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Magneto-optic spectrum and electronic structure of single-crystal MnBi
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Journal of Magnetism and Magnetic Materials 283 (2004) 95–102 www.elsevier.com/locate/jmmm
Magneto-optic spectrum and electronic structure of single-crystal MnBi D.P. Brammeier, J.-M. Park, C.G. Olson, I.R. Fisher1, D.W. Lynch a
Department of Physics and Astronomy and Ames Laboratory, USDOE, Iowa State University, Ames IA 50011, USA Received 12 February 2004; received in revised form 16 April 2004 Available online 9 June 2004
Abstract Single crystals of MnBi were used for magneto-optic Kerr-angle spectroscopy and photoelectron spectroscopy. The Kerr-angle peak at 3.35 eV was observed for our nearly oxygen-free bulk samples, but the role of the oxide overlayer, demonstrated by Auger spectroscopy, as a possible origin of this peak cannot fully be assessed. The energy bands from photoelectron spectroscopy were in general agreement with calculated band structures, but were not extensive enough, due to sample cleavage properties, to distinguish reliably between band-structure calculations that disagree. r 2004 Published by Elsevier B.V. PACS: 75.50; 78.20.L; 79.60 Keywords: Magneto-optics; Electronic structure; Photoelectron spectroscopy; MnBi; Kerr effect
MnBi is a ferromagnetic compound [1,2] used for magneto-optic recording in the form of amorphous films, often doped to reduce the Curie temperature. A great deal of work has been done on amorphous and polycrystalline films of MnBi, usually doped with Al, Si, Cr, or O, but little work has been done on single crystals. Single crystals are of less interest for magneto-optic recording, but Corresponding author. Tel.: +1-515-294-3476; fax: +1515-294-0689. E-mail address: [email protected] (D.W. Lynch). 1 Current address: Geballe Laboratory for Advanced Materials and Department of Applied Physics, Stanford University, Stanford CA 94305-4045, USA.
0304-8853/$ - see front matter r 2004 Published by Elsevier B.V. doi:10.1016/j.jmmm.2004.04.130
are important for understanding the electronic structure of this material. Electronic structure calculations on spin-polarized MnBi, discussed below, do not agree in all details of the band structure and of the off-diagonal component of the optical interband conductivity, i.e., the magnetooptic polar Kerr-angle spectrum. Moreover, there is some disagreement about the number of peaks in the magneto-optic Kerr-angle spectrum in both theory and experiment, and why one of the peaks is or is not present. In the following we report on the flux growth of single crystals of MnBi, the Kerr-magneto-optic spectrum of a single crystal of MnBi, and some angle-resolved photoelectron
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spectroscopy for comparison with the bandstructure calculations. MnBi has the hexagonal NiAs (B8) structure, space group D46h (p63/mmc) below its Curie temperature of 633 K. The magnetic moments are oriented along the c-axis for temperatures above 84 K. Below this temperature, the moments lie in the basal plane [3,4]. The property of interest, the polar Kerr-angle spectrum [2,5,6], is obtained by analyzing the state of polarization of normally incident reflected light from a sample with magnetization normal to the sample surface. The reflected light is elliptically polarized, with the major axis of the ellipse at an angle YK , the Kerr angle, with respect to the polarization direction of the incident light. The ellipticity, eK , is the ratio of the minor to major axis lengths of the ellipse. tan YK and eK form a Kramers–Kro¨nig pair, and tan YK YK for nearly all magneto-optic materials. A hexagonal crystal magnetized along the c-axis has one offdiagonal component of the complex optical conductivity that plays a role in the reflection of light normally incident along the c-axis. This quantity can be calculated from the electronic structure and determined experimentally from the Kerr-spectrum, but it requires use of a diagonal component of the optical conductivity, which can be measured, usually by ellipsometry. Alternatively, the diagonal component of the conductivity can be obtained from electronic structure calculations and a calculated Kerr-angle spectrum used for comparison with experiment [2,5–12]. The optical and magneto-optical spectra have been measured several times on thin-film samples [2]. Usually these films were prepared by evaporation or sputtering several thin alternating layers of Mn and of Bi, often capped with a thin protective layer of SiO2, followed by annealing to produce single-phase MnBi. The most extensive study was by Di et al. [13,14]. Their measured Kerr-angle spectrum for MnBi has two peaks, at 1.84 and 3.35 eV, the former having the relatively large magnitude of 2.31 at 85 K, making MnBi of some interest for magneto-optic recording (although it has a number of disadvantages [2]). Kerr-angle spectra by Huang et al. [15] were on Al-doped films of MnBiSi. They showed two peaks of
slightly smaller amplitude shifted to higher energies from those of Di et al. The electronic band structure of MnBi has been calculated several times [7–12,16], but there is still disagreement about parts of the band structure. Oppeneer et al. [9] calculated the electronic structure of MnBi and the interband optical conductivity and Kerr-angle spectrum. They found a large negative peak at 1.8 eV, in agreement with experiment, and a shoulder around 3.4 eV, where experiment often has a peak. The peak magnitude could be fit to experiment, using a reasonable value for the broadening parameter. Since the data of Di et al. were taken on a sample with the composition Mn1.22Bi, Oppeneer et al. simulated this material and found a calculated Kerr-angle spectrum with a similar, but weaker, peak at 1.8 eV and a second peak at 4.3 eV, higher in energy than that for MnBi. These peaks all arose from Bi p-p transitions. They also calculated Kerr-angle spectra for MnAs and MnSb and MnBi doped with Al. They explained the large Kerr angles in MnBi, compared with those of MnSb and MnAs, as arising from the large magnetic moments on Mn and the large spin–orbit splitting on Bi. Sabiryanov and Jaswal [8] previously had calculated Kerr spectra for MnBi and several hypothetical MnBixAly compounds, finding the low-energy peak in all but MnBiAl, but a high-energy peak only in MnBi itself. Ko¨hler and Ku¨bler [10,11] calculated the band structure and the optical and magneto-optical spectra for MnBi, and MnBiX0.5 (X=Mn, Si, Al, O, Pt), and MnBiAl, MnBiPt, and MnBiAl0.5O0.5. The calculated Kerr-angle spectrum for MnBi had only one peak, the lower energy one. Under the hypothesis that the thin-film samples may have considerable impurities from materials in contact with them, they repeated the calculations using the elements labeled X above. They found that only O gave a second peak, but the energies of both peaks were not in good agreement with experiment. They assigned the low-energy peak in the Kerr spectrum to Bi pk-Mn dktransitions (k=minority spin). Ravindran et al. [12], on the other hand, did find a second peak in their calculated Kerr-angle spectrum for pure MnBi. They assigned both peaks to Bi pk-Mn dk transitions. They also
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calculated the bands, optical conductivity and magneto-optical spectra for MnSb and MnAs as an aid to understanding why the Kerr-angle peak is so large in MnBi, agreeing with the assessment of Oppeneer et al. Fig. 1 compiles some of the polar magneto-optic Kerr-angle spectra calculated to date. It is clear that the spectra from Ko¨hler and Ku¨bler and from Oppeneer et al. agree well, with one peak and shoulder, while that of Ravindran has two main peaks. The spectrum of Kulatov et al. [7], reported in the paper of Ravindran et al. [12], consists of a single peak at about 2.2 eV and a weak shoulder in the 3.0–3.2 eV region. One should note that the off-diagonal component of the conductivity is difficult to calculate accurately. Its magnitude is of the order of a percent of that of the diagonal component due to extensive cancellation of contributions of opposite sign. In order to clarify the role of oxygen in the Kerr spectrum, Harder et al. [17] made films similar to those of Di et al., but in ultra-high vacuum, to prevent, or at least reduce, oxygen incorporation in the films. They were made on two different substrates and capped with an SiO protective film. After correcting for the optical effect of the SiO overlayer they obtained a Kerr-angle spectrum with a single peak at 1.85 eV. The higher-energy peak, assigned to interstitial oxygen by Ko¨hler
Fig. 1. Calculated polar magneto-optic Kerr-angle spectra. Filled squares: Ref. [10]; stars: Ref. [9]; open circles: Ref. [7]; asterisks: Ref. [12].
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and Ku¨bler, was not present in this spectrum. Moreover, the magnitude of the low-energy peak was in better agreement with that calculated by Ko¨hler and Ku¨bler but its peak position remained at about 1.8 eV, although the calculated lowenergy peak shifted from 1.8 eV to about 1.0 eV upon going from MnBi to MnBiO0.5. It would seem that the high-energy peak is the result of oxygen in MnBi, but, according to the calculations of Ko¨hler and Ku¨bler, it must be considered a major constituent of the MnBi. Moreover, photoelectron spectroscopy on oxidized MnBi [18] later showed that the oxygen valence electrons appear 6 eV below the Fermi level, too low to contribute to the measured spectra. The calculations of Ko¨hler and Ku¨bler place them much nearer the Fermi level [10]. In the following we report the growth of single crystals of MnBi, polar magneto-optic Kerr spectra for comparison with the calculated spectra and those measured on thin films, and some photoelectron spectra for comparison with the existing band calculations. The single-crystal Kerr spectra should suffer less from the effects of impurities, except for oxygen from the atmosphere.
1. Experimental Single crystals were grown by slowly cooling a melt of 10 at% Mn and 90 at% Bi from 410 1C to 272 1C, at which temperature the excess Bi was decanted by centrifuging. Each growth process produced dozens of crystals, often in the form of hexagonal platelets or prisms. The largest had hexagon ‘‘diameters’’ of 1–2 mm. Longer growth times yielded taller prisms, but not prisms with larger basal-plane areas. The crystals were characterized by magnetic measurements using a commercial quantum design SQUID magnetometer. The magnetization was measured for fields applied parallel and perpendicular to the c-axis, both in a steady field as a function of temperature from 2 to 450 K, and as a function of field at constant temperature. The data were in agreement with literature values on microcrystals of MnBi [19] and single crystals [20–22] of MnBi.
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Kerr-magneto-optic spectra were measured on a spectrometer described elsewhere [23,24]. MnBi saturates magnetically in the 0001 direction at around 0.3 T at 300 K [25], where the measurements were taken. The sample was a natural face of an asgrown crystal. MnBi is considered air sensitive although Yoshida et al. [26] report purer MnBi is less air sensitive. We describe our surfaces further below. The spectra stop before the high-energy limit of the spectrometer, due to the small sample size and a reflectance that decreases with increasing photon energy. Both the Kerr angle and ellipticity spectra were measured. These, and the diagonal component of the complex optical conductivity, which can be obtained by ellipsometry, give the offdiagonal component of the optical conductivity, the interband contribution of which can be calculated from the electronic structure results. Here, however, we need only the Kerr-angle spectrum. For photoelectron spectroscopy (PES), the samples were epoxied to an Al stud, oriented by Laue back-reflection X-ray diffraction, mounted on a closed-cycle He refrigerator, then an Al post was epoxied on top. They were ‘‘cleaved’’ in situ at about 15–20 K under pressures below 4 10 11 Torr by pressure applied to the top post. All measurements were made under these conditions and no sign of sample surface deterioration was observed. The crystals, however, did not really cleave parallel to the expected (0 0 0 1) planes. The fracture was closer to conchoidal. However, angleresolved spectra taken with normally emitted (11 half-angle) electrons showed features dispersing with photon energy, despite a rather large background of scattered electrons. (Low-symmetry stepped surfaces have, in the past, yielded good normal-emission ARPES spectra [27].) Angleresolved PES spectra were taken on the Ames/ Montana beam line at the Synchrotron Radiation Center [28].
with three spectra from thin films. The singlecrystal spectrum shows peaks at 1.8 and 3.2 eV. The peak at 3.2 eV is probably an intrinsic peak, as the commonest impurity likely in the bulk crystal is excess Bi, while any oxygen present should be an oxide of Mn on the surface from post-growth exposure to air (see later). The peaks in the spectra of Di and Uchiyama [14], and of Huang et al. [15] are at slightly different energies and have larger amplitudes. The films of Huang et al. were of MnBiAl and MnBiAlSi, while those of Di and Uchiyama were made by annealing multilayers of Mn, Bi, and Al, then capped them with an overlayer of SiO2. The spectra reported in Ref. [14] were, however, corrected for the optical effects of this overlayer and should represent the spectrum of bulk MnBi. Fig. 2 also shows data from Fumigalli, taken on a film of MnBi [29]. The range in magnitude of the different Kerrangle spectra is difficult to explain. Our data were taken in an applied magnetic field that produced about 62% of the saturation magnetization. Di and Uchiyama’s spectrum apparently was taken with no applied field, i.e., with the residual magnetization, of the order of 90% of the saturation [19–21], or in an applied field yielding saturation. Since the Kerr spectrum amplitude is linear in the magnetization, our spectrum should
2. Results 2.1. Magneto-optic Kerr spectra Fig. 2 shows our measured polar magneto-optic Kerr-angle spectrum of single-crystal MnBi along
Fig. 2. Measured polar magneto-optic Kerr-angle spectra. Solid squares: Refs. [13,14]; stars: Ref. [15]; open circles: Ref. [29]; open squares: present work.
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be smaller than Di’s by a factor of 0.62–0.69. However, Di and Uchiyama corrected their measured spectrum for the effect of the SiO2 overlayer used to protect his film, an effect that increases the magnitude of the true spectrum above that of the spectrum measured with the overlayer. We have previously modeled such an effect for GdCo2 [30], finding that a correction for ( of a transparent overlayer increases the 200 A amplitude of YK by a factor of about 1.5 at a peak, and by an even larger factor if the overlayer is absorbing. If such a correction applies to our MnBi data after correcting for the magnetization difference just described, the amplitude of our spectrum becomes larger than that of Di and Uchiyama. The energies of the peaks in our Kerr spectrum are close to those of Di et al. and of Fumagalli. The position of the low-energy peak agrees with that calculated [9–12], but the high-energy peak does not appear in the calculated spectra for stoichiometric MnBi of Oppeneer et al. [9] and of Ko¨hler and Ku¨bler [10,11]. The high-energy peak does appear in the calculated spectrum of Ravindran et al. [12], but its energy is considerably lower than the observed energy. This peak appears at about the right strength and energy in the calculations for non-stoichiometric MnBi, with a large excess of Mn or O [10,11], i.e., MnBiMn0.5 and MnBiO0.5. Single-crystal surfaces similar to those used in the Kerr-angle spectra were studied by Auger microscopy. They were exposed to the air for about 90–120 min before introduction into the microscope vacuum, about half the duration of the magneto-optic spectroscopy. The as-grown surfaces were not only MnBi; there were small, often circular, regions of Bi left from the growth process. These covered up to 50% of the surface area. Since they contribute to the reflectance, but not to its magnetic-field dependence, they do not alter noticeably the shape of the Kerr-angle spectra, but they do reduce its magnitude. Thus the magnitude of our single-crystal Kerr spectrum, about the same as that from polycrystalline or amorphous films, should actually be larger because of this effect. Surface regions outside the Bi islands were sputtered while Auger spectral peaks from
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Mn, Bi, and O were monitored. These initial surfaces contained mostly Mn and O, with small amounts of Bi. As sputtering progressed the O peak diminished, the Bi peak grew, and the Mn peak remained constant or grew some. After about ( had been removed, the O peak had 100–200 A fallen to a smaller, steady value (it overlapped a contribution from Bi, so the O concentration cannot be shown to be zero), and the Bi and Mn peaks had risen to steady values, indicating the bulk had been reached. The crystals were too small for XPS spectroscopy between Bi islands, so the oxidation state of the Mn in the overlayer could not be determined. The difficulty with describing the surface layer primarily as an oxide of Mn, of composition depending on depth, on top of bulk MnBi is the fact that no maximum in the Bi concentration vs. depth appeared. The Mn in MnBi that oxidized appeared not to have left surplus Bi localized enough to be detected. A thin overlayer of any non-ferromagnetic oxide should alter the magnitude of the Kerr spectrum, but not its shape. Antiferromagnetic MnO would not contribute a feature to the Kerr spectrum where it is transparent, but in the spectral range above its band gap, 3.8 eV [31,32], its absorption could affect the shape, not just the magnitude, of the Kerr spectrum. A film of ferromagnetic Mn2O3 could contribute structure directly to the Kerr spectrum, as well as alter that of the MnBi below due to its strong absorption, both at energies above its band gap, but it is less likely to be a major constituent of the film due to limited oxygen supply below the outermost few surface layers. It seems unlikely to be the cause of the peak at 3.35 eV in the Kerr-angle spectrum. 2.2. Photoelectron spectra Fig. 3 shows electron energy distribution curves (EDCs) taken at photon energies of 20, 28, and 85 eV. The latter should be nearly free of dipole matrix element effects and should resemble the density of states (DOS), except for the relative strengths of the Mn 3d and Bi 6p contributions, which have different photoexcitation cross sections [33]. Both calculated and measured DOS show a step at the Fermi level, indicating a metallic
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Fig. 4. Electron energy distribution curves of MnB taken below and in the Mn 3p resonance region. The broad peak marked with a vertical line is the Mn MVV Auger peak.
Fig. 3. Electron energy distribution curves of MnBi at three different photon energies.
sample. Both have their major peak at around 2.75 eV, but the measured spectrum extends to 12.5 eV below the Fermi level, further than the calculated 7 eV. The band calculations indicate that the Mn 3d states dominate all other contributions to the occupied part of the DOS in the 0–7 eV range of binding energies. Resonant PES on the Mn 3p core level can emphasize the 3d states in the spectra. See, for example, Ref. [34]. Fig. 4 shows EDCs taken with a photon energy of 45 eV (below the Mn 3p–3d resonance starting at 47 eV), and three EDCs taken in the broad resonance. The broad peaks with tick marks are Mn MVV Auger peaks and can be ignored here. These spectra indicate considerable Mn 3d character throughout the entire valence band. Constant initial-state (CIS)
spectra for valence-band initial states at 0.5, 2.5, 5.5, and 10.5 eV all show the Fano line shape characteristic of Mn 3p–3d resonance origin, hence of significant Mn 3d character at these four binding energies. The enhancement at 0.5 eV binding energy is less than that at the other three energies, implying less Mn 3d character at 0.5 eV than at higher binding energy. The largest enhancement is at 2.5 eV, as expected from the calculated partial DOS. At higher binding energies, the resonant enhancement falls off less slowly than the calculated Mn 3d partial DOS would lead one to expect. Normal emission EDCs at a number of photon energies show three structures, at the Fermi edge, around 0.9 eV binding energy, and at 2.75 eV binding energy. In addition, as the photon energy increases, the amplitude of the entire spectrum for binding energies greater than about 2 eV grows with respect to the part at lower binding energies. This is due to the effect of the photoexcitation cross sections for initial states based primarily on Mn 3d states (binding energy larger than 2 eV) and initial states based mainly on Bi 6p states (less than
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2 eV). The Mn 3d cross section grows monotonically with photon energy in the range used, while that for Bi 6p states decreases [33]. The 2.75-eV peak disperses very little, although the shape changes with photon energy. The lack of dispersion is common with 3d bands that are not strongly hybridized, and, although one can see a number of such flat Mn 3d-based bands around 2.75 eV in the calculated bands, the calculated bands along the kz-axis of the Brillouin zone do, in fact, disperse enough to allow one to state that the expected dispersion of the calculated band is not seen in the experimental EDC. The changes in shape with photon energy can be assigned to dipole photoexcitation matrix element effects from the initial-state band, or several overlapping initial-state bands. When there are several overlapping initial state bands, this effect can cause the apparent lack of dispersion. Electron correlation effects tend to flatten bands, and they may play a role in the reduction of the ‘‘expected’’ dispersion in this peak. The peak at 0.9 eV disperses about 300 meV. The inflection points as the photon energy varies represent initial-state band maxima and minima along the z-axis of the Brillouin zone, i.e., the G and A points. An inner potential of 14 eV places this peak at the A symmetry point, with a binding energy of 1.0 eV, when the photon energy is 16 eV. This band is primarily of Bi 6p character, based on the photon-energy dependence of its contribution to the EDC, just discussed, and on the CIS spectra. The Fermi-edge peak changes shape with photon energy, probably indicating bands crossing the Fermi level. With a 14-eV inner potential, the Fermi level peak at the G point should occur at a photon energy of 15 and 26.5 eV, and the latter is observed in the EDCs very near EF at 26 and 27 eV photon energy. The relative intensity in this spectral region does not decrease monotonically with increasing photon energy, suggesting it originates from a band with dominant Mn 3d character. Most of the Mn 3d minority-spin bands lie above EF, but the band calculations show some Mn 3d contribution just below EF. The photoelectron spectra were measured at about 20 K with no applied field. The magnetic moments were in the basal plane. The calculations
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were done with the moments parallel to the c-axis. The difference in electronic structure for the two orientations of the magnetism should, however, be small on the energy scale of our spectra [35]. Some cleaves gave regions with EDCs that showed far more dispersion than those of MnBi. Core-level spectra taken on these showed only Bi peaks. Evidently some of the cleaves took place exposing Bi inclusions from the flux growth, and these inclusions were epitaxial with the MnBi. They contributed nothing to the Laue reflection patterns taken after completion of the spectra. There was no evidence of oxygen on or just below our cleaved surfaces, no detectable O 1 s photoemission and no 6 eV oxygen valence-electron peak in any EDCs, although the latter would not be easily seen, if present, due to the large MnBi valence band contribution.
3. Summary Our angle-resolved photoelectron spectra, limited to the G–A line, are consistent with the calculated the calculated band structure, but with only two peaks along one line in the Brillouin zone, we cannot determine which of the different band structures is the most correct. Most of the observed spectrum originates from initial states with Mn 3d character. No clear statement can be made about the role of oxygen in the higher-energy peak in the Kerr-angle spectrum. We observed this peak from an essentially oxygen-free single crystal. The role of the oxide overlayer is not known in any detail, but it is more likely to alter the peak heights than to cause the occurrence of the 3.35-eV peak.
Acknowledgements We thank J.W. Anderegg for the Auger spectroscopy measurements and Prof. J. Ku¨bler for helpful correspondence. The Ames Laboratory is operated for the US Department of Energy by Iowa State University under contract No. W7405-Eng-82. This work was supported by the Director for Energy Research, Office of Basic Energy Science. The Synchrotron Radiation
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Center, University of Wisconsin-Madison, is supported by the NSF under Grant No. DMR0084402. References [1] C. Guillard, J. Phys. Radium 12 (1951) 223. [2] P.M. Oppeneer, in: K.H.J. Buschow (Ed.), Handbook of Magnetic Materials, Vol. 13, Elsevier, Amsterdam, 2001 (Chapter 3). [3] P.A. Albert, W.J. Carr, J. Appl. Phys. 32 (1961) 201S. [4] T. Hihara, Y. Koi, J. Phys. Soc. Japan 29 (1970) 343. [5] J. Schoenes, in: R.W. Cahn, P. Haasen, E.J. Kramer (Eds.), Materials Science and Technology, Vol. 3A, Part 1, VCH, Weinheim, 1992 (Chapter 2). [6] W. Reim, J. Schoenes, in: K.H.J. Buschow, E.P. Wohlfarth (Eds.), Ferromagnetic Materials, Vol. 5, Elsevier, Amsterdam, 1990 (Chapter 2). [7] E.T. Kulatov, A.G. Nargiznyan, Yu.A. Uspenskii, S.P. Khalilov, Kratk. Soobshch. Fiz. 26 (1995) 3 [Bull. Levedev Phys. Inst. 3 (1995) 22]. [8] R.F. Sabiryanov, S.S. Jaswal, Phys. Rev. B 53 (1996) 313. [9] P.M. Oppeneer, V.N. Antonov, T. Kraft, H. Eschrig, A.N. Yaresko, A.Ya. Perlov, J. Appl. Phys. 80 (1996) 1099. [10] J. Ko¨hler, J. Ku¨bler, J. Phys: Condens. Matter 8 (1996) 8681. [11] J. Ko¨hler, J. Ku¨bler, Physica B 402 (1997) 237. [12] P. Ravindran, A. Delin, P. James, B. Johansson, J.M. Wills, R. Ahuja, O. Eriksson, Phys. Rev. B 59 (1999) 15680. [13] G.Q. Di, S. Iwata, S. Tsunashima, S. Uchiyama, J. Magn. Magn. Mater. 1023 (1992) 104. [14] G.Q. Di, S. Uchiyama, Phys. Rev. B 53 (1996) 3327. [15] D. Huang, X.W. Zheng, C.P. Luo, H.S. Yang, Y.J. Wang, J. Appl. Phys. 75 (1993) 6351. [16] R. Coehoorn, R.A. de Groot, J. Phys. F: Met. Phys. 15 (1985) 2135. [17] K.-U. Harder, D. Menzel, T. Widmer, J. Schoenes, J. Appl. Phys. 84 (1998) 3625.
[18] J. Schoenes, K.-U. Harder, D. Menzel, T. Widmer, J. Magn. Soc. Japan 23 (1999) 95 quoted in [K.H.J. Buschow (Ed.), Handbook of Magnetic materials, Vol. 13, Elsevier, Amsterdam, 2001 (Chapter 3)]. [19] M. Kishimoto, K. Nakai, J. Appl. Phys. 48 (1977) 4640. [20] W.E. Stutius, T. Chen, T.R. Sandin, AIP Conference Proceedings, Vol. 18 (Part 2) (1974) 1226. [21] T. Chen, W. Stutius, IEEE Trans. Magn. 10 (1974) 581. [22] T. Chen, J. Crystal Growth 24/25 (1974) 454. [23] R.J. Lange, S.J. Lee, D.W. Lynch, P.C. Canfield, B.N. Harmon, S. Zollner, Phys. Rev. B 58 (1998) 351. [24] S.J. Lee, R.J. Lange, P.C. Canfield, B.N. Harmon, D.W. Lynch, Phys. Rev. B 61 (2000) 9669. [25] D. Chen, J.F. Ready, E. Bernal, J. Appl. Phys. 39 (1968) 3916. [26] H. Yoshida, T. Shinma, T. Takahashi, H. Fujimori, S. Abe, T. Kaneko, T. Kanomata, T. Suzuki, J. Alloys Compounds 297 (2001) 317. [27] R.F. Davis, R.S. Williams, S.D. Kevan, P.S. Wehner, D.A. Shirley, Phys. Rev. B 31 (1985) 1997. [28] C.G. Olson, Nucl. Instrum. Methods A 266 (1988) 205. [29] P. Fumagalli, Habilitationsschrift, Rheinisch-Westfa¨lisch Universita¨t, Aachen, 1996 (We do not have access to this reference, but have taken the curve from Fig. 7 of Ref. [12]). [30] S.J. Lee, K.J. Kim, P.C. Canfield, D.W. Lynch, J. Magn. Magn. Mater. 213 (2000) 312. [31] R.N. Iskenderov, I.A. Drabkin, L.T. Emel’Yanova, Ya.M. Ksendzov, Fiz. Tverd. Tela 10 (1968) 2573 [Sov. Phys. Solid State 10 (1969) 2031]. [32] D.R. Huffman, R.L. Wild, J. Shinmei, J. Chem. Phys. 50 (1969) 4092. [33] J.J. Yeh, I. Lindau, Atomic and Nuclear Data Tables, Vol. 32, 1985, p. 1. [34] J.W. Allen, in: R.Z. Bachrach (Ed.), Synchrotron Radiation Research—Advances in Surface and Interface Science, Vol. 1, Techniques, Plenum Press, New York, 1992 (Chapter 6). [35] B.N. Harmon, private communication.
Journal of Magnetism and Magnetic Materials 283 (2004) 95–102 www.elsevier.com/locate/jmmm
Magneto-optic spectrum and electronic structure of single-crystal MnBi D.P. Brammeier, J.-M. Park, C.G. Olson, I.R. Fisher1, D.W. Lynch a
Department of Physics and Astronomy and Ames Laboratory, USDOE, Iowa State University, Ames IA 50011, USA Received 12 February 2004; received in revised form 16 April 2004 Available online 9 June 2004
Abstract Single crystals of MnBi were used for magneto-optic Kerr-angle spectroscopy and photoelectron spectroscopy. The Kerr-angle peak at 3.35 eV was observed for our nearly oxygen-free bulk samples, but the role of the oxide overlayer, demonstrated by Auger spectroscopy, as a possible origin of this peak cannot fully be assessed. The energy bands from photoelectron spectroscopy were in general agreement with calculated band structures, but were not extensive enough, due to sample cleavage properties, to distinguish reliably between band-structure calculations that disagree. r 2004 Published by Elsevier B.V. PACS: 75.50; 78.20.L; 79.60 Keywords: Magneto-optics; Electronic structure; Photoelectron spectroscopy; MnBi; Kerr effect
MnBi is a ferromagnetic compound [1,2] used for magneto-optic recording in the form of amorphous films, often doped to reduce the Curie temperature. A great deal of work has been done on amorphous and polycrystalline films of MnBi, usually doped with Al, Si, Cr, or O, but little work has been done on single crystals. Single crystals are of less interest for magneto-optic recording, but Corresponding author. Tel.: +1-515-294-3476; fax: +1515-294-0689. E-mail address: [email protected] (D.W. Lynch). 1 Current address: Geballe Laboratory for Advanced Materials and Department of Applied Physics, Stanford University, Stanford CA 94305-4045, USA.
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are important for understanding the electronic structure of this material. Electronic structure calculations on spin-polarized MnBi, discussed below, do not agree in all details of the band structure and of the off-diagonal component of the optical interband conductivity, i.e., the magnetooptic polar Kerr-angle spectrum. Moreover, there is some disagreement about the number of peaks in the magneto-optic Kerr-angle spectrum in both theory and experiment, and why one of the peaks is or is not present. In the following we report on the flux growth of single crystals of MnBi, the Kerr-magneto-optic spectrum of a single crystal of MnBi, and some angle-resolved photoelectron
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spectroscopy for comparison with the bandstructure calculations. MnBi has the hexagonal NiAs (B8) structure, space group D46h (p63/mmc) below its Curie temperature of 633 K. The magnetic moments are oriented along the c-axis for temperatures above 84 K. Below this temperature, the moments lie in the basal plane [3,4]. The property of interest, the polar Kerr-angle spectrum [2,5,6], is obtained by analyzing the state of polarization of normally incident reflected light from a sample with magnetization normal to the sample surface. The reflected light is elliptically polarized, with the major axis of the ellipse at an angle YK , the Kerr angle, with respect to the polarization direction of the incident light. The ellipticity, eK , is the ratio of the minor to major axis lengths of the ellipse. tan YK and eK form a Kramers–Kro¨nig pair, and tan YK YK for nearly all magneto-optic materials. A hexagonal crystal magnetized along the c-axis has one offdiagonal component of the complex optical conductivity that plays a role in the reflection of light normally incident along the c-axis. This quantity can be calculated from the electronic structure and determined experimentally from the Kerr-spectrum, but it requires use of a diagonal component of the optical conductivity, which can be measured, usually by ellipsometry. Alternatively, the diagonal component of the conductivity can be obtained from electronic structure calculations and a calculated Kerr-angle spectrum used for comparison with experiment [2,5–12]. The optical and magneto-optical spectra have been measured several times on thin-film samples [2]. Usually these films were prepared by evaporation or sputtering several thin alternating layers of Mn and of Bi, often capped with a thin protective layer of SiO2, followed by annealing to produce single-phase MnBi. The most extensive study was by Di et al. [13,14]. Their measured Kerr-angle spectrum for MnBi has two peaks, at 1.84 and 3.35 eV, the former having the relatively large magnitude of 2.31 at 85 K, making MnBi of some interest for magneto-optic recording (although it has a number of disadvantages [2]). Kerr-angle spectra by Huang et al. [15] were on Al-doped films of MnBiSi. They showed two peaks of
slightly smaller amplitude shifted to higher energies from those of Di et al. The electronic band structure of MnBi has been calculated several times [7–12,16], but there is still disagreement about parts of the band structure. Oppeneer et al. [9] calculated the electronic structure of MnBi and the interband optical conductivity and Kerr-angle spectrum. They found a large negative peak at 1.8 eV, in agreement with experiment, and a shoulder around 3.4 eV, where experiment often has a peak. The peak magnitude could be fit to experiment, using a reasonable value for the broadening parameter. Since the data of Di et al. were taken on a sample with the composition Mn1.22Bi, Oppeneer et al. simulated this material and found a calculated Kerr-angle spectrum with a similar, but weaker, peak at 1.8 eV and a second peak at 4.3 eV, higher in energy than that for MnBi. These peaks all arose from Bi p-p transitions. They also calculated Kerr-angle spectra for MnAs and MnSb and MnBi doped with Al. They explained the large Kerr angles in MnBi, compared with those of MnSb and MnAs, as arising from the large magnetic moments on Mn and the large spin–orbit splitting on Bi. Sabiryanov and Jaswal [8] previously had calculated Kerr spectra for MnBi and several hypothetical MnBixAly compounds, finding the low-energy peak in all but MnBiAl, but a high-energy peak only in MnBi itself. Ko¨hler and Ku¨bler [10,11] calculated the band structure and the optical and magneto-optical spectra for MnBi, and MnBiX0.5 (X=Mn, Si, Al, O, Pt), and MnBiAl, MnBiPt, and MnBiAl0.5O0.5. The calculated Kerr-angle spectrum for MnBi had only one peak, the lower energy one. Under the hypothesis that the thin-film samples may have considerable impurities from materials in contact with them, they repeated the calculations using the elements labeled X above. They found that only O gave a second peak, but the energies of both peaks were not in good agreement with experiment. They assigned the low-energy peak in the Kerr spectrum to Bi pk-Mn dktransitions (k=minority spin). Ravindran et al. [12], on the other hand, did find a second peak in their calculated Kerr-angle spectrum for pure MnBi. They assigned both peaks to Bi pk-Mn dk transitions. They also
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calculated the bands, optical conductivity and magneto-optical spectra for MnSb and MnAs as an aid to understanding why the Kerr-angle peak is so large in MnBi, agreeing with the assessment of Oppeneer et al. Fig. 1 compiles some of the polar magneto-optic Kerr-angle spectra calculated to date. It is clear that the spectra from Ko¨hler and Ku¨bler and from Oppeneer et al. agree well, with one peak and shoulder, while that of Ravindran has two main peaks. The spectrum of Kulatov et al. [7], reported in the paper of Ravindran et al. [12], consists of a single peak at about 2.2 eV and a weak shoulder in the 3.0–3.2 eV region. One should note that the off-diagonal component of the conductivity is difficult to calculate accurately. Its magnitude is of the order of a percent of that of the diagonal component due to extensive cancellation of contributions of opposite sign. In order to clarify the role of oxygen in the Kerr spectrum, Harder et al. [17] made films similar to those of Di et al., but in ultra-high vacuum, to prevent, or at least reduce, oxygen incorporation in the films. They were made on two different substrates and capped with an SiO protective film. After correcting for the optical effect of the SiO overlayer they obtained a Kerr-angle spectrum with a single peak at 1.85 eV. The higher-energy peak, assigned to interstitial oxygen by Ko¨hler
Fig. 1. Calculated polar magneto-optic Kerr-angle spectra. Filled squares: Ref. [10]; stars: Ref. [9]; open circles: Ref. [7]; asterisks: Ref. [12].
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and Ku¨bler, was not present in this spectrum. Moreover, the magnitude of the low-energy peak was in better agreement with that calculated by Ko¨hler and Ku¨bler but its peak position remained at about 1.8 eV, although the calculated lowenergy peak shifted from 1.8 eV to about 1.0 eV upon going from MnBi to MnBiO0.5. It would seem that the high-energy peak is the result of oxygen in MnBi, but, according to the calculations of Ko¨hler and Ku¨bler, it must be considered a major constituent of the MnBi. Moreover, photoelectron spectroscopy on oxidized MnBi [18] later showed that the oxygen valence electrons appear 6 eV below the Fermi level, too low to contribute to the measured spectra. The calculations of Ko¨hler and Ku¨bler place them much nearer the Fermi level [10]. In the following we report the growth of single crystals of MnBi, polar magneto-optic Kerr spectra for comparison with the calculated spectra and those measured on thin films, and some photoelectron spectra for comparison with the existing band calculations. The single-crystal Kerr spectra should suffer less from the effects of impurities, except for oxygen from the atmosphere.
1. Experimental Single crystals were grown by slowly cooling a melt of 10 at% Mn and 90 at% Bi from 410 1C to 272 1C, at which temperature the excess Bi was decanted by centrifuging. Each growth process produced dozens of crystals, often in the form of hexagonal platelets or prisms. The largest had hexagon ‘‘diameters’’ of 1–2 mm. Longer growth times yielded taller prisms, but not prisms with larger basal-plane areas. The crystals were characterized by magnetic measurements using a commercial quantum design SQUID magnetometer. The magnetization was measured for fields applied parallel and perpendicular to the c-axis, both in a steady field as a function of temperature from 2 to 450 K, and as a function of field at constant temperature. The data were in agreement with literature values on microcrystals of MnBi [19] and single crystals [20–22] of MnBi.
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Kerr-magneto-optic spectra were measured on a spectrometer described elsewhere [23,24]. MnBi saturates magnetically in the 0001 direction at around 0.3 T at 300 K [25], where the measurements were taken. The sample was a natural face of an asgrown crystal. MnBi is considered air sensitive although Yoshida et al. [26] report purer MnBi is less air sensitive. We describe our surfaces further below. The spectra stop before the high-energy limit of the spectrometer, due to the small sample size and a reflectance that decreases with increasing photon energy. Both the Kerr angle and ellipticity spectra were measured. These, and the diagonal component of the complex optical conductivity, which can be obtained by ellipsometry, give the offdiagonal component of the optical conductivity, the interband contribution of which can be calculated from the electronic structure results. Here, however, we need only the Kerr-angle spectrum. For photoelectron spectroscopy (PES), the samples were epoxied to an Al stud, oriented by Laue back-reflection X-ray diffraction, mounted on a closed-cycle He refrigerator, then an Al post was epoxied on top. They were ‘‘cleaved’’ in situ at about 15–20 K under pressures below 4 10 11 Torr by pressure applied to the top post. All measurements were made under these conditions and no sign of sample surface deterioration was observed. The crystals, however, did not really cleave parallel to the expected (0 0 0 1) planes. The fracture was closer to conchoidal. However, angleresolved spectra taken with normally emitted (11 half-angle) electrons showed features dispersing with photon energy, despite a rather large background of scattered electrons. (Low-symmetry stepped surfaces have, in the past, yielded good normal-emission ARPES spectra [27].) Angleresolved PES spectra were taken on the Ames/ Montana beam line at the Synchrotron Radiation Center [28].
with three spectra from thin films. The singlecrystal spectrum shows peaks at 1.8 and 3.2 eV. The peak at 3.2 eV is probably an intrinsic peak, as the commonest impurity likely in the bulk crystal is excess Bi, while any oxygen present should be an oxide of Mn on the surface from post-growth exposure to air (see later). The peaks in the spectra of Di and Uchiyama [14], and of Huang et al. [15] are at slightly different energies and have larger amplitudes. The films of Huang et al. were of MnBiAl and MnBiAlSi, while those of Di and Uchiyama were made by annealing multilayers of Mn, Bi, and Al, then capped them with an overlayer of SiO2. The spectra reported in Ref. [14] were, however, corrected for the optical effects of this overlayer and should represent the spectrum of bulk MnBi. Fig. 2 also shows data from Fumigalli, taken on a film of MnBi [29]. The range in magnitude of the different Kerrangle spectra is difficult to explain. Our data were taken in an applied magnetic field that produced about 62% of the saturation magnetization. Di and Uchiyama’s spectrum apparently was taken with no applied field, i.e., with the residual magnetization, of the order of 90% of the saturation [19–21], or in an applied field yielding saturation. Since the Kerr spectrum amplitude is linear in the magnetization, our spectrum should
2. Results 2.1. Magneto-optic Kerr spectra Fig. 2 shows our measured polar magneto-optic Kerr-angle spectrum of single-crystal MnBi along
Fig. 2. Measured polar magneto-optic Kerr-angle spectra. Solid squares: Refs. [13,14]; stars: Ref. [15]; open circles: Ref. [29]; open squares: present work.
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be smaller than Di’s by a factor of 0.62–0.69. However, Di and Uchiyama corrected their measured spectrum for the effect of the SiO2 overlayer used to protect his film, an effect that increases the magnitude of the true spectrum above that of the spectrum measured with the overlayer. We have previously modeled such an effect for GdCo2 [30], finding that a correction for ( of a transparent overlayer increases the 200 A amplitude of YK by a factor of about 1.5 at a peak, and by an even larger factor if the overlayer is absorbing. If such a correction applies to our MnBi data after correcting for the magnetization difference just described, the amplitude of our spectrum becomes larger than that of Di and Uchiyama. The energies of the peaks in our Kerr spectrum are close to those of Di et al. and of Fumagalli. The position of the low-energy peak agrees with that calculated [9–12], but the high-energy peak does not appear in the calculated spectra for stoichiometric MnBi of Oppeneer et al. [9] and of Ko¨hler and Ku¨bler [10,11]. The high-energy peak does appear in the calculated spectrum of Ravindran et al. [12], but its energy is considerably lower than the observed energy. This peak appears at about the right strength and energy in the calculations for non-stoichiometric MnBi, with a large excess of Mn or O [10,11], i.e., MnBiMn0.5 and MnBiO0.5. Single-crystal surfaces similar to those used in the Kerr-angle spectra were studied by Auger microscopy. They were exposed to the air for about 90–120 min before introduction into the microscope vacuum, about half the duration of the magneto-optic spectroscopy. The as-grown surfaces were not only MnBi; there were small, often circular, regions of Bi left from the growth process. These covered up to 50% of the surface area. Since they contribute to the reflectance, but not to its magnetic-field dependence, they do not alter noticeably the shape of the Kerr-angle spectra, but they do reduce its magnitude. Thus the magnitude of our single-crystal Kerr spectrum, about the same as that from polycrystalline or amorphous films, should actually be larger because of this effect. Surface regions outside the Bi islands were sputtered while Auger spectral peaks from
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Mn, Bi, and O were monitored. These initial surfaces contained mostly Mn and O, with small amounts of Bi. As sputtering progressed the O peak diminished, the Bi peak grew, and the Mn peak remained constant or grew some. After about ( had been removed, the O peak had 100–200 A fallen to a smaller, steady value (it overlapped a contribution from Bi, so the O concentration cannot be shown to be zero), and the Bi and Mn peaks had risen to steady values, indicating the bulk had been reached. The crystals were too small for XPS spectroscopy between Bi islands, so the oxidation state of the Mn in the overlayer could not be determined. The difficulty with describing the surface layer primarily as an oxide of Mn, of composition depending on depth, on top of bulk MnBi is the fact that no maximum in the Bi concentration vs. depth appeared. The Mn in MnBi that oxidized appeared not to have left surplus Bi localized enough to be detected. A thin overlayer of any non-ferromagnetic oxide should alter the magnitude of the Kerr spectrum, but not its shape. Antiferromagnetic MnO would not contribute a feature to the Kerr spectrum where it is transparent, but in the spectral range above its band gap, 3.8 eV [31,32], its absorption could affect the shape, not just the magnitude, of the Kerr spectrum. A film of ferromagnetic Mn2O3 could contribute structure directly to the Kerr spectrum, as well as alter that of the MnBi below due to its strong absorption, both at energies above its band gap, but it is less likely to be a major constituent of the film due to limited oxygen supply below the outermost few surface layers. It seems unlikely to be the cause of the peak at 3.35 eV in the Kerr-angle spectrum. 2.2. Photoelectron spectra Fig. 3 shows electron energy distribution curves (EDCs) taken at photon energies of 20, 28, and 85 eV. The latter should be nearly free of dipole matrix element effects and should resemble the density of states (DOS), except for the relative strengths of the Mn 3d and Bi 6p contributions, which have different photoexcitation cross sections [33]. Both calculated and measured DOS show a step at the Fermi level, indicating a metallic
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Fig. 4. Electron energy distribution curves of MnB taken below and in the Mn 3p resonance region. The broad peak marked with a vertical line is the Mn MVV Auger peak.
Fig. 3. Electron energy distribution curves of MnBi at three different photon energies.
sample. Both have their major peak at around 2.75 eV, but the measured spectrum extends to 12.5 eV below the Fermi level, further than the calculated 7 eV. The band calculations indicate that the Mn 3d states dominate all other contributions to the occupied part of the DOS in the 0–7 eV range of binding energies. Resonant PES on the Mn 3p core level can emphasize the 3d states in the spectra. See, for example, Ref. [34]. Fig. 4 shows EDCs taken with a photon energy of 45 eV (below the Mn 3p–3d resonance starting at 47 eV), and three EDCs taken in the broad resonance. The broad peaks with tick marks are Mn MVV Auger peaks and can be ignored here. These spectra indicate considerable Mn 3d character throughout the entire valence band. Constant initial-state (CIS)
spectra for valence-band initial states at 0.5, 2.5, 5.5, and 10.5 eV all show the Fano line shape characteristic of Mn 3p–3d resonance origin, hence of significant Mn 3d character at these four binding energies. The enhancement at 0.5 eV binding energy is less than that at the other three energies, implying less Mn 3d character at 0.5 eV than at higher binding energy. The largest enhancement is at 2.5 eV, as expected from the calculated partial DOS. At higher binding energies, the resonant enhancement falls off less slowly than the calculated Mn 3d partial DOS would lead one to expect. Normal emission EDCs at a number of photon energies show three structures, at the Fermi edge, around 0.9 eV binding energy, and at 2.75 eV binding energy. In addition, as the photon energy increases, the amplitude of the entire spectrum for binding energies greater than about 2 eV grows with respect to the part at lower binding energies. This is due to the effect of the photoexcitation cross sections for initial states based primarily on Mn 3d states (binding energy larger than 2 eV) and initial states based mainly on Bi 6p states (less than
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2 eV). The Mn 3d cross section grows monotonically with photon energy in the range used, while that for Bi 6p states decreases [33]. The 2.75-eV peak disperses very little, although the shape changes with photon energy. The lack of dispersion is common with 3d bands that are not strongly hybridized, and, although one can see a number of such flat Mn 3d-based bands around 2.75 eV in the calculated bands, the calculated bands along the kz-axis of the Brillouin zone do, in fact, disperse enough to allow one to state that the expected dispersion of the calculated band is not seen in the experimental EDC. The changes in shape with photon energy can be assigned to dipole photoexcitation matrix element effects from the initial-state band, or several overlapping initial-state bands. When there are several overlapping initial state bands, this effect can cause the apparent lack of dispersion. Electron correlation effects tend to flatten bands, and they may play a role in the reduction of the ‘‘expected’’ dispersion in this peak. The peak at 0.9 eV disperses about 300 meV. The inflection points as the photon energy varies represent initial-state band maxima and minima along the z-axis of the Brillouin zone, i.e., the G and A points. An inner potential of 14 eV places this peak at the A symmetry point, with a binding energy of 1.0 eV, when the photon energy is 16 eV. This band is primarily of Bi 6p character, based on the photon-energy dependence of its contribution to the EDC, just discussed, and on the CIS spectra. The Fermi-edge peak changes shape with photon energy, probably indicating bands crossing the Fermi level. With a 14-eV inner potential, the Fermi level peak at the G point should occur at a photon energy of 15 and 26.5 eV, and the latter is observed in the EDCs very near EF at 26 and 27 eV photon energy. The relative intensity in this spectral region does not decrease monotonically with increasing photon energy, suggesting it originates from a band with dominant Mn 3d character. Most of the Mn 3d minority-spin bands lie above EF, but the band calculations show some Mn 3d contribution just below EF. The photoelectron spectra were measured at about 20 K with no applied field. The magnetic moments were in the basal plane. The calculations
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were done with the moments parallel to the c-axis. The difference in electronic structure for the two orientations of the magnetism should, however, be small on the energy scale of our spectra [35]. Some cleaves gave regions with EDCs that showed far more dispersion than those of MnBi. Core-level spectra taken on these showed only Bi peaks. Evidently some of the cleaves took place exposing Bi inclusions from the flux growth, and these inclusions were epitaxial with the MnBi. They contributed nothing to the Laue reflection patterns taken after completion of the spectra. There was no evidence of oxygen on or just below our cleaved surfaces, no detectable O 1 s photoemission and no 6 eV oxygen valence-electron peak in any EDCs, although the latter would not be easily seen, if present, due to the large MnBi valence band contribution.
3. Summary Our angle-resolved photoelectron spectra, limited to the G–A line, are consistent with the calculated the calculated band structure, but with only two peaks along one line in the Brillouin zone, we cannot determine which of the different band structures is the most correct. Most of the observed spectrum originates from initial states with Mn 3d character. No clear statement can be made about the role of oxygen in the higher-energy peak in the Kerr-angle spectrum. We observed this peak from an essentially oxygen-free single crystal. The role of the oxide overlayer is not known in any detail, but it is more likely to alter the peak heights than to cause the occurrence of the 3.35-eV peak.
Acknowledgements We thank J.W. Anderegg for the Auger spectroscopy measurements and Prof. J. Ku¨bler for helpful correspondence. The Ames Laboratory is operated for the US Department of Energy by Iowa State University under contract No. W7405-Eng-82. This work was supported by the Director for Energy Research, Office of Basic Energy Science. The Synchrotron Radiation
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