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Au(1 1 1)
Journal of Electron Spectroscopy and Related Phenomena 136 (2004) 107–115
Angle-, field-, temperature-, and size-dependent magnetic circular X-ray dichroism in Au/Co nanoclusters/Au(1 1 1) T. Koide a,∗ , H. Miyauchi a , J. Okamoto b , T. Shidara a , A. Fujimori b , H. Fukutani c , K. Amemiya d , H. Takeshita e , S. Yuasa e , T. Katayama f , Y. Suzuki e a
Photon Factory, Institute of Materials Structure Science, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan b Graduate School of Frontier Sciences, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan c Institute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305-0006, Japan d Graduate School of Science, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan e NanoElectronics Research Institute, National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568, Japan f Department of Physics, Toho University, Funabashi, Chiba 274-0072, Japan
Abstract We have studied the magnetic states of Au/2-monolayer Co clusters/Au(1 1 1) by angle-, field-, temperature-, and cluster-size-dependent magnetic circular X-ray dichroism (MCXD) measurements in the longitudinal geometry with full use of a magic angle of 54.7◦ . The absolute magnitude of the normal-incidence MCXD provides evidence for a single domain of clusters and for a phase transition from ferromagnetism (FM) to superparamagnetism (SPM) with decreasing cluster size. The spin, in-plane and out-of-plane orbital, and in-plane and out-of-plane magnetic dipole moments of almost purely interfacial Co atoms were directly determined. The interfacial spin moment is strongly enhanced and the interfacial orbital and magnetic dipole moments are highly anisotropic and enhanced as compared with those in bulk Co, verifying theoretical predictions. We argue the implications of the results in particular relation to their physical origin and to a potential technological application of the nanoclusters. © 2004 Elsevier B.V. All rights reserved. Keywords: Magnetic circular X-ray dichroism; Nanoclusters; Sum rules; Interfacial magnetic moments; Magnetic phase transition
1. Introduction The magnetism of low-dimensional systems, such as nanoclusters, ultrathin films, and multilayers, have recently attracted much interest [1–4], both because of their bridge character between zero-dimensional isolated atoms and corresponding three-dimensional condensed systems and because of their potential technological applications. In particular, studies of nanoclusters [4–6] are expected to shed new light on the magnetic evolution and to provide clues for developing new magnetic recording devices due to their microscopic size controllability. Theoretical studies have predicted that the spin (mspin ) and orbital (morb ) magnetic moments could be strongly enhanced in nanoclusters [7–10] as well as at surfaces and interfaces [11–13] as compared to those in bulk, not only
∗ Corresponding author. Tel.: +81-29-864-5673; fax: +81-29-864-2801. E-mail address: [email protected] (T. Koide).
0368-2048/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.elspec.2004.02.137
for 3d, but even for normally nonmagnetic 4d and 5d transition metal elements. Stern–Gerlach-deflection experiments [5,6,14–17] have shown that the total magnetic moment (mtot ) of size-selected Fe, Co, and Ni free clusters increases, exhibiting some oscillations, with decreasing cluster size. This enhancement could be ascribed to a surface effect, since those free clusters comprise a small number of atoms and are free of interfacial interactions. The morb of Co and Fe has been shown to be enhanced in surfaces [18,19], multilayers [20,21], ultrathin films [22], and supported clusters [23–26] as compared to that in bulk by magnetic circular X-ray dichroism (MCXD) measurements, although no enhancement of mspin had been reported until our recent study [27]. A simple extrapolation of many of those previous experimental magnetic moments to one monolayer (1 ML) limit indicates strongly, but indirectly, a remarkable enhancement of mtot and morb at surfaces or interfaces. However, a direct and separate determination of mspin and morb of purely surface or interface atoms had remained to be a challenge for experimentalists until very recently. This
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is because of difficulties in preparing samples comprising only surface or interface atoms. Difficulties also arise from requirements for sensitive detection of highly anisotropic atomic moments in such extremely dilute systems and for a simultaneous confirmation of the microscopic structure. In a recent letter [27], we reported on the essential results of an angle- [22,28], field-, temperature-, and cluster-size-dependent MCXD study of Au/Co nanoclusters/Au(1 1 1). In this paper we present additional data and more details of our basic idea, experiments, results and discussion, and a potential technological application. In particular, we report on a direct determination of mspin , in-plane (morb ) and out-of-plane (m⊥ orb ) orbital magnetic moments, and in-plane (mT ) and out-of-plane (m⊥ T ) spin-density anisotropies of almost purely interfacial Co atoms by exploiting the unique property of the constant 2-ML height of the clusters. We also present evidence that the Co clusters retain ferromagnetism (FM) at room temperature in a range of size and that a magnetic phase transition takes place from FM to superparamagnetism (SPM) with decreasing cluster size.
2. Basic idea One may naturally ask questions: Is it possible to prepare a sample comprising only interfacial or surface atoms? Is it possible to experimentally determine magnetic moments in such a sample? Our answer to these questions is “yes” by the following argument and observation. For that purpose, we shall make two-step argument. We begin with considering basic possibilities. Note first that by definition a 1-ML film can be regarded neither as an interfacial one nor as a surface one, because no similar atom layers exist behind the 1-ML film. Next, an ultrathin film of ≥3 ML inevitably contains at least one bulk-like layer, as shown in Fig. 1a. Thus, these thickness ranges are excluded from our candidates. A free-standing 2-ML film undoubtedly comprises only equivalent surface atoms, but to perform magnetic measurements on such a sample is practically almost impossible. A supported 2-ML film is thus the only remaining candidate. It is emphasized that when the other (upper) side of even a supported 2-ML film faces a vacuum (Fig. 1b), the atoms within the 2-ML film are not equivalent, because the upper-layer atoms are of surface but the lower-layer atoms are interfacial. In contrast, only if the 2-ML film is capped with layers consisting of the same atoms as for the substrate, all the 2-ML atoms are equivalent and purely interfacial ones (Fig. 1c). This is the unique solution to our Gedanken Experimente. We proceed to a practical possibility. Recent studies with scanning tunneling microscopy (STM) observations in combination with the molecular-beam epitaxy (MBE) technique have revealed that supported Co nonoclusters are self-organized on reconstructed Au (1 1 1) surface [29–33].
Fig. 1. Schematic microscopic structure for (a) supported 3-ML Co film, (b) supported 2-ML Co film with the upper layer facing a vacuum, and (c) 2-ML Co film capped with layers of the same atoms as those of the substrate. Note that all the Co atoms can be regarded as equivalent, interfacial ones only for the capped 2-ML Co, as in (c).
The SPM behavior was strongly indicated by previous experiments [29–32] and analyses were made on the assumption of SPM. However, the SPM behavior does not allow applications for magnetic recording devices operating at room temperature. The most interesting and important feature of self-assembled Co nanoclusters on Au (1 1 1) is their constant height of 2 ML, independent of the nominal Co coverage [29,31,32]. A natural question arises: Why is the cluster height always constant at 2 ML? What is its physical origin? This question remains unanswered. Nevertheless, based on the above argument, we can utilize this chance by reversing the problem to open up a new opportunity for directly approaching the interfacial magnetism [27]. Namely, if one admits the 2-ML height to be an undoubted experimental fact given by nature, and interposes Co nanoclusters between Au films, it is found that no bulk-like Co atoms exist at all and almost all of the Co atoms can be regarded as interfacial ones (a “magic height”) with a negligibly small number of perimeter atoms (Fig. 1c). This is a very simple but essential idea for our study, providing an ideal, practical system for directly determining the interfacial magnetic moments.
3. Experiment The nominal sample structure and angle-dependent MCXD experimental arrangement are shown in Figs. 2 and 3.
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Fig. 2. Nominal sample structure and arrangement for angle- and cluster-size-dependent MCXD experiments. The wedge-shaped Co with the nominal ∗ , microscopically consists of independent clusters for the range of d ∗ 1.6 ML. E and p stand for the electric field and momentum coverage, dCo Co vectors of the incident photons.
Fig. 3. (a) STM picture, (b) scanning height distribution along the white line in Fig. (a), and (c) height distribution histgrams for Dav 4.7 nm ∗ 0.85 ML). (dCo
The details of sample preparation and structural characterization are described elsewhere [30,31]. A wedge-shaped Co ∗ , ranging from 0 to 2 ML, was with a nominal coverage, dCo grown on a 200 nm-thick Au (1 1 1) seed layer with a mica substrate (not shown in Fig. 2) using the MBE technique in an ultrahigh vacuum (UHV) (Fig. 2). A 5-ML-thick Co film was produced at one edge. The microscopic surface structure of Au and Co was characterized using reflection high-energy electron diffraction (RHEED) and STM during and after each growth. An STM observation revealed atomically flat, 100–200-nm wide Au(1 1 1) terraces with the so-called “herringbone” pattern only when a proper heat treatment was made very carefully [27,30,31]. Quasi two-dimensional Co nanoclusters were self-assembled at herringbone elbow sites by the room-temperature deposition of Co, as shown in Fig. 3a [27,30,31]. An STM observation showed an almost constant height of 2 ML of the Co clusters (Figs. 3b and c). The 2-ML height implies that the average in-plane diameter, ∗ (Fig. 2), Dav , is proportional to the root-mean square of dCo ∗ but only the dCo 0.85 ML clusters had a proportional ∗ cluscoefficient somewhat different from that for other dCo ters. The Co layer was finally capped with a 2-nm-thick Au layer in both order to ensure the “magic height” and to prevent the Co from oxidation (Fig. 2). The Au-layer oxidation prevention is unbelievabaly perfect, as shown later. Angle-, field-, and temperature-dependent MCXD experiments were performed in the longitudinal geometry at the Co L2,3 and M2,3 core edges and the Au N6,7 and O2,3 core edges by detecting the X-ray absorption spectra (XAS) using the total-electron-yield (TEY) and light-reflection methods with circularly polarized synchrotron radiation on a bending-magnet (BL-11A) and helical undulator (BL-28A) beamlines at the Photon Factory (Fig. 2). Possible artifacts arising from the saturation effect on the MCXD spectra in the TEY detection can be fully neglected due to the only 2-ML
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height of the clusters. Magnetic fields, B, ranging from 0 to ±5 T were applied to a sample parallel and antiparallel to the fixed positive helicity (h) of the incident photons (longitudinal geometry) using a UHV superconducting magnet [34]. A remanent MCXD for B = ±0 T was measured in such a way that B = 0 T → B = +5 T → B = +0 T (where µ− taken) → B = −5 T → B = −0 T (where µ+ taken). Here, µ+ and µ− stand for the absorption coefficients for the photon helicity parallel and antiparallel to the 3d majority spin direction. We define MCXD as µ = µ+ − µ− . The sample was rotated about a vertical axis parallel to the Co-wedge direction, thus changing the angle θ between the photon momentum p and the sample surface normal n. The ∗ (or D ) of the Co clusters shone by the incident light dCo av was changed by a vertical translation of the sample. The sample temperature was varied from 300 to 30 K. The average degree of circular polarization, PC , of the light was directly measured to be 92 ± 3% on BL-28A [35]. The PC on BL-11A was carefully evaluated to be 78 ± 3% both by a comparison of the measured MCXD of single-crystalline Co and Ni films with the reported MCXD intensities [36,37] and by a calculation which took into account the source characteristics and the effects of beam-line optical elements on the polarization of light.
4. Theoretical background: angle-dependent sum rules In this section we present a brief review of the sum rules [38,39] in the angle-dependent mode [22,28], which are used in the next section. Let the z axis be along the surface-normal direction (n) for a quasi-two-dimensional sample. We consider the situation where a circularly polarized light beam is incident onto the sample in a direction making angle θ with respect to n and magnetic fields are applied to the sample parallel and antiparallel to the θ direction (longitudinal geometry) (see Fig. 2). The MCXD orbital [38] and spin [39] sum rules for the p → d transitions, as applied to the angle-dependent mode [22,28], read mθorb =
−4 3
[AL3 + AL2 ]θ nh µB , [AL3 + AL2 ]θ
(1)
and mspin + 7mθT =
−2[AL3 − 2AL2 ]θ nh µB , [AL3 + AL2 ]θ
(2)
where AL3 and AL2 , and AL3 and AL2 are the L3 and L2 energy-integrated MCXD and XAS sum (µ+ + µ− ) intensities, respectively, nh is the 3d hole number, mθorb = − Lθ µB /¯h, mspin = −2 S µB /¯h, and mθT = − Tθ µB /¯h with T being the expectation value of the intra-atomic magnetic dipole operator T = S − 3r(r · S)/r 2 [28]. Here, we have neglected the θ dependence of mspin , which could be theoretically expected in the second order of the spin-orbit
(SO) interaction constant ξ 3d (Co) but is indeed negligibly small. It holds for d orbitals [28] that Tx + Ty + Tz = 0,
(3)
which leads to
m⊥ T + 2mT = 0,
(4)
in the absence of in-plane anisotropy, as valid for the present sample. It also holds [22] that
2 2 mθorb = m⊥ orb cos θ + morb sin θ,
2 2 mθT = m⊥ T cos θ + mT sin θ.
(5a) (5b)
Eqs. (1), (2), (4), (5a) and (5b) allow a determination of ⊥ mspin , morb , m⊥ orb , mT , and mT from MCXD measurements for two different angles of θ [22,28]. It is further noted that the combined use of (4) and (5b) leads to mθT = mT (1 − 2 ◦ 3cos θ) = 0 at θ = 54.7 (magic angle). Thus, Eq. (2) for θ = 54.7◦ reduces to mspin =
−2[AL3 − 2AL2 ]θ nh µB , [AL3 + AL2 ]θ
(6)
which allows a direct determination of mspin by a single magic-angle measurement [27,28]. We have made an approximation in which the original expression (µ+ +µ0 +µ− ) is replaced by 3/2(µ+ +µ− ) in the denominator of Eqs. (1), (2), and (6). This could be especially well valid for the magic angle, because linear dichroism should vanish at the angle.
5. Results and discussion 5.1. Field and temperature dependencies of normal-incidence MCXD Fig. 4 shows the B dependence of the mesh-monitor-fluxnormalized, polarization-dependent, normal-incidence Co L2,3 -edge XAS and MCXD hysteresis curve for nanoclus∗ 1.6 ML) taken at 300 K ters with Dav 8.2 nm (dCo [27]. Almost the same result was obtained for Co clusters ∗ 1.2 ML). The qualitative hyswith Dav 7.2 nm (dCo teresis curves were measured by the M2,3 -edge MCXD and their absolute magnitude was determined by the L2,3 -edge MCXD. Surprisingly, even the non-surface-sensitive reflection method yielded a clear M2,3 -edge MCXD for such dilute systems, demonstrating the power of core-level MCXD. We first emphasize that no multiplet features typical for CoO was seen at all in the L2,3 XAS and that a strong MCXD was reproduced. This provides evidence for no oxidation of the Co clusters; note that the clusters’ height is only 2 ML. The Co nanoclusters with 7.2 Dav 8.2 nm ∗ (1.2 ML dCo 1.6 ML), for the present Au(1 1 1) herringbones’ terrace size, exhibit a clear remanent MCXD at 300 K, although it is smaller than that for B = ±3 T (Fig. 4a). The field dependence of the MCXD shows a clear
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∗ 1.6 ML) clusters taken at 300 K Fig. 4. (a) Polarization-dependent, normal-incidence Co L2,3 -edge XAS and MCXD spectra of Dav 8.2 nm (dCo and under B = ±3 T and ±0 T. Note a clear remanent MCXD (lower panel). (b) Co L3 -edge MCXD hysteresis curve of Dav 8.2 nm clusters at 300 K. The inset shows the expanded low-field region.
hysteresis with a coercive field HC of 330 Oe for Dav 8.2 nm (Fig. 4b). These results reveal that Co clusters with 7.2 Dav 8.2 nm retain cluster-cluster FM alignment at 300 K. It is also noted that the magnetization detected by the MCXD is fully saturated at very low fields (Fig. 4b). This clearly shows that the FM clusters are of single domains. The 5-ML film showed a remanent MCXD (B = ±0 T) equal to an MCXD for B = ±3 T (Fig. 5). Its B-dependent L3 -edge MCXD revealed a clear rectangular hysteresis curve, showing complete FM of the film with an HC of 530 Oe. We emphasize here that the equal magnitude of MCXD for zero and high fields assures negligibly small artifacts arising from the effects of the magnetic field on TEY detection. This can be reasonably understood as being due to the high symmetry of detection by considering that all photoelectrons emitted at the high-B sample position are transferred along a helix, with a reversal of B resulting in only a reversal of the sense of the rotation of the helix. The general belief that high fields would affect the TEY-detected MCXD has no physical foundation at all.
∗ = 5 ML film taken at Fig. 5. Co L3 -edge MCXD hysteresis curve of dCo T = 300 K.
Fig. 6a and b show the temperature dependence of the ∗ remanent MCXD for clusters with Dav 4.7 nm (dCo 0.85 ML), respectively and the field dependence of the ∗ 0.4 ML) MCXD for clusters with Dav 4 nm (dCo [27]. All of the Co clusters with Dav 4, 4.7, and 6.7 nm ∗ 1.1 ML) showed the behavior qualitatively similar (dCo to Fig. 6a and b. In contrast to the results for clusters with 7.2 Dav 8.2 nm, no remanent MCXD was detected at 300 K in Co clusters with Dav 4 nm, 4.7, and 6.7 nm (Fig. 6a and b), whereas a large MCXD was observed for B = ±5 T at 300 K for all of three Dav (Fig. 6b). The MCXD intensity at 300 K strongly depends on the field strength (Fig. 6b). The B dependence of MCXD can be fitted approximately, but not fully, by a single Langevin function over a whole range of B up to 5 T. This small deviation from the Langevin function could be due to a finite size distribution of the clusters. These results strongly indicate the SPM behavior of the independent Co nanoclusters with Dav 6.7 nm. In order to further verify the SPM, we examine the temperature dependence of the remanent MCXD in Fig. 6a. A clear remanent MCXD appears at T 100 K with lowering T, whereas no remanent MCXD is seen for T 125 K. This shows that the magnetic moments of Co clusters are randomly oriented due to thermal activation at high temperatures, and are ferromagnetically aligned for T 100 K, giving a blocking temperature of TB ≈ 100–120 K. A similar T-dependent MCXD of Co clusters with Dav 4 nm yields a blocking temperature of TB ≈ 70–80 K. The B-dependent, normal-incidence MCXD measured at T = 30 K for the SPM clusters with Dav 6.7 nm is displayed in Fig. 6b in comparison with that taken at 300 K [27]. It is most noted that the saturated MCXD intensity for B = ±5 T is nearly equal for T = 300 and 30 K. This can be understood only if the Co clusters form single domains and their relative orientation is aligned by external fields. The large MCXD amounting to 40%, even at 300 K for ±5 T, cannot be explained at all by the usual paramagnetism.
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Fig. 6. (a) Temperature dependence of the Co L2,3 -edge remanent MCXD for Dav 4.7 nm clusters. Note that a clear remanent MCXD appears at T 100 K. (b) Co L3 -edge MCXD hysteresis curve at T = 30 K and B-dependent MCXD at T = 300 K for Dav 4 nm.
Thus, we conclude that the independent Co clusters with Dav 6.7 nm are of SPM. All the present results provide evidence that the Co nanoclusters retain FM over a range of 7.2 Dav 8.2 nm and that a magnetic phase transition crit ≈ 6.7–7.2 nm takes place from FM to SPM around at Dav ∗crit (dCo ≈ 1.1–1.2 ML) with decreasing cluster size. This indicates the in-plane magnetic interaction between independent Co clusters via the conducting electrons of Au.
ement, from the edge-jump-normalized MCXD data (θ =0◦ and 54.7◦ ) on a single-crystalline bulk hcp Co film and the accurately known values of mspin and morb . The saturation effect in TEY detection [43] was taken into account. The second analysis allowed us to avoid the use of an accurately unknown 3d electron-occupation number for clusters in applying the MCXD sum rules. No appreciable differ-
5.2. Direct determination of interfacial magnetic moments by angle-resolved MCXD The angle (θ)-resoleved Co L2,3 -edge MCXD was measured at T = 30 K under B = ±5 T for SPM clusters with Dav 6.7 nm, and at T = 300 K and under B = ±3 T for FM clusters with 7.2 Dav 8.2 nm. Fig. 7 shows pictorially the θ-dependent XAS, MCXD, and its energy-integrated spectra for the SPM clusters with Dav 6.7 nm. Fig. 8 shows only the MCXD and its integrated spectra for FM clusters with Dav 7.2 nm in a two-dimensional form in order to make clear the angle dependence [27]. The noise in the XAS and MCXD spectra in Fig. 7 is due to liq. He flowing to cool the sample. In general, the magnetization is not necessarily parallel to the external B under low B (B 1 T), except for θ = 0◦ and 90◦ in two-dimensional systems with strong magnetic anisotropy [40]. The present high B ensures this parallelism. Though the theoretical possibility of magic angle measurements was originally suggested by Stöhr and König [28], no experimental studies utilizing this powerful technique had been reported until our recent study [27]. Since we are most interested in the purely interfacial mspin , we made full use of magic-angle (θ = 54.7◦ ) measurements. We made two independent analyses by using an nh value and not using an nh value. A first analysis was made using a theoretical nh value for Co2 Pt4 multilayers [41,42]. A second analysis was made by determining the constant C = (AL3 + AL2 )/nh , which is proportional to the square of the 2p → 3d radial transition matrix el-
Fig. 7. Angle-resolved Co L2,3 -edge (a) XAS, and (b) MCXD spectra for SPM clusters with Dav 6.7 nm taken at T = 30 K under B = ±5 T. The energy integrals of the MCXD spectra are also shown in (b).
T. Koide et al. / Journal of Electron Spectroscopy and Related Phenomena 136 (2004) 107–115
Fig. 8. Angle-resolved Co L2,3 -edge (a) MCXD spectra, and (b) their energy integrals for FM clusters with Dav 7.2 nm taken at T = 300 K under B = ±3 T.
ence was found for the results of two analyses. The mspin , ⊥ ⊥ morb , m⊥ orb , mT , mT , and mtot = mspin + 1/3 (morb + 2 morb ) were determined by applying the sum rules to the data for θ = 0◦ and 54.7◦ . The self-consistency of the analyses was confirmed by the combined use of the data for θ = 0◦ and 65◦ . The results are shown in Fig. 9 as functions of Dav and of the number of atoms per cluster (N) together with values for bulk hcp Co [27]. The mspin was found to reach large values of 2.0–2.15 B for independent Co clusters with Dav 7.2 nm, irrespective of their FM and SPM. This implies an almost full spin polarization of the Co 3d electrons in the clusters, if one considers the total 3d hole number of nh 2.5 for bulk Co [41,42] and that the clusters’ nh value is not very much different from that of the bulk, as evidenced by the present two analyses. We emphasize here again that these mspin values are of almost purely interfacial Co atoms. The present result provides the first direct experimental verification of a remarkable enhancement of the interfacial mspin predicted by theoretical calculations [7–13]. The smaller mspin value only for Dav 8.2 nm can be reasonably understood by their non-perfect 2-ML height. An STM observation showed that ∗ , approaching ∼2 ML, produced a finite an increase of dCo number of 3-ML-height clusters without forming a uniform film [44], resulting in the appearance of bulk-like Co atoms with a smaller mspin value (see Fig. 1a). The present mtot 2.2–2.4 B for clusters with Dav 7.2 nm agrees surprisingly well with mtot 2.4–2.5 B of free Co clusters
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Fig. 9. Dav and N dependencies of the magnetic moments determined from the angle-resolved MCXD measurements and the angle-dependent ⊥ sum rules: (a) mspin and mtot ; (b) morb and m⊥ orb ; (c) mT and mT . The corresponding moments of bulk hcp Co are shown for comparison. The hutched area denotes the FM/SPM transition region.
in the range of the smallest number of atoms, obtained by Stern–Gerlach-deflection experiments [5,14]. This strongly indicates that the interfacial Co atoms in Au/Co/Au(1 1 1) systems are in an environment which is very similar to the surface. This is quite plausible, since the calculated 5d band of bulk Au is located well below the Fermi level, EF , and thus the Co 3d-Au 5d hybridization could be very small. This small d–d hybridization was confirmed by the present Au N6,7 and O2,3 core-edge MCXD measurements. The Au-edge MCXD was by an order-of-magnitude smaller than the large MCXD at the Pt N6,7 and O2,3 edges in Co/Pt multilayers reported previously by the present authors [21]. ⊥ The m⊥ orb reaches a value of morb 0.30 − 0.31 B for independent clusteres with Dav 7.2 nm. This value is two-times as large as that of bulk Co. The two-times enhancement is consistent with recent results for m⊥ orb obtained by the normal-incidence MCXD in the same Co clusters/Au(111) [23] and Fe clusters/Cu(1 0 0) [24], and by angle-dependent MCXD in Fe clusters/Cu(111) [25] and Fe clusters/Au(1 1 1) [26]. It is interesting to compare the anisotropy of the present mθorb with that of Weller et al. on normal ultrathin Co films in Au/Co/Au(1 1 1) for 4 tCo 11 ML [22]. A simple extrapolation to the tCo = 1 ML limit of their results, using the 1/tCo law, gave a value of m⊥ orb,S ⊥ 0.36 B for 1 ML [22]. The present morb 0.30 − 0.31 B is close to this value. In contrast, a difference is found for
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morb between two experiments. A simple extrapolation to the 1-ML limit of their result with the use of 1/tCo law gave a value of morb,S ≈ 0 [22], which is remarkably different from the present value of morb 0.16 − 0.21 B . However, this seeming discrepancy is not unexpected, since the present samples were independent clusters, whereas their extrapolation was based on the assumption of a uniform 1-ML film. If one considers an extreme limiting case where the in-plane diameter (Dav ) becomes nearly equal to the clusters’ height, the anisotropy of mθorb should disappear. Thus, we conclude that morb initially decreases with decreasing tCo in the range of uniform films [22], but it increases back again with fur∗ in the range of independent clusters ther decreasing dCo only if the Au substrate is properly heat-treated to form a “herring-bone” pattern. Both m⊥ T and mT of the FM clusters with Dav 8.2 nm agree with a simply extrapolated value of their results using the 1/tCo law [22]. The smaller anisotropy of the present mθT for the clusters Dav 7.2 nm is reasonably understood as being due to a loss of two dimensionality. At the Co/Au interface, the reduced effective coordination number and the increased electron localization mainly in the perpendicular direction will lead to more localized atomic-like 3d wave functions. This would narrow the 3d band width, resulting in a transfer of the electron occupation number from the minority- to majority-spin bands while nearly keeping the total hole number. This effect could give rise to an enhancement of mspin [27]. A reduction of symmetry at the interfaces produces a uniaxial crystal field and lifts the orbital degeneracy, enhancing the difference of the electron occupation number for the in-plane and out-of-plane 3d orbitals. This effect causes an m⊥ orb enhancement and a θ nonzero anisotropc mT [27]. It is interesting to note that the observed nonvanishing mθT shows a partial manifestation of the intrinsic quadrupole moment in the electron-density distribution Qθθ of each 3d orbital, since mθT is related with Qθθ through mθT ∝ − Tθ ≈ Qθθ S [28].
given by ESO ≈
−αξ3d ⊥ (morb − morb ), 4µB
(8)
where α is an effective correction factor. By using ξ3d ≈ 70 meV and α ≈ 0.2 for ultrathin Co films [22], we obtain ESO ≈ −4.4 × 10−4 eV per atom and ESO ≈ −2.6 × 10−4 eV per atom for the FM clusters with Dav 7.2 and 8.2 nm, respectively. The spin–spin dipole interaction energy, which favors the in-plane magnetic anisotropy, was calculated to be 2πMs2 × 0.93 ≈ +0.86 × 10−4 eV per atom. Here, a correction factor of 0.93 is due to the finite height (2 ML) in the perpendicular direction. We find that |ESO | > 2πMs2 × 0.93, which shows a strong perpendicular magnetic anisotropy (PMA) of the FM clusters. Thus, the present Co nanoclusters in a range of 7.2 Dav 8.2 nm have simultaneously four important properties: (i) no oxidation, (ii) single domain, (iii) FM at 300 K, and (iv) PMA [27]. The magnetic moment of each FM cluster could be reversed by modern atom technologies, such as the use of magnetic force microscopy (MFM) with an appropriate radius of curvature of the tip and a suitable magnetic-field strength, as shown in Fig. 10a. Its reversed moment may be held after the MFM tip is removed, because the spin flip requires an energy larger than the reorientation energy barrier (Fig. 10b). If the cluster–cluster FM-interaction energy is smaller than the energy barrier, the single cluster’s “antiparallel” spin orientation would be maintained. This situation could be realized for Dav 7.2 nm, which is just above the FM/SPM transition cluster size. Therefore, the present FM Co nanoclusters may provide a technological possibility for utilizing each cluster as a single nano-scale magnetic bit operating at room temperature.
6. Potential technological application We estimate a magnetic anisotropy energy (MAE), ESO , caused by the SO interaction. Laan derived a formula for ESO to the second order of ξ 3d [45] 2
ESO ≈
ξ3d −ξ3d ⊥ (m − morb ) + ( 21 3 m⊥ + A), 4µB orb Eex µB 2 2 T (7)
where Eex is the 3d exchange-splitting energy and A is a term independent of the spin direction [26]. However, this formula is generally difficult to directly apply to MCXD results, because it is necessary to separately take account of morb of the minority- and majority-spin bands. Thus, we use a simpler, majority-hole corrected Bruno’s relationship [46]
Fig. 10. Schematic view for a potential technological application: (a) an MFM tip approaching Co cluster 1 could reverse its magnetic moment; (b) energy level as a function of angle θ 1 . The reversed moment of cluster 1 may be held as a quasi-stable state due to the energy barrier.
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7. Conclusion
We have directly determined the values of mspin , morb , ⊥ morb , mT , m⊥ T , and mtot of almost purely interfacial Co atoms in Au/Co anoclusters/Au(1 1 1) by angle-resolved MCXD measurements with full use of the clusters’ constant 2-ML height and of the experimental magic angle of 54.7◦ . Evidence has been presented for an FM/SPM magnetic phase transition with decreasing cluster size by the field, temperature, and size-dependent MCXD. We have pointed out the in-principle possibility of the room-temperature application of Co clusters as a nanoscale magnetic bits.
Acknowledgements The authors thank Professor H. Sugawara and Professor H. Kobayakawa for financial support and encouragement. They acknowledge Professor J. Stöhr, Dr. H.A. Dürr, and Dr. K. Koike for stimulating discussion. References [1] J.A.C. Bland, B. Heinrich (Eds.), Ultrathin Magnetic Structures I, II, Springer, Berlin, 1994. [2] J.L. Morán-Lopez (Ed.), Physics of Low-Dimensional Systems, Kluwer/Plenum, New York, 2000. [3] S. Miller, M. Drillon (Eds.), Magnetism: Molecules to Materials I, II, III, and IV, Wiley, Weinheim, 2001, 2002. [4] J. L. Dorman, D. Fiorani (Eds.), Magnetic Properties of Fine Particles, North-Holland, Amsterdam, 1992. [5] I.M.L. Billas, A. Chˆatelain, W.A. de Heer, Science 265 (1994) 1682. [6] J. Shi, S. Gider, K. Babcock, D.D. Awschalom, Science 271 (1996) 937. [7] G.M. Pastor, J. D-Dávila, S. Dick, H. Dreysse, Phys. Rev. Lett. 75 (1995) 326. [8] K. Wildberger, V.S. Stepanyuk, P. Lang, R. Zeller, P.H. Dederichs, Phys. Rev. Lett. 75 (1995) 509. [9] V.S. Stepanyuk, W. Hergert, P. Rennent, K. Wildberger, R. Zeller, P.H. Dederichs, Phys. Rev. B54 (1996) 14121. [10] J. Guevara, A.M. Llois, M. Weissmann, Phys. Rev. Lett. 81 (1998) 5306. [11] R. Wu, A.J. Freeman, Phys. Rev. B45 (1992) 7222. [12] S. Blügel, Phys. Rev. Lett. 68 (1992) 851. [13] A.M. Niklasson, B. Johansson, H.L. Skriver, Phys. Rev. B59 (1999) 6373. [14] J.P. Bucher, D.C. Douglass, L.A. Bloomfield, Phys. Rev. Lett. 66 (1991) 3052. [15] I.M.L. Billas, J.A. Becker, A. Chˆatelain, W.A. de Heer, Phys. Rev. Lett. 71 (1993) 4067.
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Angle-, field-, temperature-, and size-dependent magnetic circular X-ray dichroism in Au/Co nanoclusters/Au(1 1 1) T. Koide a,∗ , H. Miyauchi a , J. Okamoto b , T. Shidara a , A. Fujimori b , H. Fukutani c , K. Amemiya d , H. Takeshita e , S. Yuasa e , T. Katayama f , Y. Suzuki e a
Photon Factory, Institute of Materials Structure Science, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan b Graduate School of Frontier Sciences, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan c Institute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305-0006, Japan d Graduate School of Science, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan e NanoElectronics Research Institute, National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568, Japan f Department of Physics, Toho University, Funabashi, Chiba 274-0072, Japan
Abstract We have studied the magnetic states of Au/2-monolayer Co clusters/Au(1 1 1) by angle-, field-, temperature-, and cluster-size-dependent magnetic circular X-ray dichroism (MCXD) measurements in the longitudinal geometry with full use of a magic angle of 54.7◦ . The absolute magnitude of the normal-incidence MCXD provides evidence for a single domain of clusters and for a phase transition from ferromagnetism (FM) to superparamagnetism (SPM) with decreasing cluster size. The spin, in-plane and out-of-plane orbital, and in-plane and out-of-plane magnetic dipole moments of almost purely interfacial Co atoms were directly determined. The interfacial spin moment is strongly enhanced and the interfacial orbital and magnetic dipole moments are highly anisotropic and enhanced as compared with those in bulk Co, verifying theoretical predictions. We argue the implications of the results in particular relation to their physical origin and to a potential technological application of the nanoclusters. © 2004 Elsevier B.V. All rights reserved. Keywords: Magnetic circular X-ray dichroism; Nanoclusters; Sum rules; Interfacial magnetic moments; Magnetic phase transition
1. Introduction The magnetism of low-dimensional systems, such as nanoclusters, ultrathin films, and multilayers, have recently attracted much interest [1–4], both because of their bridge character between zero-dimensional isolated atoms and corresponding three-dimensional condensed systems and because of their potential technological applications. In particular, studies of nanoclusters [4–6] are expected to shed new light on the magnetic evolution and to provide clues for developing new magnetic recording devices due to their microscopic size controllability. Theoretical studies have predicted that the spin (mspin ) and orbital (morb ) magnetic moments could be strongly enhanced in nanoclusters [7–10] as well as at surfaces and interfaces [11–13] as compared to those in bulk, not only
∗ Corresponding author. Tel.: +81-29-864-5673; fax: +81-29-864-2801. E-mail address: [email protected] (T. Koide).
0368-2048/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.elspec.2004.02.137
for 3d, but even for normally nonmagnetic 4d and 5d transition metal elements. Stern–Gerlach-deflection experiments [5,6,14–17] have shown that the total magnetic moment (mtot ) of size-selected Fe, Co, and Ni free clusters increases, exhibiting some oscillations, with decreasing cluster size. This enhancement could be ascribed to a surface effect, since those free clusters comprise a small number of atoms and are free of interfacial interactions. The morb of Co and Fe has been shown to be enhanced in surfaces [18,19], multilayers [20,21], ultrathin films [22], and supported clusters [23–26] as compared to that in bulk by magnetic circular X-ray dichroism (MCXD) measurements, although no enhancement of mspin had been reported until our recent study [27]. A simple extrapolation of many of those previous experimental magnetic moments to one monolayer (1 ML) limit indicates strongly, but indirectly, a remarkable enhancement of mtot and morb at surfaces or interfaces. However, a direct and separate determination of mspin and morb of purely surface or interface atoms had remained to be a challenge for experimentalists until very recently. This
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is because of difficulties in preparing samples comprising only surface or interface atoms. Difficulties also arise from requirements for sensitive detection of highly anisotropic atomic moments in such extremely dilute systems and for a simultaneous confirmation of the microscopic structure. In a recent letter [27], we reported on the essential results of an angle- [22,28], field-, temperature-, and cluster-size-dependent MCXD study of Au/Co nanoclusters/Au(1 1 1). In this paper we present additional data and more details of our basic idea, experiments, results and discussion, and a potential technological application. In particular, we report on a direct determination of mspin , in-plane (morb ) and out-of-plane (m⊥ orb ) orbital magnetic moments, and in-plane (mT ) and out-of-plane (m⊥ T ) spin-density anisotropies of almost purely interfacial Co atoms by exploiting the unique property of the constant 2-ML height of the clusters. We also present evidence that the Co clusters retain ferromagnetism (FM) at room temperature in a range of size and that a magnetic phase transition takes place from FM to superparamagnetism (SPM) with decreasing cluster size.
2. Basic idea One may naturally ask questions: Is it possible to prepare a sample comprising only interfacial or surface atoms? Is it possible to experimentally determine magnetic moments in such a sample? Our answer to these questions is “yes” by the following argument and observation. For that purpose, we shall make two-step argument. We begin with considering basic possibilities. Note first that by definition a 1-ML film can be regarded neither as an interfacial one nor as a surface one, because no similar atom layers exist behind the 1-ML film. Next, an ultrathin film of ≥3 ML inevitably contains at least one bulk-like layer, as shown in Fig. 1a. Thus, these thickness ranges are excluded from our candidates. A free-standing 2-ML film undoubtedly comprises only equivalent surface atoms, but to perform magnetic measurements on such a sample is practically almost impossible. A supported 2-ML film is thus the only remaining candidate. It is emphasized that when the other (upper) side of even a supported 2-ML film faces a vacuum (Fig. 1b), the atoms within the 2-ML film are not equivalent, because the upper-layer atoms are of surface but the lower-layer atoms are interfacial. In contrast, only if the 2-ML film is capped with layers consisting of the same atoms as for the substrate, all the 2-ML atoms are equivalent and purely interfacial ones (Fig. 1c). This is the unique solution to our Gedanken Experimente. We proceed to a practical possibility. Recent studies with scanning tunneling microscopy (STM) observations in combination with the molecular-beam epitaxy (MBE) technique have revealed that supported Co nonoclusters are self-organized on reconstructed Au (1 1 1) surface [29–33].
Fig. 1. Schematic microscopic structure for (a) supported 3-ML Co film, (b) supported 2-ML Co film with the upper layer facing a vacuum, and (c) 2-ML Co film capped with layers of the same atoms as those of the substrate. Note that all the Co atoms can be regarded as equivalent, interfacial ones only for the capped 2-ML Co, as in (c).
The SPM behavior was strongly indicated by previous experiments [29–32] and analyses were made on the assumption of SPM. However, the SPM behavior does not allow applications for magnetic recording devices operating at room temperature. The most interesting and important feature of self-assembled Co nanoclusters on Au (1 1 1) is their constant height of 2 ML, independent of the nominal Co coverage [29,31,32]. A natural question arises: Why is the cluster height always constant at 2 ML? What is its physical origin? This question remains unanswered. Nevertheless, based on the above argument, we can utilize this chance by reversing the problem to open up a new opportunity for directly approaching the interfacial magnetism [27]. Namely, if one admits the 2-ML height to be an undoubted experimental fact given by nature, and interposes Co nanoclusters between Au films, it is found that no bulk-like Co atoms exist at all and almost all of the Co atoms can be regarded as interfacial ones (a “magic height”) with a negligibly small number of perimeter atoms (Fig. 1c). This is a very simple but essential idea for our study, providing an ideal, practical system for directly determining the interfacial magnetic moments.
3. Experiment The nominal sample structure and angle-dependent MCXD experimental arrangement are shown in Figs. 2 and 3.
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Fig. 2. Nominal sample structure and arrangement for angle- and cluster-size-dependent MCXD experiments. The wedge-shaped Co with the nominal ∗ , microscopically consists of independent clusters for the range of d ∗ 1.6 ML. E and p stand for the electric field and momentum coverage, dCo Co vectors of the incident photons.
Fig. 3. (a) STM picture, (b) scanning height distribution along the white line in Fig. (a), and (c) height distribution histgrams for Dav 4.7 nm ∗ 0.85 ML). (dCo
The details of sample preparation and structural characterization are described elsewhere [30,31]. A wedge-shaped Co ∗ , ranging from 0 to 2 ML, was with a nominal coverage, dCo grown on a 200 nm-thick Au (1 1 1) seed layer with a mica substrate (not shown in Fig. 2) using the MBE technique in an ultrahigh vacuum (UHV) (Fig. 2). A 5-ML-thick Co film was produced at one edge. The microscopic surface structure of Au and Co was characterized using reflection high-energy electron diffraction (RHEED) and STM during and after each growth. An STM observation revealed atomically flat, 100–200-nm wide Au(1 1 1) terraces with the so-called “herringbone” pattern only when a proper heat treatment was made very carefully [27,30,31]. Quasi two-dimensional Co nanoclusters were self-assembled at herringbone elbow sites by the room-temperature deposition of Co, as shown in Fig. 3a [27,30,31]. An STM observation showed an almost constant height of 2 ML of the Co clusters (Figs. 3b and c). The 2-ML height implies that the average in-plane diameter, ∗ (Fig. 2), Dav , is proportional to the root-mean square of dCo ∗ but only the dCo 0.85 ML clusters had a proportional ∗ cluscoefficient somewhat different from that for other dCo ters. The Co layer was finally capped with a 2-nm-thick Au layer in both order to ensure the “magic height” and to prevent the Co from oxidation (Fig. 2). The Au-layer oxidation prevention is unbelievabaly perfect, as shown later. Angle-, field-, and temperature-dependent MCXD experiments were performed in the longitudinal geometry at the Co L2,3 and M2,3 core edges and the Au N6,7 and O2,3 core edges by detecting the X-ray absorption spectra (XAS) using the total-electron-yield (TEY) and light-reflection methods with circularly polarized synchrotron radiation on a bending-magnet (BL-11A) and helical undulator (BL-28A) beamlines at the Photon Factory (Fig. 2). Possible artifacts arising from the saturation effect on the MCXD spectra in the TEY detection can be fully neglected due to the only 2-ML
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height of the clusters. Magnetic fields, B, ranging from 0 to ±5 T were applied to a sample parallel and antiparallel to the fixed positive helicity (h) of the incident photons (longitudinal geometry) using a UHV superconducting magnet [34]. A remanent MCXD for B = ±0 T was measured in such a way that B = 0 T → B = +5 T → B = +0 T (where µ− taken) → B = −5 T → B = −0 T (where µ+ taken). Here, µ+ and µ− stand for the absorption coefficients for the photon helicity parallel and antiparallel to the 3d majority spin direction. We define MCXD as µ = µ+ − µ− . The sample was rotated about a vertical axis parallel to the Co-wedge direction, thus changing the angle θ between the photon momentum p and the sample surface normal n. The ∗ (or D ) of the Co clusters shone by the incident light dCo av was changed by a vertical translation of the sample. The sample temperature was varied from 300 to 30 K. The average degree of circular polarization, PC , of the light was directly measured to be 92 ± 3% on BL-28A [35]. The PC on BL-11A was carefully evaluated to be 78 ± 3% both by a comparison of the measured MCXD of single-crystalline Co and Ni films with the reported MCXD intensities [36,37] and by a calculation which took into account the source characteristics and the effects of beam-line optical elements on the polarization of light.
4. Theoretical background: angle-dependent sum rules In this section we present a brief review of the sum rules [38,39] in the angle-dependent mode [22,28], which are used in the next section. Let the z axis be along the surface-normal direction (n) for a quasi-two-dimensional sample. We consider the situation where a circularly polarized light beam is incident onto the sample in a direction making angle θ with respect to n and magnetic fields are applied to the sample parallel and antiparallel to the θ direction (longitudinal geometry) (see Fig. 2). The MCXD orbital [38] and spin [39] sum rules for the p → d transitions, as applied to the angle-dependent mode [22,28], read mθorb =
−4 3
[AL3 + AL2 ]θ nh µB , [AL3 + AL2 ]θ
(1)
and mspin + 7mθT =
−2[AL3 − 2AL2 ]θ nh µB , [AL3 + AL2 ]θ
(2)
where AL3 and AL2 , and AL3 and AL2 are the L3 and L2 energy-integrated MCXD and XAS sum (µ+ + µ− ) intensities, respectively, nh is the 3d hole number, mθorb = − Lθ µB /¯h, mspin = −2 S µB /¯h, and mθT = − Tθ µB /¯h with T being the expectation value of the intra-atomic magnetic dipole operator T = S − 3r(r · S)/r 2 [28]. Here, we have neglected the θ dependence of mspin , which could be theoretically expected in the second order of the spin-orbit
(SO) interaction constant ξ 3d (Co) but is indeed negligibly small. It holds for d orbitals [28] that Tx + Ty + Tz = 0,
(3)
which leads to
m⊥ T + 2mT = 0,
(4)
in the absence of in-plane anisotropy, as valid for the present sample. It also holds [22] that
2 2 mθorb = m⊥ orb cos θ + morb sin θ,
2 2 mθT = m⊥ T cos θ + mT sin θ.
(5a) (5b)
Eqs. (1), (2), (4), (5a) and (5b) allow a determination of ⊥ mspin , morb , m⊥ orb , mT , and mT from MCXD measurements for two different angles of θ [22,28]. It is further noted that the combined use of (4) and (5b) leads to mθT = mT (1 − 2 ◦ 3cos θ) = 0 at θ = 54.7 (magic angle). Thus, Eq. (2) for θ = 54.7◦ reduces to mspin =
−2[AL3 − 2AL2 ]θ nh µB , [AL3 + AL2 ]θ
(6)
which allows a direct determination of mspin by a single magic-angle measurement [27,28]. We have made an approximation in which the original expression (µ+ +µ0 +µ− ) is replaced by 3/2(µ+ +µ− ) in the denominator of Eqs. (1), (2), and (6). This could be especially well valid for the magic angle, because linear dichroism should vanish at the angle.
5. Results and discussion 5.1. Field and temperature dependencies of normal-incidence MCXD Fig. 4 shows the B dependence of the mesh-monitor-fluxnormalized, polarization-dependent, normal-incidence Co L2,3 -edge XAS and MCXD hysteresis curve for nanoclus∗ 1.6 ML) taken at 300 K ters with Dav 8.2 nm (dCo [27]. Almost the same result was obtained for Co clusters ∗ 1.2 ML). The qualitative hyswith Dav 7.2 nm (dCo teresis curves were measured by the M2,3 -edge MCXD and their absolute magnitude was determined by the L2,3 -edge MCXD. Surprisingly, even the non-surface-sensitive reflection method yielded a clear M2,3 -edge MCXD for such dilute systems, demonstrating the power of core-level MCXD. We first emphasize that no multiplet features typical for CoO was seen at all in the L2,3 XAS and that a strong MCXD was reproduced. This provides evidence for no oxidation of the Co clusters; note that the clusters’ height is only 2 ML. The Co nanoclusters with 7.2 Dav 8.2 nm ∗ (1.2 ML dCo 1.6 ML), for the present Au(1 1 1) herringbones’ terrace size, exhibit a clear remanent MCXD at 300 K, although it is smaller than that for B = ±3 T (Fig. 4a). The field dependence of the MCXD shows a clear
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∗ 1.6 ML) clusters taken at 300 K Fig. 4. (a) Polarization-dependent, normal-incidence Co L2,3 -edge XAS and MCXD spectra of Dav 8.2 nm (dCo and under B = ±3 T and ±0 T. Note a clear remanent MCXD (lower panel). (b) Co L3 -edge MCXD hysteresis curve of Dav 8.2 nm clusters at 300 K. The inset shows the expanded low-field region.
hysteresis with a coercive field HC of 330 Oe for Dav 8.2 nm (Fig. 4b). These results reveal that Co clusters with 7.2 Dav 8.2 nm retain cluster-cluster FM alignment at 300 K. It is also noted that the magnetization detected by the MCXD is fully saturated at very low fields (Fig. 4b). This clearly shows that the FM clusters are of single domains. The 5-ML film showed a remanent MCXD (B = ±0 T) equal to an MCXD for B = ±3 T (Fig. 5). Its B-dependent L3 -edge MCXD revealed a clear rectangular hysteresis curve, showing complete FM of the film with an HC of 530 Oe. We emphasize here that the equal magnitude of MCXD for zero and high fields assures negligibly small artifacts arising from the effects of the magnetic field on TEY detection. This can be reasonably understood as being due to the high symmetry of detection by considering that all photoelectrons emitted at the high-B sample position are transferred along a helix, with a reversal of B resulting in only a reversal of the sense of the rotation of the helix. The general belief that high fields would affect the TEY-detected MCXD has no physical foundation at all.
∗ = 5 ML film taken at Fig. 5. Co L3 -edge MCXD hysteresis curve of dCo T = 300 K.
Fig. 6a and b show the temperature dependence of the ∗ remanent MCXD for clusters with Dav 4.7 nm (dCo 0.85 ML), respectively and the field dependence of the ∗ 0.4 ML) MCXD for clusters with Dav 4 nm (dCo [27]. All of the Co clusters with Dav 4, 4.7, and 6.7 nm ∗ 1.1 ML) showed the behavior qualitatively similar (dCo to Fig. 6a and b. In contrast to the results for clusters with 7.2 Dav 8.2 nm, no remanent MCXD was detected at 300 K in Co clusters with Dav 4 nm, 4.7, and 6.7 nm (Fig. 6a and b), whereas a large MCXD was observed for B = ±5 T at 300 K for all of three Dav (Fig. 6b). The MCXD intensity at 300 K strongly depends on the field strength (Fig. 6b). The B dependence of MCXD can be fitted approximately, but not fully, by a single Langevin function over a whole range of B up to 5 T. This small deviation from the Langevin function could be due to a finite size distribution of the clusters. These results strongly indicate the SPM behavior of the independent Co nanoclusters with Dav 6.7 nm. In order to further verify the SPM, we examine the temperature dependence of the remanent MCXD in Fig. 6a. A clear remanent MCXD appears at T 100 K with lowering T, whereas no remanent MCXD is seen for T 125 K. This shows that the magnetic moments of Co clusters are randomly oriented due to thermal activation at high temperatures, and are ferromagnetically aligned for T 100 K, giving a blocking temperature of TB ≈ 100–120 K. A similar T-dependent MCXD of Co clusters with Dav 4 nm yields a blocking temperature of TB ≈ 70–80 K. The B-dependent, normal-incidence MCXD measured at T = 30 K for the SPM clusters with Dav 6.7 nm is displayed in Fig. 6b in comparison with that taken at 300 K [27]. It is most noted that the saturated MCXD intensity for B = ±5 T is nearly equal for T = 300 and 30 K. This can be understood only if the Co clusters form single domains and their relative orientation is aligned by external fields. The large MCXD amounting to 40%, even at 300 K for ±5 T, cannot be explained at all by the usual paramagnetism.
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Fig. 6. (a) Temperature dependence of the Co L2,3 -edge remanent MCXD for Dav 4.7 nm clusters. Note that a clear remanent MCXD appears at T 100 K. (b) Co L3 -edge MCXD hysteresis curve at T = 30 K and B-dependent MCXD at T = 300 K for Dav 4 nm.
Thus, we conclude that the independent Co clusters with Dav 6.7 nm are of SPM. All the present results provide evidence that the Co nanoclusters retain FM over a range of 7.2 Dav 8.2 nm and that a magnetic phase transition crit ≈ 6.7–7.2 nm takes place from FM to SPM around at Dav ∗crit (dCo ≈ 1.1–1.2 ML) with decreasing cluster size. This indicates the in-plane magnetic interaction between independent Co clusters via the conducting electrons of Au.
ement, from the edge-jump-normalized MCXD data (θ =0◦ and 54.7◦ ) on a single-crystalline bulk hcp Co film and the accurately known values of mspin and morb . The saturation effect in TEY detection [43] was taken into account. The second analysis allowed us to avoid the use of an accurately unknown 3d electron-occupation number for clusters in applying the MCXD sum rules. No appreciable differ-
5.2. Direct determination of interfacial magnetic moments by angle-resolved MCXD The angle (θ)-resoleved Co L2,3 -edge MCXD was measured at T = 30 K under B = ±5 T for SPM clusters with Dav 6.7 nm, and at T = 300 K and under B = ±3 T for FM clusters with 7.2 Dav 8.2 nm. Fig. 7 shows pictorially the θ-dependent XAS, MCXD, and its energy-integrated spectra for the SPM clusters with Dav 6.7 nm. Fig. 8 shows only the MCXD and its integrated spectra for FM clusters with Dav 7.2 nm in a two-dimensional form in order to make clear the angle dependence [27]. The noise in the XAS and MCXD spectra in Fig. 7 is due to liq. He flowing to cool the sample. In general, the magnetization is not necessarily parallel to the external B under low B (B 1 T), except for θ = 0◦ and 90◦ in two-dimensional systems with strong magnetic anisotropy [40]. The present high B ensures this parallelism. Though the theoretical possibility of magic angle measurements was originally suggested by Stöhr and König [28], no experimental studies utilizing this powerful technique had been reported until our recent study [27]. Since we are most interested in the purely interfacial mspin , we made full use of magic-angle (θ = 54.7◦ ) measurements. We made two independent analyses by using an nh value and not using an nh value. A first analysis was made using a theoretical nh value for Co2 Pt4 multilayers [41,42]. A second analysis was made by determining the constant C = (AL3 + AL2 )/nh , which is proportional to the square of the 2p → 3d radial transition matrix el-
Fig. 7. Angle-resolved Co L2,3 -edge (a) XAS, and (b) MCXD spectra for SPM clusters with Dav 6.7 nm taken at T = 30 K under B = ±5 T. The energy integrals of the MCXD spectra are also shown in (b).
T. Koide et al. / Journal of Electron Spectroscopy and Related Phenomena 136 (2004) 107–115
Fig. 8. Angle-resolved Co L2,3 -edge (a) MCXD spectra, and (b) their energy integrals for FM clusters with Dav 7.2 nm taken at T = 300 K under B = ±3 T.
ence was found for the results of two analyses. The mspin , ⊥ ⊥ morb , m⊥ orb , mT , mT , and mtot = mspin + 1/3 (morb + 2 morb ) were determined by applying the sum rules to the data for θ = 0◦ and 54.7◦ . The self-consistency of the analyses was confirmed by the combined use of the data for θ = 0◦ and 65◦ . The results are shown in Fig. 9 as functions of Dav and of the number of atoms per cluster (N) together with values for bulk hcp Co [27]. The mspin was found to reach large values of 2.0–2.15 B for independent Co clusters with Dav 7.2 nm, irrespective of their FM and SPM. This implies an almost full spin polarization of the Co 3d electrons in the clusters, if one considers the total 3d hole number of nh 2.5 for bulk Co [41,42] and that the clusters’ nh value is not very much different from that of the bulk, as evidenced by the present two analyses. We emphasize here again that these mspin values are of almost purely interfacial Co atoms. The present result provides the first direct experimental verification of a remarkable enhancement of the interfacial mspin predicted by theoretical calculations [7–13]. The smaller mspin value only for Dav 8.2 nm can be reasonably understood by their non-perfect 2-ML height. An STM observation showed that ∗ , approaching ∼2 ML, produced a finite an increase of dCo number of 3-ML-height clusters without forming a uniform film [44], resulting in the appearance of bulk-like Co atoms with a smaller mspin value (see Fig. 1a). The present mtot 2.2–2.4 B for clusters with Dav 7.2 nm agrees surprisingly well with mtot 2.4–2.5 B of free Co clusters
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Fig. 9. Dav and N dependencies of the magnetic moments determined from the angle-resolved MCXD measurements and the angle-dependent ⊥ sum rules: (a) mspin and mtot ; (b) morb and m⊥ orb ; (c) mT and mT . The corresponding moments of bulk hcp Co are shown for comparison. The hutched area denotes the FM/SPM transition region.
in the range of the smallest number of atoms, obtained by Stern–Gerlach-deflection experiments [5,14]. This strongly indicates that the interfacial Co atoms in Au/Co/Au(1 1 1) systems are in an environment which is very similar to the surface. This is quite plausible, since the calculated 5d band of bulk Au is located well below the Fermi level, EF , and thus the Co 3d-Au 5d hybridization could be very small. This small d–d hybridization was confirmed by the present Au N6,7 and O2,3 core-edge MCXD measurements. The Au-edge MCXD was by an order-of-magnitude smaller than the large MCXD at the Pt N6,7 and O2,3 edges in Co/Pt multilayers reported previously by the present authors [21]. ⊥ The m⊥ orb reaches a value of morb 0.30 − 0.31 B for independent clusteres with Dav 7.2 nm. This value is two-times as large as that of bulk Co. The two-times enhancement is consistent with recent results for m⊥ orb obtained by the normal-incidence MCXD in the same Co clusters/Au(111) [23] and Fe clusters/Cu(1 0 0) [24], and by angle-dependent MCXD in Fe clusters/Cu(111) [25] and Fe clusters/Au(1 1 1) [26]. It is interesting to compare the anisotropy of the present mθorb with that of Weller et al. on normal ultrathin Co films in Au/Co/Au(1 1 1) for 4 tCo 11 ML [22]. A simple extrapolation to the tCo = 1 ML limit of their results, using the 1/tCo law, gave a value of m⊥ orb,S ⊥ 0.36 B for 1 ML [22]. The present morb 0.30 − 0.31 B is close to this value. In contrast, a difference is found for
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morb between two experiments. A simple extrapolation to the 1-ML limit of their result with the use of 1/tCo law gave a value of morb,S ≈ 0 [22], which is remarkably different from the present value of morb 0.16 − 0.21 B . However, this seeming discrepancy is not unexpected, since the present samples were independent clusters, whereas their extrapolation was based on the assumption of a uniform 1-ML film. If one considers an extreme limiting case where the in-plane diameter (Dav ) becomes nearly equal to the clusters’ height, the anisotropy of mθorb should disappear. Thus, we conclude that morb initially decreases with decreasing tCo in the range of uniform films [22], but it increases back again with fur∗ in the range of independent clusters ther decreasing dCo only if the Au substrate is properly heat-treated to form a “herring-bone” pattern. Both m⊥ T and mT of the FM clusters with Dav 8.2 nm agree with a simply extrapolated value of their results using the 1/tCo law [22]. The smaller anisotropy of the present mθT for the clusters Dav 7.2 nm is reasonably understood as being due to a loss of two dimensionality. At the Co/Au interface, the reduced effective coordination number and the increased electron localization mainly in the perpendicular direction will lead to more localized atomic-like 3d wave functions. This would narrow the 3d band width, resulting in a transfer of the electron occupation number from the minority- to majority-spin bands while nearly keeping the total hole number. This effect could give rise to an enhancement of mspin [27]. A reduction of symmetry at the interfaces produces a uniaxial crystal field and lifts the orbital degeneracy, enhancing the difference of the electron occupation number for the in-plane and out-of-plane 3d orbitals. This effect causes an m⊥ orb enhancement and a θ nonzero anisotropc mT [27]. It is interesting to note that the observed nonvanishing mθT shows a partial manifestation of the intrinsic quadrupole moment in the electron-density distribution Qθθ of each 3d orbital, since mθT is related with Qθθ through mθT ∝ − Tθ ≈ Qθθ S [28].
given by ESO ≈
−αξ3d ⊥ (morb − morb ), 4µB
(8)
where α is an effective correction factor. By using ξ3d ≈ 70 meV and α ≈ 0.2 for ultrathin Co films [22], we obtain ESO ≈ −4.4 × 10−4 eV per atom and ESO ≈ −2.6 × 10−4 eV per atom for the FM clusters with Dav 7.2 and 8.2 nm, respectively. The spin–spin dipole interaction energy, which favors the in-plane magnetic anisotropy, was calculated to be 2πMs2 × 0.93 ≈ +0.86 × 10−4 eV per atom. Here, a correction factor of 0.93 is due to the finite height (2 ML) in the perpendicular direction. We find that |ESO | > 2πMs2 × 0.93, which shows a strong perpendicular magnetic anisotropy (PMA) of the FM clusters. Thus, the present Co nanoclusters in a range of 7.2 Dav 8.2 nm have simultaneously four important properties: (i) no oxidation, (ii) single domain, (iii) FM at 300 K, and (iv) PMA [27]. The magnetic moment of each FM cluster could be reversed by modern atom technologies, such as the use of magnetic force microscopy (MFM) with an appropriate radius of curvature of the tip and a suitable magnetic-field strength, as shown in Fig. 10a. Its reversed moment may be held after the MFM tip is removed, because the spin flip requires an energy larger than the reorientation energy barrier (Fig. 10b). If the cluster–cluster FM-interaction energy is smaller than the energy barrier, the single cluster’s “antiparallel” spin orientation would be maintained. This situation could be realized for Dav 7.2 nm, which is just above the FM/SPM transition cluster size. Therefore, the present FM Co nanoclusters may provide a technological possibility for utilizing each cluster as a single nano-scale magnetic bit operating at room temperature.
6. Potential technological application We estimate a magnetic anisotropy energy (MAE), ESO , caused by the SO interaction. Laan derived a formula for ESO to the second order of ξ 3d [45] 2
ESO ≈
ξ3d −ξ3d ⊥ (m − morb ) + ( 21 3 m⊥ + A), 4µB orb Eex µB 2 2 T (7)
where Eex is the 3d exchange-splitting energy and A is a term independent of the spin direction [26]. However, this formula is generally difficult to directly apply to MCXD results, because it is necessary to separately take account of morb of the minority- and majority-spin bands. Thus, we use a simpler, majority-hole corrected Bruno’s relationship [46]
Fig. 10. Schematic view for a potential technological application: (a) an MFM tip approaching Co cluster 1 could reverse its magnetic moment; (b) energy level as a function of angle θ 1 . The reversed moment of cluster 1 may be held as a quasi-stable state due to the energy barrier.
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7. Conclusion
We have directly determined the values of mspin , morb , ⊥ morb , mT , m⊥ T , and mtot of almost purely interfacial Co atoms in Au/Co anoclusters/Au(1 1 1) by angle-resolved MCXD measurements with full use of the clusters’ constant 2-ML height and of the experimental magic angle of 54.7◦ . Evidence has been presented for an FM/SPM magnetic phase transition with decreasing cluster size by the field, temperature, and size-dependent MCXD. We have pointed out the in-principle possibility of the room-temperature application of Co clusters as a nanoscale magnetic bits.
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