Correlation between spin polarization and magnetic moment in ferromagnetic alloysTat-Sang Choy, Jian Chen, and Selman Hershfield

Citation: Journal of Applied Physics 86, 562 (1999); doi: 10.1063/1.370766 View online: http://dx.doi.org/10.1063/1.370766 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/86/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Impacts of enhanced electronic correlation in anion p-orbitals on electronic structure and magnetic properties ofnitrogen or carbon doped zinc oxide J. Appl. Phys. 111, 07E313 (2012); 10.1063/1.3672090 The electronic structure and spin polarization of Fe 3 x Mn x Si and Fe 3 y MnSi y alloys J. Appl. Phys. 107, 093911 (2010); 10.1063/1.3388640 Engineering the electronic, magnetic, and gap-related properties of the quinternary half-metallic Heusler alloys J. Appl. Phys. 103, 023503 (2008); 10.1063/1.2831224 Role of interface bonding in spin-dependent tunneling (invited) J. Appl. Phys. 97, 10C910 (2005); 10.1063/1.1851415 Electronic structures and magnetism of LaNi 5–x Fe x compounds J. Appl. Phys. 89, 7311 (2001); 10.1063/1.1357854

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

95.254.122.104 On: Tue, 08 Apr 2014 08:10:52

JOURNAL OF APPLIED PHYSICS VOLUME 86, NUMBER 1 1 JULY 1999

[This a

Correlation between spin polarization and magnetic momentin ferromagnetic alloys

Tat-Sang Choy,a) Jian Chen, and Selman HershfieldDepartment of Physics and National High Magnetic Field Laboratory, University of Florida,Gainesville, Florida 32611

~Received 3 February 1999; accepted for publication 19 March 1999!

The correlation between the spin polarization of the tunneling current in ferromagnet/Al2O3/Altunnel junction experiments and the magnetic moment in ferromagnets has been a mystery@Phys.Rev. B16, 4907~1977! and Phys. Rep.238, 173~1994!#. In this study, an attempt is made to explainthis correlation. By assuming that thes electrons are responsible for the tunneling, the tunnelingcurrents are proportional to thes density of states at the Fermi level@Phys. Rev. B8, 3252~1973!#.A tight-binding coherent potential approximation model for itinerant magnetism is applied tocalculate the band structure of Fe- and Ni-based alloys@Rev. Mod. Phys.46, 465 ~1974!#. TheSlater–Pauling curve for the bulk magnetic moment is recovered, and the spin polarization of theselectrons at the Fermi level is found to correlate well with the magnetic moment. The calculation iscarried out in a model where the approximate band structure of an alloy is calculated by using twoextra tight-binding parameters besides those of the host. As the average number of electrons ischanged by the impurities, the total Coulomb energy and hence the splitting between the up anddown spin bands has to be modified self-consistently. The modified band structure is then used toobtain the magnetic moment and the spin polarization. The relation between the magnetic momentand spin polarization can be understood by noting that within approximately 1.5 eV of the Fermilevel, the density of states of thes band for either spin is roughly anincreasing functionof energyand therefore of the number of electrons. For a fixed total number of electrons, the magneticmoment increases with the number of spin-up electrons, corresponding to a larger spin-up densityof states at the Fermi level. Thus, the spin polarization increases as the magnetic moment increases.© 1999 American Institute of Physics.@S0021-8979~99!00213-3#

eton

tic

rizel

sthntelly.thorlini

b

pi.

theedthe

of

o-

l--untym-a

a-ow-

heione

tial-

I. INTRODUCTION

There has been much recent interest in ferromagntunnel junctions. Many of the experiments areferromagnetic–insulator–ferromagnetic (F/I /F) tunneljunctions,1 which have potential applications in magnestorage devices. Another type of experiment2,3 involvesferromagnetic–insulator–superconductor junctions (F/I /S).These experiments allow one to measure the spin polation at the Fermi surface and are alternatives to fiemission4 and photoemission5 studies.

The F/I /S experiments done by ParaskevopouloMeservey, and Tedrow give two surprising results. First,tunneling spin polarizations are all positive for Fe, Co, aNi. This apparently contradicts the Stoner–Wohlfarth–Sla~SWS!6,7 theory of ferromagnetism, which has successfuexplained the Slater–Pauling curve7,8 for magnetic momentsIf the tunneling current is assumed to be proportional tototal density of states at the Fermi level, the SWS thepredicts negative spin polarizations. Second, the tunnespin polarization for Fe, Co, Ni, and various Ni base alloysroughly proportional to their magnetic moments~see Fig. 1!.The magnetic moment per atom in a ferromagnet is givenmB(N↑2N↓), wheremB is the Bohr magneton, andN↑ andN↓ are the number of electrons per atom in the majority s~spin-up! and minority spin~spin-down! states, respectively

a!Electronic mail: tschoy@phys.ufl.edu

5620021-8979/99/86(1)/562/3/$15.00

rticle is copyrighted as indicated in the article. Reuse of AIP content is sub

95.254.122.104 On: Tue,

ic

a-d

,edr

eyg

s

y

n

On the other hand, it is expected that only electrons nearFermi level take part in tunneling. Given the complicatband structure of the transition metals, it is not clear whytwo quantities, the magnetic moment and the polarizationtunneling current, are related in such a simple way.

Stearns9 explained this trend by assuming that the ferrmagnet has a small percentage of itinerantd-like electrons.On the other hand, Hertz and Aoi10 assumed that the tunneing current is predominantly due tos electrons and they calculated the tunneling spin polarization by taking into accothe self-energy due to spin-wave emission. Recently, Tsbal and Pettifor11 studied the tunneling from Fe and Co bytight-binding model in which thesss bond is used to allowonly s electron tunneling. All of the above models give resonable agreement with the experiments. It is not clear, hever, which model is closer to reality.

In this paper we point out that an implementation of tSWS theory can lead to an explanation of the correlatmentioned above. We assume thats electrons are responsiblfor the tunneling current. The total density of states~DOS!ands partial density of states (s-DOS) of ferromagnetic al-loys are calculated with a tight-binding coherent potenapproximation~CPA!12 model. We define the spin polarization of s-DOS by

Ps5ns↑2ns

↓

ns↑1ns

↓ , ~1!

© 1999 American Institute of Physics

ject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

08 Apr 2014 08:10:52

ati

noityatth

er

.

b

m

e-

563J. Appl. Phys., Vol. 86, No. 1, 1 July 1999 Choy, Chen, and Hershfield

[This a

wherens↑ andns↓ are thes-DOS of spin-up and spin-down

bands at the Fermi level. We find thatPs is related to themagnetic moment just as the tunneling spin polarizationPT

is related to the magnetic moment in the experiments.

II. MODEL

We consider a tight-binding model for a bulk alloy this structurally ordered but chemically disordered. The Hamtonian can be written as

H5(ims

uims cims

† cims1 (^ i j &mns

t i jmncims† cjns , ~2!

wherecims† (cims) is the creation~annihilation! operator of a

s-spin electron of orbitalm on the lattice sitei, uims is the

on-site potential, andt i jmn is the hoping energy betweeneighboring sites. The tight-binding parameters of the hmetal are obtained from fits to the local densapproximation.13 To simplify the calculation, we assume ththe tight-binding parameters for the impurity sites aresame as the host except for the on-site energiesui ,d

↑ andui ,d↓

of the spin-up and spin-downd bands. Although the simpli-fied model has only two extra parameters, it still producimportant features such as the virtual bound states in NiC

FIG. 1. Comparison of the tunneling spin polarization~symbols! ofParaskevopoulos, Meservey and Tedrow and the saturation magneticment ~lines!.

FIG. 2. Comparison of the calculated spin polarization of thes-DOS ~sym-bols! and the saturation magnetic moment~lines!.

rticle is copyrighted as indicated in the article. Reuse of AIP content is sub

95.254.122.104 On: Tue,

l-

st

e

sas

suggested by the Friedel model.14 This is crucial in explain-ing the anomalous branches in the Slater–Pauling curve

The major contributions to the on-site energies,ui ,d↑ and

ui ,d↓ , come from the atomic core potential and the Coulom

o-

FIG. 3. The average DOS~dashed line! ands-DOS~solid line, magnified bya factor of 10! of ~a! pure Ni,~b! Ni0.9Fe0.1, ~c! Ni0.9Cu0.1, and~d! Ni0.9Cr0.1.The s-DOS for different Ni alloys are very similar to each other. Consquently, their trends can be studied systematically.

ject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

08 Apr 2014 08:10:52

th

ve

rn-P

nereru

nfo

ue

egs

nt

he

to

l-

et-rhen

n-emi

pid,

inginilartionlsospinof

n-

564 J. Appl. Phys., Vol. 86, No. 1, 1 July 1999 Choy, Chen, and Hershfield

[This a

energy due to the opposite spin. Therefore, we rewriteparameters as

ui ,d↑ 5Ui

01UixNi ,d↓ ,

~3!ui ,d↓ 5Ui

01UixNi ,d↑ ,

where Ui0 and Ui

x are the on-site parameter and effectiCoulomb energy per pair at sitei, andNi ,d

↑ (Ni ,d↓ ) is the num-

ber of spin-up~spin-down! d electrons at sitei. SinceNi ,d↑

and Ni ,d↓ depend on the alloy band structure, which in tu

depend onui ,d↑ and ui ,d

↓ , Eq. ~3! needs to be solved selfconsistently with the band structure obtained from the Ccalculation. Magnetic moments ands-spin polarizations canbe obtained from the resulting band structure.

III. RESULTS

In Fig. 2, the calculated magnetic moment per atom as-spin polarizationPs are plotted as a function of the numbof valence electrons per atom in the alloys. The SlatPauling curve for magnetic moment, including anomalobranches, is obtained.

For the Ni-based alloys,Ps is found to be correlated withthe magnetic moment in a similar manner to the wayPT

correlates with the magnetic moment in the experimeshown in Fig. 1. The correlation can be understood aslows. As shown in Fig. 3, thes-DOS looks very similar fordifferent alloys and for spin-up and spin-down bands. Thit is helpful to think of thes-DOS as just being shifted in thdifferent alloys and spin channels. We notice that thes-DOSis an increasing function of energy in a range of about 1.5near the Fermi level. For the 3d transition metals, increasinthe number of electrons in a certain spin channel increathe Fermi energy, and therefore increases thes-DOS. As a

result, the differencens↑2ns

↓ between the spin-ups-DOS and

FIG. 4. The average DOS~dashed lines! ands-DOS ~solid lines, magnifiedby a factor of 10! of Fe0.5Cr0.5.

rticle is copyrighted as indicated in the article. Reuse of AIP content is sub

95.254.122.104 On: Tue,

e

A

d

–s

tsl-

s,

V

es

the spin-downs-DOS increases as the magnetic momemB(N↑2N↓) increases.

For FeCr alloys, which are also shown in Fig. 2, tcorrelation is less clear. There is a sudden decrease inPs

near Fe0.2Cr0.8 as the Cr percentage increases. This is duethe relatively sharp change in thes-DOS in bcc metals as theFermi level decreases~see Fig. 4!. It would be interesting totest this experimentally.

The structure in thes-DOS can be understood as folows. When thes–d hybridization is neglected, thes-DOSis constant near the Fermi level. However, in transition mals, thed states tend to pushs states to higher and loweenergies through hybridization. Thus, the location of tpeaks and valleys of thes-DOS are affected by the locatioof the d peaks. The shift of thes-DOS is a direct result ofs–d hybridization, and the SWS splitting of thed states. Thesimilarity between different Ni-based alloys can also be uderstood by the fact that thed peaks due to Ni do not changmuch among different alloys. In Ni-based alloys, the Ferlevel is just above thed peak of the majority spin, and istherefore in the range where thes-DOS is changing signifi-cantly. In the case of FeCr alloys, this change is more rawhich is a characteristic of bcc transition metals.

IV. CONCLUSION

In this article, we have presented evidence supportthe idea thats electrons are responsible for the tunnelingF/I /S experiments. Our calculation produces trends simto those observed experimentally for both the magnetizaand the polarization of the tunneling current. We have asuggested that there may be a sudden change in thepolarization in FeCr alloys as a function of the percentageCr. A detailed mechanism as to whys electrons should domi-nate the tunneling process is not clear at present.

1J. S. Mooderaet al., Phys. Rev. Lett.80, 2941~1998!.2D. Paraskevopoulos, R. Meservey, and P. M. Tedrow, Phys. Rev. B16,4907 ~1977!.

3R. Meservey and P. M. Tedrow, Phys. Rep.238, 173 ~1994!.4M. Landolt and M. Campagna, Phys. Rev. Lett.38, 633 ~1977!; M.Landolt and Y. Yafet,ibid. 40, 1401~1978!.

5G. Buschet al., Phys. Rev. B4, 746 ~1971!.6E. C. Stoner, Philos. Mag.15, 1080~1933!.7J. C. Slater, J. Appl. Phys.8, 385 ~1937!.8P. H. Derichset al., J. Magn. Magn. Mater.100, 241 ~1991!.9M. B. Stearns, Phys. Rev. B8, 4383~1973!.

10J. A. Hertz and K. Aoi, Phys. Rev. B8, 3252~1973!.11E. Yu. Tsymbal and D. G. Pettifor, J. Phys.: Condens. Matter9, L411

~1997!.12R. J. Elliott, J. A. Krumhansl, and P. L. Leath, Rev. Mod. Phys.46, 465

~1974!.13Papaconstantopoulos, D. A.,Handbook of the Band Structure of Eleme

tal Solids~Plenum, New York, 1986!.14J. Friedel, Nuovo Cimento 10VII , 287 ~1958!.

ject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

08 Apr 2014 08:10:52