between
Meq and T (Figure 1a); that is, at a spin temperature Ts the
magnetization equals Meq (Ts ) by definition.
Let us next consider a system with interacting lattice
(phonons), electronic (excluding spin) and spin degrees of
freedom. Within the so-called three-temperature (3T) model
(Beaurepaire, Merle, Daunois and Bigot, 1996), each of
the subsystems are assumed to be internally in thermal
equilibrium, and described by their own temperature (Tp , Te ,
and Ts , respectively) and heat capacity (Cp , Ce , and Cs ),
where in general the latter can be functions of Tp , Te and
Ts , respectively. Given any starting set of temperatures, the
evolution of the system is described by a set of three coupled
differential equations:
dTe
= −Gep (Te − Tp ) − Ges (Te − Ts )
(3)
Ce
dt
dTp
= −Gep (Tp − Te ) − Gsp (Tp − Ts )
(4)
Cp
dt
dTs
= −Ges (Ts − Te ) − Gsp (Ts − Tp )
Cs
(5)
dt
The mutual coupling constants, Gep , Ges , and Gsp will
strive to balance out any nonequilibrium between the subsystems by exchange of energy (Figure 1b). In laser-heating
experiments (see next subsection), absorption of photons
leads mostly to electronic excitations, causing a quasiinstantaneous increase of the electron temperature. The successive dynamics has been found to be phenomenologically
describable by equations (3–5), as already noted in the original work by Beaurepaire, Merle, Daunois and Bigot (1996).
Therefore, the model is extremely useful to parameterize
transient experiments, although only limited microscopic
insight is being provided.
As another limitation of this description, the threetemperature model does not properly take care of conserving
the angular momentum J of the total system (Koopmans, 2003; Koopmans, van Kampen and de Jonge, 2003).
Ms
∆T
∆M
Electrons
Lattice
T e, Ce
T p, C p
M eq
T s, C s
TC
(a)
Ts
(b)
Spins
Figure 1. (a) Definition of spin temperature, and representation of a
laser-induced magnetization dynamics experiment, and (b) the three
interacting reservoirs in the three-temperature model.
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Magneto-optical techniques
At present, angular momentum conservation is being considered as an important ingredient of understanding the ultrafast
equilibration process.
2.3
Transfer of angular momentum
At a subpicosecond timescale, it is natural to consider the
interacting reservoirs being isolated from the environment.
For such a closed system, not only the total energy should
be conserved (discussed in Section 2.2), but also the total
e ) moment
angular momentum J. The spin (Se ) and orbital (L
of the electronic system are related to its magnetic moment
e + g Se )
µ
= µB (L
(6)
where g ≈ 2 for the materials considered here. In addition,
these electronic moments are related to the total angular
momentum of the system. When including possible momentum carried by the laser field (photons) and the lattice
(phonons), the total angular momentum reads
phonon + L
photon
e + Se + L
J = L
(7)
Since the Hamiltonian of the entire system conserves J,
a change in magnetization of a closed system can only
be achieved by exchange among the four contributions at
the right-hand side of equation (7). This has interesting
consequences not contained within the three-temperature
model.
As an example, let us consider the exchange of energy
between the electron and the spin reservoir, heating up the
spins (lowering M) by cooling down a hot-electron gas. In
the absence of interactions with the laser field and lattice
e as
this can only be achieved by an exchange of Se and L
mediated by spin-orbit coupling. One has to realize that in the
ground state, the magnetization of ferromagnetic transition
metals is strongly dominated by the spin momentum (i.e.,
µ ≈ gµB S) because of quenching of the orbital momentum
(Ashcroft and Mermin, 1976). Then, for g ≈ 2, transferring
spin momentum to orbital momentum leads to a reduction of
µ by a factor of 2 at most. In particular, it means that this
mechanism cannot lead to a full quenching of M, whereas
a complete loss of magnetic order has been experimentally
observed at high enough fluences (see the discussion on the
full quenching regime in Section 7).
2.4
Laser-induced electron and spin dynamics
This section addresses the different scattering processes as
of relevance after laser excitation.
2.4.1 Photoabsorption and state filling
The interaction of laser pulses with matter primarily
causes electronic excitations. Exploiting light sources in
the (near)visible range, with typically photon energies from
one to several electron volts, causes thereby excited electrons with energies a hundred times the thermal energy at
room temperature. Even if the excitations conserve spin,
is conserved during the excitation, the
and thereby M
redistribution of occupied electronic levels will change the
MO response of the system (Koopmans, van Kampen and
de Jonge, 2003; Oppeneer and Liebsch, 2004). In particular,
excitations made by the pump pulse, will block the same transitions to be made by probe photons, a phenomenon denoted
‘dichroic bleaching’ (Koopmans, van Kampen, Kohlhepp and
de Jonge, 2000b).
After laser excitation, the total energy of the electron
system has increased. Although at this stage the system is
in strong thermal nonequilibrium and thereby a temperature
is not unambiguously defined, the excess energy can be
used to define an electron temperature, Te,E , according
to the equilibrium relation between excess energy and
electron temperature. For a free-electron system with a
constant density of states (DOS) DF one can derive Eex =
1 2
2
6 π DF (kB Te,E ) , where kB is the Boltzmann constant. In
the weak perturbation limit, treating only small changes in
temperature, we thus find:
Te,E =
3
Eex
π 2 DF kB2 Te,E
(8)
Alternatively, we could have defined a temperature according to the slope of the electron distribution function f (E) at
the Fermi energy EF . From the analogy with a thermalized
electron distribution, one can derive
−1
df (E) = − 4kB
dE EF
Te,F
(9)
Note that laser excitation causes an instantaneous increase
of Te,E , while Te,F displays a gradual increase in which
electronic relaxation is involved.
2.4.2 Electron–electron scattering
The lifetime of ‘hot’ carriers is very short. Within a freeelectron metal, phase space arguments can be used to
derive the hot-electron lifetime (Knorren, Bennemann and
Burgermeister, 2000; Bennemann, 2004)
τ ee (E) =
1
Kee (E − EF )2
(10)
Time-resolved Kerr-effect and spin dynamics in itinerant ferromagnets 1593
−1 is
where the electron–electron scattering constant Kee
2
2
typically 30 fs eV for Ag and 3 fs eV for nickel (Knorren,
Bennemann and Burgermeister, 2000). The difference reflects
the larger phase space for scattering provided by the high
DOS of the Ni d-band near EF . Note, however, that for such
metals, with d-states near the Fermi level, equation (10) is
not too accurately fulfilled.
After having started the cascade-like process of e–e
scattering, the electron gas rapidly thermalizes (Groeneveld,
Sprik and Lagendijk, 1995). Different approximations for the
thermalization process lead to an expression of the form
τT =
A
Kee Te2
(11)
with A ∼ 2 K2 eV2 for nickel (van Kampen et al., 2005a).
−1 = 3 fs eV2 leads to a thermalization time τ ≈
Taking Kee
T
300 fs for Ni. Significantly lower estimates (∼100 fs) are
obtained when correcting for deviations from equation (10),
in better agreement with experimental findings (van Kampen
et al., 2005a).
The simplest way of introducing laser excitation into
the 3T-model is by inserting a source term in equation (3)
(Beaurepaire, Merle, Daunois and Bigot, 1996):
Ce
dTe
= −Gep (Te − Tp ) − Ges (Te − Ts ) + P (t)
dt
(12)
where P (t) denotes the power dissipated in the electron system by absorption of photons at time t. This way, however,
the process of electron thermalization is not covered since in
the strict 3T-model the electron system is considered to be
internally in thermal equilibrium from the start (τ T = 0).
Extended models have been introduced to account for the
thermalization by adding an additional bath of nonthermal
electrons (Fann, Storz, Tom and Bokor, 1992; Sun et al.,
1994). The extended 3T model (Koopmans, 2003) is sketched
in Figure 2. Within such a ‘E3T’ model, it is essential to use
Te,F to denote the temperature of thermalized electrons. The
Electrons
Lattice
T e,F
2
T e,F
Tp
∆T (au)
T e,E
(a)
0
(b)
where T1 is the final temperature rise, proportional to the
absorbed laser power in the low-fluence limit. Note that in
equation (14) we dropped the explicit subscript ‘F’, as we
will keep on doing throughout this chapter.
2.4.3 Electron–phonon scattering
Equilibration of electrons with the lattice proceeds via
electron–phonon (e–p) scattering (for a review, see e.g.,
Groeneveld, Sprik and Lagendijk, 1995). The most efficient
process is the deformation potential scattering by longitudinal
acoustic zone-edge phonons (with an energy of the order of
the Debye energy, ωD ) (van Hall, 2001). If one assumes
that the heat capacities Ce and Cp are relatively constant
over the temperature range covered, and neglecting the spin
system for the moment (Cs = 0), equations (3) and (4) can be
solved analytically, resulting in an exponentially converging
temperature with a time constant
τE =
Ce Cp 1
Ce + Cp Gep
(15)
where subscript ‘E’ denotes ‘Energy’ equilibration. Typically, τ E ∼ 0.5 ps for the ferromagnetic transition metals
(van Kampen et al., 2005a).
Incorporating the thermalization process as well, an empirical relation for the electron temperature transient can then
be introduced (van Kampen et al., 2005a):
(16)
1
Ts
Spins
(13)
which vanishes after thermal equilibrium has been established, Te,E = Te,F . The temporal evolution of the Fermi temperature is often approximated by an empirical relation:
−t
(14)
Te = T1 1 − exp
τT
+T2 [1 − exp(−t/τ E )]
Ts
Tp
Laser
Enonthermal = Ce (Te,E − Te,F )
Te = T1 [1 − exp(−t/τ T )] exp(−t/τ E )
T e,F
‘Hot’
total energy stored in the system of nonthermal electrons is
then
0
1
2 3
t / τE
4
Figure 2. Extended three-temperature model: (a) The four reservoirs, including nonthermalized ‘hot’ electrons excited by the laser
pulse. (b) Schematic transient of the four temperatures, discussed
in the text, for a case where τ T = 0.2τ E and τ M = 0.5τ E .
where T2 is the final temperature to which Te and Tp converge, and T1 ≥ T2 . It is easy to show that T1 /T2 =
1 + Cp /Ce . In the limit τ T τ E , Te approaches T1 for
times τ T t τ E , and thereby a clear ‘overshoot’ of Te is
being witnessed.
The simplest microscopic approach, on equal footing with
the derivation of the free-electron lifetime (10), is obtained
by using a simple Einstein model with identical harmonic
oscillators representing the phonon system. Matrix elements
1594
Magneto-optical techniques
for e–e and e–p scattering (λee and λep , respectively) can
then be assigned to the scattering processes, represented
in Figure 3. Alternatively, scattering probabilities Kee ∝ λ2ee
(cf. (10)) and Kep ∝ λ2ep entering the Boltzmann equations
describing the dynamics of the system, can be introduced.
It can be derived that for Te and Tp well above TD the
phenomenological coupling constant Gep of the 3T-model is
independent of temperature, and related to the microscopic
parameter Kep according to (Hohlfeld, 1998)
Gep = Kep Ep kB
(17)
Using the Born–Oppenheimer approximation for the deformation potential scattering, and equations (15) and (17),
yields τ E of the order of 1 ps, in reasonable agreement with
experiment (van Kampen et al., 2005a).
2.4.4 Spin scattering
Often, it is of relevance to assign a characteristic timescale
τ M to an experimentally obtained MO transient – independent of the microscopic interpretation. Although the full 3Tmodel can be used for that purpose, here we limit ourselves
to a simple approximation that can be treated analytically.
We use the following assumptions: (i) the spin specific heat
is neglected, (ii) Ce and Cp are considered constant, which
can be achieved at low enough fluence, (iii) we assume that
the spin dynamics is merely controlled by Tp and Te,E (and
not Te,F ), according to:
(Te,E − Ts ) (Tp − Ts )
dTs
=
+
dt
τ M,e
τ M,p
(18)
We note that the last assumption lacks a strict, physical motivation, though it is in line with the description of the energy
flow in the 2T- and 3T-model. Moreover, it makes sense
that the highly excited (nonthermal) electrons have a significant influence on the spin relaxation, as would not be
the case if equation (18) were described in terms of Te,F .
Finally, we use the electron and phonon temperature transients: Te,E (t) = T2 + (T1 − T2 ) exp(−t/τ E ) and Tp (t) =
e
(a) e
e
eσ
e
p
Impurity
or
aλii
(b)
e
e
e −σ
e −σ
p +1
aλep
eσ
p
+
λep
λee
e −σ
(c)
e
e
p −1
+
eσ
Figure 3. Feynmann diagrams for (a) e–e scattering, (b) e–p
scattering, and (c) e–p scattering accompanied with spin flip.
T2 (1 − exp(−t/τ E )), in agreement with equation (16). Then,
we find as a general solution:
Ts (t) = T2 +
+
(τ E T1 − τ M T2 ) exp(−t/τ M )
τE − τM
τ E (T2 − T1 ) exp(−t/τ E )
τE − τM
(19)
−1
−1
with τ −1
M = τ M,e + τ M,p , and T1 = T1 τ M /τ M,e . An ‘overshoot’ of Ts is achieved in the case that the e–s channel
dominates over the s–p channel, that is τ M,e τ M,p , unless
τ M τ E , all as expected.
The result shows that an overall τ M (including both contributions via the s–p and s–e channel) can be fitted, without
prior knowledge of which of the two channels dominates,
and without needing information from transient reflection. If
the latter is available, and thereby T1 , the ratio of the fitted
T1 /T1 can be used to extract τ M,e and τ M,p separately.
Often, in literature, an even more empirical fitting function
is being used that can be described generally as:
−t
Ts (t) = 1 − exp
Te (t)
(20)
τM
It should be emphasized that although the shape of the
resulting profile Ts (t) can be quite similar to the one produced
by (19), the extracted value of τ M can be off by a factor two!
Examples thereof are discussed in Sections 6 and 7.
As to the microscopic origin of the laser-induced demagnetization, quite a number of spin-scattering processes have
to be considered. We discuss them in the context of conservation of J . First, the hot-electron lifetime can be spin
dependent (Aeschlimann et al., 1997; Knorren, Bennemann
and Burgermeister, 2000; Bennemann, 2004). Experiments
using two-photon photoemission (TPPE) have indeed found
significant differences between majority and minority carriers for the ferromagnetic transition metals Co, Fe, and
Ni (Aeschlimann et al., 1997). The results have been interpreted in terms of the huge difference of phase space for
scattering majority and minority carries within the spin-split
DOS of these materials. Relevant timescales are in the lowfemtosecond regime. It should be emphasized, however, that
the spin-dependent lifetime has no relation to a change in
magnetic moment of the system.
Secondly, spin scattering by redistribution of angular
momentum within the electron system is considered. It
has been argued that hot electrons will have high enough
energy to overcome the Stoner gap (Scholl, Baumgarten,
Jacquemin and Eberhardt, 1997), and thereby create Stoner
excitations–changes of the local spin moment. These spin
flips would be accompanied by emission (or absorption) of
magnons (spin waves). However, also this process does not
provide a net change of the magnetic moment of the system.
Time-resolved Kerr-effect and spin dynamics in itinerant ferromagnets 1595
An other purely electronic process to be considered is
transfer from spin to orbital momentum as mediated by spinorbit coupling. From the typical energy scale exc ∼ 0.1 eV
fast time scales /exc ∼ 10 fs could be anticipated indeed.
In Section 2.3, however, we already derived that, unlike
experimental observations, this mechanism cannot account
for a full quenching of M while conserving J . Moreover,
the final state would be characterized by a large orbital
momentum. Using arguments to be introduced in Section 3.2,
this should lead to an increase rather than a decrease of MO
signals upon laser heating, again contrary to experimental
observations.
Thirdly, transfer of energy between the lattice and spin
system can occur (Koopmans, Kicken, van Kampen and
de Jonge, 2005; Koopmans, Ruigrok, Dalla Longa and
de Jonge, 2005). This can be considered as ordinary spinorbit mediated spin-lattice relaxation (Yafet, 1963). Angular
momentum is being transferred from the spin to the lattice, by absorption or emission of phonons carrying orbital
momentum. On a macroscopic scale, this transfer is being
witnessed as a finite rotation of a magnetic bar upon changing its magnetic moment, as in the classical De Haas and
Einstein experiment (Scott, 1962). For nonmagnetic metals
spin-lattice scattering has been well addressed, and described
by Eliot–Yafet type of scattering (Yafet, 1963). A finite probability a is assigned for an electron to flip its spin upon
momentum scattering with phonons or impurities. This process is schematically represented in Figure 3(c). Although
values of a have been tabulated before for some nonmagnetic metals (Beuneu and Monod, 1978), little is known about
implications for ferromagnetic transition metals. In passing
we not that, in principle, a similar factor a can also be related
to the spin diffusion length (lsf ), used to describe magneto
transport in, for example, current-perpendicular to the plane
giant magnetoresistance (GMR) pillars (Dubois et al., 2006).
However, a comparison between the spin-flip probability in
the transport regime and the strongly nonequilibrium laserheating case is far from trivial – and has not been discussed
in literature yet. Therefore, in the present review, we will
refrain from such a detailed analysis.
Finally, scenarios including the laser field itself or hybrid
mechanism have been proposed, but all have their intrinsic
complications. At this stage, the reader may wonder what
is causing the demagnetization after all. Although a full
understanding has not been achieved yet, a more quantitative
discussion of the present insights is discussed in Sections 6
and 7.
3
EXPERIMENTAL APPROACHES
Over the past decade a number of techniques have been
developed that give access to the dynamics of spin systems
down to femtosecond timescales. Most of them rely on the
use of subpicosecond laser pulses. This section provides a
detailed description of the relation between magneto-optics
and spin dynamics, and discusses different experimental
approaches.
3.1
Excitation sources
In order to access subpicosecond magnetization dynamics, extremely short rise time or pulse-lengths should be
exploited. From conceptual point of view, magnetization
dynamics is triggered in the most straightforward way by
short magnetic field pulses. Conventional approaches using
electronic pulse generators are limited to a rise time of several tens of picoseconds at least, even when taking utmost
care to feed pulses into- and guide them through microscopic
strip lines (Elezzabi and Freeman, 1996; Elezzabi, Freeman and Johnson, 1996; Hiebert, Stankiewicz and Freeman,
1997). An exciting alternative has been provided by using
picosecond electron bunches from a linear accelerator (Siegmann et al., 1995) Experiments so far (Back et al., 1998,
1999; Tudosa et al., 2004; Stamm et al., 2005) have been
restricted to static microscopic characterization after single
pulse excitation. Time-domain extrapolations of the technique could be imaginable, although stroboscopic approaches
are very unlikely. In passing, we also stress the importance of spin-torque induced switching, which recently has
been observed spatio-temporally resolved by ultrafast x-ray
microscopy (Acremann et al., 2006).
Hybrid schemes, using femtosecond optical pulses to
produce picosecond rise time magnetic field pulses have been
demonstrated in a multitude of configurations. The standard
approach employs a photoconductive switch to launch an
electrical pulse into a strip line. Typically, around picosecond
rise times and – when desired – tunable duration can be
produced (e.g., Gerrits et al., 2002). An alternative, in which
switch and sample are integrated, is the use of laser pulses
to trigger breakthrough of a Schottky barrier that supports a
thin-film FM sample (Woltersdorf, Buess and Back, 2005).
Integrating pulse generator and sample even further is
established in all-optical configurations. In order to study
precessional dynamics similar to the field-induced cases,
a configuration can be employed in which an internal
anisotropy field pulse is being generated by pulsed-laser
heating of a magnetic thin-film system (van Kampen et al.,
2002). We stress that this approach has been demonstrated
to be widely applicable. However, it cannot be applied in,
for example, magnetic configurations in which the applied
and effective field are both along a symmetry axis of the
sample. Further details will be discussed in Section 8. The
next section will focus on thermodynamic processes triggered
by the laser heating.
1596
3.2
Magneto-optical techniques
Ultrafast probes and time-resolved
magneto-Optics
A number of femtosecond laser-based approaches to probe
the subpicosecond magnetization dynamics have been developed. Detecting photoemitted electrons has been exploited in
different schemes: spin-polarized time-resolved photoemission (SP-TRPE) (Scholl, Baumgarten, Jacquemin and Eberhardt, 1997), time-resolved photoemission (TRPE) probing
the evolution of the exchange splitting (Rhie, Dürr and Eberhardt, 2003, 2005; Lisowski et al., 2005), or probing the
spin dynamics via the image-potential states at FM surfaces
(Schmidt et al., 2005). With the advance of new generations
of synchrotrons, X-ray magnetic circular dichroism – with
the unique potential of probing spin and orbital momenta
separately – is expected to play an important role in the near
future. Within the present chapter, though, we concentrate on
all-optical approaches.
The latter are based on the MO-Kerr effect. The key
link between the magnetic state of a material and the
MO response is provided via the dielectric tensor. As
an instructive case, for an optically isotropic material,
magnetized along ẑ, the dielectric tensor reads:

xx
=  − xy
0
↔
xy
xx
0

0
0 
xx
(21)
Note that εxy transforms antisymmetrically under reversal
↔ −M,
providing the ‘magnetic
of the magnetization, M
contrast’.
Thus, polarized light experiences a rotation upon transmission (Faraday effect) or reflection (Kerr effect) from a
magnetic medium. The resulting complex MO rotation is
written as θ̃ = θ + i, where θ and are the induced MO
rotation and ellipticity, respectively. The relation between
can be written as (Koopmans, 2003)
MO rotation and M
θ̃ = F̃ M
(22)
where a generalized Fresnel coefficient F̃ has been introduced that involves all details of the experimental configuration and sample layout. We restricted ourselves to the
simplified case where θ̃ depends on the magnitude (or a sin only, and refer to (Koopmans, 2003)
gle component) of M
for the general case.
Measuring θ̃ in a time-resolved experiment, one should be
aware of the possibility that the perturbation does not only
but also the generalized Fresnel coefficient F̃ .
modify M,
This can significantly hinder a simple interpretation solely in
terms of M
Another, even more subtle complication arises because
MO experiments are only possible by the sake of spinorbit coupling, through which the spatial degree of freedom
(electric field) is correlated with the spin degree of freedom
(magnetic ordering). In fact, it can be stated that optics
is merely capable of measuring the orbital moments in a
is possible only
material, whereas a prediction about M
to orbital
after assuming a certain fixed ratio of spin (S)
(L) momenta. This ratio is not a priori conserved upon
a
perturbation of the material. As to the dependency on L,
sum-rule has been derived that links the frequency integrated
absorptive past of the off-diagonal element of the dielectric
tensor to a part of the orbital momentum (Oppeneer, 1998).
we will
Rather than writing equation (22) in terms of L,
include those potential deviations within the explicit time
dependence of F̃ .
In the further analysis we assume the weak perturbation
regime, in which changes of the Kerr rotation are relatively
small. In that case, the relation θ (t) = F (t)M(t) can be
linearized (Koopmans, 2003):
θ(t) = M0 F (t) + F0 M(t)
(23)
where index ‘0’ denotes unperturbed values (at t < 0) and
indicates pump-induced values. From equation (23) it is
easily seen that, whenever F (t) = F0 independent of t, the
relation
θ (t)
(t)
M(t)
=
=
(24)
θ0
0
M0
is fulfilled, that is, the normalized transient rotation and
ellipticity should be equivalent. Therefore, any deviation
from equation (24) demonstrates the presence of an explicit
t-dependence of F . A similar identification of ‘optical
artifacts’ can be based on a spectroscopic analyses. Whenever
optical artifacts play a role, one may expect the normalized
MO transients to depend on the probing frequency ω. If not,
the relation
(ω2 , t)
M(t)
θ (ω1 , t)
=
=
θ 0 (ω1 )
0 (ω2 )
M0
(25)
holds for any set of frequencies (ω1 , ω2 ).
Complementary to measuring the linear optical response,
higher order optical signals can be monitored to acquire
information on the magnetization dynamics. A well-known
example is provided by magnetization-induced optical second-harmonic generation (MSHG) (See also Magnetizationinduced Second Harmonic Generation, Volume 3). Also
there, the aim is to extract information on those tensor ele Well-known
ments that transform odd under reversal of M.
advantages of MSHG are its interface sensitivity (Pan, Wei
and Shen, 1989; Hübner and Bennemann, 1989; Shen, 1989)
Time-resolved Kerr-effect and spin dynamics in itinerant ferromagnets 1597
and the huge nonlinear Kerr angles that can be achieved
(Koopmans, Groot Koerkamp, Rasing and van den Berg,
1995). Disadvantages are the small signals, down to the photon counting regime, and an even less-trivial interpretation.
In principle, the analysis in terms of a generalized Fresnel
factor F̃ can be extended to the nonlinear case, leading to
similar explicit time-dependencies that affect magnetization
dynamics studies in the same way as in its linear counterpart
(Regensburger, Vollmer and Kirschner, 2000).
3.3
Implementations
The simplest realization of an all-optical time-resolved
magneto-optical Kerr effect (TRMOKE) experiment in a
crossed-polarizer configuration is sketched in Figure 4.
Pump and probe pulses are focused to overlapping spots on
the sample. The pump pulses pass a mechanical delay line
to adjust the time delay. The influence of the pump beam
on the polarization state of the reflected probe pulse is measured using an analyzer at an angle α A and any type of
photodetector. Either a measurement of θ̃(t) with and without pump pulses is performed, or, to enhance the sensitivity,
a mechanical chopper is placed in the pump beam, and a
lock-in amplifier is used to directly measure θ̃(t).
It can easily be derived that the pump-induced change in
output signal is described in lowest order of θ̃ and α A by
(Koopmans, 2003)
I (t) = 2R0 α A θ (t) + α 2A R(t)
(26)
where R0 and R(t) are the reflectivity and pump-induced
transient thereof. Within the basic implementation, no sensitivity on ellipticity is achieved, and care has to be taken
to rule out artificial signals due to a R(t) of nonmagnetic
origin. Bigot et al. argued that part of the drawbacks of the
crossed-polarizer approach are avoided by performing measurements at a multitude of analyzer angles (Bigot, Guidoni,
Beaurepaire and Saeta, 2004).
Pump
Sample
Delay
line
(a)
ep
P
Probe
aA
∆t
aP
A
ε (∆t )
es
TRMOKE
θ (∆t )
(b)
Figure 4. Schematic illustration of a TRMOKE setup. (a) In the
crossed-polarizer experiment, a polarizer is inserted at ‘P’ and an
‘analyzer’ almost crossed at ‘A’. (b) Definition of the polarization
vectors es and ep .
A particularly attractive, alternative scheme is provided by
replacing the analyzer by a polarizing beam splitter, using a
pair of balanced photodiodes and generating the difference
signal by a differential amplifier (Ju et al., 1998b). Thereby,
a highly sensitive measure of the MO transient is achieved.
When working exactly at the balanced configuration, a
dependency on R(t) can be avoided (Koopmans, 2003):
I (t) = 2R0 θ (t)
(27)
When required, a sensitivity to the complementary ellipticity
channel is obtained by using a quarter-wave plate, an option
also available for the crossed-polarizer configuration.
A final scheme is achieved by exploiting polarization
modulation using, for example, a photoelastic modulator
(PEM) placed before the sample (Koopmans, van Kampen,
Kohlhepp and de Jonge, 2000a). Then, the detected signal
displays oscillating signals Inf at harmonics nf of the PEM
frequency f . A number of configurations has been reported,
some of them solely depending on θ̃(t), others also on R
(Koopmans, 2003). As an example, having the main axis of
the PEM parallel or perpendicular to the plane of incidence,
one obtains to a fair approximation (Koopmans, van Kampen,
Kohlhepp and de Jonge, 2000a; Koopmans, 2003):
I1F (t)
= 2J1 (A0 )ε(t)
I0f
(28)
I2F (t)
= 2J2 (A0 )θ(t)
I0f
(29)
where Jn (A0 ) is the nth order Bessel function at the
retardation A0 of the PEM. It is obtained that the 1f signal is proportional to the transient ellipticity, whereas
the 2f -signal corresponds to rotation. Thus, the approach
is highly applicable when identifying optical artifacts (cf.
equation (24)).
Aiming at a full deconvolution of transient dielectric
tensor elements of the magnetic materials, rather than just
the transient (MO) reflection, a combination of experiments
is required. Combining rotation and ellipticity, both in
the magnetic and nonmagnetic channel, and/or combining
rotation (Kerr) and transmission (Faraday) measurements,
have been reported. Examples of such a transient MO
ellipsometry can be found in (Guidoni, Beaurepaire and
Bigot, 2002). When further striving for parallel detection of
a broad spectral range, the simplest configuration, that of the
crossed-polarizer, is most appropriate. Bigot introduced such
a method of femtosecond spectrotemporal magneto-optics,
in which spectrally broadened probe pulses (480–750 nm)
were used, and the Kerr and Faraday rotation spectra where
measured at a multitude of analyzer angles (Bigot, Guidoni,
Beaurepaire and Saeta, 2004).
1598
Magneto-optical techniques
In the analysis so far, cases were treated where only the
magnitude M(t), or one of its vector components, Mi (t),
was of relevance. Vectorial schemes, to measure three com
ponents of M(t),
using a high-aperture microscope objective and four-quadrant detection are widespread by now (for
details, see Freeman and Hiebert, 2002). While so far being
restricted to studies of magnetic field-induced dynamics, very
recently, an extension to all-optical investigations down to
the femtosecond regime has been reported (Vomir et al.,
2005).
It has been discussed that dichroic bleaching can hinder a
proper view on the ultrafast demagnetization process during
the first hundreds of femtoseconds. Attempts to establish a
full separation of F (t) and M(t) have been reported
by van Kampen et al. In particular, they suggested to
measure the MO transients at different ambient temperatures
to establish this separation (Koopmans, van Kampen and
de Jonge, 2003; van Kampen, 2003). The key approach is
as follows. We start by writing the normalized M(t) in terms
of a spin temperature Ts (t),
θ(t)
F (t)
1 dM0
=
+
Ts (t)
θ0
F0
M0 dT0
(30)
We now consider transient experiments at two ambient
temperatures (T0,1 and T0,2 ) and denote thermal differences
by δ. As an important approximation, we assume that the
state-filling effects are relatively independent of temperature,
that is, δF (t) ≈ 0 and δF0 ≈ 0, since broadening the
Fermi-profile by a few millielectron volts hardly changes the
hot-electron (> eV) behavior. Then we obtain:
1 dM0
1 dM0
θ (t)
=δ
Ts (t) +
δTs (t)
δ
θ0
M0 dT0
M0 dT0
(31)
Note that |M0−1 dM0 /dT0 | is strongly T -dependent. In fact,
it diverges while approaching TC , providing further support
for the neglect of the term δ(F (t)/F0 ) in equation (30).
In order to proceed, we make a second approximation:
the evolution of the spin temperature is independent of the
starting temperature of the experiment, that is, δTs (t) = 0.
Within the 3T-model, for example, this is fulfilled if Ce , Cp ,
and Gep are T -independent, and Cs can be neglected. Then,
the spin dynamics can be derived from
Ts (t) ≈
δ (θ(t)/θ 0 )
0
δ M0−1 ddM
T
(32)
0
where the numerator is experimentally measured, and the
denominator is obtained from the materials specific M(T ).
Preliminary results of this thermal difference scheme have
been recently reported by our group (Koopmans, van Kampen and de Jonge, 2003; van Kampen, 2003).
As a final more sophisticated approach, one might want
to perform a ‘thermal difference scheme’ but drop the
approximation of constant Ce and Cp . Such an approach
has been outlined in Koopmans (2004). While potentially an
interesting route for future studies, we refrain from a detailed
discussion in the present review.
4
PIONEERING WORK ON
LASER-INDUCED DYNAMICS
Early attempts on estimating timescales with laser-induced
magnetization dynamics were by Agranat and coworkers in
the mid-1980s (Agranat, Ashikov, Granovskii and Rukman,
1984, 1986). The demagnetization of transition metal thin
films was studied by measuring the remnant MO contrast
with a dc probing laser after pulsed-laser heating with pulses
of different duration. It was concluded that the spin relaxation
time in the FM lies in the interval 1ns < τ M < 40ns.
First real-time experiments were performed using SPTRPE in the beginning of the 1990’s (Vaterlaus, Beutler
and Meier, 1991; Vaterlaus et al., 1992). Detailed experiments were conducted on the rare-earth FM gadolinium
(Gd), yielding τ M = 100 ± 80 ps, and iron. The accuracy
in those experiments was limited, however, by the relatively long duration of the heating pulses (∼10 ns). Nevertheless, the experimentally determined relaxation time τ M
was found to be in good agreement with theoretical estimates
based on spin-lattice relaxation by Hübner and Bennemann
(1996). Therefore, around 1995, it was concluded that the
demagnetization upon laser heating is dominated by spinlattice relaxation, and proceeds at a typical timescale of
τ M ∼ 0.1–1 ns.
In view of the previous context, a surprising result was
obtained in 1996 by Beaurepaire, Merle, Daunois and Bigot
(1996). They reported on a combined TRMOKE and transient
reflection study. The spin temperature, as extracted from
TRMOKE, was found to display a maximum around 2
ps, while the initial decay rate was a few tenths of a
picosecond only, suggesting τ M < 0.5 ps (Figure 5). The
complete behavior was shown to be described adequately
by a 3T-model (equations (12), (4), and (5)). A complete
dominance of the spin-electron coupling over the spin-lattice
coupling needed to be assumed.
The experimental finding of an ultrafast (τ M < 500 fs) spin
relaxation was confirmed soon thereafter by several groups.
Hohlfeld et al. exploited time-resolved SHG (Section 3.2) to
study Te (t) and Ts (t) in bulk polycrystalline nickel (Hohlfeld,
Matthias, Knorren and Bennemann, 1997). In contrast with
the work of Beaurepaire, it was found that already after 300
fs the magnetization is governed by the electron temperature,
Time-resolved Kerr-effect and spin dynamics in itinerant ferromagnets 1599
1
MSHG contrast (%)
MO contrast
0.8
0.7
0.6
0.5
90
80
70
0
(a)
Laser profile
100
0.9
5
10
Delay (ps)
−100
15
(b)
−50
0
50
100
150
Delay (fs)
Figure 5. (a) Pioneering experiments by Beaurepaire, showing the loss of MO contrast of a nickel thin film within 1 ps after laser excitation.
(Reproduced from Beaurepaire et al., 1996, with permission from the American Physical Society.  1996.) (b) Similar data by Güdde and
Hohlfeld, using MSHG, and showing a quasi-instantaneous demagnetization. (Reproduced from J. Güdde et al., 1999, with permission from
the American Physical Society.  1999.)
that is, Ts (t) = Te (t), even before electrons and lattice have
mutually thermalized, that is, τ M < τ E . For even smaller
delay times, t < τ T , at which the electron thermalization has
not set in yet, a break down of the classical magnetization
behavior was found. On the basis of this, one could conclude
that τ M ≈ τ T .
In later experiments, using shorter pulses, even a quasiinstantaneous break down of the MO contrast was found
(Güdde et al., 1999; Hohlfeld et al., 1999); τ M ≈ 0 τ T .
Within the experimental resolution, the loss of ‘magnetic
order’ was described by the time integral of the absorbed
pump power, that is, the absorbed energy was seen to be
converted directly to the spin system. Other experiments
showed a 100% quenching of M, when using high enough
fluence and films with a reduced TC (Güdde et al., 1999;
Conrad, Güdde, Jähnke and Matthias, 1999). A similar
FM→PM transition was demonstrated in more detail for
CoPt3 by Beaurepaire et al. (1998).
An alternative confirmation for an ultrafast subpicosecond
loss of magnetic order in Ni thin films (τ M = 300 fs) came
from TRPE by Scholl, Baumgarten, Jacquemin and Eberhardt
(1997). In contrast with previous work, a second, slower
transition of hundreds of picoseconds was reported. The two
timescales were assigned to Stoner excitations and ordinary
spin-lattice relaxation, respectively. However, such a second
process has never been reproduced, despite specific search
for it (Hohlfeld, 1998; Hohlfeld et al., 1999).
On the basis of these first experiments it was concluded
that the loss of MO contrast is extremely fast, at least
within a few hundred femtoseconds, that is, well before
the electron and lattice system are mutually equilibrated;
(τ M < τ E ). Speculations were around on a demagnetization
directly linked to electron thermalizaton (τ M ≈ τ T ), or even
being quasi instantaneous (τ M τ T ), meaning that M(t) =
Meq (Te,E (t)). Particularly the last claim triggered some
concerns as to the simple interpretation of the data, and a
potential role of ‘optical artifacts’. Such optical effects will
be addressed in the next two sections. After that, we will
return to the genuine demagnetization process in more detail.
5 POPULATION DYNAMICS
Around the year 2000, a number of groups started to question
the simple interpretation of the TRMOKE experiments that
seemed to indicate an almost instantaneous demagnetization.
Doubting a direct proportionality between MO signal and M
is equivalent to considering a potential explicit time dependence of the effective Fresnel coefficient F̃ in equation (22).
First experimental evidence that this was indeed the case
came from Koopmans, van Kampen, Kohlhepp and de Jonge
(2000a,b), who measured the rotation and ellipticity separately in a TRMOKE experiment on (epitaxial) nickel thin
films (Figure 6a). It was found that during the first hundreds
of femtoseconds after laser excitation, a profound difference
between the two normalized channels arose: ε(t)/ε 0 =
θ (t)/θ 0 . Those experiments provided unambiguous proof
that, at least in some cases, the MO transient after pulsedlaser heating does not reflect the genuine magnetization
dynamics. Effects were attributed to ‘dichroic bleaching’, or
state blocking effects, as introduced in Section 2.4.1.
Similar conclusions were drawn from MSHG experiments
on Ni(110) single crystals by Regensburger, Vollmer and
Kirschner (2000). MSHG experiments can be performed in
several configurations, selecting different (combinations of)
second-harmonic susceptibility tensor elements. In one of the
configurations, the authors observed a reversal of the MO
contrast when pumping at high enough laser fluence, whereas
it was carefully excluded to be related to a true magnetization
reversal. It was concluded, again, that the fast initial drop
of the MO signal cannot be unambiguously attributed to an
ultrafast demagnetization.
Magneto-optical techniques
Relative MO contrast
1600
(a)
−0
0
−0.1
−0.01
1
0
2
Delay (ps)
0
(b)
0.1
Delay (ps)
∆escal
K
∆q scal
K
0.1
0
−0.1
f exc = 0.01
fexc =p 0.02
0
(c)
2
4 0
2
4
Photon energy (eV)
Figure 6. (a) TRMOKE ellipticity and rotation for nickel thin film.
(After Koopmans, 2000b.) (b) Complementary channels for CoPt3 .
(After Guidoni, 2000.) (c) Calculated dichroic bleaching for same
excitation density as (a); the laser frequency corresponds to the
vertical dashed line. (Reproduced from Oppeneer et al., 2004, with
permission from IOP Publishing Ltd.  2004.)
By now, a clear consensus on the explicit time dependence
of F̃ has been achieved. However, it has been found also that
the relative importance of such ‘optical artifacts’, as well as
the timescale over which they contribute, depends strongly
on sample layout and experimental settings. Comin reported
results for 50-nm cobalt thin films, observing the strongest
differences persisting for a few hundred femtoseconds, very
similar to the original nickel work (Comin et al., 2004). Pronounced differences in the transients of different MSHG
tensor elements of nickel and permalloy thin films were
reported by Melnikov, Güdde and Matthias (2002). Beaurepaire performed detailed experiments on CoPt3 (Guidoni,
Beaurepaire and Bigot, 2002). It was again found that during
electron thermalization (t < τ T ) a difference between the real
and imaginary signal exists, however, full overlap was found
after thermalization was established (Figure 6b). Finally, van
Kampen carefully controlled the ‘chirp’ (i.e., the time lag
between high- and low-frequency components) of the laser
pulses to investigate the optical artifacts (van Kampen, 2003;
Koopmans, van Kampen and de Jonge, 2003). The MO trace
depended on the chirp indeed, in a way that was fully consistent with expectations from simple models. This served as
additional proof for the absence of a direct relation between
θ̃ (t) and M(t).
Differences persisting for much longer times, up to several
tens of picosecond, were observed both by van Kampen
on Cu(001)/Ni (Koopmans, van Kampen, Kohlhepp and
de Jonge, 2000b; van Kampen, 2003), and by Kampfrath on
iron thin films (Kampfrath et al., 2002). In this context, it also
noteworthy mentioning similar results for manganites (more
specifically PCMO and LCMO) by McGill et al. (2004). In
that case, artifacts playing a role for nanoseconds could be
attributed to contrasting carrier dynamics.
In general, it has been argued that the strongest deviations
would occur in cases where either of the two signals strongly
dominates the static MO response, that is, cases where
θ 0 0 or vice versa. In such a case even small changes
in the minor channel (e.g., θ(t)) would yield huge effects
in the normalized signal (θ(t)/θ 0 ). In MO spectra such
cases would occur near zero crossings of θ (ω) or (ω), with
obvious divergences at the zero crossings themselves.
In cases where θ 0 and 0 are of similar magnitude,
smaller differences – or even no measurable difference at
all – have been reported. Identical traces have been observed,
for instance, for nickel films on silicon wafers (Wilks,
Hughes and Hicken, 2002) (although subtle differences were
reported in Wilks et al., 2004), and Si/Si3 N4 /Ni films (van
Kampen, 2003). Moreover, Bigot used femtosecond spectroscopy with supercontinuum pulses (spectrum spreading
from 480 nm to 750 nm) to demonstrate that for CoPt3 films
the identity θ (t)/θ 0 = (t)/ 0 ) holds for the whole spectral range measured (Bigot, Guidoni, Beaurepaire and Saeta,
2004), although the temporal resolution was somewhat lower
(≥200 fs) in this experiment.
Altogether, lots of evidence has been gathered for optical artifacts. The few reports on long lasting effects are
not fully understood yet. In contrast, dichroic bleaching
during the thermalization phase of the electronic system
after optical excitation has been interpreted in a quantitative way. In a naive picture, one would expect the relative
change of the MO response θ/θ 0 to be of the order of
the excitation density fexc , defined as the number of optically excited electrons per atom. Such a behavior can easily
be derived for an ensemble of two-level systems. However,
effects for dichroic bleaching as reported in the original
work (Koopmans, van Kampen, Kohlhepp and de Jonge,
2000b) were as high as θ /θ 0 ∼ 0.1 for laser fluences
corresponding to fexc = 0.01. It was conjectured that such
an effect could be understood by the fact that because
of momentum conservation during optical excitations, the
transitions are concentrated in specific parts of the Brillouin zone. As a result, the few states that are involved
are much more effective in blocking additional transitions
when using probe and pump pulses of the same photon
energy (Koopmans, van Kampen, Kohlhepp and de Jonge,
2000b).
Recently, Oppeneer and Liebsch (2004) performed ab initio calculations of the magneto-optics for nonequilibrium
electron distributions in nickel to put these hand waving
arguments on more solid ground. More specifically, they
Time-resolved Kerr-effect and spin dynamics in itinerant ferromagnets 1601
investigated the MO response right after optical excitation,
treating the electronic structure and optical matrix elements
within the density-functional theory. They found a quantitative agreement with the experiments, but only when properly
taking the momentum conservation during optical excitation
into account. At the laser frequency of 1.7 eV the calculated dichroic bleaching corresponded to / 0 ≈ 9fexc , in
good agreement with experimental results (Figure 6c). It is
fair to stress that the calculations represent a worst-case scenario in the sense that electronic relaxation of hot electrons
is not included. Such a relaxation is taking place within tens
of femtoseconds, most probably leading to a fast decay of
the bleaching effects. Detailed calculations thereof would be
of considerable interest, but require an enormous numerical
effort and have not been reported to date.
Concluding this section, both experimental and theoretical
results have demonstrated the nonequivalence of the MO
response and the transient magnetization in the regime of
the strongly excited state before thermalization has set in. By
focusing on the strongest of the complementary MO signals
(rotation vs ellipticity) one may hope to obtain a more direct
view on the magnetization dynamics. Nevertheless, a full
understanding has not yet been achieved, as also evidenced
by artifacts remaining for tens of picoseconds of unknown
origin that appear in some of the experiments.
6
EXPERIMENTS ON ORBITAL
MOMENTUM TRANSFER
In the process of laser-induced loss (or, more generally, modification) of magnetic order, a contribution by the transfer
of angular momentum between the laser field and the FM
sample cannot be excluded a priori. As to emphasize its
potential relevance, it is of interest pointing recent developments in optical control of ferromagnetic garnets. It was
demonstrated by Kimel and Hansteen et al. that circularlypolarized light can be used to nonthermally excite and
coherently control the spin dynamics via the inverse Faraday effect in, for example, DyFeO3 (Kimel et al., 2005)
and Lu3−x−y Yx Biy Fe5−z Gaz O12 (Hansteen, Kimel, Kirilyuk
and Rasing, 2005). Other related work is that on ultrafast modification of the order parameter in AF materials
that has been addressed both in theory (Gomez-Abal, Ney,
Satitkovitchai and Hübner, 2004) and experiment (Kimel,
Pisarev, Hohlfeld and Rasing, 2002; Duong, Satoh and
Fiebig, 2004). In the latter case, however, conservation of
J does not play a role, since the AF ordered state carries no
net M.
The feasibility of the role of the laser field to the demagnetization process in itinerant FMs could be concluded from
theoretical work by Zhang and Hübner. They developed a
particularly interesting model, in which an ultrafast magnetic response (within ∼10 fs) is explained by the dephasing induced by a cooperative effect of spin-orbit coupling
and the external laser field (Zhang and Hübner, 2000).
Although not stated explicitly, either direct angular momentum transfer from/to the laser field, or laser-enhanced transfer
between orbital and spin momentum should be at the basis
of the described effect. It is questionable, however, whether
the laser-induced mechanism plays a dominant role in the
demagnetization after laser heating of the ferromagnetic transition metals, as will be discussed in the subsequent text.
The first experiments on laser-induced angular momentum transfer for itinerant FMs were reported by Ju et al.
(1998b). They used circularly-polarized pump pulses to study
ultrafast spin dynamics in CoPt3 . More recently, Wilks and
coworkers reported on polarization dependent studies on the
ultrafast MO response of nickel thin films (Wilks et al.,
2004). Whereas linearly polarized pump pulses provided relatively conventional transient demagnetization results (τ M =
130 fs; minor difference between rotation and ellipticity),
pronounced effects showed up in the rotational channel
around zero delay when using circularly-polarized pump
pulses. Nevertheless, this additional signal was demonstrated
to transform even under reversal of the magnetic field, while
transforming odd under reversal of the handedness of the
polarization. Therefore, it cannot be considered a real magnetic effect, as also becomes clear from the observation
of similar features for nonmagnetic materials (Wilks and
Hicken, 2004). The additional features are well described
by the specular inverse Faraday effect (SIFE) and specular
optical Kerr effect (SOKE) (Wilks et al., 2004), related to
(3)
the third-order optical susceptibility tensor, χ (3)
xxyy and χ xyyx .
More recently, Dalla Longa performed additional circularly-polarized pumping experiments on nickel thin films
(Dalla Longa, 2007), fully confirming results of Wilks.
In the work of Dalla Longa, however, focus was particularly on a potential influence of the handedness of the
pump polarization on the demagnetization timescale τ M . It
was argued that when the angular momentum of the photon was parallel to the original magnetic moment of the
thin film, transfer of angular momentum could never promote a fast demagnetization on itself. Results (Figure 7)
showed τ M to be independent of the pump polarization
within experimental accuracy (τ M = 135 ± 10 fs when using
equation (20); τ M = 74 ± 4 fs when using equation (19)),
ruling out a significant role of the photon angular momentum in the laser-induced ultrafast demagnetization process in
nickel. In passing we emphasize that these results are in line
with earlier, more qualitative, conclusions on an insignificant
role of circular polarization for CoPt3 (Beaurepaire et al.,
1998).
1602
Magneto-optical techniques
3
RCP
2
MO contrast
LCP
+M
1
+M, RCP
+M, LCP
−M, RCP
−M, LCP
0
−1
−2
−M
−3
(a)
0
(b)
1
2
Delay (ps)
3
MO(+M )–MO(−M )
MO(RCP)–MO(LCP)
MO contrast
2
+M
−M
1
RCP
0
−1
(c)
LCP
0
1
Delay (ps)
0
2
(d)
1
2
Delay (ps)
Figure 7. (a) Schematic diagram of the configuration. Applying a field perpendicular to the thin film, causes an upward (+M) or downward
canting of the magnetization (−M). Photon angular momentum in a polar geometry is parallel or antiparallel for right-handed (RCP) or
left-handed (LCP) polarized light, respectively. (b) TRMOKE in polar geometry on a 10-nm Ni thin film, using RCP and LCP pump light
and canting magnetization upward and downward. (c) Polarization contrast (difference in contrast between RCP and LCP), and (d) magnetic
contrast (difference between +M and −M) in the same experiment. (After Dalla Longa, 2007.)
The latter conclusion cannot be considered as a complete surprise, because it agrees with earlier predictions:
For example, in (Koopmans, van Kampen, Kohlhepp and
de Jonge, 2000b) an excitation density fexc = 0.01 led to
a maximum demagnetization of 5%. For nickel, with an
atomic magnetic moment of 0.6 µB . This corresponds to a
loss of 0.03 µB per Ni atom. Even if all absorbed photons
would have transferred one quantum of angular momentum, the photon flux would have been a factor of 3 too
small. Even more strongly, taking into account the quenching
of orbital momentum in the transition ferromagnetic metals
(Ashcroft and Mermin, 1976), which generally leads to a
lowering of MO efficiency by one to two orders of magnitude, fully excludes a possible role of the photon-induced
mechanism.
It should be emphasized that the foregoing estimate does
not disqualify a photon-induced transfer between orbital and
spin momenta, mediated by the laser field. However, in
Section 2.3 it was argued that such a mechanism cannot
lead to a full quenching of magnetization in the systems
considered.
In conclusion, circularly-polarized light triggers interesting
processes in the itinerant FMs, but these cannot be considered
of relevance for the ultrafast demagnetization process. A
simple estimate shows that the amount of photons is too
small to account for the observed decrease of magnetic
moment. Moreover, the experiments demonstrate that a
possibly small transfer does not act as a seed for the
process.
7
DEMAGNETIZATION DYNAMICS
After having read Section 5, the reader might have wondered
whether TRMOKE is capable of probing the ultrafast magnetic behavior properly, and even whether a genuine demagnetization is occurring within a picosecond at all. Fortunately,
the situation is far more positive. At present, it is generally
1.
2.
3.
4.
5.
6.
A loss in MO contrast within a few hundred femtoseconds is observed in almost all itinerant ferromagnetic metals (apart from Ni, e.g., Fe (Kampfrath et al.,
2002), NiFe (Melnikov, Güdde and Matthias, 2002),
Co (Güdde et al., 1999; Conrad, Güdde, Jähnke and
Matthias, 1999; Comin et al., 2004), CoPt3 (Beaurepaire et al., 1998; Guidoni, Beaurepaire and Bigot,
2002), and Co25 Ni75 /Pt multilayers (Wilks, Hicken, Ali
and Hickey, 2005)).
In almost all experiments, starting with (Hohlfeld,
Matthias, Knorren and Bennemann, 1997), it has been
found that after approximately 300–500 fs, θ̃ (t) is
consistent with a spin temperature that is approaching
the electron temperature, that is, M(t) ∼ Meq [Te (t)].
From about half a picosecond, the demagnetization
transient θ̃ (t) reflects both the subpicosecond e–p
equilibration, as well as the diffusive cooling of the
thin film thereafter. Deviations from this behavior only
occur in those exceptional cases where differences
between θ (t)/θ 0 and (t)/ 0 persist for longer
times.
The magnitude of the demagnetization (as measured
after a few hundred femtoseconds) displays a temperature dependence that would have been expected from a
laser-heating induced change of the equilibrium magnetization at different ambient temperatures, that is,
θ̃ ∝ (dMeq (T )/dT )T , where T is determined by
the laser fluence and heat capacity (van Kampen, 2003).
Even in cases where differences between θ (t)/θ 0 and
(t)/ 0 persist for tens of picosecond, the thermal
differences of the complementary channels (the real
and imaginary part of dθ̃ /dT ) nicely overlap (Koopmans, van Kampen and de Jonge, 2003), as shown in
Figure 8.
If, in spite of the preceding arguments, at 1 ps the spin
system would not have reached thermal equilibrium
with electrons and lattice, a second (slower) transient
to the final fully equilibrated state should be observed
(most probably on a timescale of at most hundreds
of picoseconds). Except for initial work by Scholl,
Baumgarten, Jacquemin and Eberhardt (1997), in which
a slower transition to the fully demagnetized state after
a few hundred picosecond was claimed, such a twostep process has never been observed for the elementary
itinerant FMs.
At large laser fluence (or reduced Curie temperature)
and at a reversed bias field (i.e., H antiparallel to M) it
Induced rotation (%)
believed that – in most cases – TRMOKE closely images
the genuine M(t) behavior, and agrees on a characteristic
timescale well below a picosecond, as based on the following
arguments:
0
−2
303 K
−4
373 K
−6
−8
−1
(a)
Induced ellipticity (%)
Time-resolved Kerr-effect and spin dynamics in itinerant ferromagnets 1603
Rotation
0
1
2
3
303 K
373 K
Ellipticity
4
Delay (ps)
0
(b)
1
2
3
Delay (ps)
4
0
−1
Tm
Tnm
0
(c)
Difference
1
2
3
Delay (ps)
4
−2
Figure 8. Transient MO response for Cu(001)/Ni/Cu at ambient
temperatures of 307 K (filled) and 373 K (open). Normalized
rotation (a) and ellipticity (b), respectively. (c) Thermal difference
curves for rotation (filled) and ellipticity (open symbols). The line
labeled Tnm (dark gray) indicates the fitted loss of electron plus
phonon excess energy in the Ni layer (in au), the line labeled
TM (light gray) represents the fitted spin temperature (in au) (van
Kampen, 2003).
has been shown possible to fully quench the MO contrast well within a picosecond, after which recovery is
in the opposite orientation (Beaurepaire et al., 1998;
Hohlfeld et al., 2001). It is difficult to come up with
any interpretation other than a successful magnetization
reversal, seeded within the first picosecond. We emphasize that the possibility to achieve full quenching in Ni
thin films is not entirely uncontroversial. For example,
Cheskis et al. claimed to see a saturation of the contrast loss at high excitation densities (Cheskis et al.,
2005). However, such a saturation can equally well be
explained by the finite penetration depths of the pump
light and the relatively thick film thickness (30 nm, i.e.,
twice the extinction depth) used in that work. Thereby,
as a rough estimate, the laser power to heat the bottom
part of the film above the Curie temperature is almost
ten times higher than needed for the surface.
7.
It has been demonstrated that the loss of MO contrast
is accompanied by emission of a picosecond terahertz
radiation pulse; which is interpreted as being due to
the sudden change in magnetic moment within the
first picosecond (Beaurepaire et al., 2004; Hilton et al.,
2004).
1604
8.
9.
10.
11.
Magneto-optical techniques
In addition to the ultrafast demagnetization probed
by TRMOKE and TRPE, it has been found from
TRPE that also the exchange splitting is being reduced
within approximately 300 fs (Rhie, Dürr and Eberhardt,
2003, 2005). Although also the interpretation of the
photoemission data is far from trivial, it should be seen
as an additional evidence for genuine magnetic effects
during the first half a picosecond.
Despite the differences between θ (t)/θ 0 and (t)/ 0
observed for some systems during the first hundreds
of femtoseconds, in many other cases complementary
channels do provide the same response. As an example,
this has been verified in particular detail for a broad
spectrum of laser frequencies in recent studies on CoPt3
(Bigot, Guidoni, Beaurepaire and Saeta, 2004).
It has been found that the sudden reduction of magnetic
moment can create an ‘anisotropy field pulse’ (van
Kampen et al., 2002), its duration being estimated to
be typically <2 ps for nickel thin films (cf. Section 8).
Thereby, indirectly it provides additional proof of a
genuine picosecond magnetic response.
In a special material (FeRh, cf. Section 9) a transition
from an AF to FM state within 1 ps has been demonstrated unambiguously (Ju et al., 2004; Thiele, Buess
and Back, 2004). One could well argue: if it is even
possible to generate magnetism within 1 ps, then there
is no reason to disbelieve a lowering of the ferromagnetic moment at a similar timescale.
Finally, we would like to stress that equally interesting
results have been observed in other FM systems, such as
Gd(0001) surfaces (Melnikov et al., 2004; Lisowski et al.,
2005), magnetic semiconductors such as InMnAs (Wang
et al., 2003, 2005), and several colossally magnetoresitive
mangantites and other oxides (e.g., Kise et al., 2000; Ogasawara et al., 2005).
Altogether, ample of evidence for the loss of magnetic
order in the elementary itinerant FMs within hundreds of
femtosecond has been gathered by now. In search for the
underlying mechanisms, it is of relevance agreeing on a
number of relevant timescales. Here we will focus on a
set of coherent experiments, both TRMOKE and transient
reflection, performed for nickel thin films. Care was taken to
have optically transparent films (homogeneously heating the
layer), thermally well isolated from the substrate. Thereby,
transport of hot electrons and thermal diffusion could be
excluded, and a local description in terms of an extended
3T-model will be valid (van Kampen et al., 2005a). A set of
characteristic data is displayed in Figure 9. It is concluded
that the demagnetization time τ M ≈ 100–200 fs (when using
equation (20); just below 100 fs when using equation (19)
(Dalla Longa, 2007)) is approximately equal or slightly
longer than the thermalization time τ T ≈ 80 fs, but shorter
than the e–p equilibration τ E ∼ 0.4 ps. Weak temperature
dependencies in τ M have been found in (van Kampen, 2003),
but will not be discussed any further here.
Quite a few mechanisms have been proposed to account
for such a subpicosecond demagnetization. However, as
discussed in Sections 2.3 and 2.4, many of the proposed
mechanisms excluding the lattice degree of freedom do
not obey conservation of angular momentum. (i) Some
interesting theoretical studies demonstrated femtosecond MO
response, however, more in the spirit of state-filling effects
than a transient M(t) (Hübner and Zhang, 1998; Zhang and
200
−0.1
−0.2
τth = 80 fs
−0.3
−0.4
τth = 0
0
(a)
Induced spin temperature (K)
Induced reflection (%)
0
100
50
0
0.5
Delay (ps)
150
(b)
0
0.5
1
Delay (ps)
Figure 9. (a) Transient reflection on a nickel thin film, resolving τ T and τ E as indicated. Filled circles: measured reflection changes, thin
dashed line: pump-probe autocorrelation, fat dashed line: 2T-model fit using infinitely fast thermalization (τ T = 0), fat line: fit including
finite thermalization, and gray line: adding a coherent signal on top (representing weak state-filling effects). A background signal due to
lattice expansion is corrected for (van Kampen et al., 2005a). (Reproduced from M. van Kampen et al., 2005, with permission from IOP
Publishing Ltd.  2005.) (b) TRMOKE data on the same film, resolving τ M . Open circles display measured data. The black and gray lines
represent 3T-model fits without- and with a coherent signal (dichroic bleaching) respectively (van Kampen, 2003).
Time-resolved Kerr-effect and spin dynamics in itinerant ferromagnets 1605
Spins
Electrons
Temperature (K)
Hübner, 1999; Vernes and Weinberger, 2005). (ii) In some
explanations, the transfer of spin itself was not addressed
explicitly, and it was merely stated to be occurring during
electron thermalization (Hohlfeld, Matthias, Knorren and
Bennemann, 1997; Guidoni, Beaurepaire and Bigot, 2002,
and others). (iii) Elsewhere, a link was made with Stoner
excitations (Scholl, Baumgarten, Jacquemin and Eberhardt,
1997), or a collapse of the Stoner gap (Cheskis et al.,
2005), in both cases angular momentum conservation seems
not fulfilled. (iv) Spin-orbit scattering in which spin and
orbital momenta are exchanged would lead to an enhanced
orbital moment upon lowering M. Thereby an increase of
the MO contrast rather than a reduction would be expected
(MO measuring mostly orbital effects (Oppeneer, 1998)),
which has never been observed. (v) Transfer of orbital
momentum during laser excitation has been demonstrated
to be negligible (Section 6). (vi) Finally, emission of Tera
Hertz radiation has been observed to accompany the laserinduced demagnetization (Beaurepaire et al., 2004; Hilton
et al., 2004). The configuration was such, however, that it
cannot explain the loss of angular momentum. At this stage,
we consider it unlikely that such a scenario will provide the
key answer.
Motivated by the controversy that arose, we have readdressed the possibility to include the lattice interactions in
order to take care for a potential bath of angular momentum. Let us first restate two general arguments against such
a scenario: (i) It is too slow, or, phrased differently, it
would require an unrealistically large spin-flip probability
a (see subsequent text, and Section 2.4.4). (ii) If the lattice
is involved, one would expect the spin temperature to lag
behind the lattice temperature that is, τ M > τ E .
A first numerical model including e–p induced spin-flip
scattering was published in Koopmans, Kicken, van Kampen
and de Jonge (2005). In search for the simplest model that
just contained the essential ingredients three reservoirs were
defined. A simplified electron and lattice system were defined
as introduced in Section 2.4. In addition, the spin system was
described as a set of identical two-level systems obeying
Boltzmann statistics and with an exchange splitting ex
that depends in a self-consistent way on the average spin
moment S, that is, using a mean-field (Weiss) description:
ex = J S, where the exchange energy J is related to the
Curie temperature via kB TC = J /2. A spin-flip probability
a, for an e–p event to be accompanied by spin flip, was
introduced. All dynamics was performed within the random-k
approximation.
Numerically solving the Boltzmann equations after optical excitation of the electron system, revealed traces for
Te , Tp and Ts very similar to the ones obtained by the
3T model (Koopmans, Kicken, van Kampen and de Jonge,
2005). Some results for an arbitrary set of parameters and
asf = 0.50
600
asf = 0.10
asf = 0.01
500
400
Lattice
300
0
1
2
3
Time (ps)
(a)
Electrons
‘Hot’
tT
Lattice
tE
Te,F
Tp
Te,E
tM
Ts
Laser
(b)
Spins
Figure 10. (a) Calculated traces of electron, lattice and spin temperature for different spin-flip probabilities a, according to the
model discussed in the text. (Reproduced from B. Koopmans et al.,
2005, with permission from Elsevier.  2005.) (b) Schematic flow
scheme of the phonon-mediated model.
as a function of spin-flip probability a are displayed in
Figure 10(a). As expected, the higher a, the faster the
equilibration of the spin temperature. However, as a surprising observation it can be seen that for some sets
of parameters it is possible to achieve a spin response
faster than the heating of the lattice (i.e) τ M < τ E , even
though phonons are involved in the model. This clearly
disproves argument (ii) against a phonon-mediated demagnetization.
These numerical efforts were later backed by an analytical
approach, both including spin-flip scattering with phonons
and with impurities. Equations could be derived for τ M
and τ E in the limit of infinitely fast thermalization τ T → 0
(Koopmans, Ruigrok, Dalla Longa and de Jonge, 2005).
More specifically, for the phonon-mediated model, and for
temperatures ‘well-enough below TC ’, a ratio
τM
3c0 Ds (ωD )2
= 2
τE
π aDF kB3 T 2 TC
(33)
was found. For a reasonable set of parameters for Ni, it
required a ∼ 0.1 to end up with τ M ∼ τ E . On the basis of the
1606
Magneto-optical techniques
band structure considerations – in particular the knowledge
that band degeneracies near the Fermi level can enhance
a by orders of magnitude (Fabian and Sarma, 1998) – it
was concluded that phonon-mediated spin-flip scattering in
the spirit of Elliot and Yafet may provide a non-negligible
contribution to the subpicosecond magnetic response for
realistic values of a. This significantly weakens argument
(i) against a phonon-mediated demagnetization.
All of this can be understood diagrammatically as sketched
in Figure 10(b): The energy flow from the electron to the
spin bath, whereby Ts approaches Te , is strongly influenced
by (the temperature of) the lattice. The fact that even a = 0.1
is sufficient to achieve τ M ∼ τ E is related to the fact that it
needs many e–p events (ωq ∼ 0.05 eV) to lower the kinetic
energy of an optically excited electron (<1 eV), whereas a
single spin flip per atom is more than sufficient to quench
all magnetization in nickel (with a magnetic moment of
0.6 µB ).
Finally, of even more generic interest, a potential link
between the demagnetization process and Gilbert damping of
precessional dynamics was derived in (Koopmans, Ruigrok,
Dalla Longa and de Jonge, 2005). Therefore, the same model
Hamiltonian was used to derive an analytical expression
for the Gilbert parameter α. The approach followed was
quite similar to the spin-flip scattering treated by Kamberský
(1970), though did not include ordinary scattering between
spin-dependent band levels (Kamberský, 1970; Kunes and
Kamberský, 2002). Interestingly, for all mechanisms considered, that is, both the impurity- and phonon-mediated
spin-flip scattering, practically the same relation between α
and τ M was found (Koopmans, Ruigrok, Dalla Longa and
de Jonge, 2005):
τ M ≈ c0
1
kB TC α
(34)
again valid for T well-enough below TC . The parameter
c0 is between 1/8 and 1/4, slightly depending on details
of the models and regimes worked in. Although a strongly
simplified model it sets the relevant timescale with surprising
accuracy. For example, using α = 0.02–0.03 (being the
intrinsic value for nickel (Heinrich, Meredith and Cochran,
1979)), and TC = 630 K, readily predicts τ M ∼ 100 fs, within
a factor of 2 of the measured value!
Thus, two major areas of contemporary research in magnetism were linked: (i) the ultrafast (subpicosecond) manipulation of magnetic matter, and (ii) the switching and precessional dynamics in multilayered and micromagnetic systems.
Maybe, relating the two fields provides future answers to
the origin of the femtosecond-scale magnetization processes
in itinerant FMs as triggered by pulsed-laser heating. For
sure, the new insight will inspire the community to come
up with new and even more dedicated investigations aiming
at further unraveling the secrets of ultrafast magnetization
dynamics.
8
ANISOTROPY DYNAMICS AND
LASER-INDUCED PRECESSION
Magnetic anisotropies arise from a subtle balance of the magnetic energy in an applied field, dipole–dipole interactions
(in case of shape anisotropy) and spin-orbit interactions that
give rise to coupling to the lattice (magnetocrystalline- and
surface anisotropies). It has been found that sudden laser
heating of a FM material can perturb the balance between
the different anisotropy contributions and the applied field,
launching a precessional motion of the magnetization vector. Such an approach provides access to both the precessional dynamics (frequency and damping), as well as the
picosecond-dynamics of the magnetic anisotropy itself.
Ju et al. demonstrated the ability to use the ultrafast optical
modulation of the AF/FM interaction of an exchange-biased
(Ju et al., 1998a,
(EB) bilayer to launch a precession of M
2000). In these experiments, such a modulation was obtained
by heating a NiFe/NiO bilayer close to the blocking temperature TB . A more general scheme was introduced by van
Kampen et al. They found a similar laser-induced precession
for a single magnetic layer with a canted equilibrium orienta (Koopmans, van Kampen, Kohlhepp and de Jonge,
tion of M
2000b; van Kampen, Koopmans, Kohlhepp and de Jonge,
2001). Initially, the phenomenon was observed for specially
engineered systems with a canted ground state orientation
of the magnetization, such as epitaxial Cu(111)/Ni/Cu and
Cu(001)/Ni/Cu at a proper (intermediate) Ni-layer thickness.
Owing to the contrasting temperature dependence of the various anisotropy contributions, the canting angle c is strongly
T -dependent when starting at a nontrivial angle (c = 0◦ and
c = 90◦ ).
Later, it was reported that the phenomenon was even
more general, and could be observed in polycrystalline films
to a
with an in-plane anisotropy as well, by pulling M
canted orientation in an applied magnetic field (van Kampen
et al., 2002) (Figure 11). For such a nickel polycrystalline
film, the equivalence of the laser-induced precession with
microwave driven magnetization oscillations was verified in
a conventional ‘FMR’ experiment (van Kampen et al., 2002).
Many applications of the approach have followed. The
dispersion of perpendicular standing spin waves could be
resolved (van Kampen et al., 2002). In later experiments,
discrete modes in artificial spin chains, that is, submicrometer
pillars of [NiFe/Al2O3]n (n repetitions), were investigated
(van Kampen et al., 2005b). The all-optical approach is
Time-resolved Kerr-effect and spin dynamics in itinerant ferromagnets 1607
(a)
0.5
IIa
q′c
1
IIb
1.5
2
−1 0 1 2
qc
z
500 1000 1500
Delay time (ps)
III
(b)
Figure 11. (a) Laser-induced precession in a polycrystalline nickel
thin film, showing demagnetization (<2 ps) and successive preces and (b)
sion, by measuring the polar component of the canted M,
is canted out of
schematic explanation: (I) In the external field, M
plane; (II) laser heating changes the equilibrium orientation, thereby
triggering a precession; (III) after thermal recovery, the final precession is almost in the original anisotropy field.
particularly convenient for measuring dynamics on wedgeshaped samples, in which one of the film thicknesses is
continuously varying over the sample area. Józsa used this
configuration to explore correlations between damping and
coercivity as well as damping by means of spin pumping
(Józsa, 2006). Furthermore, the technique has been used to
probe anisotropies, such as in the Fe/AlGaAs(001) system
(Zhao et al., 2005). The role of anisotropy on the ultrafast
dynamics in cobalt has been addressed by Bigot, Vomir,
Andrade and Beaurepaire (2005). Finally, it should be
emphasized that the all-optical approach is particularly suited
to measure materials with a high anisotropy (thereby a
high precessional frequency) and a high damping (where a
frequency domain approach is troublesome), such as hard
disk recording media (Bergman et al., unpublished).
Returning to the initial ‘anisotropy field pulse’, it has been
demonstrated that the anisotropy is being modified really at
the picosecond timescale. This can be concluded qualitatively
already after
from the observation of the first rotation of M
several picoseconds. A more accurate estimate is obtained
by backtracing the anisotropy field pulse from the complete
precessional signal. A scheme therefore has been developed
by Józsa (2006). For a nickel thin film, a characteristic
timescale of at most 1–2 ps was derived this way.
Finally, a particularly interesting problem, with both scientific and technological aspects, is the quenching of the
anisotropy interaction between a FM and an AFM, as originally being explored by Ju et al. for NiFe/NiO (Ju et al.,
1998a,b, 2000). More recently, Weber and coworkers reported
on a collapse of the exchange-bias field HEB within the first
10 ps after laser excitation, for three different EB systems
(NiFe/FeMn, IrMn/CoFe and NiMn/CoFe) (Weber, Nembach
and Fassbender, 2004; Weber et al., 2005; Weber, Nembach,
Hillebrands and Fassbender, 2005), the time scale basically
−200 ps
10 ps
100 ps
300 ps
2
qc
q′c
Kerr rotation (au)
I
0
2.5
M
1.5
1
0.5
0
−0.5
0
250
500
750
1000
Magnetic field (Oe)
(a)
700
EB field (Oe)
Induced MO contrast (%)
H
600
500
400
300
−500
(b)
IrMn / CoFe
H 8b(t ), t = 205 ps
0
500
1000 1500 2000 2500 3000 3500
Delay (ps)
Figure 12. Exchange-bias shift field as a function of pump-probe
delay measured for a IrMn/CoFe sample. (a) Easy axis transient
hysteresis loops for various pump-probe delays as indicated. (b)
Time evolution of HEB . (Reproduced from M.C. Weber et al., 2005,
with permission from EDP Sciences.  2005.)
determined by the relatively long pulse duration used (9
ps – see Figure 12). The fast thermal unpinning is followed by
a slower heat diffusion dominated recovery of HEB . Using a
similar approach and identical samples, Hoffmann et al. found
that even for 100-fs pulses the collapse of HEP seemed to
be just limited by the pulse duration (Hoffmann, 2006) – an
observation that is not well being understood by now.
Future studies would certainly profit from the availability
of well-defined, epitaxial systems. As a first attempt, Dalla
Longa et al. started to explore the ultrafast dynamics of the
EB effect in epitaxial Co/Mn films (Dalla Longa, Kohlhepp,
de Jonge and Koopmans, 2006). This system displays large
monolayer oscillations in both coercivity and EB field as
a function of the Co thickness (Kohlhepp, Kurnosikov and
de Jonge, 2005). First laser-induced precessional effects have
been demonstrated for this intriguing system (Dalla Longa,
Kohlhepp, de Jonge and Koopmans, 2006).
1608
9
Magneto-optical techniques
ULTRAFAST PHASETRANSITIONS AND
GROWTH OF MAGNETISM
After having established the possibility to quench ferromagnetic order on a subpicosecond timescale, a new challenge
is in generating magnetic order. Not only is this of profound fundamental interest it would also open up more
serious applications of the laser-induced ultrafast magnetic
manipulation.
The simplest approach is provided by cooling down a
FM after laser heating above TC (Figure 13a). Beaurepaire
reported on such a laser-induced FM to PM transition within
0.5 ps in CoPt3 , and the successive recovery to the original
FM state (Beaurepaire et al., 1998). Such experiments were
extended to the real switching domain by Hohlfeld et al.
(2001). The material of choice was the recording material
GdFeCo, and pairs of set and reset magnetic field pulse
allowed to follow the reversal process in a stroboscopic
experiment (Figure 13b). However, the growth of M is
basically limited by the cool-down time of the magnetic film,
a slow diffusion driven process taking tens to hundreds of
picoseconds.
A potentially much faster generation of magnetic order
could be achieved for materials that display a magnetic phase
transition (Figure 13c). A typical example is provided by
FeRh. Recently, Ju et al. (2004) and Thiele, Buess and Back
(2004) demonstrated independently the feasibility of driving
therein the AF→FM phase transition within a picosecond
by laser heating. When properly prepared, FeRh has the
chemically ordered CsCl structure. At low temperatures, the
material has an antiferromagnetic spin orientation, with iron
local moments of ±3 µB and no appreciable moment on
rhodium. At a phase transition temperature of ∼370 K, a
first-order transition to a ferromagnetic phase takes place,
with iron- and rhodium local moments of 3 µB and 1 µB ,
100
MO signal (%)
M
(a)
FM
M
AF
TP
(c)
+Hsat
50
H=0
0
−50
−Hsat
0
TC
(b)
250
500
Delay (ps)
750
Figure 13. Schematic representation of growth of magnetic
moment by cooling down below TC (a) and by driving a AFM
to FM phase transition (c). An experimental realization of the first
option is displayed in (b) for a GdFeCo thin film, and applying
different external fields. (Reproduced from J. Hohlfeld et al., 2001,
with permission from the American Physical Society.  2001.)
respectively. The fact that the phase transition shows up
slightly above room temperature makes it particular attractive
for applications. The latter has been recently emphasized by
Thiele, Maat and Fullerton (2003). They proposed the use of
an exchange spring bilayer FePt/FeRh as a storage medium
for heat-assisted recording.
A typical time-resolved experiment is displayed in
Figure 14(a). Using FeRh thin films, Ju et al. observed that
about 20% of the final net MO signal establishes within
the first picosecond, converging to a full signal after ∼50 ps
(Ju et al., 2004). Different fingerprints have been suggested
to decide on a genuine laser-induced phase transition: (i)
Appearance of a MO signal when performing the experiments in a magnetic field. (ii) The observation of a ‘threshold fluence’, as reported by Ju et al. (2004), and shown in
Figure 14(b). A certain minimum laser fluence is needed
to heat up the film above the transition temperature, TP .
Moreover, the higher the fluence, the longer the MO signal persists, because it takes longer to cool down below
TP – all exactly as observed in Figure 14(b). (iii) A ‘twopeak feature’ in the MO transient, as claimed originally by
both teams (Ju et al., 2004; Thiele, Buess and Back, 2004).
The magnetization may be expected to go twice through a
maximum – that is, during heat up as well as while cooling
down – since right above TP the magnetic moment is highest.
Also, at increasing laser fluence the time at which the second
peak occurs should be larger. This ‘two-peak argument’ will
next be addressed in more detail.
If the magnetic system would be in a constant equilibrium with electrons and lattice, a double pass of the
state with highest M would be expected indeed. However, in the nonequilibrium experiment, the electron temperature is almost suddenly raised well above TP . It is
questionable whether in such a case the equilibration of
electron and spin system is indeed accompanied by first a
buildup of magnetic order, after which it is quenched again.
Bergman, Ju et al. rephrased this consideration recently
in terms of two separate timescales: τ s to account for a
process in which Ts increases monotonically, driving M
through an optimum indeed, and τ M accounting for a process in which the magnetization (rather than Ts ) grows
monotonously from zero to its final value (Bergman et al.,
2006).
Support for the second model came from magnetic field
dependent experiments, in which it was shown that the
two features originally observed had to be assigned to
the onset of a laser-induced precession, similar to the
ones described in Section 8. This behavior was successfully
accounted for by an LLG simulation in which both the
were described (Bergman
magnitude and orientation of M
et al., 2006) – including heat diffusion and a gradual increase
of M after passing TP . More specifically, the effective field
Time-resolved Kerr-effect and spin dynamics in itinerant ferromagnets 1609
Induced MO (au)
1
Increasing
fluence
11 kG
8 kG
0.5
5 kG
2 kG
0
(a)
0
20
Delay (ps)
40
0
(b)
500
Delay (ps)
1000
0
100
(c)
Delay (ps)
200
Figure 14. (a) Experimental realization of a subpicosecond growth of FM moment after pulsed-laser heating, demonstrated by TRMOKE
on a thin FeRh film. (Reproduced from G. Ju et al., 2004, with permission from the American Physical Society.  2004.) (b) A threshold
fluence is needed to reach TP , and the higher the fluence, the longer the system remains in the FM state. (Reproduced from B. Bergman
can be clearly observed.
et al., 2006, with permission from the American Physical Society.  2006.) (c) At higher fields, a precession of M
(Heff (t|)) was calculated from time dependent orientation
and magnitude of the magnetization vector throughout the
film, M(z,
t)|), (z being the depth coordinate), and used
in the LLG equation for the normalized magnetization:
m(t)
= M(z,
t)/M(z, t) requiring all spins in the system to
be parallel:
dm
dm
(35)
= γ µ0 m
× Heff + α m
×
dt
dt
For more details we refer to Bergman et al. (2006). At higher
fields, a faster precession was found indeed as shown in
Figure 14(c). This new interpretation shows that a two-peak
feature as originally postulated is not observed upon laser
heating of FeRh, asking for a description in terms of τ M .
By observing an ultrafast, subpicosecond component in
the MO response, both teams concluded to have solved the
long-standing issue whether the magnetic phase transition
in FeRh is driven by lattice expansion, or whether it
is a purely electronic phenomenon. The observation of a
growth of magnetism well before the lattice is expanded
(several picoseconds) unambiguously demonstrates the latter
(Ju et al., 2004; Thiele, Buess and Back, 2004).
The successive growth of the final MO contrast during a period of tens of picoseconds has been addressed in
more detail in Bergman et al. (2006), exploiting a combined TRMOKE and transient reflectivity approach. It was
concluded that all data are consistent with a subpicosecond
nucleation of magnetic moments that grow and align during
the next tens of picoseconds – driven by effective field and
mutual exchange interactions.
Our understanding of the whole process on a microscopic
scale is still limited. On the other hand, the material with
its two coupled spin systems may provide a very efficient
playground for acquiring more in-depth understanding of
magnetic processes at the subpicosecond timescale. It is
anticipated that exploring laser-induced magnetic phase transitions in general, and the FeRh case in particular, will grow
toward a very rich and challenging field of research in the
forthcoming years.
10 CONCLUDING REMARKS
Within a decade after the first report on femtosecond
magnetization dynamics an exciting and active field of
research has emerged. Hand in hand with developments
in spintronics, ever new phenomena have been discovered.
By now, a whole toolkit of methods for manipulating and
probing FM matter on a subpicosecond time scale has
become available. Main emphasis in this chapter was on
all-optical approaches. It was shown that femtosecond laser
pulses can demagnetize a ferromagnetic film within a few
hundred femtosecond, but also drive an AF to FM phase
transition and thereby generate a magnetic moment at a
similar timescale. By changing the magnetic anisotropy at
the subpicosecond timescale, precessional phenomena can be
triggered and probed in an elegant all-optical scheme.
As will have become clear, our understanding of many of
the phenomena is still at rather a phenomenological level.
While the basic interactions leading to the equilibration of
the electron and lattice system after pulsed-laser heating
are relatively well understood, no consensus on the microscopic mechanisms underlying the femtosecond quenching
and growth of magnetic order has been achieved yet. Nevertheless, the bare fact that a genuine change in magnetic order
does occur within a few hundred femtoseconds is generally
accepted by now. A larger number of supporting arguments
were discussed, although it should be stressed that utmost
care remains necessary to interpret optical data in the strong
1610
Magneto-optical techniques
nonequilibrium regime, where state-filling effects do mix up
with the ‘magnetic’ signal. Within the chapter, the role of
transfer of angular momentum has been emphasized, and
some of the recently proposed dissipation channels were
discussed. Recent approaches seem to point out a potential
universal link between dissipation of precessional motion of
the magnetization vector (Gilbert damping) with the relaxation time of microscopic spin fluctuations (represented by
τ M ). Moreover, a possible role of phonons in the magnetic
relaxation process even at picosecond timescale was estimated.
Clearly, a more comprehensive understanding of the
underlying physics requires more dedicated theoretical efforts
as well as novel, targeted experiments. New insight could
be expected, for example, from the rapid development
of synchrotron radiation sources, which may open up the
possibility of performing element specific measurements of
the spin dynamics at subpicosecond timescale, with the
potential to discriminate between orbital and spin angular
momenta. Also, rapid progress has been witnessed in the
use of TRPE. Other routes, such as directly exciting and
probing lower energy excitations (such as spin waves) in the
system could be anticipated to provide deeper insight, but
have not been explored intensively in the picosecond regime
yet. Clearly, particular progress is expected from combing
several of the aforementioned approaches in a clever way.
Apart from progress by improving our analytical techniques, exciting opportunities arise by engineering novel
structures. Experiments on FeRh, but also spin dynamics
in oxides that was not explicitly discussed in the present
chapter, have shown the exciting phenomena that can be
observed when moving to specific alloys and compounds.
Also, a growing awareness is being witnessed that new
classes of dynamics can be explored when entering the
regime of exchange-coupled systems. Finally, the development of nano-structuring techniques opens up a particular
challenging route for a combined spatiotemporal manipulation of the flow of energy and angular momentum in the
nonequilibrium regime.
Upon completing this chapter, I’m particularly grateful to
my (former) PhD and undergraduate students Maarten van
Kampen, Csaba Józsa, Jeroen Rietjens, Bastiaan Bergman,
Francesco Dalla Longa, Harm Kicken, and Dijon Boesten
for their skillful experiments and original contributions to
the research program – much of which contributed in an
essential way to this chapter. Furthermore, I have profited considerably from instructive discussions and joint
projects with many colleagues. Out of them, I specifically
want to mention Ganping Ju and coworkers at Seagate
Research, and Jaap Ruigrok at Philips Research, for our
recent collaborations on FeRh (Section 9) and theory of
femtosecond dynamics (Section 7), respectively. Finally, I
acknowledge support by the European Communities Human
Potential Programme (contract number HRPN-CT-200200318 ULTRASWITCH), and by the Netherlands Foundation
for Fundamental Research on Matter (FOM).
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