RAPID COMMUNICATIONS PHYSICAL REVIEW B, VOLUME 64, 140405 R Layer-dependent magnetization at the surface of a band ferromagnet R. Pfandzelter and M. Potthoff Humboldt-Universita¨t zu Berlin, Institut fu¨r Physik, Invalidenstraße 110, 10115 Berlin, Germany Received 17 May 2001; published 17 September 2001 The temperature dependence of the magnetization near the surface of a band ferromagnet is measured with monolayer resolution. The simultaneous application of highly surface-sensitive techniques enables one to deduce the layer-dependent magnetization curves at a Fe 100 surface. Analysis of data is based on a simple mean-field approach. Implications for modern theories of itinerant-electron ferromagnetism are discussed. DOI: 10.1103/PhysRevB.64.140405 PACS number s : 75.70.Rf, 75.50.Bb, 79.20.Hx, 79.20.Rf A ferromagnetic material is characterized by a spontane- within Hubbard-type models of correlated itinerant electrons ous magnetization m which decreases with increasing tem- using slave-boson, decoupling and alloy-analogy perature T until the paramagnetic state with m 0 is reached approaches.10 Roughly, the results are similar to those for at the Curie point Tc . For very low temperatures the form of Ising or Heisenberg systems in the range of intermediate the magnetization curve m(T) is governed by spin-wave ex- temperatures. Yet, the precise form of m (T) for a band- citations according to Bloch's law. For temperatures very ferromagnetic surface must still be considered as largely un- close to Tc critical fluctuations result in a power-law depen- known. dence m(T) (Tc T) with a critical exponent . In the On the experimental side, determination of the layer- wide range of intermediate temperatures the form of m(T) dependent magnetization curve at a surface is a demanding depends on the specific system. In case of a band- task as well, which has not been achieved so far. In order to ferromagnetic material, such as Fe as a prototype, the de- measure m (T), experimental techniques sensitive to surface tailed form of m(T) in this intermediate regime must be magnetism are required with a magnetic probing depth tun- explained from the underlying electronic structure.1,2 able with monolayer ML resolution. Common surface- Density-functional theory within the local-spin-density sensitive techniques like spin-resolved secondary-electron approximation is known to give a quantitatively accurate de- emission11 or inverse photoemission12 average over several scription of several ground-state properties.3 For finite tem- layers beneath the surface resulting in a nearly bulklike peratures, however, there is no satisfying implementation behavior of m(T). Nevertheless, in a number of sophisticated available. A microscopic theory must account for the exis- experiments a roughly linear temperature trend of m(T) has tence of local magnetic moments above Tc in particular.4 been observed and attributed to the surface magnetization This requires one to deal with correlations among itinerant see Refs. 13­15 for Fe surfaces and Ref. 16 for experimen- valence electrons as, for example, within the framework of tal techniques . an orbitally degenerate Hubbard-type model with realistic Here we report on an experiment to determine m (T) at parameters.5 The long history of itinerant-electron ferromag- the 100 surface of bcc Fe. The crucial feature of our ex- netism shows that this is a demanding task.2 On the other periment is the simultaneous application of different in situ hand, comparatively simple mean-field approaches based on techniques which are highly sensitive to the magnetization spin models are known to provide a successful phenomeno- near the surface, but slightly differ in their magnetic probing logical description in many cases see, e.g., Ref. 6 . Remark- depths. ably, while the Weiss mean-field theory fails to reproduce the Ultimate surface sensitivity magnetic probing depth known T 0 and T Tc limits and substantially overesti- 0 ML) is achieved by spin-polarized electron capture.17,18 mates Tc , the form of the Fe magnetization curve m(T) at 25 keV He ions are grazingly scattered incidence angle to intermediate reduced temperatures T/Tc is reasonably well the surface plane 1 ­2°) off a magnetized Fe 100 surface. described: For spin-quantum number S 1/2 there are devia- The ions are reflected and capture target electrons into ex- tions from the measured bulk magnetization curve of Fe cited atomic states. The spin polarization of captured elec- within a few percent only.7,8 trons is deduced from the observed degree of circular polar- At the surface of a band ferromagnet the magnetization ization of emitted fluorescence light. Excited atomic states may be different for different layers parallel to the surface can only survive collisions for impact parameters exceeding because of the reduced translational symmetry. Hence, a key the mean radius of the corresponding electronic orbital. Thus quantity that characterizes the surface magnetic structure is the final formation of atomic states takes place on the outgo- the layer-dependent magnetization curve m (T). Within the ing part of the trajectories, resulting in a sensitivity of elec- framework of classical spin models, the lowered surface co- tron capture to a region at or above the top surface layer. ordination number implies that certain exchange interactions An established technique to study magnetism near a sur- are missing. This directly leads to a reduced magnetic stabil- face is spin-polarized secondary-electron emission, induced ity at the surface:9 The top-layer ( 1) magnetization is by keV electrons at normal or oblique incidence.19 Based on substantially reduced as compared with the bulk. However, a mean-field study, Abraham and Hopster11 infer from their significant deviations from the bulk magnetization curve are observed temperature-dependence of the spin-polarization of confined to the first few layers in the intermediate tempera- secondary electrons from Ni 110 a magnetic probing depth ture range. This is confirmed qualitatively by calculations of 3 ­4 ML with an upper limit of 7 ML for electrons 0163-1829/2001/64 14 /140405 4 /$20.00 64 140405-1 ©2001 The American Physical Society RAPID COMMUNICATIONS R. PFANDZELTER AND M. POTTHOFF PHYSICAL REVIEW B 64 140405 R of about 0 or 10 eV kinetic energy. A compilation of electron scattering cross sections by Scho¨nhense and Siegmann20 sug- gests a similar value for Fe ( 4.2 ML), in accordance with a recent overlayer experiment by Pfandzelter et al.21 The probing depth in secondary-electron emission can be considerably reduced by using energetic ions instead of elec- trons as primary particles.22,21 Grazingly incident ions are reflected from the top surface layer and do not penetrate into the bulk ``surface channeling'' . In practice, structural im- perfections like surface steps mediate penetration of some projectiles, leading to a contribution of excited electrons from layers beneath the surface. From computer simulations emulating ion trajectories23 and an overlayer experiment,21 we infer for scattering of 25 keV protons from our Fe 100 surface a probing depth of (0.5 0.2) ML for electrons of 10­20 eV kinetic energy. We note that seems to in- crease for lower electron energies owing to cascade multipli- cation governed by electron-electron scattering.21 Hence, en- ergy resolution is mandatory if maximum surface sensitivity is aspired. Electron capture and electron emission yield information on the spin part of the magnetization. Although a general quantitative relationship between experimental observable electron spin polarization and magnetization has not been worked out so far, it is generally assumed that one can derive the normalized temperature dependence of the magnetiza- tion. This assumption appears to be justified in view of the, at least for the conditions of our experiment, weak selectivity of capture and emission processes in k space. Considering the small, well-defined, but different information depths of the techniques, a simultaneous application at the same sur- face thus should enable one to deduce the layer-dependent magnetization curves near the surface. In our experiment, a 100 Fe single crystal disk is mounted to close the gap of a magnetic yoke with a coil. For FIG. 1. Temperature dependence of a Kerr rotation, b spin the measurements the crystal is magnetized by current pulses polarization of secondary electrons, induced by electrons and graz- ingly scattered protons open and solid circles, respectively , and through the coil along an easy axis of magnetization 001 or c spin polarization of electrons captured into atomic states of He 001¯ in the 100 surface plane. This reproducibly yields a ions, grazingly scattered off Fe 100 . The curves represent mean- full remanent magnetization near the center of the crystal as field calculations according to Eqs. 1 and 2 with different prob- checked by the magneto-optic Kerr effect. The 100 surface ing depths as indicated. is prepared by cycles of grazing Ar sputtering and anneal- ing, until the surface is clean, atomically flat, and well or- formed during grazing scattering of 25 keV He ions is stud- dered, as inferred from Auger electron spectroscopy, grazing ied via fluorescence light emitted in the 2s3S-3p3P, ion scattering, and LEED. The target temperature is con- 388.9 nm transition. The circular polarization fraction of trolled by a thermocouple attached directly near the crystal. the light is measured by means of a rotatable quarter-wave Systematic differences between the thermocouple reading plate, a linear polarizer, a narrow bandwidth interference fil- and the crystal temperature are calibrated by Kerr effect Cu- ter, and a cooled photomultiplier. The transition being in the rie temperature Tc) and pyrometer measurements and cor- UV spectral range, detection is affected on a tolerable level rected. by stray light from the filaments for heating the crystal up to Electrons are emitted by 25 keV protons at grazing inci- temperatures below about 900 K. dence (1.2°) or by 4 keV electrons at oblique incidence Experimental results are depicted in Fig. 1 as a function (33°) and enter an electrostatic energy analyzer cylindrical of the reduced temperature T/Tc , Tc 1043 K. The data are sector field in a direction of about 10° from normal. Spin collected from several quick heating and cooling runs. Short analysis is performed for electrons with 10­20 eV kinetic measurement times turned out to be important in order to energy in a subsequent LEED spin polarization detector.21 avoid significant segregation of C at intermediate tempera- Each polarization spectrum is obtained from two identical tures and S at temperatures close to Tc .15 No systematic measurements with reversed magnetizations to eliminate in- differences exceeding the statistical error about 0.03 for strumental asymmetries. the normalized polarization were observed for heating and Electron capture into the excited He I 1s3p3P term cooling runs, respectively. In Fig. 1 a we show for compari- 140405-2 RAPID COMMUNICATIONS LAYER-DEPENDENT MAGNETIZATION AT THE . . . PHYSICAL REVIEW B 64 140405 R son the rotation of the polarization axis associated with the by an exponential factor exp( / ) where is the probing longitudinal magneto-optic Kerr effect solid circles . The depth characteristic for the experimental technique applied. temperature dependence is in agreement with previous Kerr- From the layer-dependent magnetization curves m (T), we rotation measurements at Fe 100 by Sirotti et al.15 and re- thus calculate a quantity P(T) as flects the bulk magnetization, because of the large penetra- tion depth of visible He-Ne-laser light typically 20 nm Ref. 24 . P T e / m T . 2 Clearly different temperature-dependences are observed 1 with the surface-sensitive techniques electron-induced elec- The results are shown in Fig. 1 curves . The mean-field tron emission Fig. 1 b , open circles , proton-induced elec- P(T) nicely reproduces the temperature trend of the prop- tron emission Fig. 1 b , solid circles , and electron capture erly normalized measured data for the respective informa- Fig. 1 c , solid circles . The curvatures gradually decrease, tion depth . A value 5 ML is consistent with the esti- until, for electron capture, an almost linear behavior is ob- mates for the probing depth in electron-induced electron served. Remarkably, for electron-induced electron emission, emission ( 4 ­5 ML). We have also checked against the a prominent technique to study surface magnetism, the data choice S 1/2. This does not change the temperature trend of closely resemble the data from the Kerr effect. m /m (0) as a function of T/Tc significantly. Surprisingly, Information on the layer-dependent magnetization cannot considering an enhancement of the T 0 top-layer magnetic be extracted from the data directly, as these have to be inter- moment see Ref. 27 does not lead to a significant change of preted as exponentially weighted averages over a number of the temperature trend either. Following Ref. 28 one may ex- layers corresponding to the probing depth. We use an indirect pect a different exchange between the top- and the sub- way by comparing with results of a simple mean-field calcu- surface-layer moments: J12 J. Within the experimental er- lation which is known to reproduce the bulk magnetization ror, we find that the measured data are reproduced by curve fairly well, provided that reduced quantities calculations for a modified surface exchange in the range m(T)/m(0) and T/Tc are used. from J12 /J 0.8 to J12 /J 1.1. Accordingly, the spin-S Heisenberg model for the 100 We conclude that the mean-field calculation gives a rather surface of a bcc lattice with layer-independent nearest- accurate description of the layer-dependent magnetization at neighbor exchange J is considered: H J i ,j Si Sj . the Fe 100 surface at intermediate temperatures. Clearly, Here i labels the sites within a layer parallel to the surface mean-field theory must be considered as a poor starting point and 1, . . . , the different layers. The mean-field free to explain surface magnetism. Nevertheless the result is in- energy is F teresting as any theoretical approach that conceptually im- MF kBT ln tr exp( HMF /kBT) where HMF is obtained from H by the usual decoupling S proves upon the Weiss theory should give the same results i Sj Si Sj S within our experimental error . i Sj Si Sj . Assuming collinear ferromagnetic or- der, m In summary, this study gives detailed information on the m ez , and minimizing FMF with respect to the order parameter, m z layer-dependent magnetization at the surface of a prototypi- g B Si (g: Lande´ factor; B : Bohr magneton , yields a coupled set of Weiss self-consistency cal band ferromagnet. We report on an experiment to mea- equations sure temperature-dependent magnetization curves near the 100 surface of bcc Fe. We simultaneously apply different m m 0 BS Sb /kBT , 1 techniques, two of which are based on grazing scattering of energetic ions, resulting in an ultimate surface sensitivity. with m (0) g BS, the Brillouin function BS Ref. 25 and The magnetic information depths of the techniques being the layer-dependent Weiss field b (2J/g B)(z m well defined but slightly different enables one to achieve a z m 1 z m 1). z 0 and z 4 are the intra- and near monolayer resolution. The form of the layer-dependent inter-layer coordination numbers for the 100 surface. The magnetization curve is an important key quantity of surface total coordination number is z z 2z 8. The equations magnetism which, for intermediate temperatures, represents 1 are easily solved numerically for a film of finite but suf- a benchmark to discriminate between different microscopic ficiently large thickness. For the actual calculations we have theoretical approaches to explain surface magnetism from taken S 1. Assuming the orbital contribution to the mag- the underlying temperature-dependent electronic structure. netic moment to be quenched completely (g 2), this ap- pears to be the proper choice in the case of Fe since the T The experimental part of this work was performed in col- 0 spin moment is 2.13 B per atom.26 laboration with T. Igel, M. Ostwald, and Professor H. Winter. To compare with the experiment we assume that each Financial support by the Deutsche Forschungsgemeinschaft layer gives a contribution proportional to m but weighted Sonderforschungsbereich 290 is gratefully acknowledged. 1 A. Aharoni, Introduction to the Theory of Ferromagnetism Ox- 3 W. Kohn and P. Vashishta, in Theory of the Inhomogeneous Elec- ford University Press, Oxford, 1996 . tron Gas, edited by S. Lundqvist and N. H. March Plenum, 2 Band-ferromagnetism, edited by K. Baberschke, M. Donath, and New York, 1983 , p. 79. W. Nolting Springer, Berlin, in press . 4 T. 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