Journal of Magnetism and Magnetic Materials 233 (2001) 119–122

Magnetic domain fluctuations observed by coherent X-rayscattering

F. Yakhoua,*, A. L!etoublonb, F. Livetb, M. de Boissieub, F. Bleyb

aEuropean Synchrotron Radiation Facility, 6 Rue Jules Horowitz, BP 220, F-38043 Grenoble Cedex 9, FrancebLTPCM-ENSEEG, BP 75, F-38402 St Martin d ’H "eres Cedex, France

Abstract

Coherent X-ray-scattering measurements were performed in the type-I antiferromagnetic phase of UAs at the MIV

uranium absorption edge. Speckle patterns from a magnetic reflection were followed up through the magnetictransition. The origin of the speckles is discussed in terms of antiferromagnetic domain configuration and fluctuations.r 2001 Elsevier Science B.V. All rights reserved.

Keywords: Coherent X-ray scattering; Actinides; Antiferromagnets; Domains

1. Introduction

Over the past few years, the availability of highfluxes of coherent hard X-rays from third-genera-tion synchrotron sources has opened up new fieldsof investigation of disordered systems, through theanalysis of the random diffraction or ‘‘specklepatterns’’. A disordered material may be viewed asa distribution of coherently scattering volumesintroducing random phase-shifts that result in astrongly modulated diffraction pattern when illu-minated by coherent incident radiation. Each suchspeckle pattern is uniquely related to the exactinstantaneous spatial distribution of the disorder;if this spatial arrangement changes with time, thecorresponding speckle pattern also changes. In-formation on the dynamics of the disorderedsystem can thus be retrieved from the time

correlation analysis of a single speckle, while thespatial information is contained in the inverseFourier transform of the diffraction pattern.

The dynamic coherent-scattering technique withhard X-rays has proven successful, mainly in thefield of soft condensed matter [1] by giving accessto a higher q-range than dynamic light scattering,and to slower phenomena than neutron scattering.Condensed-matter problems, such as antiphasedomain structure in Cu3Au [2], equilibrium criticalfluctuations in Fe3Al [3,4] and, more recently,phason fluctuations in quasicrystals [5], have alsobeen successfully addressed by coherent scatteringtechniques in the 8 keV energy range, where a highflux of coherent X-rays can be ‘‘easily’’ obtained.The imaging aspect of the technique, thoughestablished [6], requires daunting computingefforts and remains anecdotic for the time being.

An exciting new domain of application of such acombination of both an imaging and a dynamictechnique is the study of antiferromagnetic do-mains. Because of crystal symmetry, domain

*Corresponding author. Tel.: +33-4-7688-2491; fax: +33-4-

7688-2542.

E-mail address: yakhou@esrf.fr (F. Yakhou).

0304-8853/01/$ - see front matter r 2001 Elsevier Science B.V. All rights reserved.

PII: S 0 3 0 4 - 8 8 5 3 ( 0 1 ) 0 0 2 4 1 - 4

formation is inherent to most types of magneticordering but little is known up to now aboutdomain size and arrangement in antiferromagneticmaterials. A speckle pattern from a magneticsystem should prove to be of considerable interestin this respect, since only a few neutron topogra-phy results [7], and very recently, antiferromag-netic domain imaging by the photo-electronemission microscopy technique (PEEM) [8], havebeen reported.

However, the extreme weakness of the magneticscattering signal makes it a challenging experi-ment. UAs was chosen as a test system for whichadvantage can be taken from the huge enhance-ment of the magnetic intensity through a resonantprocess [9,10] at the MIV uranium absorption edge(3.728 keV).

2. Experimental

In a preliminary experiment, we have observedfor the first time a static speckle pattern frommagnetic domains in the type-I antiferromagneticphase of UAs, at T ¼ 100 K [11]. UAs crystallizein the cubic NaCl structure and, at TND123 K,the system undergoes a first-order phase transi-tion to a magnetically ordered phase with alter-nating ferromagnetic sheets stacked along thec-axis, and moments along the propagationvector [12].

In a recent experiment on the ID20 beamlineat ESRF, we have followed up the specklepatterns of both the (0 0 1) magnetic and the(0 0 2) charge reflections throughout the magnetictransition. A coherent beam was obtained byproperly collimating a 3.73 keV beam from two-phased 42mm period undulators, monochroma-tized by a double Si(1 1 1) monochromator ofbandwidth dlXl ¼ 1:3 � 10@4. The resultinglongitudinal coherence length l� lXdlE1 mmat 3.73 keV and it is large enough not tosmear out the coherent effects. The transversecoherence length could be matched to the 20 mmcollimating pinhole by controlling the apertureof a set of secondary slits placed after theoptics. Special care was taken to lessen thenumber and the thickness of windows along

the X-ray path, which resulted in a 3.5�109 ph/s integrated coherent flux at the sample at200 mA ring current, and a 2000 cts/s peakintensity on the magnetic (0 0 1) reflection atT ¼ 100 K (60 cts/s achieved in the preliminaryexperiment).

The crystal with a [0 0 1] cleaved surface was putinto a standard 4He cryostat in horizontal scatter-ing geometry. Both an NaI scintillation detectorand a direct illumination 384� 576 22.5 mm-chipCCD camera were used for intensity optimisationand speckle-pattern recording, respectively. TheCCD camera could be used as a photon counter byapplying a droplet algorithm taking into accountthe detector resolution [12].

The temperature dependence of the integratedmagnetic intensity was recorded. As expected[9,10], the continuous character of the transitionobserved at low temperatures suddenly locks intoa first-order phase transition at TN ¼ 122:69 K.Most of the subsequent measurements wereperformed over a narrow temperature range of1 K around this temperature.

Two different measuring procedures were usedto record the speckle patterns: the temperature waseither stabilized for 5 min before each acquisition(200� 5 s frame images) or continuously variedduring the acquisitions (50� 1 s frame images).For the recording of the charge scattering, only thesecond method was used. At 122.69 K, theintegrated magnetic intensity drops and reachesthe background level within 0.01 K. At the sametime, the mean apparent coherence (or contrast) of10 subsequent frames summed up decreases asplotted in Fig. 1, indicating that either thedisorder-domain-configuration is evolving or thatthe sample is moving (either in reciprocal or in realspace). The sample movements due to thermalexpansion of the sample stick were determined tobe less than 10 mm/K and cannot account for theobserved decrease of the coherence over 0.01 K. Avery small magnetostriction could be detected onthe charge scattering with a slight shift in q-spaceof the peak position, that could explain thesmearing of the speckles. This actually happensfor the charge speckle pattern whose degree ofcoherence drops at the transition and then comesback to the initial value of E40%. The situation is

F. Yakhou et al. / Journal of Magnetism and Magnetic Materials 233 (2001) 119–122120

different though for the magnetic speckles, mea-sured once the temperature was stabilized (firstmeasuring procedure): the q-space position of eachimage, and within each frame of a single image,was determined by a 2D Gaussian fit and wasfound stable within 2 pixels (E4.5� 10@5 (A@1).Thus, neither magnetostriction nor thermal ex-pansion can account for the smearing of themagnetic speckle patterns. On the other hand,fluctuations of the domain configurationFthus ofthe instantaneous speckle patternFon a time scaleshorter than the typical measuring time of 1 s,would result in a similar smearing out of thespeckles.

Another hint in this direction is the averagesize of the observed coherently scatteringvolumes as retrieved from the full-width at half-maximum (FWHM) of the 2D diffraction patternsshown in Fig. 2. The apparent anisotropy ofthe diffraction spot results from the considerablelongitudinal smearing of the diffusion vector,due to the very low X-ray penetration depth

(2500 (A at 151 incidence). The recorded patternmay be viewed as a planar cut at the Bragg angle ywith respect to the diffusion vector with ananisotropy factor 1 : sin y. The average domainsize is then simply the inverse FWHM corrected

Fig. 1. The apparent coherence and intensity of the magnetic

(0 0 1) reflection through the magnetic transition, plotted

against the image number in the recording series. The

measurements were performed while continuously warming

up the sample from 122.66K (first image) to 123.01K (last

image). The coherence decreases with the intensity, indicating

that the domain configuration changes within the measuring

time (see text).

Fig. 2. Horizontal (a) and vertical (b) cuts through the 2D

magnetic speckle pattern. The apparent anisotropy can be easily

explained considering the low X-ray penetration depth at

3.73 keV and the resulting longitudinal smearing of the

diffusion vector (see text). The inferred average domain size is

4 mm, to be compared to a 2.5-mm size for the charge scattering.

F. Yakhou et al. / Journal of Magnetism and Magnetic Materials 233 (2001) 119–122 121

for this asymmetry ratio; it is found to be 4 mmfor the magnetic domains and 2.5 mm for thecharge domains, in good agreement with theilluminated volume size and the approximatenumber of observed speckles. The charge domainsmay be related to a small angular disorientation ofthe lattice within the Darwin width of the Braggreflection; it should not perturb the magneticordering that can, therefore, propagate on a longerlength scale.

Finally, the correlation of each subsequentimage to the starting speckle pattern was calcu-lated for a cycling procedure through the magnetictransition and is very close to 1 for the last imageof the cycle, indicating that a similar domainconfiguration has been established and that themagnetic domains are probably pinned by crystaldefects.

3. Conclusion

In summary, magnetic speckle patterns in thetype-I antiferromagnetic phase of UAs wererecorded as a function of temperature at theMIV uranium absorption edge. The smearing ofthe speckles at the transition and a domainsize larger than that of the charge scatteringstrongly suggest that this is the first observa-tion of antiferromagnetic domain fluctuationsat a first-order phase transition. Real-spaceimaging through the inverse Fourier transformof the 2D diffraction pattern remains yet tobe done, but the feasibility of coherent-scattering experiments on magnetic systems hasbeen proven, and it opens up an exciting new fieldof investigations.

Acknowledgements

Technical help from R. Chagnon, G. Pepellinand B. Caillot is greatly acknowledged.

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