IEEE TRANSACTIONS ON MAGNETICS, VOL. 51, NO. 4, APRIL 2015
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Curie Temperature Distribution in FePt Granular Media
Simone Pisana1,2 , Shikha Jain1 , James W. Reiner1 , Oleksandr Mosendz1, Gregory J. Parker1 ,
Matteo Staffaroni1 , Olav Hellwig1 , and Barry C. Stipe1
1 San
2 Department
Jose Research Center, HGST, a Western Digital Company, San Jose, CA 95135 USA
of Electrical Engineering and Computer Science, York University, Toronto ON M3J 1P3, Canada
The Curie temperature distribution is an important parameter affecting transition noise in heat-assisted magnetic recording.
In this paper, we follow up on our recent report on a technique to evaluate the Curie temperature distribution and provide modeling
that validates the method as well as provides the experimental bounds for its validity. Thermal modeling is used to determine
whether the technique is sensitive to extrinsic sources of grain temperature variations, such as distributions in thermal boundary
resistance. The technique is applied to a variety of FePt granular media films of varying alloy composition and chemical ordering,
and we find the Curie temperature distribution to depend primarily on grain ordering kinetics. We also present results of grain
switching probability as a function of the applied magnetic field and find a non-trivial dependence on the alloy magnetization.
Index Terms— Curie temperature, FePt, heat-assisted magnetic recording (HAMR), magnetic media.
I. I NTRODUCTION
T
HE MAGNETIC data storage industry has been pursuing next-generation magnetic recording technologies to
follow perpendicular magnetic recording. For more than a
decade, this activity has concentrated on heat-assisted magnetic recording (HAMR) [1]–[3], which is based on plasmonic
devices in the recording head and hard magnetic materials
(typically FePt) in the granular medium to achieve higher
effective write field gradients and hence higher data storage
density. The introduction of HAMR is faced by many new
implementation challenges that span the topics of laser integration, plasmonic device fabrication, thermal management, hightemperature head-disk interactions, novel magnetic media, to
name a few. In terms of the fundamentals of magnetic recording, HAMR presents a range of new performance limiting
factors and magnetization reversal processes near the Curie
temperature (TC ) that are not yet fully understood.
In this paper, we present modeling and experimental results
aimed at evaluating the Curie temperature distribution (σTc )
in FePt granular magnetic media. This distribution is an
additional and significant contributor to transition noise in
the magnetic recorded data pattern in HAMR [4] and can be
linked to other common magnetic parameter variations, such
as saturation magnetization (Ms ) and anisotropy field (Hk ), as
well as physio-chemical grain properties, such as grain size
and degree of L10 chemical ordering [5]. The importance
of σTc to HAMR originates from the relation between the
location of a magnetic transition and the medium temperature
at the time the transition is recorded. In addition, similar
effects on transition noise can come from extrinsic sources
of grain temperature variation (σT ) by the absorption of nearfield radiation and/or dissipation of heat [6]. This paper builds
on our previous paper [7] and provides additional modeling
and experimental results.
Manuscript received August 6, 2014; revised August 29, 2014; accepted
September 2, 2014. Date of current version May 18, 2015. Corresponding
author: S. Pisana (e-mail: [email protected]).
Color versions of one or more of the figures in this paper are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TMAG.2014.2355493
II. M ODELING OF R EMANENT M AGNETIZATION
F OLLOWING A H EAT P ULSE
It has been found that σTc can be recovered from the
switching temperature distribution of a grain ensemble when
the heat exposure time is at the nanosecond time scale [7].
To demonstrate the validity of this approach, we model the
thermal behavior of our magnetic media and present the
relevant time scale in which σTc can be experimentally determined.
The thermal model is run with a finite-element multi-physics
COMSOL package and consists of a multi-layer medium
exposed to a far-field near infrared pulse lasting ∼6 ns.
The medium layer composition is FePtC(7 nm)-MgO(12 nm)HS(30 nm)-UL(100 nm)-glass, where HS is a metallic heat
sink layer and UL is an adhesion underlayer. The structure
is similar to the samples that have been measured in this
paper, and its optical and thermal properties were determined experimentally by spectroscopic ellipsometry and time
domain thermoreflectance. The thermal parameters consisted
of thermal conductivity and thermal boundary conductance and
included anisotropy in the granular FePtC layer.
The magnetic modeling is performed on a grain ensemble with a Landau–Lifshitz–Bloch formalism as previously
described [1], [8]. The grain properties are distributed as
determined by various characterization techniques [8], and
include grain size and orientation variations, Hk and TC
distributions. To model the switching temperature distribution,
the grains are first set with uniform magnetization and exposed
to a particular maximum temperature (TMAX ). The grains are
kept at this temperature for a varying amount of time (dwell
time) and then cooled in a constant reversing magnetic field.
The strength of the magnetic field is kept below the roomtemperature nucleation field of the medium. The cooling rate
is characterized by a simple exponential decay with time
constant τ , which was also varied. The switching temperature
distribution is obtained by plotting the remanent magnetization
state as a function of TMAX . For each TMAX , the medium
was reinitialized to the uniform magnetization state. This
procedure is similar to the experimental method to determine
the switching temperature distribution.
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Fig. 1. (a) Simulation result of the temperature dependence of the FePt
layer in typical HAMR media following a ∼6 ns infrared laser pulse. The
main panel shows the detailed behavior near the peak temperature. Inset:
complete time range simulated. The temperature dependence is approximated
in the magnetic model as shown in red. (b) Simulated cumulative switching
temperature distribution of an ensemble of FePt grains. The model can be fitted
to an erf function leading to a σTc of 4.2% and mean switching temperature
T50 of 698 K. (c) Surface plot of T50 as a function of dwell time at TMAX
and cooling time constant. The colors are binned in intervals of 1% of TC
and the red dashed line indicates TC .
Fig. 1(a) shows the temperature swing of the FePt layer
following a laser pulse. In this case, the intensity of the laser
pulse was selected so that TMAX = 800 K. The dwell time
and cooling rate in the magnetic model simplify the shape
of the thermal response of the medium and span a range
of values. In the thermal model of Fig. 1(a), for example,
the dwell time represents the temperature plateau near TMAX ,
which is ∼0.5 ns, and the cooling rate time constant was set
IEEE TRANSACTIONS ON MAGNETICS, VOL. 51, NO. 4, APRIL 2015
to ∼32 ns. The thermal response of the medium 10 ns or more
after TMAX deviates from an exponential decay, but its shape
is no longer relevant as the medium has cooled sufficiently for
the magnetization to be stable.
Fig. 1(b) shows an example of a cumulative switching temperature distribution curve, with the remanent magnetization
state of the grain ensemble in the y-axis and TMAX in the xaxis. The simulation was made with an applied field of 0.5 T, a
dwell time of 0.5 ns, and a cooling rate time constant of 30 ns,
similar to the expected temperature dependence extracted
previously, and as shown in Fig. 1(a). The magnetization level
does not reach +/−Ms due to a small fraction of superparamagnetic or low thermal stability grains. The grain’s TC distribution is modeled as having two origins: 1) a grain volume distribution and 2) an additional Gaussian component of 2.5%, for
a total of ∼4% standard deviation and 699 K mean <TC >. The
curve in Fig. 1(b) can be approximately fit to an erf function,
and the obtained fit matches the input Curie temperature distribution, highlighting the validity of the experimental approach.
A small fraction of the grains switches well below TC , between
500 and 650 K. This is due to a distribution in grain thermal
stability, which results in thermally activated magnetization
reversal rather than switching by magnetization freezing when
cooling through TC as for the majority of the grains.
Fig. 1(c) contains the results for a number of simulations
in which the cooling rate time constant and dwell time was
varied, whereas the applied field was kept at 0.5 T. As can
be seen in most of the cases, the grain mean switching
temperature (T50 ) is found to be within 1% of <TC >, except
for the lower left corner which shows grains switching well
above TC , due to the fact that the grains are exposed to TMAX
for times approaching the magnetization relaxation times.
Therefore, for the experimental dwell times and cooling rates
reached in our experiment, the grains are found to switch
<1% below TC . Given that the time scales of our experiments
are still longer than typical recording time scales, we also
analyzed, in the same manner of Fig. 1(b), the cumulative
switching temperature distribution for a dwell time of 63
ps and cooling rate time constant of 1 ns. The fit yielded
T50 = 699.5 K and σTc of 4.0%, indicating that even at
recording time scales the switching temperature distribution is
an accurate measure of the Curie temperature distribution. It is
also to be noted that additional simulations obtained for larger
applied fields showed that the discrepancy between switching
temperature and TC can increase due to thermal activation.
Nonetheless, accurate σTc measurements can be obtained for
applied fields below the room temperature nucleation fields
of the grains (∼1 T), or above the threshold for deterministic
switching, as described in Section III. Caution should be used,
if the grain ensemble is expected to have poorer anisotropy
distributions, as this can cause a larger error due to thermally
activated switching, in which case lower applied fields are
warranted.
As discussed in Section I, extrinsic effects altering the
amount of power absorbed or dissipated by a grain can
introduce a grain temperature distribution σT , which can
potentially affect a σTc measurement. The measurement takes
place by far-field illumination, therefore, there is no source of
light power absorption distribution, as the grain size is much
smaller than the wavelength of the incoming light. To evaluate
the effects of grain thermal boundary conductance distribution,
PISANA et al.: CURIE TEMPERATURE DISTRIBUTION IN FePt GRANULAR MEDIA
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we model extreme cases in which this parameter has been
lowered by up to 4×. In all cases, the FePt medium is found to
cool at rates almost identical to the underlying MgO layer. This
is not surprising as the FePt/MgO thermal boundary resistance
accounts for <10% of the total thermal resistance incurred
between the FePt layer and the deepest layer reached by the
thermal wave (i.e., the adhesion under-layer). In the limiting
case of a 4× reduction of thermal boundary conductance,
there would be a negligible variation in cooling rate and
hence a negligible difference in grain switching temperature
according to the results of Fig. 1(b). For the same limiting
case, we find a maximum FePt-MgO interface temperature
difference of 12 K for a 500 K FePt temperature rise, or ∼2.2%
of TC , i.e., a grain with poorer thermal coupling would be
hotter. If present, this effect would add in quadrature to σTc ,
and contribute significantly to the lowest values of switching
temperature distribution reported in this paper (3%). However,
we treat σT contributions to our measurement as unimportant,
as only extremely broad distributions in thermal boundary
conductance (a factor of 4× at 1σ in the example above) would
affect the measurement, and only for switching temperature
distributions of 4% or below.
III. M EASUREMENT OF C URIE T EMPERATURE
D ISTRIBUTION
The experimental optical pump-probe setup and measurement procedure are as previously described [7]. Briefly, the
setup consists of an infrared pulsed laser as pump to briefly
heat the sample and continuous wave laser as probe for Kerr
magnetization measurement. Both beams are focused on the
sample surface, with the pump size being 12× larger than
that of the probe to measure a uniformly heated area. The
sample is placed between the poles of an electromagnet that
provides out of plane magnetic bias fields. The switching
temperature distribution is obtained by ramping the pump laser
pulse power, one pulse at a time in a constant applied reversal
field that is smaller than the room temperature nucleation
field of the HAMR medium. After each pulse, the medium is
initialized to the same uniformly magnetized state by reversing
the applied field and selecting a pump laser power sufficiently
high to cause a temperature rise in the medium above the Curie
temperature distribution.
The HAMR media samples presented in this paper consist
of three series (some of the results from two of which
have been presented before): 1) a growth temperature series;
2) a growth pressure series; and 3) a Cu doping series.
In all cases, the samples have been deposited in a commercial
Intevac Lean 200 sputter tool as previously described [9].
The growth temperature series consists of samples exposed
to differing growth temperatures to affect the degree of mean
chemical ordering. In the growth pressure series, the differences in sputter gas pressure lead to variations in Fe:Pt
composition due to pressure-dependent sputter yield for our
target geometry. Last, in the Cu alloy series, varying amounts
of CuPt were codeposited with FePt. The CuPt and FePt
target compositions and sputter rates were carefully chosen
to obtain a composition of Fe50−x Cux Pt50 , where x is the
atomic Cu concentration in percent. The Cu is commonly
introduced in FePt to lower the alloy TC without drastically
reducing Hk [3].
Fig. 2(a) shows an example of a measured cumulative
switching temperature distribution. The change in grain
Fig. 2.
(a) Example of a measured cumulative switching temperature
distribution taken at a constant applied reversing field of 1 T. Kerr rotation
is proportional to the number of switched grains and the laser pump pulse
energy is proportional to TMAX . Data are fitted to an erf function resulting
in a measured σTc of 3.1% ± 0.3%. (b) Magnetization curve obtained by
measuring the media magnetization state following a single pump pulse of
9 μJ at each applied field value. Pump pulse energy is high enough for each
grain to reach TC , therefore the measurement reveals the grains’ switching
probability at a given applied magnetic field and peak temperature reached.
remanent magnetization state as a function of applied pump
pulse energy can be interpreted as the cumulative distribution
function of switching (Curie) temperatures, as explained
in Section II. Assuming a Gaussian distribution of Curie
temperatures, we fit the measurement to an erf function
to extract the mean and distribution width of the laser
energies needed to switch the medium, which we label σLaser .
This quantity is the Curie temperature distribution, we seek,
referenced to room temperature (i.e., zero pulse energy yields
no heating, and TMAX = room temperature). To obtain σTc
in typical units referenced to degrees K , an independent
measurement of the mean Curie temperature <TC > is needed,
for example, by vibrating sample magnetometry (VSM), as
shown below. Then, σTc = σLaser (<TC > −TAMB )/<TC >,
where TAMB is the ambient temperature. Note that this
conversion assumes a linear relation between laser energy
delivered to the medium and the medium’s temperature rise.
We have carefully verified that this linearity holds for our
experiment by modeling the temperature rise of the medium
as a function of laser energy, including the temperature
dependence of the heat capacity.
The curve in Fig. 2(a) shows some grain switching below
<TC >, most visible at 5–6 μJ pulse energies. This was also
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Fig. 3. XRD analysis and Curie temperature distribution for FePt HAMR
media as a function of (a) and (b) deposition temperature and (c) and (d)
Fe:Pt composition.
visible in the model in Fig. 1(b) and is due to a small fraction
of grains having poor thermal stability K u V product that
switch prematurely by thermal activation (K u is the uniaxial
magnetocrystalline anisotropy energy density and V is the
grain volume). Some noise present in the transition between
7 and 8 μJ is due to laser source energy instabilities and can
be alleviated by acquiring more data points.
Fig. 2(b) shows the result of another measurement that
yields the field-dependent grain switching probability. In this
case, the pump pulse energy is fixed at a value sufficiently
high to insure that all grains cool through TC . The curve is
obtained by sweeping through the applied field and delivering
one pump pulse at each field, then measuring the Kerr rotation.
The curve is symmetric and shows zero coercivity as expected.
The data show that for this medium ∼0.5 T is sufficient
to deterministically switch all the grains through TC for the
given experimental cooling rate time constant of 29 ns. This
information can be used in conjunction with media and head
models to optimize the HAMR recording system. We shall see
how varying the FePt medium composition can yield different
grain switching probability curve shapes.
Fig. 3 shows the results of measurements made on
the first two series of samples considered in this paper.
X-ray diffraction (XRD) analysis and VSM are used to highlight the variations in crystal and magnetic structure, along
with the measured Curie temperature distributions σTc . In the
first set of samples, the deposition temperature was varied,
resulting in different degrees of L10 order obtained in the
FePt grains. Fig. 3(a) shows the expected increase in XRD
(001)/(002) peak intensity ratio with deposition temperature.
Higher deposition temperatures increase the mean ordering
parameter due to the enhancement in the thermodynamic
driving force for ordering [10]. σTc is found to decrease, as
shown in Fig. 3(b), and we attribute this to the improvement
in ordering kinetics. There is a 165 K difference between the
Curie temperatures of the A1 and L10 phases of FePt [11].
As the deposition temperature increases, the kinetics improve,
resulting in higher mean ordering as well as lower ordering
distribution. In other words, the improved kinetics causes the
IEEE TRANSACTIONS ON MAGNETICS, VOL. 51, NO. 4, APRIL 2015
Fig. 4. XRD and VSM analysis, and Curie temperature distribution for
FePt HAMR media as a function of additional Cu content. (a) and (b) Curie
temperature estimation and its variation with Cu content. The dashed red line
in (a) highlights the kink in Ms (T ) at TC . (c) Dependence of the XRD (002)
peak and coercive field (Hc ). (d) Dependence of σTc .
grains to order better and reach their ordering equilibrium
faster, reducing the grain-to-grain variations.
The second set of samples shown in Fig. 3(c) and (d) shows
the characterization results for FePt media with varying Fe:Pt
stoichiometry. The changes in relative Pt content in the alloy
results in strong variations in mean ordering, anisotropy, and
magnetization (not shown) [1] as well as σTc . Note that in this
case, the samples were also grown at a reduced deposition
temperature near 580 °C. In addition, the conversion from
σLaser to σTc was done following the compositional variation
of <TC > reported in [12], due to the lack of direct <TC >
measurements from these samples. Barmak’s group has made
careful measurements of the ordering kinetics of FePt alloys,
and has found that the kinetic drive to order lowers away from
1:1 stoichiometry [12]. Therefore, if the reduced kinetics are
not balanced out, by increasing the deposition temperature,
for example, the mean ordering lowers and the ordering
distribution rises away from equiatomic compositions.
The third set of samples in Fig. 4 is for media films in
which Cu was added such that the resulting ternary alloy
was of the form Fe50−x Cux Pt50 , where x is the atomic Cu
concentration in percent. Fig. 4(a)–(c) shows the XRD and
VSM data obtained for these samples. Fig. 4(a) shows an
example of how <TC > is estimated by VSM. Given that the
geometry in the instrument is constrained for high-temperature
measurements to applying a field in-plane, we measure the
total magnetization as a function of temperature in a constant
applied field of several Tesla. This rotates a significant fraction
of the sample’s total magnetization in-plane so that it can be
detected, but it also adds large paramagnetic and diamagnetic
contribution to the total signal. Therefore, the detailed Ms (T )
curves cannot be isolated owing to the large temperature
dependence of diamagnetic contribution. However, both blocking and Curie temperatures can be obtained, respectively, by
comparing zero-field-cooled to field-cooled curves and by
identifying the characteristic kink at Tc . Fig. 4(b) and (c)
shows the Curie temperature, coercivity, and c-axis (002) peak
position as a function of Cu alloying. The ordering parameter
PISANA et al.: CURIE TEMPERATURE DISTRIBUTION IN FePt GRANULAR MEDIA
3200205
follow unique trends with respect to Ms or K u . The lack of
dependence on Ms implies that there is no trivial dependence
between grain switching probability and Zeeman energy as
the grains cool through Tc . For example, alloys with lower
Ms might be expected to need a higher applied field for full
deterministic switching in order to have total Zeeman energies
comparable with alloys with higher Ms . The magnetization
plays an important role in determining the strength of the
thermally induced fluctuation fields important near the Curie
temperature, therefore careful micromagnetic modeling may
be needed to understand these results.
Fig. 5. Media switching probability as a function of alloy composition. Raw
data have been smoothed to highlight the differences and normalized to the
same saturation moment.
was not calculated given the added difficulty in accounting for
the variations in diffraction intensity as Cu is added. On the
other hand, one can see that the c-axis (002) peak position
shifts to lower lattice spacings, and the alloy coercivity and
Curie temperature lower, consistent with the addition of Cu.
Measurements of σLaser were accompanied with measurements
of <TC > to extract σTc . As can be seen, the addition of
Cu does not result in deterioration of the Curie temperature
distribution. Note that the other experiments resulted in worse
Curie temperature distributions as the mean ordering was
lowered. Here, however, the reduction in coercivity is not
associated with drastic reductions in chemical ordering as the
Curie temperature distribution does not vary within the error
of our measurement, suggesting that the addition of Cu is not
leading to a reduction of the drive to order. Barmak’s group
has found that Cu alloying yields the same variations in kinetic
ordering temperature as the binary FePt alloy [12]. That is,
having a Pt content that is off the optimum results in lower
drive to ordering, but adding Cu up to 17 at% does not alter it
further as compared with the binary alloy having the same Pt
content. Given that our Cu alloying preserves the Pt fraction
at 50 at%, no reduction of kinetic drive to order would be
expected, and this is consistent with our results of constant
Curie temperature distribution with the addition of Cu. The
reduction in Hc in our samples is therefore mostly attributed
to reduction in K u due to alloying, rather than reduction in
chemical ordering.
The effects of alloying are further investigated in measurements of grain switching probability, as shown in Fig. 5. The
figure shows one quadrant of the measured M versus H curve
in which at each field a pump pulse was applied. In all
cases, the pump energy was selected by first measuring the
cumulative switching temperature distribution and selecting
an energy 3σ above the mean switching temperature (T50 ), to
insure comparable temperature exposure conditions. The data
were smoothed to highlight the differences. Measurements
taken for FePt media deposited at varying temperatures as well
as similar Fe:Pt stoichiometries were indistinguishable, and
only a representative curve for Fe50 Pt50 is shown. It was found
that stronger variations from optimal stoichiometry resulted in
departures from the typical grain switching probability curve,
with binary FePt alloys needing a higher field to deterministically switch all grains, and ternary FeCuPt alloys needing
lower fields. It is important to note that the behavior does not
IV. C ONCLUSION
We have presented a method to evaluate the Curie temperature distribution in granular magnetic media. We modeled the remanent magnetic state of grain ensembles, while
cooling through the Curie temperature and found that the
switching temperature distribution obtained, when grains cool
at characteristic cooling times of 1–100 ns is representative
of the Curie temperature distribution. The applied reverse
field should be strong enough to deterministically switch the
grains and lower than the room-temperature nucleation fields,
provided no significant fraction of the grains switch by thermal
activation, in which case, lower applied fields are preferable.
The Curie temperature distribution measured for a variety of
alloy compositions and deposition temperatures seems to be
dominated by the ordering kinetics, whereas the switching
probability is found to have no trivial dependence on the
magnetization and needs careful micromagnetic investigation
to be better understood.
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