Structural and magnetic dynamics of a laser induced phase transition in FeRh

0.17 MB·English

by  S. O. Mariager

Structural and magnetic dynamics of a laser induced phase transition in FeRh
S. O. Mariager,1,∗ F. Pressacco,2 G. Ingold,1 A. Caviezel,1 E. Mo¨hr-Vorobeva,1 P. Beaud,1 S. L. Johnson,1 C. J.
Milne,3 E. Mancini,2 S. Moyerman,4 E. E. Fullerton,4 R. Feidenhans’l,5 C. H. Back,2 and C. Quitmann1
1Swiss Light Source, Paul Scherrer Institut, 5232 Villigen, Switzerland
2Fakult¨at fu¨r Physik, University of Regensburg, 93053 Regensburg, Germany
3E´cole Polytechnique Fed Lausanne, 1015 Lausanne, Switzerland
4University of California, San Diego, La Jolla, CA 92093-0401, USA
5Niels Bohr Institute, University of Copenhagen, 2100 København, Denmark
2 (Dated: 4 January 2012)
1
Weusetime-resolvedx-raydiffractionandmagneticopticalKerreffecttostudythelaserinduced
0
antiferromagnetic to ferromagnetic phase transition in FeRh. The structural response is given by
2
the nucleation of independent ferromagnetic domains (τ1 ∼30ps). This is significantly faster than
n the magnetic response (τ2 ∼60ps) given by the subsequent domain realignment. X-ray diffraction
a shows that the two phases co-exist on short time-scales and that thephase transition is limited by
J
the speed of sound. A nucleation model describing both the structural and magnetic dynamics is

1 presented.
1

] Todatethefastestmanipulationofmagneticfilmsand moments [15].
i
c elementsareinducedbysinglefslaserpulsesandinclude In order to unravel the physical processes underlying
s
- domain switching and demagnetization on sub-ps time- the phase transition a prerequisite is the ability to dis-
rl scales [1–4]. On similar time scales magnetization has tinguish the contributions arising from the lattice- and
mt been switched by ultrashort but strong magnetic field magnetic- dynamics. In this letter we report a time re-
pulses generated by relativistic electron bunches [5] and solvedx-raydiffraction (XRD) experiment directly mea-
.
t stripline techniques [6], while a third intriguing option suring the structural dynamics and providing the evolu-
a
m is the manipulation of the magnetic energy landscape tion of the AFM and FM volume fractions with a time
by strong single cycle electric field pulses [7]. Gener- resolution of ∼ 200 fs. The results are combined with
-
d ation of a magnetic moment is equally interesting but TR-MOKE measurements on the same sample and are
n harder to achieve on an ultrafast timescale. Ferromag- explainedusingasimplemodeldescribingthenucleation
o
netic (FM) ordercan be established inordinaryFM ma- and subsequent alignment of FM domains.
c
[ terials by cooling from the paramagnetic phase, but the The FeRh epitaxial thin film (d = 47 nm) was grown
processis limited by heat transferandtypicaltimescales on MgO(001) by co-magnetron sputtering from elemen-
2
are nanoseconds. In this context the antiferromagnetic tal targets. The film is epitaxial with a (001) surface.
v
5 (AFM) to FM phase transition in FeRh (TT ≈ 375K) is Uponheatingthroughthephasetransitionthelatticeex-
3 interesting because it can be induced by fs laser pulses. pands 0.7 % along the surface normal, in contrastto the
4 The first order phase transition from the low tempera- isotropic expansion of bulk samples, indicating a strong
6 ture AFM phase is accompanied by a ∼0.5 % volume in-plane strain.
.
1 increase, and though this has been known since 1939 [8] The time-resolved XRD was performed at an x-ray
1 the physical mechanism behind the transition has never energy of 7 keV using a synchrotron slicing source
1 been resolved and is still debated [9–11]. (200 ph/pulse at 2 kHz and 1.2 %bw) as probe and an
1
: The ultrafasttransitionhas been studiedin all-optical 800 nm 120 fs p-polarized laser pulse with an incidence
v o
pump-probe experiments using both transient reflectiv- angle of 12 as pump, resulting in a total time resolu-
i
X ity and time resolved magneto optical Kerr effect (TR- tion of 200 fs [16]. The x-ray gracing incidence angle
o o
r MOKE) [12, 13]. While the reflectivity measures a was either α = 0.51 or 0.71 , in order to match the
a combination of electronic and structural properties, TR- penetration depth of the x-ray probe to either the laser
MOKE measures the magnetization. In addition x-ray pump (penetration depth 15 nm) or to the film thick-
magnetic circular dichroism (XMCD), which is element ness (47 nm). Due to the grazing angle the x-ray spot
specific, has been used to probe the transition [14]. This size was 0.4×1 mm2. The (101) Bragg reflection was
study found a gradual growth of the magnetization on a recorded with a two dimensional PILATUS 100K pixel
time-scaleof∼100ps. Innone ofthese experimentswas detectorandrockingcurveswith60discreteimageswere
a separate determination of the lattice dynamics possi- acquired by rotating the sample around the surface nor-
ble. The magnetization dynamics have been simulated mal (±2.5o) [17].
with the Landau-Lifshitz-Gilbert equation and a model The TR-MOKE measurements were performed at
which considers growth of a non-homogenous magneti- 72kHzasatwo-colorpump-probeexperimentwith200fs
zation proportional to the spin-temperature followed by cross-polarized 800 nm p-polarized pump and 400 nm
a slower alignment and precession of the local magnetic probe pulses. The probe (58×26µm2) hadanincidence
2
−3 −3
x 10 x 10 0ps A B
0 0 1.5ps
1mJ/cm2, 340K 3ps
440K 3
6ps
−2 2.7mJ/cm2, 440K −2 9ps
400ps
q⊥ −4 2mJ/cm2, 340K −4 b.] 2
/⊥ ar
q [
∆ −6 2.7mJ/cm2, 340K −6
I
−8 −8 340K 1
5.2mJ/cm2, 340K
A B
0 5T0ime [ps1]00 150 0 F [m2.J5/cm2] 5 00.9 7 0.98 0.99 1 0.98 0.99 1 1.01
q [r.l.u.] q [r.l.u.]
⊥ ⊥
FIG. 1: (Color online) Shift of the center of the (101) Bragg
peak after laser excitation. (A) As a function of time delay.
FIG.2: (Color online) Bragg reflectionsobtained at different
(B) As a function of fluence at a fixed time delay of 145 ps
for temperatures aboveand below TT =375K. taimpuemdpelaflyuse,n(cAe)offo2r.a7pmuJm/cpmfl2u.eTncheeosfo5li.d2mlinJe/icsmt2heansidm(uBla)tfeodr
Bragg reflection at t=6psunderthesole influenceof thermal
strain.
o
angle of 60 with respect to the surface while the pump
o
was incident along the surface normal (90 ). We used a
longitudinal geometry with an applied in-plane external thresholdfluenceof∼1mJ/cm2correspondstoatemper-
field of 0.1 T. The time dependent traces were recorded ature increase of 32 K [25]. This matches the difference
foroppositeorientationsoftheexternalfieldandtheKerr between the sample (340 K) and the transition temper-
rotation is the difference of the two traces [18]. ature (TT=375 K) and is consistent with the thermal
nature of the laser induced transition. As a final verifi-
InFIG.1AweshowtheshiftofthecenteroftheBragg
cation that the peak shift arises from the AFM to FM
peak as a function of time and laser fluence. As the ex-
phase transition the sample was heated to 440 K, well
pansion due to the film geometry is purely one dimen-
sional, the shift occurs along the surface normal (q⊥). above TT. At this temperature the peak shift is given
solely by thermal expansion. We thus unambiguously
Anegativepeakshiftcorrespondstoanexpansionofthe
confirm the laser induced AFM to FM phase transition.
lattice,andforasingleunstrainedphasethepeakshiftis
proportionaltothelatticeexpansion,∆a/a≈−∆q⊥/q⊥. In FIG. 2A we further show the full Bragg peaks
We firstconsider dataobtainedata sample temperature for several time delays and a fixed pump fluence of
ofT =340K<TT. Atapumpfluenceof1mJ/cm2 the 5.2 mJ/cm2. At t = 0 ps the entire film is in the AFM
Bragg peak shifts to a new equilibrium position through phase. Att =400psthe entirefilmhasbeendriveninto
a single damped oscillation. This is the signature of a the FM phase. The full transformation is evident as the
thermally induced strain wave [19] and the period T= two peaks have the same shape. At intermediate times
18.6±0.9ps(95%confidenceinterval)isgivenbythetime thepeakisasumofthetwodistinctpeakscorresponding
it takes a strain wave to travel back and forth through to the two phases. We thus directly confirm the coexis-
the film, T = 2d/v. The resulting speed of sound v = tence of the two structural phases at short time scales.
5.1 km/s is consistent with the literature [20]. At higher This is supported by the solid line which is the calcu-
pump fluences the strain wave is still present but ac- lated Bragg peak at t = 6 ps under the sole influence of
companied by an increased peak shift. At intermedi- thermal strain[19]. It is thus evident that the transition
ate (2-2.7 mJ/cm2) laser fluences this extra peak shift proceedsthroughthedecreaseoftheAFMphaseandin-
is slower than the strain wave, while at high laser flu- creaseoftheFMphase,ratherthanthroughacontinuous
ences (5.2 mJ/cm2) the time scales are comparable. We change of the lattice constant. The phase coexistence is
attribute this peak shift to the transformation from the a common trait of first order transitions and has been
AFM to the FM phase, and since the peak shift at in- observed statically in FeRh for both the magnetic [14]
termediate fluences is slower than the strain wave, the and the crystallographic structure [21]. FIG. 2B shows
strain wave can not be the driving force of the transi- similar Bragg peaks obtained at a fixed pump fluence
tion. In FIG. 1B the peak shift is shownas a function of of 2.7 mJ/cm2. In this case the final state (t = 400ps)
fluence for a time delay of 145 ps. A deviation from the consists of both AFM and FM structure.
linear fluence dependence given by thermal expansion, In FIG. 1A it can be seen that the amplitude of the
is observed above 1 mJ/cm2. This threshold behavior initial strain wave does not scale with fluence above the
is the signature of a laser-induced phase transition. The threshold. Thus the phase transition adds to the mag-
3
nitude of the strain wave. The fact that the phase of
the FM peak is initially strainedis also seenin FIG. 2A.
Since the stress is relaxed at the speed of sound at least
A
forpartsofthefilmtheunderlyingchangeinenergyland-
0.6
scape from AFM to FM appears faster than τ ∼ d/v.
This timescale is the limit for the structural transition.
To obtain a quantitative measure of the structural M 0.4
F
change due to the phase transition we separate it from V
3
the effects of the strain wave. In our experiment the 0.2 2.7mJ/cm2, 0.51° 2
grazing incidence geometry and the relatively low x-ray 2.7mJ/cm2, 0,71° 1
energy limit the separation ∆q⊥ between the AFM and 0 2.0mJ/cm2, 0.71° 0
0.98 0.99 1 1.01
FM peaks, but the two contributions can be systemati-
cally extracted from the measured data by fitting it to 3 B 4.5mJ/cm2
thesumoftwosymmetricfunctions(a/cosh((x−b)/c)2) 3.1mJ/cm2
[26]. One such fit is shown in the insert in FIG. 3A. b.] 1.3mJ/cm2
This way the integrated intensities which are propor- ar 2 30 15
tbieoneaxltrtaocttehde, ascnadttienriFnIgGv.o3luAmtehseovfoltuhmeetwfroacpthioanseosfctahne θ [kerr 1 τ [ps]1 1200 5102χ
FM phase (VFM) is shown as a function of time delay. ∆ 02 4 6 8 10120
Beforethearrivalofthelaserpumpthefilmisentirelyin n
0
the AFM phase and VFM=0. After laser excitation the
FM volume grows to saturation within 100 - 200 ps. In- 0 100 200 300 400
creasingthe fluence from2.0to 2.7mJ/cm2 increasesthe Time [ps]
∗
transformedvolumefractionofthe FMphaseV from
FM
32% to 59%. By decreasing the x-ray penetration depth FIG. 3: (Color online) (A) Evolution of the volume fraction
o o
from 47 nm (α = 0.71 ) to 15 nm (0.51 ) we see that oftheexpandedFMphaseasafunctionoftimedelay,shown
for smaller probe depths VFM rises significantly faster, for two different pump fluences and incidence angles. The
while the transformed volume is only increased slightly. insertillustratesthefittingprocedure(t=6ps,2.7mJ/cm2),
showingtheAFM(dashed)andFM(dotted)fitfunctions,and
This implies that the nucleation of the FM phase starts
theirsum(solid). (B)TransientKerrrotationforcomparable
at the free surface while the final phase consists mainly
fluences. Theinsetshowsthedependenceofthetimeconstant
of domains penetrating the entire film depth. τ1(o)andachi-squareestimator(+)onthemodelparameter
To compare the change in structure to the change in n. Thesolidlinesarefitstothedataasdescribedinthetext.
magnetization we measured the change in Kerr rotation
(∆Θkerr) on the same sample but at 313 K, as shown in
namics in terms of nucleation and alignment of FM do-
FIG. 3B. The higher pump fluences applied compensate
mains. Weassumethatthefilmisinstantaneouslyheated
for the lower sample temperature. As for the x-ray data
weobserveathresholdinlaserfluence. Belowthethresh- above TT and that the nucleation of the FM phase pro-
oldthereisnochangeinmagneticmoment(1.3mJ/cm2) ceedsthroughnucleationatmanyindependentsites. The
while above the threshold the Kerr rotation increases rateofchangeofVFM isthenproportionaltoVAFM and
described by a single time constant τ which may differ
and reaches saturationafter severalhundred ps (3.1 and 1
4.5 mJ/cm2). For the first 100 ps the dynamics appears for the structural and magnetic changes. Because the
transition is of first order the final state may be mixed.
tofollowapowerlaw,instrongcontrasttothegrowthof
Toaccountfor this we introducethe finalfractionofFM
VFM. Asshowninthemodelbelowthisdifferencearises ∗
becauseXRDmeasuresthevolumeofFMdomains,while phase VFM. As VFM + VAFM = 1 we then find:
TR-MOKE measures their alignment. Our TR-MOKE dVFM VAFM −(1−VF∗M) VF∗M −VFM
results are in agreement with previous XMCD [14] and = = (1)
dt τ τ
TR-MOKE [12, 13] experiments, except for the previ- 1 1
ouslyreportedultrafastTR-MOKEcomponentwhichwe This is essentially the Avrami model without growth of
do not observe. The absence of the ultrafast response existing domains [22] and the solutionis the exponential
may have two reasons. First, TR-MOKE is prone to op- functionV∗ (1−exp(−t/τ )). Thedepthdependenceis
FM 1
tical artifacts in the first hundreds of fs after excitation. only included by allowing different time constants when
Second, the absence might be due to the different probe averagingacrossdifferentprobedepths. Thisexponential
spot size usedin the different experiments,as this deter- functionhasbeenusedtofitthedatainFIG.3Aandde-
mines whether ornotthe magnetizationis averagedover scribes the data very well. Within errorbars we find the
many FM domains or just a few. same time constant τ =33±4 ps for both intermediate
1
We now present a model describing the observed dy- fluences,whileτ =14±3psatα=0.51o. Theexponen-
1
4
tialgrowthofVFM isonlyobservedwhenthenucleation thegoodagreementbetweendataandmodelweconclude
of independent domains is dominant while the growthof that the FM domains initially nucleate with un-aligned
existing domains is suppressed. As the x-ray spot size is moments which are subsequently aligned. We speculate
0.4×1 mm2 the distance between nucleation sites must thattheinitialdomainstructureisgivenbythe underly-
then be less than ∼10 µm. ing AFM phase and that the mechanism responsible for
Inordertodescribethemagnetizationweassumethat the re-alignment process is domain wall motion.
the FM domains nucleate with the magnetization fixed
Thesimplestalternativemodelwoulddescriberealign-
into one of n directions and that all n directions are
mentasarotationofthetotalmomentofadomain. The
equally probable. We assume one of these directions is
realignment term in (2) and (3) would then be ∓Vn/τ2,
favoredby the applied magnetic field and define the vol- independent of VA. For this model χ2 ≈ 30 which is
ume fractionVA ofFMphasealignedtothe appliedfield significantly worse than χ2 =1.8 obtained above. In ad-
and the volume fraction Vn not yet aligned. These sat- dition the fit is independent of n and results in different
isfy VFM = Vn + VA. We finally assume that alignment nucleation times τ for structure and magnetism. This
1
ofthemagnetizationoccursbygrowthofthealignedFM
would imply that the phase transition is independent of
domains at the expense of non-aligned FM domains, as
the anisotropy and that the magnetic domains nucleate
describedbyaproducttermVAVn/τ2 andasingletime- slower than the structure. Both conclusions appear less
constant τ . As this model depends on the existence of
2 likely than those reached from (1) - (3). We thus reject
both aligned and un-aligned FM domains it supports a
the alternative explanation.
theory whereshort-rangeinteractionsareresponsible for
aligning neighboring FM domains through domain wall Insummarywehavemeasuredthestructuralandmag-
motion. Given these assumptions the time evolutions of netization dynamics of the AFM to FM phase transition
Vn and VA are described by two differential equations: in FeRh on an ultra-fast timescale. XRD allowed us to
directly observe the co-existence of the two phases and
dVn n−1dVFM VAVn toderiveasimplemodelwhichdescribestheevolutionof
= − (2)
dt n dt τ both the structure and the magnetization. We find two
2
intrinsic timescales: One for the initial nucleationof FM
domains which is the same for both magnetic and struc-
dVA 1dVFM VAVn
= + (3) tural dynamics, and a second for the subsequent growth
dt n dt τ
2 ofFMdomainsalignedtotheappliedmagneticfield. The
co-existence of FM and AFM domains is clearly seen in
The MOKE signal is proportional to the magnetization
along the preferred direction: <m> ∝ VA - Vn/(n-1). theXRDdata. Atintermediatepumpfluencesthephase
transition to a large extent proceeds similarly to static
This is valid when one of the n-1 directions is opposite
heating, while at higher fluences the structural change
tothe appliedfieldandthe magnetizationoftheremain-
is limited by the speed of sound. This speed limit on
ing n-2 directions averages to zero. The underlying as-
structural change in principal allows for a significantly
sumptionsofnucleationandcoexistenceofphasesinthis
faster magnetic response, which we do not observe. It
modeldifferfromtheworkbyBergmanetal. [15]whoas-
thus appears that magnetic and structural nucleationgo
sumedthat the localmagnetizationgrowsmonotonously
hand in hand rather than one driving the other. While
with spin-temperature throughout the film.
the microscopic nature of the magnetization change has
The threedifferentialequationsaresolvednumerically
been considered theoretically [11], a more definitive an-
for integervalues of n, andthe resultoffitting the result
swer will require the use of spatially resolved magnetic
to the TR-MOKE data is shown in FIG. 3B for n=4,
probes in order not to average the dynamics over many
which optimizes the fit. The agreement between experi-
ment and fit is excellent with χ2 = 1.8. The result n=4 domains.
is consistent with the in-plane magnetization expected The x-ray experiments were performed on the X05LA
for a cubic thin film, and has been confirmed by static beam line at the Swiss Light Source, Paul Scherrer In-
XMCD PEEM images obtained for the same film. For stitut, Villigen, Switzerlandand wethank D. Grolimund
the nucleationtime τ =17.8±0.9 ps we find, as for the and C. Borca for help. SOM thanks P. Derlet and FP
1
XRDdata,thesamevalueforbothpumpfluenceswithin thanks G. Woltersdorf for fruitful discussions. We ac-
errorbars. Since the probedepthforthe laserinthe TR- knowledge discussions with K. Sokolowski-Tinten of our
MOKE experiment is ∼11 nm this must be comparedto results. This work was supported by the Swiss National
the 14±3 ps obtained with XRD at α=0.51o. We thus Foundation through NCCR MUST, by Marie Curie Ac-
conclude that the timescales of nucleation for magnetic tions through the FANTOMAS Project within the Sev-
andstructuraldomainsarethesamewithintheerrorbars. enthFrameworkProgramme(FP7),bytheDanishnatu-
Forthe finalparameterτ whichdescribesthe alignment ralsciencecouncilthroughDANSCATTandbytheDan-
2
ofdomainsweobtain72±1ps and57±1psfor fluences ish National Science Foundation. Work in UCSD was
of 4.5 mJ/cm2 and 3.1 mJ/cm2 respectively. Based on partially supported by DOE-BES Award de-sc0003678.
5
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∗
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