Ultrafast electron-phonon-magnon interactions at noble metal-ferromagnet interfaces
V. Shalagatskyi,1 O. Kovalenko,1, 2 V. Shumylo,1 T. Pezeril,1 D.
Mounier,1 V. E. Gusev,3 D. Makarov,4, 5 and V. V. Temnov∗1
IMMM CNRS 6283, Université du Maine, 72085 Le Mans cedex, France
2
IPCMS CNRS 7504, Université de Strasbourg, BP 43,
23 rue du Loess, 67034 Strasbourg Cedex 02, France
3
LAUM CNRS 6613, Université du Maine, 72085 Le Mans cedex, France
4
Institute of Ion Beam Physics and Materials Research,
Helmholtz-Zentrum Dresden-Rossendorf e. V., 01328 Dresden, Germany
5
Institute for Integrative Nanosciences, IFW Dresden, 01069 Dresden, Germany
(Dated: December 1, 2015)
Ultrafast optical excitation of gold-cobalt bilayers triggers the nontrivial interplay between the
electronic, acoustic and magnetic degrees of freedom. Laser-heated electrons generated at the goldair interface diffuse through the layer of gold and strongly overheat the lattice in cobalt resulting
in the emission of ultrashort acoustic pulses and thermal excitation of exchange magnons. Several
experimental configurations are applied to quantify the thermal boundary (Kapitza) resistances and
hot electron diffusion. A new way to reduce the thermal boundary resistance by a thin phononically
matched metal layer is demonstrated.
PACS numbers: 43.35.+d,63.20.kd,73.40-c,75.78.-n
which results in the temperature jump ∆T across the
1
Data Au (90 nm)
Data Au (150 nm)/Pt (30 nm)
0.8
Data Au (150 nm)/Co (30 nm)
Fit Au
RKap = 20e-9
Fit Au/Pt RKap = 5.0e-9
0.6
Fit Au/Co RKap= 2.5e-9
Co or Pt
0.4
Al2O3
Au
PUMP
0.2
PROBE
{
Ultrafast heat transport in nanophotonic devices plays
a crucial role in modern nanotechnology, in particular in the quest of information processing at ultrahigh
(Tbit/second) rates. It is well established [1] that thermal effects dominate in nanophotonic devices based on
semiconductor quantum dots when excited by trains of
femtosecond laser pulses with THz repetition rate. When
using complex metal-ferromagnet multilayer structures,
which are particularly important in ultrafast plasmonic
applications [2, 3], the most exciting way is to control
the optical properties via ultrafast manipulation of the
magnetic order at the nanoscale [4, 5]. Whereas the
most recent investigations consider the role of the nonequilibrium spin dynamics at metal-ferromagnet interfaces [6, 7], our current study focuses mainly on the thermal aspects. As we are going to show in this manuscript,
ultrafast optical excitations in gold-cobalt bilayer structures on a sapphire substrate result in the non-trivial
dynamics of electrons, phonons and magnons. These dynamics are triggered by heat transport via superdiffusive hot electrons in gold through the metal-ferromagnet
interface and can be described without considering the
spin.
To quantify the rate of heat transfer across the metaldielectric interfaces we have first inspected the cooling
dynamics of several metal samples, which were grown by
magnetron sputtering on sapphire substrates [3](Fig. 1).
In case of sub-micrometer thin metallic layer on a substrate possessing high thermal conductivity the cooling
dynamics are dominated by the relatively large interfacial
thermal boundary (Kapitza) resistance [8]
Q (1)
RKap = ,
∆T
Transient reflectivity (a.u.)
arXiv:1511.09060v1 [cond-mat.mtrl-sci] 29 Nov 2015
1
L
0
0
5
10
15
20
Time delay (ps)
FIG. 1: Nanosecond time-resolved reflectivity measurements
on a 90 nm thin gold layer and 150 nm Au/30 nm Pt and
150 nm Au/30 nm Co bilayer structures show that the thermal
boundary (Kapitza) resistance RKap between gold and sapphire can be significantly reduced by phononically matched
layer.
interface slowing down the heat flow Q = −κ(∂T /∂z)
[9]. Previous studies by transient thermoreflectance
technique allowed to understand the mechanism of
heat transfer across metal-dielectric interfaces, which is
strongly affected by the difference in the phononic density of states between two materials quantified by their
Debye temperatures [10, 11].
By fitting the measured transient reflectivity data for
a 90 nm Au and 150 nm Au/30 nm Pt and 150 nm
Au/30 nm Co bilayer structures on a sapphire substrate in Fig. 1 with the numerical solutions of the onedimensional heat diffusion equation we obtained values
for Kapitza resistance of RAu−sapphire = 20 × 10−9 ,
RP t−sapphire = 5 × 10−9 and RCo−sapphire = 2.5 ×
10−9 m2 K/W, respectively. These results corroborate
2
(a)
Transient reflectivity (a.u.)
0.8
0.4
Al2O3 Au (90 nm)
0
PROBE
PUMP
−0.4
RKap = 20e-9
RKap = ∞
Experimental data
−0.8
0
100
200
300
400
500
Time delay (ps)
(b)
Transient reflectivity (a.u.)
1
0.8
Al2O3 Co (90 nm)
0.6
PROBE
PUMP
0.4
0.2
RKap = 1e-9
RKap = 2.5e-9
RKap = 4e-9
Experimental data
0
−0.2
0
100
200
300
Time delay (ps)
τCo+ τAu
τCo+ 2τAu
(c)
400
500
τCo+ 3τAu
2
Transient reflectivity (a.u.)
the general trend that the best thermal metal-substrate
matching is obtained for cobalt, which possesses the
closest to that of sapphire Debye temperature Θ (compare ΘAu = 178 K, ΘP t = 225 K, ΘCo = 436 K
to Θsapphire = 1047 K). A thin layer of phononically
matched cobalt reduces the value of the effective thermal
boundary resistance between gold and sapphire almost
by an order of magnitude.
In order to quantify the role of electronic transport
across the metal-metal interfaces we have performed femtosecond time-resolved optical pump-probe experiments
(Fig. 2). Ultrashort optical pump pulses (800 nm, 120 fs,
500 kHz repetition rate) were used to excite the samples and the dynamics of surface reflectivity at the opposite side were measured by time-delayed femtosecond
probe pulses (400 nm, 120 fs). Having said that the thicknesses of all investigated samples largely exceed the optical skin depth (around 10-15 nm), such front pump back probe measurements are suited to study the dynamics of heat transport across the metal-metal interfaces on
a sub-nanosecond time scale. In case of a single gold layer
(Fig. 2a) the heat transport is dominated by diffusion of
laser-excited hot electrons, which are able to cross the
entire film (hot electron diffusion length ¿100 nm) before
cooling down in the process of electron-phonon relaxation
on a sub-picosecond time scale [12]. The pronounced
reflectivity oscillations in Fig. 2(a) caused by reflection
of coherent acoustic phonons from the acoustically mismatched (22% acoustic reflectivity) gold-sapphire interface decay within 100 ps. A small temperature decrease
on 200-300 ps timescale is consistent with the onset of
slow cooling into sapphire substrate, confirming the value
for the Kapitza resistance at the cobalt-sapphire interface obtained from nanosecond reflectivity measurements
(Fig. 1).
The dynamics in cobalt (Fig. 2(b)) are different: the
temperature at the back interface grows slowly, reaches
its maximum after 200 ps and starts cooling down into
the substrate later. The numerical solution of heat diffusion equation appears to be in a good quantitative
agreement with experimental data assuming the Kapitza
resistance RCo−sapphire = 2.5 × 10−9 m2 K/W. Apart
from different values of Kapitza resistances there are two
significant differences between cobalt and gold. First
of all, due to the larger electron-phonon coupling g =
6 × 1017 W/m3 K [13] and smaller thermal conductivity
p
κ/g ≃
κ = 100 W/Km the diffusion length δhot =
13 nm of hot electrons in cobalt is much shorter than in
gold, resulting in the localized lattice heating. Second,
the opto-acoustic part of the signal displays much weaker
acoustic reflections due to the good acoustic impedance
matching between cobalt and sapphire (< 10% acoustic
reflection).
Experiments in gold-cobalt bilayer structures
(Fig. 2(c)) appear to be more difficult to interpret.
In case of pump excitation through the sapphire sub-
1
0
Al2O3 Co
Au (150 nm)
PROBE
PUMP
PUMP
PROBE
−1
0
50
100
150
Time delay (ps)
FIG. 2: Transient reflectivity curves for (a) 90 nm Au, (b)
90 nm Co single layer and (c) 150 nm Au/30 nm Co bilayer
structures on sapphire excited by femtosecond laser pulses.
Numerical solutions of the heat-diffusion equation in (a) and
(b) confirm the values of Kapitza resistance at Au-sapphire
and Co-sapphire interfaces. The dynamics of transient reflectivity in (c) is different for pumping gold-air and cobaltsapphire interfaces.
strate the energy is absorbed in cobalt, which generates
a roughly 3 ps short acoustic pulse resulting in the
opto-acoustic modulation of the transient reflectivity
signal at the gold-air interface after traversal of the gold
layer in τCo + τAu ∼ 40 picoseconds [3]. A short spike at
zero time delay indicates that some fraction of energy
is also transported by superdiffusive hot electrons in
gold [14]. The dynamics of reflectivity signals are dominated by opto-acoustic and hot-electron contributions
rendering the extraction of thermal dynamics extremely
challenging. The situation becomes different when the
same gold-cobalt bilayer is excited from the gold side
and the dynamics are probed at the cobalt-sapphire
3
200
50
200
150
150
Au
50
100
Au
Co
Thickness (nm)
Co
250
250
Al2O3
Pump
0
0.5
1
1.5
2
Thickness (nm)
300
(c)
Pump
pulse
Al2O3
100
(a)
2.5
0
50
Time delay (ps)
100 150 200
250 300
Time delay (ps)
300
(d)
Pump
pulse
Al2O3
200
150
200
Au
250
Co
250
Co
Au
100
Al2O3
Pump
0
0.5
1
1.5
2
Time delay (ps)
2.5
50
Thickness (nm)
(b)
150
where Ce (Te ) is the electronic heat capacity (assumed to
depend linearly on Te in our range of excitations [16]),
κ(Te ) is the temperature-dependent electronic thermal
conductivity, Cl is the lattice heat capacity. The heat
transport through the gold-cobalt interface is determined
by a phenomenological (electronic) Kapitza resistance
(Co)
(Au)
RKap = −κ(∂Te /∂z)/(Te
− Te ).
Hot electrons, which are initially generated within
13 nm skin depth of pump light at the gold-air interface
transport their energy through a much thicker (240 nm,
see the experiment in Fig. 4) gold layer, where they
are injected into cobalt on a sub-picosecond time scale
(Fig. 3(a)). Due to a large value of electron-phonon
coupling constant in cobalt these hot electrons heat the
cobalt lattice at a much higher rate resulting in its transient overheating (Fig. 3(b)). We use the transient profile of lattice temperature at 1 ps as an initial condition
to solve the heat diffusion equation (Fig. 3(c)) and the
acoustic equation (Fig. 3(d)). Two critical parameters in
these simulation are (i) the heat diffusion length in gold
caused by the temperature-dependent thermal conductivity and the heat capacity of hot electrons in gold [17]
and (ii) the phenomenological value of Kapitza resistance
for hot electrons at the gold-cobalt interface.
We have used these simulations to fit in a selfconsistent manner a set of femtosecond time-resolved
measurements on gold-cobalt samples with L=30 nm
thick cobalt and a variable gold thickness. An example of such a measurement is shown in Fig. 4(a). A biexponential distribution of lattice temperature in goldcobalt structure (see inset in Fig. 4(c)) governs the cooling dynamics of the overheated cobalt into the much
thicker gold layer, serving as a heat sink on a 100 ps time
scale. This time scale unambiguously determines the
value of Kapitza resistance at Au-Co interface RCo−Au =
0.5 × 10−9 m2 K/W. Figure 4(b) shows the acoustic transient obtained by subtracting the thermal background
100
(2)
Thickness (nm)
∂ 2 Te
∂Te
= κ(Te ) 2 − g(Te − Tl )
∂t
∂z
∂Tl
Cl
= g(Te − Tl )
∂t
Ce (Te )
from the experimental reflectivity data in Fig. 4(a). The
acoustic part of the reflectivity signal is in quantitative
agreement with the solution of the acoustic wave equation
seeded with the self-consistent initial conditions obtained
from the two-temperature model.
The only part of the signal where we observe substantial differences between the theory and the experiment is the amplitude of the acoustic pulse emitted by
the overheated cobalt layer. In order to obtain quantitative agreement we had to assume a smaller value of
the Kapitza resistance RAu−Co = 0.17 × 10−9 m2 K/W.
There might be several explanations for this difference.
First, it could be the manifestation of previously reported decrease of the thermal boundary resistance at the
metal-metal interface at high temperatures [18]. While
varying the pump power within a factor of 10 we were
not able to notice any difference. Second, the intrinsic non-reciprocity of the thermal boundary resistance,
RAu−Co 6= RCo−Au , also known as a thermal rectification [19] may come into play.
50
interface (Fig. 2(c)). A small opto-acoustic modulation
is superimposed on a large thermal background. A fast
rise of lattice temperature within 10 picoseconds after
laser excitation is followed by its fast cooling within
200 ps and reach the quasi-stationary value.
We were only able to explain the dynamics of the thermal background assuming that the lattice temperature
in cobalt becomes much higher than in gold on a picosecond time scale and it cools down through gold-cobalt
interface on a time scale of a few hundreds of picoseconds. In order to understand the physics behind the observed non-monotonous temperature dynamics we have
performed numerical simulations within the framework
of a two-temperature model (TTM) [15]:
0
50
100 150 200
250 300
Time delay (ps)
FIG. 3: The two-temperature model is used to calculate the
dynamics of electron (a) and lattice (b) temperatures in goldcobalt bilayer excited by a femtosecond laser pulse from the
gold side. A remarkable overheating of cobalt (see text) a
few picoseconds after laser excitation triggers the dynamics
of heat diffusion (c) and coherent acoustic vibrations (d) on
a 100 ps time scale. Solid colored lines display the temporal (horizontal) and spatial (vertical) profiles (along the
dashed lines) of transient electron and lattice temperatures
and acoustic strain, respectively.
In addition to the determination of the overheating
factor we were able to measure the hot electron diffusion
depth. Figure 4(c) displays the results of two pumpprobe measurements with detection at the gold-air in-
4
spectrum. The comparison of excitation amplitudes of
the first (n = 1) and second-order (n = 2) magnons
∼ ((L/δhot )2 + (πn)2 )−1 as well as their detection efficiencies ∼ ((L/δskin )2 + (πn)2 )−1 give a ratio of 15%, in
agreement with our experimental data.
Transient reflectivity (a.u.)
(a)
1
= 0.25e−9
= 2.5e−9 R Au/Co
R Co/Sapp.
Kap
Kap
R Co/Sapp.
= 2.5e−9 R Au/Co
= 0.45e−9
Kap
Kap
R Co/Sapp.
= 2.5e−9 R Au/Co
= 0.65e−9
Kap
Kap
0.8
Experimental data
Acoustic pulse
from cobalt
0.6
Au (240 nm)
t = 4 ps
PUMP
0.2
t = 7 ps
PROBE
t = 50 ps
t = 250 ps
0
50
100
150
200
300
Experimental data
0.2
TTM fit: RKap= 0
TTM fit: RKap= 0.17e−9
TTM fit: RKap= 0.5e−9
0.1
G(t), a.u.
0
−0.1
−10 −5
−0.2
0
50
100
150
0 5
Time, ps
200
10
250
300
Time delay (ps)
5
150 nm
PROBE
R2(t)
R1(t)
R2(t)
PUMP
Au Co
0
dR1 (t)/dt
10
dR(t)/dt (a.u.)
(c)
250
Time delay (ps)
(b)
Transient reflectivity (a.u.)
Co Al2O3
0.4
0
Transient reflectivity (a.u.)
terface, for comparison. We have shown recently that
the time-derivative of simple reflectivity measurements
matches the acoustic pulses shape in case it is shorter
than 3.8 ps acoustic travel time through the skin depth in
gold at 400 nm probe wavelength [20]. The time derivatives of reflectivity in the inset in Fig. 4(c) compare the
acoustic pulse shapes generated by the direct optical absorption in cobalt and by hot electrons through gold.
Both pulses are consistent with the exponential heat penetration. A τhot =2 ps short acoustic pulse gives the hot
electron diffusion depth in cobalt δhot = τhot cs = 12 nm
(cs = 6 nm/ps is the sound velocity in hcp-cobalt). It is
shorter than a 3 ps pulse generated by the direct optical
excitation of cobalt corresponding to the heat diffusion
length of 20 nm [3].
Experimental observation of 2 ps short acoustic pulses
generated in cobalt by thermo-elastic mechanism unambiguously demonstrate the spatial localization of transient lattice heating, which has important consequences
for the magnetization dynamics. Figure 5(a) shows
the temporal evolution of Kerr rotation at the cobaltsapphire interface, which can be explained by the spatially inhomogeneous thermal excitation of magnetization precession in ferromagnetic cobalt. Similar to the
results of the direct optical excitation of ferromagnets
with ultrashort optical pulses [5], here we observe magnetization oscillations triggered by superdiffusive hot electrons. The magnetization precession is quantitatively reproduced by the superposition of two damped oscillations: a low-frequency ferromagnetic resonance (FMR,
n = 0) and high-frequency first-order magnon mode
(n = 1). The physical interpretation is identical to that
by van Kampen and co-workers [5], who reported the
in-phase excitation of homogeneous FMR and inhomogeneous magnon modes as a result of rapid thermally
induced changes in the magnetocrystalline anisotropy in
a ferromagnet. Two experimental observations corroborate our conclusion that a high-frequency oscillation can
be interpreted as a standing mode of exchange coupled
magnon in cobalt. First, the high frequency oscillation
is shifted by π with respect to FMR-oscillation. Taking
into account the sinusoidal spatial distribution of magnetization in a first-order magnon mode M (z) = cos(π Lz )
(see the inset in Fig. 5(a)) we conclude that the Kerr rotation measurement within the optical skin depth at the
cobalt-sapphire interface should result in a π-phase shift.
Second, the frequency ω1 of the high-frequency oscillation
agrees well with the estimates for the exchange-coupled
magnon in cobalt [21]: h̄ω1 = h̄ωFMR + D(π/L)2 with
D ≃ 550 meV Å2 . In some samples we were able to observe a short-living second-order (n = 2) magnon mode
at a frequency of h̄ω2 = h̄ωFMR + D(2π/L)2 . Excitation of second-order magnons is evidenced in a wavelet
transform [22] of the magneto-optical Kerr signal, which,
analogous to a windowed Fourier transform, provides information about the temporal evolution of the signal
−5
dR2 (t)/dt
150 nm
5
PUMP
0
PROBE
R1(t)
Au Co
−5
−10
0
30
35
40
45
10
20
30
40
Time delay (ps)
50
60
70
80
Time delay (ps)
FIG. 4: Femtosecond pump-probe measurements (a) evidence
the non-monotonous temperature dynamics in the inhomogeneously heated gold-cobalt structure (see the inset). The coherent acoustic transients (b) contain a short acoustic pulse
emitted by thermal expansion of the overheated cobalt layer.
Inset shows the photo-elastic response function G(t) [20, 23].
Reflectivity measurements at the gold-air interface (c) evidence the generation of ultrashort acoustic pulses resembling
heat penetration profile in cobalt (see the inset and Ref. [20]
for details).
To summarize, we have explored non-equilibrium pathways of energy transport in gold-cobalt bilayers mediated
by superdiffusive hot electron. The experimental observation of nonmonotonous temperature dynamics, emission of coherent acoustic pulses and excitation of coherent
exchange-coupled magnons (with n=1,2) are supported
5
(a)
Experiment
FMR+magnon
FMR
Magnon
0.5
Loire, Alexander von Humboldt Stiftung and the European Research Council (FP7/2007-2013) / ERC grant
agreement no. 306277 for funding.
Kerr rotation (a.u.)
0
−0.5
−1
Au (190 nm) Co
PUMP
Heat
diffusion
depth
Al2O3
Probe
depth
n=0 (FMR)
PROBE
(Kerr rotation)
n=1 (magnon)
−1.5
n=2 (magnon)
−2
−2.5
Frequency (GHz)
(b)
100
80
n=2 (magnon)
60
40
n=1 (magnon)
n=0 (FMR)
20
0
100
200
300
Time delay (ps)
FIG. 5: (a) Spatially inhomogeneous heating of cobalt triggers
a complex magnetization dynamics consisting of the FMRprecession (21 GHz, n = 0) and exchange-coupled magnon
(37 GHz, n = 1). (b) Continuous wavelet transform of Faraday rotation signal evidences the excitation of a weak shortliving second order (n = 2) magnon at 80 GHz.
by TTM numerical simulations. The latter account for
the Kapitza resistance for hot electrons at the gold-cobalt
interface, which strongly affects the transient overheating
of the lattice in cobalt with respect to gold.
The above analysis allows to explain our initial observation, an order-of-magnitude difference in the Kapitza
resistances between a gold single layer and thick gold thin cobalt bilayer structure on sapphire. Laser-heated
electrons in gold penetrate with little resistance into
cobalt, where they give their energy to cobalt lattice on a
12 nm length scale. Hot phonons in cobalt transport heat
into sapphire substrate and the overall thermal resistance
is reduced to RCo−sapphire . This new mechanism to tailor heat transport through the acoustically mismatched
metal-dielectric (gold-sapphire) interface by adding an
additional metal (cobalt) layer, which is phonon-matched
to the dielectric substrate, is important for device physics
at the nanoscale.
The authors are indebted to P. Ruello, A. Melnikov,
I. Razdolski and R. Tobey for stimulating discussions
and to Nouvelle équipe, nouvelle thématique et Stratégie
internationale NNN-Telecom de la Région Pays de La
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