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7-1998

Ellipsometric and Kerr-effect studies of Pt3−X

(X=Mn,Co)

R. J. Lange

Iowa State University

S. J. Lee

Iowa State University

David W. Lynch

Iowa State University, [email protected]

Paul C. Canfield

Iowa State University, [email protected]

Bruce N. Harmon

Iowa State University, [email protected]

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Ellipsometric and Kerr-effect studies of Pt3−X (X=Mn,Co)

Abstract

The conductivity tensor of polycrystalline Pt3X (X=Mn,Co) was determined between 1.6 and 5.2 eV. Samples

were arc melted, mechanically polished, and annealed at 500°C for 1 h in Ar. The complex dielectric function

was measured from 1.3 to 5.2 eV at room temperature with a rotating analyzer ellipsometer. The

magneto-optic Kerr effect was studied between 10 and 293 K in magnetic fields up to 3 T. We used the tight-binding

linear-muffin-tin-orbital method in the local spin-density approximation to determine the band structure,

density of states, and optical conductivity. Including an empirical quasiparticle self-energy and a lifetime

broadening yields good agreement of experimental and calculated spectra.

Keywords

Ames Laboratory, conductivity tensor, rotating analyzer ellipsometer

Disciplines

Atomic, Molecular and Optical Physics | Condensed Matter Physics | Physics

Comments

This article is from

Physical Review B

58 (1998): 351, doi:

10.1103/PhysRevB.58.351

. Posted with permission.

Authors

R. J. Lange, S. J. Lee, David W. Lynch, Paul C. Canfield, Bruce N. Harmon, and S. Zollner

Ellipsometric and Kerr-effect studies of Pt

₃

-X

_„

X

5

Mn,Co

_…

R. J. Lange, S. J. Lee, D. W. Lynch, P. C. Canfield, B. N. Harmon, and S. Zollner*

Ames Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011

~Received 5 August 1997; revised manuscript received 3 November 1997!

The conductivity tensor of polycrystalline Pt3X (X5Mn, Co) was determined between 1.6 and 5.2 eV.

Samples were arc melted, mechanically polished, and annealed at 500 °C for 1 h in Ar. The complex dielectric function was measured from 1.3 to 5.2 eV at room temperature with a rotating analyzer ellipsometer. The magneto-optic Kerr effect was studied between 10 and 293 K in magnetic fields up to 3 T. We used the tight-binding linear-muffin-tin-orbital method in the local spin-density approximation to determine the band structure, density of states, and optical conductivity. Including an empirical quasiparticle self-energy and a lifetime broadening yields good agreement of experimental and calculated spectra.@S0163-1829~98!07625-5#

I. INTRODUCTION

Transition metal compounds containing Pt show interest-ing magnetic properties and have attracted much interest over the past years.1–7 A large magneto-optic Kerr effect

~MOKE!, good readout performance, and high chemical sta-bility make those compounds superior to other materials used in magneto-optical recording. In order to gain a better understanding of the MOKE in Pt based materials we studied Pt₃-transition metal compounds which order in the simple cubic Cu3Au phase. These prototypical materials have a

simple crystal structure and are more amenable to analysis using first principles electronic structure methods than are materials containing rare earth elements whose 4 f electronic states are too strongly correlated for the usual local density approximation ~LDA!.8

Magneto-optic investigations of bulk Pt3Mn were made

by Buschow et al.4 who measured zero Kerr rotation and ellipticity at 633 and 830 nm at room temperature. Kato

et al.5measured the MOKE of Pt₃Mn alloy films and found a maximum rotation of 21.18° at 1.2 eV~1 mm!. No infor-mation on temperature or magnetic field was given. Mea-surements were made through the glass substrate which gives an enhancement of the MOKE of the order of the re-fractive index of the substrate.6,9 Another group measured the polar Kerr effect of Pt3Mn in an applied magnetic field of

8 T and observed a maximum rotation of20.55° at 1.2 eV.6 More recently Wierman and co-workers7 measured the di-electric function and MOKE of Pt3Mn films deposited on

quartz using magnetron sputtering. A maximum of over

22.5° at 1.4 eV at 95 K was obtained. However, the samples have a protective SiOxoverlayer and the intrinsic Kerr effect

of the film can only be obtained from the measured values after data reduction. In the review article by Buschow et al.4 experimental data for polycrystalline Pt3Co were also

pre-sented. A maximum Kerr roation of 20.65° was found at 4.4 eV. Pt1₂xCox alloy films near the 3:1 composition were

measured by Weller and co-workers10–12 at room tempera-ture. They found a decrease in amplitude of the Kerr signal after annealing the sample. However, a direct comparison with our results is difficult since the data presented by Weller

et al.10–12are for a Pt78Co22film deposited on sapphire and

may not represent the properties of bulk Pt3Co.

First principles calculations have been performed to gain an understanding of the origin of the large Kerr effect in 3d transition metal compounds. Oppeneer et al.9,13 used aug-mented spherical waves ~ASW! and the fully relativistic linear-muffin-tin-orbital ~LMTO! method to calculate the Kerr spectra of Pt3X ~where X5V, Cr, Mn, Fe, and Co!.

Orbital and spin magnetic moments of the same group of compounds were obtained from full potential linear aug-mented plane wave ~FPLAPW! calculations by Iwashita

et al.14The magnetic moments calculated with the FPLAPW method agree with those obtained by Maruyama et al.15 us-ing x-ray dichroism and neutron data presented by Booth.16 Tohyama et al.17 used a spin-polarized self-consistent tight-binding scheme to calculate the band structure and magnetic moments of Pt3X. The results obtained for the magnetic

mo-ments agree with those found earlier in polarized neutron experiments.18–20However, their calculations did not predict the correct magnetic ordering for Pt3Mn and Pt3Co.

Accord-ing to their results the lowest energy configuration for those two compounds is the antiferromagnetic phase whereas it is known that the Mn and Co compounds order ferro-magnetically.19–21Recently a theoretical study was published by Kulatov et al. using the FPLMTO scheme to calculate the spin, orbital moments, and magneto-optical properties of Pt3

transition metal compounds.22

In this work we will present MOKE spectra at low tem-peratures. We also use the tight-binding, relativistic, LMTO

~TB-LMTO! scheme to calculate the charge density, mag-netic moments, density of states ~DOS!, and band structure of Pt3 transition metal compounds. We will show that the

TB-LMTO is capable of explaining the measured Kerr spec-tra and even the fine structure is reproduced.

II. EXPERIMENT

A. Sample preparation and characterization

Pt₃X samples were arc-melted under an Ar atmosphere.

Before arc-melting the chamber is purged to 20 mT and backfilled with ultra-high-purity argon ~99.9995%!to about 0.75 atm five times. A Zr button is used to getter the atmo-sphere during the arc-melting process. After a

homogeniza-PHYSICAL REVIEW B VOLUME 58, NUMBER 1 1 JULY 1998-I

PRB 58

tion anneal at 500 °C for 72 h for Pt₃Mn and at 600 °C for 500 h for Pt3Co the ingots were cut in thin disks with a

diameter of 3–5 mm and mechanically polished with alu-mina powder. To achieve surface reconstruction without Pt segregation at the surface the samples were annealed for 1 h at 500 °C. Figure 1 shows the effect of annealing on the dielectric function~a!and the magneto-optic Kerr effect~b!. Although the dielectric constant is increased by only a few percent there is a drastic change in the Kerr spectra. An increase of the dielectric function indicates a higher surface quality. However, so far we do not understand the increased Kerr effect, although magnetic properties at surfaces can be different from the bulk and sensitive to details in structure.

In order to determine the stochiometry of the samples x-ray diffraction was used and the lattice parameter of the samples was fit. The obtained lattice constants were 3.910 and 3.857 Å for Pt3Mn and Pt3Co, respectively, which are in

excellent agreement with earlier results.1Pt3X crystallizes in

the simple cubic~sc!Cu3Au (L12) structure with four atoms

per unit cell ~point group Oh). In this structure

order-disorder transitions are common. At around 600 °C Cu3Au

undergoes a first order phase transition to a disordered phase in which all fcc sites are randomly occupied. Therefore we may use x-ray diffraction to confirm the ordered Cu3Au

structure. For a fcc structure the first peak observed in a 2u scan originates from ~111! reflections. After the annealing process we also observed ~100!, ~110!, etc., peaks which were not found in the fcc lattice structure. For Pt3Mn we can

identify the sc structure from the x-ray spectra. In the case of Pt3Co the peak intensities do not match those expected for

the sc lattice although all the peaks expected for the sc struc-ture were present. This may indicate a strucstruc-ture between sc

and fcc for this sample. Also this may be due to partial alignment in the sample which is rather unlikely in a cubic crystal structure.

Pt3Mn and Pt3Co in the ordered L12 phase are known to

be ferromagnets with Curie temperatures (T_C) of 460 and 288 K, respectively.1 In Pt3Mn disorder destroys the

ferro-magnetism whereas T_Cof Pt₃Co varies between 288 K in the ordered and 468 K in the disordered phase.21This enables us to use magnetization measurements to determine the order-ing of the sample. Table I shows the magnetic moments at the transition metal and Pt site obtained by TB-LMTO and magnetization measurements and also includes results from other groups. Polarized neutron experiments showed a mag-netic moment of (0.1760.04)mB on the Pt site and ~3.60 60.09!mB at the Mn atoms in Pt3Mn.

18,19

For Pt3Co a

slightly larger moment of (0.2660.02)mB at the Pt site and

(1.6460.04)m_B for the Co site were found.20 Theoretical investigation of the orbital and spin magnetic moments by Iwashita et al.14agree with the observations made in neutron experiments. We calculated the magnetic moments of both compounds and the moments obtained compare well with previous experimental and theoretical results ~Table I!. The major contribution to the total magnetic moment is due to spin polarization on the transition metal site whereas the or-bital moment of the 3d elements is quenched except for a small but essential amount arising from spin-orbit coupling. In ferromagnetic materials the MOKE is proportional to the net magnetization rather than the applied magnetic field. The net spin polarization is therefore a crucial factor determining the absolute magnitude of the Kerr effect.

Magnetization measurements on our polycrystalline sample at 10 K indicated a saturation magnetization of 3.92m_B/f.u. for Pt₃Mn in satisfactory agreement with the value 3.9mBfor the ordered Pt3Mn phase which can be

esti-mated from measurements published by Auwa¨rter and Kussmann.23 Figures 2 and 3 show magnetization data ob-tained for the Pt3Co sample. Data at 10 K were obtained after

cooling the sample from 395 K in zero field. Saturation is reached in an external field of 1 T. At 10 K the measurement yields a total magnetic moment of 2.80mB which is higher

[image:4.612.82.270.55.291.2]

than the total moment of 2.42mB estimated from neutron

FIG. 1. Dielectric function~a!and Kerr effect~b!in Pt3Co

be-fore and after annealing at 500° C for 1 h.~a!shows the dielectric function before ~dotted line! and after ~solid line! the annealing process.~b!s andh show the Kerr ellipticityeKand rotationQK before annealing, respectively. The spectra obtained after annealing the sample are shown withd,j.

TABLE I. Magnetic moments inmB/f.u. on the Pt and transition metal site for Pt3X (X5Mn, Co).

X mPt mX mtot

Mn 0.1760.04 3.6060.09 4.1160.21~Ref. 18! 0.1260.03 3.6860.08 4.0460.17~Ref. 19!

0.12 3.72 4.1~Ref. 22! 3.9~Ref. 23!

0.1 3.6 3.9~Ref. 14!

0.17 3.59 4.1a

3.92b Co 0.2660.02 1.6460.04 2.4260.10~Ref. 20!

0.29 1.86 2.73~Ref. 22! 0.35 1.7 2.75~Ref. 14!

0.25 1.72 2.47a

2.80b

a_{This work: tight-binding linear-muffin-tin-orbital calculations.} b_{This work: magnetization measurements.}

[image:4.612.313.560.81.257.2]

experiments on fully ordered samples at 77 K ~see Table I!. We also show M (H) at 395 K which is above T_C of the ordered phase and below the ordering temperature of the disordered phase.21 Instead of saturation we observe an in-creasing magnetization. The magnetization of a paramagnet can be described by Curie’s law which is an expansion of the Brillouin function. Taking the full Brillouin function instead of Curie’s law allows a description of M (T) for a ferromag-net even below T_C.24The solid line in Fig. 3 shows a fit of the magnetization data with the Brillouin function for an effective TC of 361 K and S52.7.25The parameter

describ-ing the applied magnetic field is TH5bgH0/k57.0 K,

wherebis the coupling constant, g is the Lande´ g factor, H0

is the external magnetic field, and k is Boltzmann’s constant. This, then, would imply that the sample simply has a TC of

361 K and the broadening~as parametrized by T_H) is due to the size of the applied field. If this is the case we can calcu-late the magnetization as a function of temperature in a smaller field. The solid line in the inset in Fig. 3 shows

M (T) as determined with the parameters obtained from the

fit for 1.5 T but with the magnetic moment reduced to 0.52mB due to the smaller applied field. The dotted line

shows the magnetization with THreduced by a factor of 150,

i.e., representing a field of 0.01 T, and a reduced moment of 0.52mB. The well-known shape of M (T) for a ferromagnet

is recovered except for a small but negligible broadening close to TC. As data at a lower field show ~inset in Fig. 3!

the fit does not agree well with the data from our sample. It is clear that the broadening of the transition is not due to the applied magnetic field but to disorder. If the sample con-sisted of two separate phases, i.e., ordered and disordered phase we would expect to see a change in the slope of M (T) in Fig. 3 at 288 K. Since there is no clear feature in the magnetization we do not think the sample is two phased, i.e., the sample has some disorder that is homogeneous through-out the sample volume.26We will therefore treat the sample as single phase with a degree of site disorder intermediate to the ordered and disordered phases of Ref. 1.

The cryostat windows ~suprasil quartz!alter the polariza-tion of the light due to strain effects and Faraday rotapolariza-tion (;10° at 3 T and 4 eV!, but this can be subtracted by mea-suring an aluminum reference mirror and switching the di-rection of the magnetic field. Therefore, each spectrum shown here is the result of four measurements taken over a period of 3 to 4 h. The saturation magnetization is reached at an external field of 1.0 T at 10 K. Measurements at low temperatures can therefore be performed in small magnetic fields reducing the induced background due to Faraday rota-tion in the windows.

B. Ellipsometry

In general, for an appropriate choice of axes, the dielectric response of a non-magnetic sample is described by the di-electric tensor27

e

J5

S

exx 0 0

0 ey y 0

0 0 e_zz

D

. ~1!

This reduces in the case of an isotropic sample to the com-plex dielectric function e5e11ie2 where e5exx5ey y 5ezz. With a rotating analyzer ellipsometer ~RAE! ~Refs.

27–29!one measures the complex reflectivity ratio

r5rp

rs

, ~2!

where rp, rs are the complex amplitude reflection

coeffi-cients for p and s polarized light, respectively. Using the angle of incidence f one gets the relation

e5

S

11r

12r

D

2

sin2f tan2f1sin2f. ~3!

[image:5.612.97.251.55.186.2]

We used a RAE following the design by Aspnes and Studna.28Data can be collected from 1.2 to 5.6 eV depend-ing on the surface quality of the sample. All ellipsometric measurements were made at room temperature with no mag-netic field applied.

[image:5.612.88.265.462.645.2]

FIG. 2. Magnetization of Pt3Co at 10 K (h) and 395 K~n!.

FIG. 3. Temperature dependence of the magnetization of Pt3Co

in an applied magnetic field of H051.5 T (h). The solid line

represents a fit to a Brillouin function with TC5361 K, S52.7, and TH5bgH0/k57.0 K, whereb is the coupling constant, g is the

Lande´ g factor, and k is Boltzmann’s constant. The inset shows data taken at 0.01 T. The solid line represents the magnetization for the parameters obtained from the fit for 1.5 T but with a reduced saturation magnetization of 0.52mB. The dotted line shows M (T) with THreduced by a factor of 150, i.e., representing a field of 0.01 T, and a magnetic moment of 0.52mB.

C. MOKE

The polar Kerr effect is measured near normal incidence (f,4°). Reflection by an isotropic surface will not change the polarization state of the light at normal incidence. How-ever, in the case of a cubic sample magnetized along z, i.e., along the surface normal, the optical conductivity is given by

s

J5

S

sxx sxy 0 2sxy sxx 0

0 0 szz

D

, ~4!

which can be converted to the dielectric function

ei j5di j1i

si j

e0v

, ~5!

where we used the Kronecker d symbol. The magnetization induces off-diagonal elements in the conductivity and dielec-tric tensor. In the polar configuration these off-diagonal ele-ments are ~to lowest order! linear functions of the sample magnetization. Eigenvectors of sJ are left ~LCP! and right

~RCP!hand circular polarizations. In general the reflectivi-ties for RCP~1!and LCP~2!,

r₆5ur₆u eiD6, ~6! are different. Incoming, linearly polarized light will be ellip-tically polarized after reflection with an ellipticityeKand the

major axis of the ellipse will be rotated by an angleQK. The

complex quantityQK1ieKis the magneto-optic Kerr effect.

The difference in the reflectivities induces an ellipticity

eK5

ur₁u2ur₂u

ur₁u1ur₂u. ~7!

The rotation of the major axis, the Kerr angle, of the ellipse is due to a phase shift between RCP and LCP

QK52

1

2~D12D2!. ~8! In the polar geometry the MOKE can be expressed in terms of the complex optical conductivity30,31

QK1ieK52

sxy

sxx

S

11isxx

e0v

D

21/2

. ~9!

The Kerr effect can be measured with a polarization modulation technique employing a photoelastic modulator.32–39From the detected dc, 1 f , and 2 f signals one determines the Kerr ellipticity and rotation. We take spectra between 1.3 and 5.4 eV. At room temperature sample char-acterization can be performed using a NdFe2B14 permanent

magnet40 with a magnetic field of approximately 0.4 T. For lower temperatures and higher magnetic fields the sample is mounted in an optical cryostat with an 8 T split coil super-conducting magnet system. Data were taken at temperatures ranging from 10 to 293 K and magnetic fields between 0.4 and 3 T.

III. THEORY

In Secs. II B and II C we described the macroscopic fea-tures of a reflecting surface. However, the microscopic origin of the MOKE is very complicated. Early explanations of magneto-optic effects in solids based on the theory of inter-band transitions were given by Bennett and Stern,41 Cooper,42 and Pershan,43 followed by work of Erskine and Stern44on Gd where they included intraband contributions to the conductivity. This intraband term is important at lower energies ~below 1.5 eV! and can lead to a considerable change in the MOKE.45,46Its origin is scattering processes of Bloch electrons. A simplified approach is to include intra-band contributions to the conductivity through an empirical Drude term.45,47However, we have not included this in our calculations and good agreement of experiment and calcu-lated spectra was found in our measured energy range above 1.3 eV. Following the notation of Bennett and Stern41 and Erskine and Stern44 we can write the absorptive part of the off-diagonal conductivitys_2xy as the sum of separate contri-butions from up and down states neglecting spin-flip transitions. The spin-up states give a conductivity

s2x y↑~v!5 pe2

4\vm2V

(

a,b @u

^

b↑up

2_ua↑

_&

_u2

2u

^

b↑up1_ua↑

_&

_u2_#3d~v

ab↑2v!, ~10!

where the sum is over all occupied statesua↑

&

and all empty states ub↑

&

that are separated by an energy\v_ab↑. For the conductivity arising from spin-down states we replace all states in Eq. ~10! by the corresponding spin-down eigen-states. The operators p65px6ipy are linear combinations

of the kinetic momentum operator

pW5pW1 \

4mc2s

W_3¹WV~rW!. ~11!

The second term represents the spin-orbit interaction. Oppe-neer and co-workers9 mapped out spin-orbit and exchange splitting contributions to the MOKE by using ASW and fully relativistic LMTO methods and scaling the corresponding terms in the Hamiltonian. Calculations showed that the ori-gin of the Kerr effect in the Pt3X is a mixture of large

spin-orbit splitting of Pt and the exchange splitting of the transi-tion metal.

We used the TB-LMTO scheme with spin-orbit coupling48–50 in the LSDA to calculate the band structure, magnetic moments, and density of states of Pt3Mn and

Pt3Co. Compared to conventional LMTO’s the TB-LMTO’s

have a rather short range and only nearest-neighbor contri-butions have been considered. Calculations were performed in the irreducible wedge of the simple cubic first Brillouin zone ~BZ!. The direction of spin alignment was taken to be

@001#. Oppeneer et al.9 compared the Kerr spectra for mag-netization along @001# and @111# for Pt3 transition metal

compounds. The largest anisotropy was observed in the case of Pt3Co. However, the anisotropy is small due to the high

symmetry of the Cu3Au structure. The interband contribution

to the conductivity was calculated using matrix elements in-cluding the spin-orbit coupling term. Figure 4 shows the band structure for the two compounds. The bands are plotted

along symmetry lines of the first BZ of the simple cubic lattice.51In Figs. 5 and 6 we show the spin projected density of states ~DOS! for the two systems. Both compounds ex-hibit a large peak in the minority spin DOS. In the case of Pt3Mn we have a 1 eV wide band with a high DOS centered

1.5 eV above the Fermi level. This peak originates from Mn 3d bands with a small contribution from 5d Pt derived states. There is negligible contribution from s, p bands in this region. At higher energies Pt 5d and 6 p states together with

Mn 3d states lead to a peak in the minority spin DOS 3.5 eV above the Fermi energy. The situation is very similar for Pt₃Co. Above the Fermi level only 3d bands contribute to the DOS at the Co sites. The peak in the minority spin DOS occurs in a 1 eV wide region around the Fermi level and is due to Co 3d as well as Pt 5d states. At higher energies the DOS at the Co site vanishes completely and the total DOS is the sum of Pt 6s, 6 p, and 5d DOS.

An analysis of the origin of the Kerr rotation in the simi-lar compound Pt3Cr was performed by Oppeneer et al.9

Ex-plicitly excluding optical matrix elements from the calcula-tion of the conductivity shows that transicalcula-tions between hybridized p-d bands of Pt have a strong influence on the structure of the Kerr spectra. When the optical matrix ele-ment of the p-d transition on the Pt site is excluded the absorptive part of sxx is reduced by roughly 60%. The

ab-sorptive part of the off-diagonal conductivity nearly vanishes below 2 eV whereas there is hardly any change at higher photon energies. Effects of s-p and d-f transitions are small and are not believed to alter the energy dependence of the polar Kerr effect in a significant way.

[image:7.612.360.511.54.287.2]

Calculations of optical response functions from ground-state band structures using the direct interband transition model usually produce good quantitative agreement with the experimental spectra when only s-p bands dominate optical absorption.52 However, this model is less appropriate for fairly localized states, e.g., 3d bands of transition metals. The ground-state band structure cannot describe the many-body interactions which lead to a shift in the energies of the excited state quasiparticles, i.e., screened electrons and holes. Empirically this can be included by adding a complex self-energy shift53

[image:7.612.82.262.57.274.2]

FIG. 4. Spin-polarized band structure for Pt3Mn~a! and Pt3Co ~b!obtained from TB-LMTO with LSDA in the atomic sphere ap-proximation.

FIG. 5. Spin-projected DOS for Pt3Mn obtained from

TB-LMTO. The upper and lower panel show the DOS on the Pt and transition metal site, arrows indicate majority (↑) and minority (↓), respectively. Thick solid lines show the total DOS for Pt3Mn. Major

contributions to the total DOS are from 3d states of Mn and 5d states of Pt below EFand empty 3d states on the transition metal site about 1 eV above the Fermi level.

FIG. 6. Spin-projected DOS for Pt3Co obtained from

TB-LMTO. The upper and lower panel show the DOS on the Pt and transition metal site, arrows indicate majority (↑) and minority (↓), respectively. Thick solid lines show the total DOS for Pt3Co. Major

contributions to the total DOS are from 3d states of Co and 5d states of Pt below EF and empty 3d states on the transition metal site in a 1 eV wide band around the Fermi level.

[image:7.612.98.249.444.676.2]

S5S11i S2 ~12!

to the energy eigenvalues obtained from TB-LMTO band structures. The real part of the self-energy represents a shift in the quasiparticle energy from the energy value obtained with the ground state calculation, while the imaginary part of the self-energy represents the lifetime of the excited quasi-particle. In general the self-energy depends on wave vector and band index.

IV. RESULTS AND DISCUSSION

We measured the dielectric function of nonmagnetized Pt3X (X5Mn, Co) using a RAE. Measurements were

per-formed at room temperature between 1.2 and 5.6 eV. In or-der to compare our experimental spectra with results from band structure calculations we determined the optical con-ductivity for both samples using Eq.~5!. Figure 7 shows the measured and calculated conductivity for both samples. For comparison we show the absorptive, i.e., real, parts1xx. The

dispersive part s2xx ~not shown in Fig. 7! is obtained by

Kramers-Kronig transformation of s1xx. Figure 7~a!shows

the data for Pt3Mn. A self-energy correction of 0.15 eV shifts

the peak in the calculated spectra to about 2.2 eV and gives good agreement with the measured peak position. Although a lifetime broadening of 0.4 eV was included there is a signifi-cant difference in the absolute magnitude of Re@sxx#.

Ellip-sometry as well as MOKE is surface sensitive with typical penetration depths of 50–100 Å with measured conductivi-ties frequently falling below calculated values for rough or contaminated surfaces. Therefore this difference is most likely due to surface effects, i.e., roughness, or an oxide

overlayer. However, the trends are well reproduced by our calculation. The results for Pt3Co, shown in Fig. 7~b!, show a

similar trend. A peak seen in the calculated spectra at around 1.8 eV is not found in our ellipsometric data.

MOKE measurements were performed at temperatures between 10 and 293 K and magnetic fields up to 3 T. How-ever, neither of the two samples showed a dependence of the Kerr effect on magnetic field for fields above 1.5 T, indicat-ing that all magnetic moments are aligned along the direction of the external magnetic field. Figure 8 shows the MOKE of Pt3Mn for three different temperatures. The signal at room

temperature does not show any significant structure. The ap-plied magnetic field was limited to 0.4 T, the field of a NdFe14B2 permament magnet. Obviously this is not enough

to achieve a considerable magnetization of the sample. Not only does the amplitude of the signal increase as we lower the temperature but the spectra show very clearly fine struc-ture that is not seen at elevated temperastruc-tures. The spectra at 10 and 100 K are essentially equal. We see a shoulder in the Kerr rotation and a peak in the ellipticity at about 2 eV. At 3 eV we observe a peak rotation of 0.31°. Finally the rotation drops towards higher energies and shows another minimum at 4.4 eV. This structure in the optical data is also observed in the Kerr ellipticity. Kramers-Kronig analysis of the mea-sured MOKE ~Ref. 54,55! ~valid only if u_K is small: tan uK'uK) confirmed the observed structures. Finally we

[image:8.612.343.534.54.290.2]

show the spectra obtained from TB-LMTO calculations. We included a lifetime broadening of 0.4 eV and a self-energy correction of 0.15 eV was chosen to obtain better agreement between experimental data and the theoretical spectra. The overall shape of the spectra reproduces the observed rotation and ellipticity well. The amplitude of the calculated spectra is about 1.6 times that of the measured spectra. The peak in

FIG. 7. Diagonal optical conductivity sxx of Pt3Mn ~a! and

Pt3Co~b!. Measured real~dashed! and imaginary~dotted! part of sxx derived from ellipsometric data using Eq.~5!. The solid line shows the absorptive, i.e., real, part ofsxxobained from TB-LMTO calculations. In both cases a lifetime broadening of 0.4 eV was included in the theoretical spectrum. In addition we used a self-energy shift of 0.15 eV for Pt3Mn to lower the theoretical peak

[image:8.612.99.251.55.288.2]

position. There is no self-energy correction used for Pt3Co.

FIG. 8. Kerr ellipticity~a!and rotation~b!of Pt3Mn for different

temperatures and magnetic fields.~n,m!show data taken at 293 K with a 0.4 T magnetic field. (s,d) and (h,j) designate scans at 10 and 100 K, respectively, in an external field of 1.5 T. The solid line is the Kerr effect calculated from TB-LMTO reduced by a factor of 1.6. A lifetime broadening of 0.4 eV and a self-energy correction of 0.15 eV was included.

the LMTO results at 3 eV agrees well with the experimental data and even the peak at 4.4 eV appears in the calculated Kerr effect.

Figure 9 shows the MOKE for Pt3Co at 10 and 100 K

with an applied magnetic field of 1.5 T and we also show the spectrum obtained at room temperature with a 0.4 T perma-nent magnet. The Kerr effect at 293 K resembles the spectra at low temperatures indicating a considerable magnetization of the sample. However, low temperature scans reveal a small structure in the Kerr ellipticity at 2.5 eV that remains nearly undetected in the rotation spectrum. At higher ener-gies a shoulder in the ellipticity becomes obvious which ap-pears also in the rotation at about 4 eV. As we go to higher energies we observe a monotonic behavior in the MOKE. It was not necessary to include a self-energy correction in the calculated spectra. Peak positions from band structure calcu-lations agree with those seen in the experimental data. How-ever, we used a Lorentzian line broadening of 0.4 eV to account for the finite lifetime of the excited states. This value gives reasonable agreement for our spectra and was also used by Oppeneer et al.9,46to calculate Kerr spectra for transition metal compounds. The overall agreement of the measured and calculated spectra is good. The magnitude of the MOKE is overestimated by our calculations for photon energies be-low 3 eV. We note that for the Kerr ellipticity even the small

peak at 2.5 eV as well as the shoulder at about 4 eV are obtained from TB-LMTO.

V. CONCLUSIONS

The dielectric function and the magneto-optical response of polycrystalline Pt₃X (X5Mn, Co) have been measured between 1.6 and 5.2 eV and compared with theoretical spec-tra obtained using the TB-LMTO scheme. The diagonal part of the optical conductivity was obtained at room temperature using a rotating analyzer ellipsometer. The measured s_xx spectra for both samples are relatively featureless, with a magnitude some 30% smaller than the calculated value, sug-gesting surface roughness or an oxide overlayer is present. The magneto-optical response was measured for various temperatures and magnetic field strengths, with the largest magnitudes and sharpest features occuring at the lowest tem-perature~10 K!and highest field ~1.5 T!as expected. There is good agreement between the measured MO spectra and the theoretical calculations, particularly for Pt3Co. For Pt3Mn we

shifted the theoretical spectra 0.15 eV to lower energies and scaled it by a factor of 1.6 to obtain optimal agreement with experiment. Such energy shifts are frequently discussed in terms of self-energy corrections for the optical properties of transition metals, however, the scaling of the magnitude is fairly large and it is not known if it is fundamental~i.e., an inadequate treatment of MO effects in the LDA! or if the suspected surface imperfections affect the surface magnetic properties and MO response. The fact that disorder destroys ferromagnetism for Pt3Mn but enhances it for Pt3Co suggests

surface conditions may be responsible. With the energy shift and scaling, the theoretical spectra for Pt3Mn agree well with

experiment. There is good agreement with the Pt3Co spectra

between theory and experiment and one may conclude that the TB-LMTO method is doing a reasonable job in the evaluation of MO spectra for these compounds in spite of the relatively narrow 3d bands involved. This does not seem to be the case for compounds containing rare earth elements where the localized 4 f states are not adequately treated within the LDA. For such materials the so-called LDA1U method, which explicitly includes the on-site Coulomb inter-action among highly correlated localized electrons, seems to offer an improved description of the MO spectra.8

ACKNOWLEDGMENTS

We would like to thank M. Kramer for the x-ray measure-ments and I.R. Fisher, A.F. Panchula, and K.D. Myers for the magnetization data. Ames Laboratory is operated for the U.S. Department of Energy by Iowa State University under Contract No. W-7405-Eng-82. This work was supported by the Director for Energy Research, Office of Basic Energy Science.

*Current address: Motorola Semiconductor Technology, Maildrop M360, 2200 West Broadway, Mesa, AZ 85202.

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