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Static and dynamic X-ray resonant magnetic scattering studies on magnetic
domains
Soriano, J.M.
Publication date
2005
Link to publication
Citation for published version (APA):
Soriano, J. M. (2005). Static and dynamic X-ray resonant magnetic scattering studies on
magnetic domains.
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4 4
STUDYY OF MAGNETIZATION
DYNAMICSS OF
G D F E
THIN
FILMS S
TheThe magnetization dynamics under the influence of strong magnetic field pulses of two
ferrimagneticferrimagnetic thin films is studied using time-resolved X-ray resonant magnetic scat-teringtering and Magneto-Optical Kerr Effect techniques. In both cases the samples are mag-neticallynetically excited by a 7 kOe pulse provided by a microcoil. The two amorphous GdFe filmsfilms differ in composition and consequently in magnetization. For a composition close
toto the ferrimagnetic compensation composition, the Gd subnetwork magnetization van-ishesishes during the pulse, while the Fe magnetization initially does not reach the satura-tiontion value. Also, this sample shows a very slow relaxation stretching over hundreds of
nanoseconds.nanoseconds. This surprising behaviour points to a loss of magnetization by non-linear generationgeneration of spin waves which affect the Gd subnetwork more than the Fe subnetwork.
InIn the second sample the Fe subnetwork magnetization dominates the properties more
completelycompletely and here the response follows the magnetic pulse closely. Still, traces of spin wavewave effects are visible in this sample also.
4.1.. Introduction
Thee study of magnetic reversal is a subject that has been attracting vast amountss of interest. It underlies much of our computerized civilization, in whichh magnetic data storage has become the default primary way of storing in-formation.. In the current devices, the switching speed is breaking through the
macrospinn of a magnetic structure switches coherently by a precessional mo-tionn driven by specially tailored field pulses [114,115,116,117]. The important questionss here are what the ultimate attainable speed will be, and how one cann avoid the non-linear generation of spin waves that tend to break up the macrospinn [118,119]. In the ultrafast dynamics limit, the formation of the mag-netizationn is hampered by bringing the electron, lattice and spin systems out of thee thermal equilibrium [120,121,122].
Inn this work, we stay in the slow thermally assisted domain. Here mag-netizationn switching by an external field occurs by nucleation of domains at sitess in the material where the magnetic anisotropy is lower or the magnetiza-tionn higher than in the rest of the system. Once nucleated, domains grow by motionn of domain walls. This motion can be accompanied by magnetostric-tivee effects which tend to limit the domain walls to speeds in the range of the speedd of sound in the material, although speeds up to 10 k m / s have been re-ported.. Most practically, structural inhomogeneities can pin the domain walls, andd further thermal excitations are required to depin them. Therefore, reversal inn homogeneous films tends to be dominated by nucleation of many domains thatt then coalesce to a completely reversed state, while in very homogeneous systemss a few nucleated domains can rapidly expand by domain wall motion too reverse the whole system. Both types of behaviour can be described by the modell originally developed by Fatuzzo [123, 124]. However, realistic micro-magneticc simulations [4] are necessary to discern the role of pinning centers in thee reversal process.
Ass magnetic storage media advance in capacity and speeds, new tools off investigating the underlying physics on ever smaller spatial scale and ever shorterr time scales are required. For fundamental observation of domains, Kerr microscopy,, using the change of polarization of visible light upon reflection by magneticc surfaces, is a convenient and simple method. However, the resolu-tionn is two orders of magnitude larger than the domain wall width. Lorentz microscopy,, a form of transmission electron microscopy, is able to probe the do-mainn structure using the deflection of the electron beam by the stray field of the magneticc domains with a few tens of nanometer resolution. The invention of the muchh simpler magnetic force microscope with the same spatial resolution has
beenn a major breakthrough. Spin-polarized STM gives even atomic resolution, butt it is proportionally more difficult and, like MFM, gives only information on thee surface magnetization.
Inn the time domain, the fastest switching time scales can be investigated usingg pump-probe experiments with ultrashort laser pulses. In these experi-ments,, most of the energy of the laser pulse is used to excite the system mag-neticallyy thermally, while a small fraction is used to probe the magnetization afterr a small time delay using the magneto-optical Kerr effect. This precessional switchingg domain is out of reach for current synchrotron-based experiments, sincee the time width of the electron bunches is in the 0.1 ns range. This time structuree has been used already for dynamical magnetization studies in spec-troscopyy [125] and photoelectron emission microscopy [114, 126]. However, futuree X-ray free electron lasers will be able to access this time window, and inn some respects, the investigation presented here can be seen as a step in the directionn of the exploitation of these new incredible sources.
Inn this pilot study, we show that X-ray resonant magnetic scattering is potentiallyy a useful technique for nucleation studies on time scales between 0.1 andd 100 ns and length scales between 50 and 1000 nm. We use low-defect amor-phouss GdFe films in which we find evidence for an unexpected decoupling of thee two ferrimagnetically coupled Gd and Fe subnetworks. We show that this decouplingg depends very sensitively on the magnetic properties of the GdFe film. .
Thee scope of this chapter is as follows: Section 4.2 gives a detailed de-scriptionn of the magnetic pulse generation and characterization. In Section 4.3, wee present the experimental techniques and the main results for the sample closerr to compensation composition, which will be discussed and a tentative modell will be presented. Section 4.4 shows the results for the second sample andd analyzes its different behaviour. In Section 4.5 we compare the results of thee two samples and draw conclusions.
4.2.. Magnetic pulse generation
Thee magnetic excitation was realized with microcoils and special power suppliess developed at the Laboratoire Louis Néel in Grenoble, France. This
sys-Figuree 4.1: Left: layout of the coil. Overall size 5x5 mm, details not to scale. Grey: copperr conductor, the darker shade indicates the contact areas. Right: SEM image of thee coil bore (courtesy of I. Snigireva, ESRF).
ternn provides the strongest magnetic excitations shown so far, and allows us to studyy reversal in relatively hard magnetic systems. Fig. 4.1 (left) shows an artis-ticc view of the coil, which was lithographically patterned in a 30 ^m thick Cu layerr deposited on a SiC>2-coated Si wafer of 5 x 5 mm2 [127]. Under the 50 }im bore,, the Si wafer has been etched away.
Thee darker areas at the top are the contacts to the power supply. Strong currentt pulses are provided by discharging a capacitor bank using fast high-powerr MOSFETs. The current is confined in the bore region by the radial lines. Thee rest of the coil provides mechanical strength and heat dissipation. A full descriptionn of the pulse coil setup can be found in Ref. [128].
Thee right side of the figure shows a scanning electron microscopy (SEM) imagee of the bore, and the white circles indicate the 50 }im coil diameter and thee 25 jim. X-ray beam size, which could be centered to within 2 ^m. The visi-blee scratches and the slight deformation of the bore were the result of breaking awayy with an ultrathin tungsten pin the SiC>2 membrane on which the Cu layer wass deposited.
Fig.. 4.2 shows the calculated lateral (a) and axial (b) profiles of the mag-neticc pulse produced by the micro-coil under the conditions used in our ex-periments.. The temporal profile (c) is shown for two different pulse lengths,
2100 0 1750 0 1400 0 1050 0 PP 700 E E C°° 1050 700 0 350 0 -- '-'--20 0 II ' i i r(r( m) -100 0 10 TT • I • I beamm size i . i . i i 20 0
a a
/ / / / / /b b
. '' i ' --.. i : — r . i .r^-^~\r^-^~\
c"
.. i. i. i. i. i. i. i. i. t. • 700 0 600 0 500 0 400 0 300 0 200 0 100 0 0 0 00 10 20 30 40 50 -5 0 5 10 15 20 25 30 35 40 45 50 hh ( m) Time (ns)Figuree 4.2: Magnetic field provided by the microcoil system when it is operated at the singlee bunch frequency of the ESRF (357 kHz), (a) Radial distribution of the magnetic fieldd strength at the coil surface, (b) Id. along the coil axis. The grey areas indicate the edgess of the coil, (c) Temporal evolution of the maximum current of 18 and 40 ns wide pulses. .
andd was obtained by measuring the voltage difference in the coil contacts. The shortestt pulse has a width at the base of 18 ns and a FWHM of 14.5 ns. The longerr pulse is 40 ns long at the base and differs by having a more extended flat top.. Typical rise and fall times are 3-4 ns.
4.3.. Magnetic reversal in Gdo.19Feo.8i films
Thee magnetic properties and the quasistatic domain evolution of Gdo.19Feo.8i (previouslyy sample B) have been discussed in Chapter 3. This sample is close too the ferromagnetic compensation point and has a relatively low magnetiza-tion.. In this section we will discuss its nucleation behaviour as revealed by time-resolvedd magneto optical Kerr effect measurements and complementary time-resolvedd XRMS at the Gd M5 edge.
Figuree 4.3: Layout of the t-MOKE setup: (1) laser, (2) polarization filter at , (3) mirror,, (4) microscope objective, (5) sample, (6) permanent magnet, (7) polarization analyser,, (8) lens, (9) diode detector.
4.3.1.. Time-resolved MOKE
MOKEE is a traditional technique to measure the magnetization of thin filmss [2]. Here we describe the time-resolved version of this technique devel-opedd at the Laboratoire Louis Néel, and the results obtained with it. This t-MOKE setupp uses a fast digital storage oscilloscope to sample the Kerr signal within a selectedd time window and averages it over many cycles.
Fig.. 4.3 shows the schematics of the t-MOKE setup. A 5 mW continuous HeNee (A = 633 nm, E = 1.95 eV) laser (1) beam passes a dichroic polarizer (2), iss redirected by a mirror (3) and focussed by a microscope objective (4) onto the sample+coill set (5). The bias field B0 (positive when parallel to the pulse) is
providedd by a position-controlled permanent magnet (6). The reflected beam travelss across the analyser (7). Finally, a lens (8) focuses the beam on a 1 MHz bandwidthh Si photodiode detector (9). Both the diode intensity and the voltage overr the coil are sampled during a selected time window around the pulse by thee digital storage oscilloscope with a sampling rate of 1 Gigasamples/s. The Kerrr signal is obtained by subtracting data sets taken with the analyser at + and -45°° as controlled by the computer. This procedure maximizes the sensitivity off the system [128]. The time traces averaged over several thousands of pulse
100 100
Delayy (ns)
Figuree 4.4: Normalized Kerr rotation of Gdo.19Feo.8i for increasing bias fields (in mT). Thee dashed line indicates the end of the 25 ns pulse.
cycless are transferred via GPIB interface from the oscilloscope to the computer.
Thee sample substrate was clamped tightly on the coil, so that the film wass pressed against the bore. In order to check for possible heating of the film byy the coil, the whole system was heated up to ~60°C, but no differences in the magneticc response could be observed. The bias field generated by the movable permanentt magnet was calibrated against a Hall sensor placed at the position off the sample.
Fig.. 4.4 shows the Kerr response to a 700 mT, 25 ns pulse for bias fields rangingg from -210 to -50 mT, represented on a logarithmic-time axis. The sig-nall is shown on a logarithmic axis and is normalized to the interval [-1, 1] to representt the reduced magnetization. For the strongest bias field (-210 mT), the pulsee is just able to nucleate some domains, after a delay of more than 10 ns and thereforee in the second half of the 25 ns pulse. The decay to equilibrium in this biass field range takes only 5 to 10 ns.
Uponn reduction of the bias field, this response increases and starts earlier until att -124 mT it shows a flat top, followed by a long tail, for -104 mT, the response startss at 8 ns after the start of the pulse and the relaxation to negative saturation takess more than 100 ns. These curves are similar to what Labrune et al. [124] havee observed in low anisotropy GdFe films, albeit at much slower timescales.
f
--g --g
-o -o CO O CD D 200 40 70 100 200 300 Delayy time + 20 (ns)Figuree 4.5: Contour plot of the reduced magnetization in, where white is corresponds too mz=-l and black is mz=\. Again a vertical white line indicates the end of the pulse. In orderr to plot the delay on a logarithmic time scale, 20 ns have been added to the delay time.. The thick white line indicates the middle of the mz=\ ridge (see text).
H o w e v e r ,, t h e curves taken at even lower bias s h o w that the magnetization in thiss p l a t e a u reaches only 90% of the saturation value.
Inn fact, for these lower bias fields, t h e signal continues to increase long after the p u l s ee h a s finished, reaching saturation only at 80 n s delay time.
Finally,, in the absence of bias, the r e m a n e n t state contains d o m a i n s a n d the r e s p o n s ee starts p r o m p t l y at the beginning of the pulse. C o m p l e t e saturation is reachedd n o w already after 10 n s , and decay to t h e original state sets in only after 2500 ns. The r e s p o n s e in this region is very irreproducible, a p p a r e n t l y because off the presence of v e r y slow magnetic b a c k g r o u n d fluctuations.
Fig.. 4.5 s h o w s the contour plot of all t-MOKE curves for bias fields rang-ingg from -50 to -210 mT, w h e r e the time base h a s b e e n shifted by 20 n s in order too allow the u s e of a logarithmic scale. T h e 0.9 m a g n e t i z a t i o n p l a t e a u a n d the s a t u r a t i o nn ridge at later times are clearly seen. The thick w h i t e line indicates the m i d d l ee of the ridge.
-100 0
-150 0
B B B« B« i i 18 8
h h
nss magnetic pulse 1000 ps X-ray pulse Magneticc response vv jVV /
t t s s \\ lFiguree 4.6: Schematic layout of the stroboscopic XRMS experiment. As in the MOKE experimentt the sample, saturated in the negative direction by the bias field Bo, is excited byy a magnetic pulse. A f is the delay time between the start of the pulse and the 100 ps X-rayy pulse.
4.3.2.. Time-resolved XRMS
Thee puzzling result of the previous section is that when starting out from aa saturated state, the MOKE intensity initially only reaches 90% of the satura-tionn value, and reaches the latter only with long delay. In order to resolve this issue,, we performed time-resolved dichroism and X-ray scattering data taken at thee Gd M5 edge. Fig. 4.6 shows the timing schematics. The power supply was triggeredd by a delay generator that was synchronized to the synchrotron bunch markerr signal. The pulse duration was 18 ns. We used the single bunch mode off operation, in which the X-ray pulse length is about 80 to 100 ps, and the time betweenn pulses 2.8 jis, allowing the sample to relax back to equilibrium.
Thee Gd magnetic response was probed by the X-ray pulse at a delay time At.. Unfortunately lack of time prevented us from measuring also the Fe L3 re-sponse.. Most of the data were collected by integrating the scattered intensity withh an X-ray diode. Data-acquisition times were typically several seconds per delayy time, corresponding to ~ 106 cycles. In addition, ^-resolved data were ob-tainedd with the 2D detector described in Sect. 3.2.2. Compared to those experi-ments,, here the count rate is strongly reduced: firstly, the single-bunch intensity iss typically 20 times lower than under normal conditions; secondly, the use of a 25-^mm beam costs a factor ~ 150. Finally, during nucleation, there is not much too scatter from, and we had to use image acquisition times of 15 minutes.
-55 O 5 10 15 20 40 60 80100 200 400 600
Delayy time (ns)
Figuree 4.7: (a) Raw data of the scattered intensity with +1 and -1 helicity. (b) Relative magnetizationn mz ) and normalized scattering S (o). Full line: shape of the 18 ns pulse.
Dataa treatment
Fig.. 4.7-a shows an example of the time trace of the intensity if- , col-lectedd at the diode after blocking the transmitted beam with the beam stop. Itt unavoidably contains a spurious background intensity St, generated by pin-holess and optics before the sample, which can be large compared to the true scatteringg signal S, especially when observing domain nucleation. As discussed before,, both signals are attenuated by the dichroic sample transmission factor. Thus,, we can write
lldio dio
^^ = T {S+Sb) HH(S(S + Sb
wheree IQ is the incident intensity, T+ is the helicity dependent transmission, iss the dichroic absorption coefficient and t the film thickness.
Sincee the absorption dichroism \ic = \i+ — \i- is linearly dependent on the
z-componentt of the Gd magnetization, we find for the helicity scattered intensity
andd the reduced magnetization m^d
SS + Sb oc 1/2(1+ + / " ) , in in Gd Gd 1+ 1+
r r
lldio dio dio dio (4.1) ) (4.2) )00 5 10 15 20 0 5 10 15 20 Delayy time (ns) Delay time (ns)
Figuree 4.8: Contour plots of (a) m^d(t, B) and (b) s(f, B) from sample Gdo.19Feo.8i in the
highh bias-short delay time region. The grey bars indicate the corresponding intensity scales.. The vertical full lines indicate the duration of the magnetic pulse.
AfterAfter subtracting the background Sj, and normalizing the result from zero to unity,, we obtain the relative scattered intensity s(t) = S(t)/S(t = 0, B = 0), whichh is a measure of the number of scattering magnetic domains [63,110,129]. Fig.. 4.7-b shows an example of these signals in comparison with the time trace off the magnetic pulse.
Results s
Dataa like those in Fig. 4.7 were collected for many different bias field values.. The results were condensed in mfd(t) and s(t) vs t contour plots as in
Figs.. 4.8-4.9. These figures correspond to two different data sets: the first one showss the early stages of the pulse (from -1 to 24 ns) and the high bias field rangee from -225 to 10 mT, while the second dataset gives the low bias range betweenn -51 to 10 mT over a much longer time window of 600 ns.
Thee high bias contour plot of the Gd subnetwork magnetization Figs. 4.8-aa shows an overall agreement with the MOKE data, although the detailed com-parisonn is slightly hampered by the different pulse widths. Note that the con-trastt is reversed as the Gd magnetization is opposite to that of the Fe. As in the MOKEE data, the change in the magnetization sets in about 5 ns after the start of
Att bias fields beyond -150 mT, the induced Gd magnetization lasts only a few nanoseconds.. The MOKE signal seems to peak later than the Gd signal. In thiss region there is some scattering, apparently from the induced domains, with moree intensity at the end of the pulse.
Att lower bias fields, between -150 and -50 mT the magnetic response increases inn amplitude and basically follows the pulse. The scattering however splits up inn two ridges centered on the regions where the time rate of change of the mag-netizationn is highest. In this region the MOKE signal basically shows similar behaviour. .
Forr bias fields between -50 and -20 mT, the sample is still saturated between pulses,, but the field pulse first produces a huge scattering ridge, after which thee magnetic signal completely vanishes, as does the scattering signal. This extremelyy surprising state (seen in more detail in Fig. 4.9), moreover lasts up too 90 ns, well beyond the end of the pulse. Note however that this anomalous behaviourr coincides with the reduced magnetization plateau of the MOKE data.
Finally,, for the lowest biases the sample is no longer saturated before thee pulse. As in the MOKE data, the magnetization now reacts promptly to the pulse,, and the recovery to equilibrium lasts up to 600 ns. The scattered intensity reactss synchronously with the magnetization and is decreased for all bias fields. Inn order to get an impression of the correlation lengths involved, we mea-suredd the ^-resolved scattering at the fields indicated by the dashed horizontal liness in Fig. 4.8. The high-field data, taken at Bo = -48 mT, are shown in Fig. 4.10-a.. The extremely weak signal indicates long correlation length as indicated on thee top scale, and perhaps an average distance between nucleation centers of aboutt 200 nm during the first scattering ridge at the moment where the mag-netizationn is changing fastest. At the second ridge at the end of the pulse, the correlationn lengths are even longer.
Thee time evolution of the ^-resolved intensity distribution for the strongly scatteringg remanent case is shown in Fig. 4.10-b. Surprisingly, during the pulse, thee diffraction curve does not seem to change noticeably, except for the 50% reductionn of the intensity already visible along the upper dashed line in the contourr plot (Fig. 4.8). This is in marked contrast with the increase of the period
200 40 60 100 200 400 600 20 40 60 100 200 400 600 Delayy time + 20 (ns) Delay time + 20 (ns)
Figuree 4.9: Contour plots of (a) m^d{t, B) and (b) s(f, B) from sample Gdo.19Feo.8i in
thee low bias-long delay time region. The grey bars indicate the corresponding intensity scales.. The vertical full lines indicate the duration of the magnetic pulse. 20 ns have beenn added to the delay time to use logarithmic time scale.
observedd in the quasi-static case and we have to conclude that apparently the correlatedd domain system is quite rigid under the fast pulse. The average do-mainn size f = 8 nm with a correlation length £ = cj/Aq = 0.92 is very similar too the values of the remanent system (934 nm and 1.2 respectively) obtained in thee previous chapter. It is however still quite possible that the pulse increases thee width of the up domains at the expense of that of the down domains. In principlee such a breathing of the domains without a change in the periodicity wouldd reduce the first order intensity. In principle the second and higher even orderr intensities should increase, however, already in the quasi-static situation thesee are not visible in these disordered samples.
Inn the previous chapter we have used Parseval's theorem to show that thee scattered intensity is proportional to 1 — (mz)2. In all quasi-static datasets
thatt we encountered so far, this relation was observed. Inspection of the magne-tizationn and scattering contour plots suffices to see that in these dynamic mea-surementss this is not the case. Instead, we see that the strongest scattering oc-curss on the edges of the magnetization contour, where the rate of change of the magnetizationn is highest.
MUI I *== - — - - ^ aa ~
»-ft »-ft
^ ^
^ ^ ^ ^3.'3.' ~^^i
IN N
ïCW|' '
(DD ^ l i L ,| »» L nW.ss Nu.1
\ \ -16.00 f \ \ 4 55 r \ \ \ #»» 5.o f Y y O x ^ ^ .Jfl^fMAV^^ ^
8 , 0 / \ \ \ \V N , M^^ ^"^ 9 00 l ^ \ \ V vv' > T \ /y^ \ \ \ \\ > v ^ V k . ^ 444 - U V v V Vrti 204:: ^ 0 A ^ ^ v \ 304;; ^ v . * - 1 3 3 3 3 4 4 5. . 6 6 1 1 9 9 J J 54, , 104 4 204--304 4 404 4 0.022 0.04 0.06 0.08 0.01 0.02 0.03 0.04 qrr (nm 1 ) qr (nm')Figuree 4.10: Semi-log plot of diffraction patterns from Gdo.19Feo.8i taken during the pulsee for (a) saturated sample and (b) relaxed domain state (dashed white lines in Fig.. 4.9). On the right of each curve the delay time is given in ns.
Violationn of Parseval's theorem means that either the Gd magnetization hass turned in-plane or the length of the magnetization vector has decreased. We cann not discriminate directly between the two cases. However, the absence of scatteringg in the plateau region means that the Gd subnetwork is in a homoge-neouss magnetization state. The ultimate reduction of the length of the magne-tizationn occurs when the sample is driven above the Curie temperature. That thiss is not the case is obvious from the MOKE data which show a clear magnetic signal.. We surmise that the Gd magnetization is reduced by the generation of spinn waves, as will be discussed in more detail below.
4.3.3.. Discussion
Inn order to interpret these time-resolved MOKE and XMRS results we havee to consider the origin of the MOKE signal and the magnetic structure of amorphouss GdFe alloys.
Crystallinee Fe has a negative Kerr rotation between 0.5 and 5 eV and reaches 0.28'' at 1.1 eV, while pure Gd has a positive Kerr rotation in the entire spectral rangee with a strong peak at 4.2 eV due to p-d interband transitions. Accord-ingg to Hansen [98], in the infrared and red spectral range, the MOKE signal of GdFee alloys is dominated by Fe 3d and Gd 5d intraband transitions, while at higherr energies p-d and d-f interband transitions dominate. Since the Gd and Fee subnetworks are antiparallel, the total Kerr angle is negative above the com-pensationn point. For our samples and at the HeNe laser frequency, the Fe Kerr contributionn is 20 times larger (9% «-30' [130]) than the Gd (6%d « 1.4' [131]), soo that the MOKE signal is primarily sensitive to the behaviour of the Fe sub-networkk [98,130,131,132,133,134].
Thee magnetic order in RT systems involves an Fe-Fe exchange tionn that is dominating the Gd-Fe indirect exchange, while the Gd-Gd interac-tionn does not play any role [134]. In the amorphous system, the details of the magneticc structure are not clear. There may be dispersion in the Fe directions, andd Mansuripur [4] claims the importance of both parallel and antiparallel cou-plingss in the Fe subnetwork. While in L ^ 0 rare-earth elements, the R moments aree strongly dispersed around the surface normal, in GdFe the Gd spin-only momentt should be well aligned. In the rest of the chapter we will ignore possi-blee moment dispersion as it does not seem to play an important role.
InIn our samples the Fe moment is larger than the Gd moment, so that be-foree the beginning of the pulse, the Fe magnetization is along the bias field di-rection.. The pulsed field completely overwhelms the bias field and, as a result, thee Fe magnetization reverses. Clearly, at the start of the pulse, the Gd magne-tizationn is initially parallel to the pulse-field direction. As the Fe subnetwork reverses,, the Fe-Gd exchange prevails over the pulse field and tries to rotate the Gdd moment against the pulse field. Indeed, in the Gd signal we do see a few ns off scatter indicating nucleation of domains. For high bias fields, these domains aree annihilated at the end of the pulse. However, for bias fields between -50 and -200 mT the Gd magnetization disappears, only to resurface much after the end
Ferrimagneticc RT films are known to be susceptible to field-driven spin reorientationn transitions when they are close to the compensation point. In thatt case, a ferrimagnet is quite similar to an antiferromagnet which, in high appliedd fields, can make a spin-flop transition. In this spin-flopped state, the antiferromagneticc anisotropy direction is normal to the field but the moments off the two subnetworks rotate away from this direction into the field direc-tionn [135, 136, 137, 138]. Indeed, in an XMCD study of the amorphous ErFe compound,, a sister compound of the GdFe system, it was found that at the com-pensationn temperature, the Er and Fe moments are parallel in applied fields.
AA simple interpretation of this behaviour could invoke the dynamic anal-ogyy of such a reorientation transition. However, if this were the only explana-tion,, the Gd moment should not vanish but become positive. We therefore have too look to a further mechanism that can reduce the magnetization in the way observedd here. Such a mechanism can be the generation of spin waves.
Coherentt spin reorientation is well described by the Landau-Lifshitz-Gilbertt equation [139]:
dm dm
—— = - 7 m x Beff + ay m x (m x Beff). (4.3) Inn this equation, 7 is the gyromagnetic frequency and a. a phenomenological
dampingg parameter. The first term describes the precessional motion of a spin thatt has been deflected from its equilibrium position in the field Be/y. The
Gilbertt damping term causes the precessing spin to spiral back to the equilib-riumm magnetization axis. In this equation, the magnetization is assumed to be conserved.. However, in hard driven systems the non-linear precessional mo-tionn of the spin generates spin waves. When enough spin waves are generated, differentt parts of the system start to lose phase coherence, causing the net spin momentt of the system to decrease. This phenomenon was first observed as a saturationn effect in ferromagnetic resonance experiments [140], and was theo-reticallyy described by Callen [118]. In recent laser-driven pump-probe experi-mentss by Silva et al. [141], these effects were also found to be observable in the timee domain in the form of a reduction of the length of the magnetization vec-tor.. These results were subsequently explained by Safonov [142] in an approach
P P E E -100 -08 -06 -04 -02 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 •••••••••••••••• ••••••••••••• 100 0 50 0 -50 0 -100 0 -150 0 100 20 30 Delayy time (ns) 40 0 100 20 30 Delayy time (ns) 40 0
Figuree 4.11: Contour plots of (a) mfrf(f,B) and (b) s(f,B) from sample GdFe5. The
verticall full lines indicate the duration of the magnetic pulse. The white dashed lines indicatee the bias fields at which the (^-resolved data were collected.
basedd on the Callen model, in which the precessing spins generate magnons whichh eventually break up the coherent precessional motion.
Itt should be stressed that in the work of Silva and most other studies, the responsee of soft permalloy films is studied using somewhat faster but relatively weakk field pulses. In the present case, the field pulse is large compared to the anisotropyy and bias fields. Under these conditions, the generation of spin waves iss a likely origin of the vanishing Gd moment and the reduced Fe moment. Apparently,, the Gd network is affected more than the Fe network. A possible explanationn is that the Gd is aligned primarily by the Fe-Gd indirect exchange. Thee pulse field is opposite to this interaction. The Fe network on the other hand iss subject to the strong Fe-Fe direct exchange.
4.4.. Magnetic reversal in GdFes
4.4.1.. Time-resolved XRMS
Time-resolvedd XRMS data from GdFe 5 (sample A in the previous chap-ter)) are condensed in the form of contour plots in Fig. 4.11, showing the Gd
4.8 8
0.022 0.04 0.06 0.02 0.03 0.04 0.05 0.06 qrr (nm') qr (nm')
Figuree 4.12: Diffraction patterns from GdFes as explained in Fig. 4.10.
magnetizationn mj1 and the scattered intensity. We see that the pulse induces an increasee in mfd that disappears when the pulse is finished. The amount of de-flectionn of the contour lines decreases as the modulus of the bias field decreases. Thee MOKE results showed very similar time scales.
Inn saturating bias fields, the scattered intensity increases during the pulse duee to the nucleation of domains. For weaker fields, the start of the domain scatteringg is similar as in Gdo.19Feo.s1- However, the return to the equilibrium positionn is very prompt. Also, there is no direct sign of a vanishing Gd moment. However,, also in this case Parseval's theorem is not fulfilled, pointing to a de-creasee of the Gd moment.
Againn we measured ^-resolved data in the saturated and domain states, att bias fields Bo = -113 and 32 mT, indicated by dashed white lines in Fig. 4.11. In thee saturated state (Fig. 4.12-a), the top of the field pulse is just able to produce
somee nucleated domains, which scatter to a very weak ring. As in the previ-ouslyy discussed sample, there is a weak scattered signal at very low q which, afterr 6.3 ns, develops a broad maximum corresponding to a correlation length off 225 nm. Due to the low signal intensity, it is very difficult to extract infor-mationn from these curves, and the presence is mainly justified as an experiment thatt is worth improving.
Thee diffraction curves from the system in the domain state (Fig. 4.12-b) displayy a clear first diffraction order peak. The average period T = 1 9 8 nm agrees againn reasonably well with the static period T = 2 3 2 nm. As in the other sample, thee peak position does not appreciably change during the pulse while the inten-sityy is reduced, in contrast to the change in period observed in the quasi static case.. This stiffness of the domain lattice suggests the presence of domain-wall resonancee modes [143], the archetypical response to perpendicular excitations. Wee argue that the reduction of the scattered intensity is due to a partial reduc-tionn of mfd magnetization during the pulse. In the down-domains that have theirr Fe magnetization in the direction of the pulse, the Gd moments are ori-entedd against the pulse field by the Gd-Fe exchange. When the Fe magnetiza-tionn is saturated in the pulse field direction, it drags the Gd spins along, leading too a considerable spin canting of the Gd moments. This would reduce the scat-teringg contrast without affecting the average period.
Fromm the t-XRMS results we conclude that the response of GdFes to the pulsee is mainly driven by nucleation and domain wall motion. However, the scatteringg S disagrees with 1 — (mz)2 around remanence. This suggests that thee spin-flop transition proposed for the other sample is also present. However, thiss effect is weaker here, since m^d is reduced but not cancelled, and the system relaxess immediately after the pulse finishes.
4.5.. Conclusions and outlook
Wee have shown that time-resolved XRMS is a useful technique for stud-iess on nanoscale magnetic phenomena. With the current synchrotron sources, it providess the magnetization and scattering from domains, as well as the domain sizess with a current spatial and time resolution of 30 nm and 100 ps.
compensationn composition, we observe a reduction of the Fe magnetization in thee reversed state and the complete disappearance of the Gd magnetization. Also,, relaxation to the equilibrium state of the total magnetization lasts much longerr than the pulse. If domains are present prior to the pulse, the reduced Gdd contrast seems to affect only the domains initially oriented against the pulse direction.. In this case relaxation times are even longer.
Thee loss of magnetization is interpreted as a dynamical spin-flop transi-tionn in combination with spin wave excitation. Spin-flop transitions have been predictedd and observed in amorphous ferrimagnets, but always under qua-sistaticc conditions of applied field and temperature. Apparently, in the dynam-icall situation described here, the Fe magnetization follows initially the pulse, butt the weak Fe-Gd exchange coupling is not strong enough to keep the Gd antiparallell to the Fe subnetwork. This could be due to the generation of vast amountss of non-linear spin waves that lead to the decoupling and the reduction off the Fe magnetization and the complete disappearance of the Gd magnetiza-tion.. Very likely, these spin waves transfer energy to the phonon bath, leading too a temperature rise of the sample in the early stage of the pulse. After the pulsee has ended, the sample cools down again, and in equilibrium with it the spinn waves damp down, resulting in a restoration of the coupling. Only then thee reunited magnetic structure starts to decay back to the equilibrium situation viaa thermally assisted nucleation as described by Labrune [124].
Inn contrast, in a sample with composition further away from compen-sation,, that is, with higher Fe content, the magnetization closely follows the temporall evolution of the pulse. Here also, the loss of scattered intensity is a signn of a decrease of the Gd sublattice magnetization. The largest difference in thee magnetic properties of the samples are the saturation magnetization Ms and thee quasistatic nucleation field B^uc, which both decrease on nearing the
com-pensationn composition. Thus, the ratio between the maximum pulse field and thee quasistatic nucleation field is 10 for GdFes and 150 for Gdo.19Feo.8i- This meanss that for the pulse amplitude used here, the former sample is excited less stronglyy than the latter, and spin wave excitation is not as important. The dif-ferencee in relaxation times back to equilibrium then is only due to a difference inn magnetization, as is normal in thermally assisted nucleation processes.
Thiss pilot study opens a new experimental approach in the study of mag-netizationn dynamics. Since scattering is an incoherent technique, it is not limited too systems with well-defined nucleation centers, as in the case of time-resolved imagingg techniques, but can be used for the study of nucleation studies as pre-sentedd here. Unfortunately, our g-resolved results suffered from a lack of signal, nott enough to record higher harmonics which would have allowed an assess-mentt of the relative width of up and down domains. We estimate that an in-tensityy gain of three orders of magnitude would be readily achievable by using aa better focused beam line and a back-thinned CCD camera optimized for soft XX rays. Obviously, future work will require more extensive characterization off the pulse height dependence and should include the Fe response measured att the Fe L3 edge. More extensive XMCD studies might reveal changes in the orbitall and spin moments which could shed more light on possible spin reorien-tationn transitions. On the theory side, micromagnetic or analytical simulations withh time-dependent exchange constants would help to understand better the presentt energy transfer mechanisms.
Futuree X-ray Free Elector Lasers (XFELs) will provide coherent 100 fs pulsess with intensities comparable to the integrated intensity in one second at a thirdd generation synchrotron. These sources offer huge potential for magneto-opticall studies well into the coherent spin rotation regime, and may enable the studyy of spin-lattice interactions. Time resolved resonant magnetic scattering willl certainly feature prominently among the techniques used at these sources.
