PHYSICAL REVIEW B VOLUME 61, NUMBER 13 1 APRIL 2000-I Resonant x-ray scattering studies of the magnetic structure near the surface of an antiferromagnet G. M. Watson Department of Physics, University of Maryland Baltimore County, Baltimore, Maryland 21250 Doon Gibbs Department of Physics, Brookhaven National Laboratory, Upton, New York 11973-5000 G. H. Lander European Commission, Joint Research Center, Institute for Transuranium Elements, Postfach 2340, D-76125 Karlsruhe, Germany B. D. Gaulin Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, Canada L8S 4M1 L. E. Berman National Synchrotron Light Source, Brookhaven National Laboratory, Upton, New York 11973-5000 Hj. Matzke European Commission, Joint Research Center, Institute for Transuranium Elements, Postfach 2340, D-76125 Karlsruhe, Germany W. Ellis Los Alamos National Laboratory, Los Alamos, New Mexico 87545 Received 18 October 1999 Resonant x-ray magnetic scattering is used to study magnetic order near the 001 surface of the antiferro- magnetic oxide UO2 for temperatures between 10 and 35 K. It is found that for temperatures below the bulk NeŽel temperature a magnetically disordered region exists at the surface, and is separated from the magnetically ordered bulk by a diffuse magnetic interface. The width of the magnetic interface is temperature dependent, and appears to diverge as the sample temperature approaches the bulk NeŽel temperature. In contrast to the bulk, which exhibits a discontinuous magnetic ordering transition, the surface layers order continuously. These results are shown to be qualitatively consistent with the theory of surface induced disorder. I. INTRODUCTION ments in which the magnetic reflectivity is used to study antiferromagnetic disordering near the surface as a function The magnetic properties of surfaces and interfaces have of temperature. Our motivations for the experiments were, recently become a topic of great interest, in part due to the first, to determine whether antiferromagnetic truncation rods technological importance of spin-engineered thin-film could be observed by x-ray scattering and, second, to study devices.1 Coincident with this attention has been the devel- the effect of the surface on a bulk magnetic order-disorder opment of techniques for the study of magnetism in thin phase transformation. films and at surfaces. Several of these techniques utilize pho- Earlier studies utilizing soft x-ray resonance techniques tons in the soft and hard x-ray wavelength regimes, and rely have also characterized the magnetic specular reflectivity, on resonant processes, which occur when the incident photon mainly near the L absorption edges of 3d transition elements. energy is tuned near an absorption edge. The magnetic sen- For example, Kao et al.,6 observed the change in reflectivity sitivity is due to a virtual electronic transition from a spin- vs momentum transfer from an iron film when the magneti- orbit split core level into spin-polarized final states. Whereas zation was flipped by 180°, and related it to the interfacial a number of these techniques have the sensitivity required to magnetic structure. Since then, a number of related experi- measure the magnetization of films as thin as a single ments have been performed at the L edges of other 3d tran- monolayer,2 and others are directly sensitive to surface sition metals.7­9 As a result of the long wavelength of the magnetism,3 few are able to determine how the magnetiza- photons at these edges, the measurements have been limited tion changes as a function of distance from the surface or to magnetic structures with unit cells larger than 10 Ć. interface.4 In this regard, resonant x-ray and neutron mag- In order to benefit from the large resonant enhancement of netic reflectivity techniques appear unique.5 the magnetic scattering at the M absorption edges of uranium In this paper, we illustrate how resonant x-ray magnetic compounds,10 we decided to look for the magnetic trunca- reflectivity may be used to obtain sublattice magnetization tions rods of UO2. In addition, for antiferromagnetic profiles at the surface of a bulk antiferromagnet, in particu- samples, some of the magnetic rods exist separately from the lar, at the 001 surface of UO2. We then describe experi- chemical truncation rods. In contrast, the magnetic and 0163-1829/2000/61 13 /8966 10 /$15.00 PRB 61 8966 ©2000 The American Physical Society PRB 61 RESONANT X-RAY SCATTERING STUDIES OF THE . . . 8967 chemical periods of ferromagnets are identical so that the 1010 photons per second. At the insertion device beamline bulk charge and magnetic truncation rods overlap in recipro- X25, approximately 2 1011 photons per second are incident cal space. To observe ferromagnetic rods therefore it is nec- on the sample, and focused into a spot of 0.5 mm2 by a essary to perform difference experiments in which Bragg in- platinum coated silicon mirror. A nondispersive, two-crystal tensities are measured for two directions of an applied Si 111 monochromator with adaptive optics was employed magnetic field, or for right and left circularly polarized inci- to tune the photon energy to the uranium MIV edge. The dent beams. In an elegant set of experiments on the ferro- experiments were performed with a standard four-circle magnetic alloy CoPt, Ferrer et al. recently related the in- vertical-scattering diffractometer at X25 and with a six-circle duced magnetism of Pt atoms at the surface to the surface diffractometer at X22C. stoichiometery by working at the Pt LIII edge.11 By measur- Two different samples were characterized. Both were cut ing the flipping ratio over a large portion of the truncation and polished to produce a surface aligned to within 0.25° rod they were able to show that the magnetization of the Pt of the 001 direction. The first sample sample 1 , used in atoms at the surface is reduced from that in the bulk. the majority of the work, was provided by Los Alamos Na- There has been considerable interest in magnetic phase tional Laboratory. The second sample sample 2 came from transitions at surfaces during the last 30 years. Perhaps the the European Institute for Transuranium Elements. Prior to best studied examples are the 001 and 110 surfaces of Ni these measurements, both samples were annealed at 1400 °C and the 001 surface of Gd, which have all been character- in a reducing atmosphere, consisting of 3.5% hydrogen and ized using spin-polarized low-energy electron diffraction. 96.5% Ar. The anneal served to reduce any near surface The exponent s , which describes the temperature depen- damage produced in the polishing process and to guarantee a dence of the surface order parameter, has been determined bulk oxygen stoichiometry of UO2. All of the magnetic scat- for Ni 001 .12 It was found that its value at the surface ( s tering experiments were performed with sample 1 mounted 0.825) differs considerably from that of the bulk ( b in a Be can backfilled with He exchange gas. Temperature 0.33). The Gd 001 surface exhibits the remarkable prop- control was achieved by means of a closed-cycle He refrig- erty of surface freezing,13 that is, it is magnetically ordered at erator for which the temperature stability was 0.02 K over temperatures above the bulk Curie temperature. Unfortu- periods of hours. The bulk mosaic was measured to be 0.05° nately, in neither case was it possible to determine how the at the 002 reflection. near surface magnetic order couples to the underlying bulk The incident x rays were linearly polarized with the elec- magnetic order. tric field in the horizontal plane.10 Both specular and non- For UO2 001 surfaces at low temperatures, we show that specular truncation rods were characterized. Specular scatter- a magnetically disordered region exists at the surface. This ing was carried out in a vertical scattering plane whereas the disordered region is separated from the ordered bulk by a scattering plane for nonspecular measurements had a small magnetic interface. At the lowest temperatures studied the horizontal component. Two types of detectors, a simple lin- interface is diffuse and has a width of approximately 6 Ć. As ear detector and a standard Bicron detector, were used to the temperature increases towards the bulk NeŽel temperature, determine the intensity of the rods along the surface normal the thickness of the disordered surface layer remains constant direction. Since charge and magnetic scattering overlap while the width of the diffuse magnetic interface appears to along the specular direction, it was necessary to use a polar- diverge. In addition, the temperature dependence of the mag- ization analyzer to isolate the magnetic reflectivity. For lin- netic intensities at the surface vary continuously near the early polarized incident x rays, the polarization of the mag- transition, in contrast to the bulk, which is discontinuous. netic scattering in UO2 001 is rotated by 90°, whereas the These intriguing results are qualitatively consistent with the charge scattering remains unrotated.20 A Au 111 crystal was theory of surface induced disorder put forward by Lipowsky used to analyze the polarization of the scattered beam, and and co-workers,14,15 and summarized by Schweika, et al.16 thereby to discriminate against charge scattering.21 At the U Surface induced disorder has previously been observed in MIV edge, the scattering angle of the Au analyzer is 89.8°. x-ray scattering studies of alloy ordering at the Cu3Au surface.17,18 The present paper describes our earlier results obtained for UO B. Bulk magnetic structure 2 001 in more detail,19 together with more recent experiments which help clarify the nature of the dis- UO ordering near the surface. 2 has the CaF2 crystal structure see Fig. 1 a with a lattice constant of 5.47 Ć at room temperature. The bulk structure consists of U4 ions arranged on an fcc lattice each II. EXPERIMENTAL PROCEDURES with eight nearest-neighbor O2 ions. UO2 is a type-I anti- ferromagnet with a discontinuous magnetic-ordering trans- A. Experiment formation at TN 30.2 K.22­24 The bulk magnetic structure The experiments described here were carried out using consists of ferromagnetically aligned 001 -type atomic Beamlines X22C and X25 at the National Synchrotron Light planes, stacked antiferromagnetically along the 001 direc- Source NSLS . At beamline X22C, approximately 6 mrad tion. UO2 is also triple q, which means that all three 001 - of radiation from a bending magnet were focused by a Ni- type magnetic modulations exist simultaneously within a coated, bent, cylindrical mirror into a spot approximately 1 single domain. The magnetic order associated with one of mm in diameter at the sample. Monochromatic x rays set at the three coexisting magnetic modulations is shown in Fig. the energy of the U MIV edge 3.728 keV were selected by 1 a . a double crystal Ge 111 monochromator. At these energies, A representation of the bulk allowed Bragg reflections in the incident flux on the sample is estimated to be 1 the (001) (010) plane is shown by the solid circles in Fig. 8968 G. M. WATSON et al. PRB 61 FIG. 2. Specular x-ray reflectivity from UO2 001 surfaces after various surface preparations, plotted vs momentum transfer L. Data are shown by the open circles. Solid lines show fits to the encapsu- lated and annealed data, which correspond to bulk truncation. Curves have been offset for clarity. The singularities at L 2, 4, 6 correspond to bulk allowed Bragg reflections. The geometry of the FIG. 1. a Crystal and magnetic structure of UO2. The U atoms scattering is illustrated in the figure. open spheres occupy an fcc lattice with a room-temperature lattice constant of a 5.47 Ć. The oxygen atoms solid spheres sit on a tribution for temperatures below TN . We refer to these rods simple cubic lattice offset from the U lattice by 1 as being mixed. For UO 4, 14, 14 . The arrows 2, a* b* c* 2 /a 1.14 Ć 1 at represent one component of the triple q antiferromagnetic structure. room temperature. It should be noted that the orientation of the moments within the 001 planes is not known, but they do lie in the plane perpendicular C. Surface preparation and characterization to the propagation direction q. b Reciprocal space map for the Due in part to the importance of the material as a fuel in UO2 001 surface showing charge solid circles and magnetic nuclear reactors, surfaces of UO2 have been studied for many open circles bulk Bragg reflections. Magnetic truncation rods years.26­28 Along the 001 direction, the ideally terminated dashed lines and truncation rods with both magnetic and charge UO2 structure consists of alternating planes of U4 and O2 components solid lines are also shown. ions see Fig. 1 b . It has been shown, however, that clean, stable surfaces with a c(2 2) reconstruction can be pre- 1 b . When the sample is cooled to temperature below TN , pared in vacuum.27 Because the sample is an oxide, and rela- additional bulk Bragg reflections appear, arising from the tively inert, we originally thought that exposure to air would magnetic structure. The allowed magnetic bulk Bragg reflec- not significantly alter the surface properties. Accordingly, tions are displaced from the atomic Bragg reflections by a none of our experiments were performed in ultrahigh 001 -type wave vector, and are shown by the open circles in vacuum. More recently, we have initiated simple tests of Fig. 1 b . Truncation rods are defined as rods of scattering these assumptions. As shown in Fig. 2, the x-ray which lie along the surface normal direction and pass reflectivity25,29 from the chemical surface is unaltered when through the bulk Bragg reflections.25 In Fig. 1 b , the solid the exposure to atmosphere is for a time less than 1 h, but it lines are rods resulting from the chemical or atomic structure evolves on a time scale of hours and days. Fits of the mag- of the surface, which we will call chemical truncation rods. netic reflectivity discussed in Sec. III suggest that an ap- In analogy with the chemical truncation rods, one may also proximately 10-Ć-thick region near the surface is altered define magnetic truncation rods aligned along the surface upon exposure to air for more than two weeks. Allen showed normal and passing through the magnetic bulk Bragg that exposure of polycrystalline surfaces to oxygen26 pro- reflections.5 Their existence originates in the truncation of duces UO2 with 0 0.25. We infer from this that the the magnetic structure at the surface. The dashed lines in Fig. near surface region of the surfaces studied in our experi- 1 b show the expected pure bulk magnetic truncation rods. ments may possess an oxygen stoichiometry just greater than Since the solid lines also pass through magnetic bulk Bragg 2. For comparison, the specular reflectivity expected from a reflections, they will have both a magnetic and a charge con- bulk terminated surface is shown by the solid line in Fig. 2. PRB 61 RESONANT X-RAY SCATTERING STUDIES OF THE . . . 8969 To characterize the stability of this surface upon exposure to air, and to eventually learn how to prepare better surfaces, sample 2 was mounted in a vacuum chamber held at 10 5 torr. The sample was annealed in situ in the H2 /Ar mixture at 200­300 °C. Following the anneal, the x-ray specular reflectivity showed nearly perfect bulk truncation. This data is labeled ``annealed'' in Fig. 2. The sample was then exposed to air for 1 h, after which the vacuum chamber was pumped down and another set of specular reflectivity data taken. This procedure was repeated for a total exposure to air of 6 h. The reflectivity curves for these surfaces are FIG. 3. Scattering diagram showing the linear polarization states also included in Fig. 2. From the figure it appears that the of the incident and scattered photons as well as the incident and scattered wave vectors. oxidization of the annealed surface is continuous and that only slight changes in the surface have occurred for exposure by Matveev and Matveev31 are beyond the scope of the times of the order of an hour. present data set, and have been neglected. Based on these results, sample 1 was vacuum annealed The x-ray cross section has been calculated in the kine- and sealed in the Be can with less than 5 min exposure to air. matical approximation and is given by The specular reflectivity taken more than three months after the anneal is labeled ``encapsulated'' in Fig. 2. The best fit to d 2 r this data solid line indicates that the surface is atomically 0 2 fn q e iq*rne Wn q 2, 2 flat in domains greater than 1000 Ć, which is the x-ray co- d A v2 all atoms n herence length, and has an outermost U-U spacing within 2% of the bulk value. Because the scattering of x rays by ura- where A is the illuminated surface area, r0 the Thomson nium is considerably stronger than that of oxygen, we were radius, v the unit-cell volume, rn the position of the nth unable to determine if the surface was terminated by oxygen atom, and Wn(q) and fn(q) are the Debye-Waller factor and or uranium. atomic scattering amplitude, respectively, of atom n. Typi- All of the magnetic scattering data reported in this paper cally, the outermost planes of atoms are allowed to have were obtained from the slightly oxidized surface. Prelimi- Debye-Waller factors which differ from the bulk,25,29 how- nary measurements of the encapsulated sample have shown a ever, for simplicity, we have used bulk values for the Debye- significant enhancement of the magnetic scattering intensity Waller factors in the fits described below. along the truncation rods relative to the oxidized sample, and The anomalous terms f and f in the atomic form factor will be published separately. The widths of the magnetic f (q) f 0(q) f f can become significant when the pho- truncation rods appear to be the same in both cases, which ton energy is tuned to an absorption edge. Following the suggests, but does not prove that the in-plane structures are work of Hannon et al.,30 these terms may be written within similar in the two samples. We attribute the reduced intensity the dipole approximation as along the magnetic truncation rod in the present sample to the x-ray attenuation by the layer of higher oxide. 3 f f 8 F11 F1 1 s** i i F11 F1 1 s* i D. X-ray resonant magnetic reflectivity n 2F10 F11 F1 1 s**n i*n . 3 In this section we describe the resonant scattering ampli- tude, including the magnetic terms, and use these to calculate Here, the FLM are proportional to the transition probability the magnetic scattering from a surface. Our approach is to of order L, where L 1 for electric dipole transitions, and model the truncation rods using the standard kinematical ap- contain resonant denominators. It is these resonant terms that proach for chemical truncation rods.25,29 Magnetic effects are produce the enhancements in the magnetic scattering that are inserted by including the magnetic terms in the scattering observed at absorption edges. The polarization of the inci- amplitudes.30 The number of photons per second scattered dent and scattered photons are i and s , respectively, and n into the detector, n is the direction of the magnetic moment of the atom. In our s , is experiments, the incident beam is linearly polarized in the d horizontal plane.10,20 The scattering geometry is illustrated in ns ni /A0 d id s T i 2 T s 2ai i as s d , Fig. 3. 1 The first term in Eq. 3 has the same polarization depen- dence as Thomson scattering and is called the anomalous where ni is the number of photons per second in the incident charge scattering amplitude. The second term is responsible beam, A0 its cross-sectional area, T( ) the Fresnel transmis- for the magnetic scattering observed in our experiments. Due sion coefficient which varies with the incident ( i) and scat- to the s* i factor, the incident polarization is rotated tered ( s) angles, and d /d is the x-ray scattering cross into scattered polarization. The fact that the polarization of section. The Fresnel transmission function differs from one the magnetic and charge scattering are orthogonal allows one only when i or s are near to the critical angle. The angular to utilize a polarization analyzer to distinguish between distribution of the incident photons is given by ai( i) while them.21 The third term in Eq. 3 produces a resonant second the acceptance of the detector is given by as( s). The mag- harmonic of the magnetic scattering and is ignored in our netic effects on the Fresnel reflectivity recently considered analysis. In order to simplify the calculations we treat the 8970 G. M. WATSON et al. PRB 61 FIG. 5. (01L) magnetic truncation rod profiles for various inci- dent photon energies near to the U MIV edge. Data were obtained at beamline X22C. Figure 4 b shows a transverse scan through the (01L) rod at an L of 0.06c*. The data are well described by a Lorentzian-squared line shape. The best fit line results in a FIG. 4. a Intensity along the (01L) magnetic truncation rod at transverse full width at half maximum FWHM of 0.06°, four different temperatures and for an incident photon energy of which is slightly larger than the bulk mosaic 0.05° . Trans- 3.728 KeV. b Rocking curve through the (01L) magnetic trunca- verse scans taken at different positions along the rod indicate tion rod at L 0.06c*. c Scattering intensity of the (01L) mag- that the line shape is independent of L although its width netic truncation rod as a function of the energy of the incident increases from 0.05° at small L to approximately 0.15° at L photon energy. 0.25c*. Both the line shape and FWHM were observed to be independent of temperature at the present signal levels. FLM term in Eq. 3 as a constant, independent of the scat- Quantitative statements about the extent of inplane magnetic tering wave vector q, but fit the energy dependence explic- order at the surface will require detailed modeling, which is itly. This simplification is reasonable as long as the range of beyond the scope of the present work. q, considered in the analysis, is limited. A good test of the origin of the observed scattering is to study its dependence on incident photon energy. If the signal III. RESULTS AND DISCUSSION were due to charge rather than magnetic scattering, we might expect that the intensity would still be observable for ener- A. Nonspecular magnetic truncation rods gies away from the MIV absorption edge. The scattered in- The intensity measured along the (01L) magnetic trunca- tensity at 0 1 0.06 is plotted as a function of incident pho- tion rod see Fig. 1 b is shown in Fig. 4 a at four different ton energy in Fig. 4 c . The observed resonance is virtually temperatures. This rod corresponds to pure magnetic scatter- identical to that of the bulk magnetic Bragg reflections20,32 ing as seen in Fig. 1 b . Integrated rod profiles, obtained by and is clear evidence that the scattering is magnetic in origin. rocking at each L, gave similar results and are not shown. This is further supported by tests of the scattered polariza- Each nonzero profile increases from L 0, takes a maximum tion, which show that it is predominantly . at the critical angle, and then falls off for larger L. As the The dependence of the magnetic truncation rod profile on temperature increases, the magnetic scattering weakens, and the incident photon energy is shown in Fig. 5. At entirely disppears above TN 30.2 K. The maximum peak 3.722 keV the peak in the profile appears near L 0.055. intensity at 10 K is of order 10 counts per second at X22C As the photon energy is increased, it shifts to larger L reach- and approximately 200 counts per second at the wiggler ing 0.068 at the MIV edge. Above the edge, the peak shifts beamline X25. back to lower L as the photon energy is further increased. PRB 61 RESONANT X-RAY SCATTERING STUDIES OF THE . . . 8971 FIG. 7. Anomalous scattering factors for U at the MIV absorp- tion edge. Data are from absorption measurements solid lines , specular reflectivity near the critical angle solid circles , shifts in the 220 bulk Bragg reflection crosses , and from fits to the (01L) magnetic truncation rod profiles open circles . compiled in Fig. 7. In one set of experiments, the specular x-ray reflectivity at small angles was utilized to determine f FIG. 6. Intensity of the (01L) magnetic truncation rod as a and f solid circles , following Ref. 33. These measure- function of incident photon energy at various positions along the ments suffered from the small size of our samples relative to rod. Data were obtained at beamline X22C. the large footprint of the beam at grazing incidence, but gave results which agree well with absorption measurements of The largest signals occur when the incident and scattered thin UO2 films solid line .34 angles i and s are close to the critical angle for total We next fitted the profiles shown in Fig. 4 a and 5 by external reflection. The fact that the peak shifts is not sur- assuming that the surface and bulk antiferromagnetic struc- prising since the critical angle depends on f and at an ab- tures are the same at T 10 K and then varying the atomic sorption edge both the real and imaginary parts of the atomic scattering amplitudes with the incident photon energy. The scattering factor change rapidly with photon energy.25 best fits are shown by the solid lines in the figures. The As described in Sec. II D, there are two major contributors results of these fits open circles in Fig. 7 are in good agree- to the rod profile: the magnetic structure, which enters ment with the results from specular reflectivity. through the differential cross section, and the Fresnel trans- Finally, due to the large change in f 50 electrons at mission coefficients. At angles much larger than the critical an absorption edge, refraction at the surface is important. As angle, the dominant effect is the resonant magnetic scattering noted many years ago,35,36 these effects lead to a shift in the amplitude. However, near the critical angle, both the mag- position of a bulk Bragg reflection with photon energy, and netic scattering amplitude and the Fresnel effects are impor- from this, the real part of the anomalous scattering factor can tant. This is illustrated in Fig. 6, where the scattered intensity be determined. The data shown by crosses in Fig. 7 were versus incident photon energy is shown at a number of dif- obtained from measurements of the peak position of the ferent L. At large values of L, i , and s are larger than the 220 bulk Bragg reflection as a function of photon energy in critical angle, so that a single peak, fixed in position and an earlier experiment.32 width, and characteristic of the energy dependence of the magnetic scattering amplitude, is observed. At smaller L, the peak shifts to lower photon energy and broadens. The shift of B. Temperature dependence of nonspecular magnetic the peak away from the U M truncation rods IV edge shows that the Fresnel effects become important at small L. In order to characterize the temperature dependence of the In order to model the data shown in Figs. 4 and 5 it is near surface magnetic structure, we measured the intensity of necessary to know the atomic scattering factors. Unfortu- the scattering at several positions along the (01L) magnetic nately, the atomic scattering factors for U are not well known truncation rod, including the bulk magnetic reflection at L for photon energies near the M edges, and it was necessary to 1. The results obtained for three different L's, are shown in measure them. A variety of techniques for determining the Fig. 8. These data correspond to peak intensities and were anomalous terms was employed. The collected results are obtained by varying the temperature at a fixed scattering 8972 G. M. WATSON et al. PRB 61 FIG. 8. Temperature dependence of the magnetic scattering at the 001 magnetic bulk Bragg reflection solid circles and at vari- ous positions along the (01L) magnetic truncation rod open sym- bols . Data are normalized to unity at low temperatures. Inset: log- log plot of the scattering intensity at two different positions along the (01L) magnetic truncation rod as a function of reduced tem- FIG. 9. Models for the absolute value of the magnetization for a perature. Solid lines are a power-law fit to the data. few atomic planes near a surface solid lines and the associated envelope function dashed lines . Shown are the thickness of the wave vector. -integrated intensities gave a similar behavior, disordered layer l and the width of the interface separating the which is expected from the observed temperature indepen- ordered bulk from the disordered surface. a Surface-induced dis- order model of Lipowsky. b Model used in our analysis. dence of the transverse widths, at least at the present signal levels. Since the atomic planes all scatter in phase at L 1, In Lipowsky's model, the coupling of the disorder at the the intensity at the magnetic bulk Bragg reflection is propor- surface to the underlying order in the bulk leads to an order tional to the square of the magnetic order parameter. Note parameter profile such as shown in Fig. 9 a . Each Gaussian that, given the strong absorption at the U M in the figure represents the average sublattice magnetization IV edge, the penetration depth at the bulk Bragg reflection is less than on the specified atomic plane. The amplitude of the Gaussian 1000 Ć. Nevertheless, the temperature dependence of the reflects the degree of magnetic order with widths that are scattering is identical to that observed by neutron held fixed. Then, two length scales characterize the falloff of the magnetization at the surface: l, the thickness of the layer scattering.32 Specifically, the intensity is nearly constant at at the surface with reduced order, and the width of the low temperatures and abruptly drops to zero at TN , consis- interface which separates the magnetically ordered bulk from tent with a discontinuous phase transition. the disordered surface layer. Interestingly, whereas the temperature dependence of the Efforts to fit the observed magnetic truncation rods to a scattering at the magnetic bulk Bragg reflection appears dis- magnetic order profile similar to that shown in Fig. 9 a were continuous, the scattering along the rod at grazing incidence unsatisfactory. Specifically, this profile can be considered as open symbols appears continuous. As illustrated by the in- having two interfaces, one at the surface of the sample and sert, which shows the truncation rod results plotted as a func- the other between the ordered bulk and the disordered sur- tion of reduced temperature t (TN T)/TN on a log-log face layer. Between the two interfaces the scattering ampli- scale, the intensities near TN are well described by a power tude is reduced. In this regard, the scattering is similar to that law in reduced temperature, I(t) I0t2 . The solid lines give of a thin film of a low-density material deposited on a high the corresponding fits for temperatures greater than 25 K. density substrate, which implies that the truncation rods Similar behavior has been observed at the discontinuous should have intensity oscillations with a periodicity deter- chemical order-disorder transformation of Cu3Au.17,18,37 In mined by the thickness of the overlayer. No such oscillations their grazing incidence x-ray scattering studies, Dosch and are observed in the magnetic truncation rods of UO2. co-workers17,18,37 observed that the temperature dependence The temperature dependence of the scattering along the of the intensity along a truncation rod varied continuously, (01L) rod in UO2 also differs from that observed for Cu3Au also following a power-law dependence on reduced tempera- in that it apparently becomes more continuous or less bulk- ture. This led them to suggest that the near surface volume is like with increasing L. This can be seen directly in Fig. 8. more disordered than the bulk at temperatures near the tran- The exponent which characterizes the temperature depen- sition. Further, they found that the temperature dependence dence of the scattering at L 0.150 is larger than that at L of the scattering became more bulklike at larger values of L, 0.075 see inset , leading to a more rounded profile. The which they argued resulted from the increase in penetration fitted values of obtained from four different runs along depth with L. The collected results were explained in terms ( 1L) are plotted as a function of L in Fig. 10. Clearly, of the model of surface-induced disorder introduced by Lip- increases with L, in contrast to the results reported for owsky for discontinuous bulk transitions.14,15 Cu3Au.17,18,36 PRB 61 RESONANT X-RAY SCATTERING STUDIES OF THE . . . 8973 FIG. 10. Variation of the exponent with position along the (01L) magnetic truncation rod. The results of four separate experi- ments are shown by the different symbols. More generally, we have found that increases not with L, but with L, the separation from bulk Bragg reflections. This is shown in Fig. 11, which shows the value of de- duced along the (01L) rod near the bulk Bragg reflection at L 1 and along the specular rod near the bulk Bragg reflec- tion at L 1. These data were fitted to a power law in re- duced temperature over the same temperature range as in Fig. 10. The fitted values for are presented as a function of the distance from the nearest bulk Bragg reflection L . The measured values are in qualitative agreement with each other, and increase with distance from the nearest bulk Bragg reflection. Since the diffracting planes do not scatter in phase at an arbitrary position along a truncation rod, the scattered inten- sity at any particular position is not a direct measure of the average magnetic order in the volume determined by the FIG. 11. Variation in the exponent with position along the penetration depth. Rather, the intensity at every position rods near the a 011 and b 001 magnetic bulk Bragg reflec- along the rod depends on the profile of the magnetic order. tions. Solid symbols correspond to L 0 and open symbols to L 0. Lines are a guide to the eye. For a diffuse or disordered interface in which the correla- tions can be described with a Gaussian function, the scattered intensity I( ,L) can be related to the intensity that would be tation of the measured exponents in terms of surface induced observed for an identical but flat interface I disorder. In view of the already weak signals, we have not 0 via pursued this analysis further. I ,L I0e L 2, 4 C. Specular magnetic reflectivity where L is the distance to the nearest bulk Bragg reflection.25,29 This is a simple Debye-Waller-like term with The discussion above provided a motivation to refit the the rms roughness replaced by the interfacial width. In the truncation rod profiles with the modified Lipowsky profile model of surface-induced disorder, the interfacial width var- illustrated in Fig. 9 b , in which the partially disordered mag- ies as a function of the reduced temperature as (t) netic surface layer of thickness l is assumed to be fully dis- ordered. Due to the fact that the penetration depth varies 0 ln(t).15 Substituting this into Eq. 4 we find that it introduces a temperature dependence to the scattering of the rapidly at small L, it turns out that it is difficult to extract form both and l from fitting the truncation rod profiles at higher temperatures. This problem is avoided along the specular rod I t,L I near the magnetic bulk Bragg reflection at L 1 for which 0t 0 L 2. 5 i and s are much greater than the critical angle. As described This implies that the temperature dependence of the scatter- in Sec. II A, both charge and magnetic scattering contribute ing along a truncation rod should follow a power-law depen- to the intensity along the specular direction for temperatures dence on reduced temperature with an exponent that in- below TN . However, the charge scattering may be consider- creases with L. It is consistent with the general trend of the ably reduced by using polarization analysis and accepting data of Figs. 10 and 11, however, it complicates the interpre- only the rotated signal. 8974 G. M. WATSON et al. PRB 61 FIG. 13. Temperature dependence of the derived magnetic in- terfacial widths for two different samples. FIG. 12. Magnetic specular reflectivity circles obtained near conclusions in the present study. Even smoother and cleaner the 001 reflection using a polarization analyzer to suppress the samples will be required in experiments carried out at third charge scattering background. generation sources before more quantitative conclusions can be drawn. We are nevertheless encouraged that both the en- The specular magnetic reflectivity obtained in the neigh- capsulated and oxidized samples 1 and 2 give such similar borhood of the bulk 001 reflection is presented in Fig. 12 results for the temperature dependence of the interfacial width. It suggests that the effects we are observing are in- for two temperatures. The intensity of the magnetic scatter- trinsic, or at least, not strongly dependent on the thin oxide ing at the bulk reflection is over 300 000/sec and falls off by surface layer. five orders of magnitude within a few tenths of an inverse Ć. The wings of the scattering are clearly much weaker at higher temperatures near TN 30.2 K open circles than at IV. SUMMARY AND CONCLUSIONS 10 K closed circles . This suggests that the magnetic inter- face is more diffuse at higher temperatures, since broadly Resonant x-ray magnetic scattering was used to determine speaking a sharper profile in reciprocal space is consistent the magnetic structure near the 001 surface of the antifer- with a more extended density profile in real space. romagnetic oxide UO2 by direct measurement of the mag- Fits of the specular and truncation rod intensities were netic reflectivity and truncation rods. For temperatures near made to a model of the magnetic interface, consisting of an to, but below, the bulk NeŽel temperature, there is a magneti- interfacial width and thickness l of magnetically disordered cally disordered layer at the surface approximately 8 Ć in volume see Fig. 9 . The magnetic profiles were otherwise thickness in sample 1 . A magnetic interface, separating the assumed to match the profile of the electronic charge density, magnetically disordered surface layer from the magnetically which was also determined using reflectivity techniques. The ordered bulk exists at all temperatures below the NeŽel tem- latter correspond closely to ideal termination, supplemented perature. At the lowest temperatures studied this magnetic by a thin absorbing layer. The best fits are shown by the solid interface has a width of slightly more than one lattice con- lines in Figs. 4 a and 12. The thickness of the disordered stant. With increasing temperature, the interfacial width in- layer l was found to be relatively insensitive to variations in creases and appears to diverge at the NeŽel temperature. This the temperature, and could be fixed at a value of about 13 Ć. leads to a continuous variation of the surface magnetic scat- The corresponding value of the interfacial width at low tem- tering near the magnetic ordering transition, in contrast to the peratures 10 K was about 6 Ć. Thus, in contrast to the bulk which is discontinuous. The magnetic scattering along electronic charge density, the magnetic structure is disor- the rods further exhibits a power-law behavior in reduced dered very near the surface, and has a more rounded profile, temperature, with an exponent that increases with increasing even at 10 K in the magnetically ordered phase. separation from bulk Bragg peaks. For increasing temperatures, the interfacial width exhib- These results are qualitatively consistent with the theory ited a dramatic increase, starting at about 25 K and diverging of surface induced disorder, and motivate continued effort on as T approached TN . This is illustrated in Fig. 13 where the smoother and still-cleaner samples at third generation syn- fitted widths are plotted versus temperature for two different chrotron sources. In particular, our specular reflectivity stud- UO2 001 samples samples 1 and 2 . Whereas the limiting ies of the chemical surface at 8-keV photon energy indicate values of the disordered volume and interfacial width of the that approximately 10 Ć of a superoxide may exist at the two samples are different at low temperatures 6 vs 11 Ć , surface on both samples 1 and 2. It is still possible that the the temperature dependencies appear similar. The divergence near-surface behavior observed in these samples is in part of the widths near TN is qualitatively consistent with the due to the effect of excess oxygen on the magnetic structure, theory of surface induced disorder, which predicts a logarith- which is known to decrease TN .38 Whether the excess oxy- mic increase. The limited range of L over which the mag- gen acts only to disorder the near surface region at zero netic reflectivity has been obtained limit us to qualitative temperature and the resulting temperature dependence of the PRB 61 RESONANT X-RAY SCATTERING STUDIES OF THE . . . 8975 magnetization profile is governed by a Lipowsky-type ACKNOWLEDGMENTS model, or whether the magnetic order profile is determined at all temperatures by the doping profile, is unknown. Further We would like to thank V. Meyritz for help with the experiments on carefully prepared samples with stoichio- sample preparation. Work at Brookhaven was supported by metric surfaces are underway to test these ideas. The prelimi- the U.S. DOE under Contract No. DE-AC02-98CH10886. nary results obtained for the encapsulated sample in the B.D.G. acknowledges financial support from NSERC of present study are very encouraging. Canada, OCMR of Ontario. 1 G. A. Prinz, Nature London 250, 1092 1990 . Berman, Hj. Matzke, and W. Ellis, Physica B 221, 405 1996 ; 2 W. L. O'Brien and B. P. Tonner, Phys. Rev. B 52, 15 332 1995 . Phys. Rev. Lett. 77, 751 1996 . 3 See, for example, J. G. Tobin, K. W. Goodman, F. O. Schumann, 20 C. C. Tang, W. G. Stirling, G. H. Lander, D. Gibbs, W. Herzog, R. F. Willis, J. B. Kortright, J. D. Denlinger, E. Rotenberg, A. P. Carra, B. T. Thole, K. Mattenberger, and O. Vogt, Phys. Rev. Warwick, and N. V. Smith, Surf. Sci. 395, L227 1998 . B 46, 5287 1992 . 4 A notable exception to this is neutron reflectometry. See, for ex- 21 D. Gibbs, G. Grušbel, D. R. Harshman, E. D. Isaacs, D. B. ample, G. P. Felcher, R. T. Kampwirth, K. E. Grey, and R. McWhan, D. Mills, and C. Vettier, Phys. Rev. B 43, 5663 Felici, Phys. Rev. Lett. 52, 1539 1984 . 1991 . 5 22 A. Fasolino, P. Carra, and M. Altarelli, Phys. Rev. B 47, 3877 B. C. Frazer, G. Shirane, D. E. Cox, and C. E. Olsen, Phys. Rev. 1993 ; G. P. M. Poppe and A. Fasolino, Surf. Sci. 331, 1186 140, A1448 1965 ; B. T. M. Willis and R. I. Taylor, Phys. Rev. 1995 . Lett. 17, 188 1965 . 23 6 C.-C. Kao, J. B. Hastings, E. D. Johnson, D. P. Siddons, G. C. O. G. Brandt and C. T. Walker, Phys. Rev. 170, 528 1968 . 24 J. Faber and G. H. Lander, Phys. Rev. B 14, 1151 1976 . Smith, and G. A. Prinz, Phys. Rev. Lett. 65, 373 1990 . 25 7 R. Feidenhans'l, Surf. Sci. Rep. 10, 105 1989 ; I. K. Robinson J. F. MacKay, C. Teichert, D. E. Savage, and M. G. Lagally, and D. J. Tweet, Rep. Prog. Phys. 55, 599 1992 . Phys. Rev. Lett. 77, 3925 1996 . 26 G. C. Allen, P. M. Tucker, and J. W. Tyler, Vacuum 32, 481 8 J. M. Tonnerre, L. Se ve, D. Raoux, G. SoullieŽ, B. Rodmacq, and 1982 . P. Wolfers, Phys. Rev. Lett. 75, 740 1995 . 27 T. N. Taylor and W. P. Ellis, Surf. Sci. 77, 321 1978 ; 107, 249 9 C.-C. Kao, C. T. Chen, E. D. Johnson, J. B. Hastings, H.-J. Lin, 1981 . G. H. Ho, G. Meigs, J.-M. Brot, S. L. Hulbert, Y. U. Idzerda, 28 Hj. Matzke and A. Turos, J. Nucl. Mater. 114, 349 1983 ; Solid and C. Vettier, Phys. Rev. B 50, 9599 1994 ; M. Sacchi, J. State Ionics 49, 189 1991 ; A. Turos, R. Falcone, A. Drigo, A. Vogel, and S. Iacobucci, J. Magn. Magn. Mater. 147, L11 Sambo, L. Nowicki, N. Madi, J. Jagielski, and Hj. Matzke, Nucl. 1995 ; V. Chakarian, Y. U. Idzerda, C.-C. Kao, and C. T. Chen, Instrum. Methods Phys. Res. B 118, 659 1996 . ibid. 165, 52 1997 ; J. W. Freeland, V. Chakarian, Y. U. Idz- 29 D. Gibbs, B. M. Ocko, D. M. Zehner, and S. G. J. Mochrie, Phys. erda, S. Doherty, J. G. Zhu, J.-H. Park, and C.-C. Kao, Appl. Rev. B 42, 7330 1990 . Phys. Lett. 71, 276 1997 ; M. Sacchi, C. F. Hague, E. M. Gul- 30 J. P. Hannon, G. T. Trammell, M. Blume, and D. Gibbs, Phys. likson, and J. H. Underwood, Phys. Rev. B 57, 108 1998 . Rev. Lett. 61, 1245 1988 . 10 D. B. McWhan, C. Vettier, E. D. Isaacs, G. E. Ice, D. P. Siddons, 31 V. M. Matveev and V. V. Matveev, Physica B 208-209, 768 J. B. Hastings, C. Peters, and O. Vogt, Phys. Rev. B 42, 6007 1995 . 1990 . 32 G. M. Watson, B. D. Gaulin, D. Gibbs, T. R. Thurston, P. J. 11 S. Ferrer, J. Alvarez, E. Lindgren, X. Torrelles, P. Fajardo, and F. Simpson, S. M. Shapiro, G. H. Lander, Hj. Matzke, S. Wang, Boscherini, Phys. Rev. B 56, 9848 1997 . and M. Dudley, Phys. Rev. B 53, 686 1996 . 12 S. F. Alvarado, M. Campagna, and H. Hopster, Phys. Rev. Lett. 33 F. Stanglmeier, B. Lengeler, W. Weber, H. Gobel, and M. 48, 51 1982 . Schuster, Acta Crystallogr., Sect. A: Found. Crystallogr. A48, 13 D. Weller, S. F. Alvarado, W. Gudat, K. Schroden, and M. Cam- 626 1992 . pagna, Phys. Rev. Lett. 54, 1555 1985 . 34 J. O. Cross, M. Newville, J. J. Rehr, L. B. Sorenson, C. E. Boul- 14 R. Lipowsky, Phys. Rev. Lett. 49, 1575 1982 ; R. Lipowsky and din, G. M. Watson, T. Gouder, G. H. Lander, and M. I. Bell, W. Speth, Phys. Rev. B 28, 3983 1983 . Phys. Rev. B 58, 11 215 1998 . 15 R. Lipowsky, Ferroelectrics 73, 69 1987 . 35 R. W. James, The Optical Principles of the Diffraction of X Rays 16 W. Schweika, D. P. Landau, and K. Binder, Phys. Rev. B 53, G. Bell and Sons, London, 1962 . 8937 1996 . 36 J. M. Cowley, Phys. Rev. 77, 669 1950 ; J. Appl. Phys. 21, 24 17 H. Dosch, L. Mailander, H. Reichart, J. Peisl, and R. L. Johnson, 1950 . Phys. Rev. B 43, 13 172 1991 . 37 H. Dosch, L. Mailander, A. Lied, J. Peisl, F. Grey, R. L. Johnson, 18 H. Reichert, P. J. Eng, H. Dosch, and I. K. Robinson, Phys. Rev. and S. Krummacher, Phys. Rev. Lett. 60, 2382 1988 ; H. Dosch Lett. 74, 2006 1995 . and J. Peisl, Colloq. Phys. 50, C7-257 1989 . 19 G. M. Watson, D. Gibbs, G. H. Lander, B. D. Gaulin, L. E. 38 A. Arrott and J. E. Goldman, Phys. Rev. 108, 948 1957 .