APPLIED PHYSICS LETTERS
VOLUME 82, NUMBER 17
28 APRIL 2003
Prediction of large polar Kerr rotation in the Heusler-related alloys
AuMnSb and AuMnSn
Laila Offernes, P. Ravindran, and A. Kjekshusa)
Department of Chemistry, University of Oslo, Box 1033, Blindern, N-0315, Oslo, Norway
共Received 4 November 2002; accepted 27 February 2003兲
Theoretical spectra for the magneto-optical Kerr effect have been obtained for the Heusler-related
alloys AuMnSb and AuMnSn, and repeated calculations are performed for the isostructural PtMnSb
phase. Using experimental lattice constants, our calculations predict a Kerr rotation exceeding ⫺1°
in the 0.5–0.8 eV region for AuMnSb and a somewhat smaller rotation for AuMnSn. Supercell
calculations indicate that half-metallic behavior can be induced on hole/electron doping in the
AuMnSn1⫺x Sbx solid-solution phase for 0.50⬍x⬍0.75. © 2003 American Institute of Physics.
关DOI: 10.1063/1.1569425兴
Recently attention has been paid to soft ferromagnetic,
Mn-based, Heusler-related alloys with the general formula
TMnX (T⫽transition metal,X⫽Sb,Sn). These alloys are
found to exhibit interesting magneto-optical 共MO兲 properties, like the magneto-optical Kerr effect 共MOKE兲, important
in MO recording technology. MOKE is observed when linearly polarized light is reflected from a magnetized material.
After reflection, MOKE is observed as the rotation of the
polarization plane by the Kerr angle, ␪ K . The reflected light
is also elliptically polarized, defining the Kerr ellipticity by
an angle, ␩ K . In most technological applications MOKE is
used in the so-called polar geometry, in which the incident
light and magnetization direction are oriented perpendicular
to the plane of the magnetized surface. In this geometry, the
Kerr effect is given by
⫺ ␴ xy
␪ K ⫹i ␩ K ⫽
␴ xx
冑
1⫹
4␲i
␻
,
共1兲
␴ xx
where ␴ xx and ␴ xy are the diagonal and off-diagonal component of the optical conductivity, respectively. The sign convention is chosen so that ␪ K is positive for a clockwise rotation of the polarization ellipse, as viewed from the direction
of the incoming beam. The sign, which is directly related to
the magnetization direction, is important for applications,
since small magnetic domains can be read optically and interpreted as binary numbers.
One of the Heusler-related phases, PtMnSb, is regarded
as a potential MO recording material and is studied extensively both experimentally1–5 and theoretically.6 –9 The exceptionally large 共for 3d phases兲 Kerr rotation angle of
PtMnSb is around ⫺2° at 1.7 eV and room temperature
共almost ⫺5° at 80 K兲.3,4,10 PtMnSb has been classified as a
half-metallic ferromagnetic 共HMF兲 material,6 viz. metallic
behavior for the majority-spin channel and a semiconductorlike gap at the Fermi level (E F ) for the minority-spin channel. In such materials, the conduction electrons should theoretically be 100% spin polarized at E F . Highly spina兲
Electronic mail: arne.kjekshus@kjemi.uio.no
polarized materials, like the HMFs, are incorporated in
magnetic multilayers, so-called spin valves. Due to the spin
dependent scattering of electrons the spin valves exhibit giant magnetoresistance and are used in magnetic recording
technology.11
To ease the continuing search for good MO materials a
set of guide lines has been set forward. 共i兲 One of the constituting elements should have a large magnetic moment
共e.g., Cr, Mn, or Fe兲. 共ii兲 Another constituting element should
be heavy 共e.g., Pt, Au, or Bi兲 in order to exhibit large spinorbit 共SO兲 coupling. 共iii兲 There should be a strong hybridization between orbitals of the elements of type i and ii.12
Through the hybridization the SO-split bands become spin
polarized, giving rise to MO-active transitions. PtMnSb
clearly fulfills these criteria. Suitable MO materials must also
meet several other requirements, e.g., have sufficiently large
reflectivity, Curie temperature (T C ) appropriate for thermomagnetic writing, and magnetic anisotropy favoring an orientation of the magnetization direction perpendicular to the
MO disk plane. Cubic PtMnSb lacks magnetic anisotropy,
but this phase still remains attractive as a possible soft ferromagnetic material in multilayer structures.13
This report primarily concerns the calculated Kerr rotation spectra for AuMnSb and AuMnSn including both interand intraband contributions, but in order to facilitate comparison with earlier studies calculations have also been repeated for PtMnSb.
The crystal structure of these Heusler-related alloys are
of the cubic AlLiSi-type; space group F4̄3m with T in 4c,
Mn in 4b, and X in 4a. 14 Compared with the Cu2 MnAl-type
structure of the proper Heusler alloys, one of the four interpenetrating fcc lattices of the latter type is empty in the
Heusler-related variant. An effect of this unoccupied site is to
reduce the degree of overlap between the wave functions,
and subsequently giving rise to narrower bands, enhanced
moments, and appearance of gaps in the density of states
共DOS兲.15 The Heusler-related-type structure easily allows for
structural disorder, either by the occurrence of vacancies,
interchange of atoms or partial addition of atoms to the 4d
site. The phases subject to this study have narrow composition ranges at 400 °C, apparently excluding the exact 1:1:1
composition.16,17 Experimental lattice parameters used in the
0003-6951/2003/82(17)/2862/3/$20.00
2862
© 2003 American Institute of Physics
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Appl. Phys. Lett., Vol. 82, No. 17, 28 April 2003
Offernes, Ravindran, and Kjekshus
2863
TABLE I. Experimental lattice parameters, magnetic moments, and Curie
temperatures for PtMnSb 共see Ref. 1兲, AuMnSn 共see Ref. 14兲, and AuMnSb
共see Ref. 17兲. Calculated magnetic moments, using the FPLMTO method,
and unscreened plasma frequency ( ␻ P ), using the FLAPW method.
Exp. a 共pm兲
Exp. ␮ F ( ␮ B /Mn)
Exp. T C 共K兲
Calc. ␮ F ( ␮ B /f.u.)
Calc. ␻ P 共eV兲
a
PtMnSb
AuMnSb
AuMnSn
620.1
4.1
582
4.050
4.01
637.9
4.2
135
4.555
3.18
634.1
3.8
⬃740a
4.089
4.63
Upper stability limit of AuMnSn.
present study and magnetic moments for the phases under
consideration are listed in Table I.
The electronic structure calculations are performed
within the framework of the generalized gradient corrected
fully relativistic full-potential density-functional theory. The
full potential linear muffin-tin orbital 共FPLMTO兲
calculations18 are all-electron, and no shape approximation to
the charge density or the potential has been used. Spin-orbit
terms are included directly in the Hamiltonian matrix elements for the part inside the muffin-tin spheres. The direction
of the moment was chosen perpendicular to the basal plane
共viz. along 关001兴兲. The self consistency was obtained with
440 irreducible k points in the whole Brillouin zone and
1468 k points for the optical as well as MO calculations. The
plasma frequency ( ␻ P ) used for the estimation of intraband
contributions to the optical conductivity has been derived by
the full potential linearized augmented plane wave method
共FLAPW兲 using the WIEN97 code.19 We have used well converged basis sets. More details about the computations will
be given elsewhere.20 Calculated ␻ P values are given in
Table I. The damping parameters used in the calculations of
the intraband contribution for PtMnSb were chosen by fitting
to the experimental curves and the thus derived parameter
values were used in the calculations for AuMnSb and
AuMnSn.
In agreement with earlier investigations9 our tightbinding linear muffin-tin orbital calculations show full halfmetallic behavior for PtMnSb, whereas the more accurate
full-potential methods reveal finite 共but very small兲 DOS values in the band-gap region for both spin channels. The
FPLMTO calculated total DOSs for PtMnSb, AuMnSb, and
AuMnSn are depicted in Fig. 1. The FPLMTO calculated
magnetic moments are in good agreement with experimental
values 共Table I兲, and the main contribution to the moments
comes from the Mn atoms, as expected.
The band structures of the three phases are strikingly
similar with deep valleys or pseudogaps, indicating strong
hybridization, characteristics of covalent bonding, and poor
ductility.15 For all three phases a gap in DOS appears in the
minority-spin direction in the vicinity of the Fermi level, for
AuMnSb just below E F and for AuMnSn and PtMnSb just
above E F ; for all owing to large exchange splitting from the
Mn atoms. The gaps in DOS for AuMnSb and AuMnSn are
narrower than in PtMnSb 共0.27 and 0.24 vs 0.84 eV兲. The
band structures for both the gold phases are very similar, and
it should accordingly, as a reasonable first approximation, be
justified to treat mutual exchange of Sb and Sn atoms within
the rigid-band approximation. Since there is a complete solid
FIG. 1. Calculated 共according to the FPLMTO method兲 total DOS for
PtMnSb, AuMnSb, and AuMnSn. The calculated DOS at E F 共in states
f.u.⫺1 eV⫺1 ) is 0.10, 0.81, and 0.22 for minority and 0.80, 0.36, and 0.60 for
majority spin channel of PtMnSb, AuMnSb, and AuMnSn, respectively.
solubility between AuMnSb and AuMnSn,17 a range of HMF
materials is likely to appear within the AuMnSb1⫺x Snx
solid-solution series. Supercell calculations for x⫽0.25,
0.50, and 0.75 suggest a range of possible HMF materials for
0.50⬍x⬍0.75 共rigid-band considerations give a slightly
wider range兲.
The calculated Kerr rotation profile for PtMnSb is shown
in Fig. 2, together with earlier calculated7–9 and
experimental2–5 spectra. On considering experimental Kerr
rotation spectra it should be remembered that sampledependent effects may significantly influence the spectral
features. Peak positions appears to be rather sensitive to
composition parameters 共stoichiometry, homogeneity, impurities, etc.兲,21 whereas the magnitude of the peaks depends on
the sample preparation, in particular the annealing.4 Surface
effects may in certain cases play a major role.
The calculated spectra for PtMnSb 共Fig. 2兲 reproduce the
magnitude and shape of the experimental curves rather well,
but the calculated profiles are shifted relative to the experimental profiles. This may be due to the choice of an idealized
1:1:1 composition for the calculations. Peak positions are
also sensitive to ␻ P , which in turn is directly related to the
FIG. 2. Calculated 共from FPLMTO兲 polar Kerr rotation spectrum for
PtMnSb. Earlier experimental and calculated spectra are included for comparison. 共Note the effect of annealing, open vs filled circles; legends on the
illustration; references in parentheses.兲
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2864
Appl. Phys. Lett., Vol. 82, No. 17, 28 April 2003
FIG. 3. Calculated 共from FPLMTO兲 polar Kerr rotation 共solid line兲 and
ellipticity 共dotted line兲 spectra for AuMnSb and AuMnSn.
number of electrons at E F . This implies that impurities
共which are indirectly related to ␻ P ) may have a major effect
on the peak positions in experimental spectra. It should be
noted that a free-electron-like approach has been used to estimate the intraband contributions 共at 0 K兲 and broadening to
account for temperature effects, and this may also cause distinctions between the theoretical and experimental spectra.
Moreover, the usual density-functional-theory approach does
not take into account correlation effects properly, and this
may also give rise to shifts in calculated peak positions.22
The Kerr rotation and ellipticity spectra of AuMnSb and
AuMnSn are given in Fig. 3. The shape of the Kerr rotation
spectrum for AuMnSb resembles that of PtMnSb with one
dominant peak, while the AuMnSn spectrum exhibits two,
but less prominent peaks. The predicted Kerr rotation is
around ⫺1.2° at 0.6 eV for AuMnSb and around ⫺0.7° and
⫺0.3° at 1.2 and 2.4 eV, respectively, for AuMnSn. The
calculated maximum Kerr rotation for AuMnSb is about
twice as large as for pure Co and Fe.23 Previous
measurements5 indicate that the Kerr rotation profile changes
continuously with composition within a solid-solution series,
implying that the Kerr rotation characteristics may be tailored
within
series
like
AuMnSn1⫺x Sbx 17
or
24
Pt1⫺x Aux MnSb. The T C of AuMnSb 共see Table I兲 is far too
low for thermomagnetic writing, but T C changes smoothly
with x in AuMnSn1⫺x Sbx 17 共for AuMnSn above its upper
stability limit of 740 K兲 and should be optimal for such a
purpose at certain values of x. However, the lacking anisotropy for these cubic phases still remains as a challenge. It
should be emphasized that the debate on as to what extent
the half-metallic behavior of PtMnSb directly or indirectly is
responsible for its unique MO properties is not yet
concluded.9 It would therefore be of considerable interest to
explore the MO properties of thin films of AuMnSn1⫺x Sbx to
verify if the phase actually passes from a normal ferromagnetic metal to an HMF and back to a normal ferromagnet
again as function of x.
In order to get insight into the origin of the peaks
in the Kerr rotation spectra the separate contributions
Offernes, Ravindran, and Kjekshus
from the diagonal and off-diagonal parts of the optical
conductivity tensor has been derived as Re(⫺␴xy) and
Re(D)⫺1 兵 D⬅ ␴ xx 关 1⫹(4 ␲ i/ ␻ ) ␴ xx 兴 1/2其 ; see Eq. 共1兲. Diagonal as well as off-diagonal elements contribute to these peaks
for PtMnSb and AuMnSb. The large calculated ␪ K for PtMnSb at 1.17 eV appears because the maximum in the offdiagonal tensor element coincides with a peak in Re(D)⫺1 at
this energy. The less prominent Kerr rotation peak for
AuMnSb is caused by a slight relative displacement of the
maxima in absolute values for Re(⫺␴xy) and Re(D)⫺1 around
␪ K . The relative contributions to ␪ K for AuMnSn 共with two,
less pronounced peaks; Fig. 3兲 is less obvious.
To summarize, the prediction of a maximum Kerr rotation for AuMnSb and AuMnSn of some ⫺1° makes these
phases and, in particular, the solid solution between them,
interesting for MO recording applications.
L.O. and P.R. appreciate the financial support from the
Research Council of Norway. Part of these calculations were
carried out on the Norwegian supercomputer facilities.
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