Origin of magnetic anistropy in transition metal spinglass alloysP. M. Levy and A. Fert Citation: Journal of Applied Physics 52, 1718 (1981); doi: 10.1063/1.329688 View online: http://dx.doi.org/10.1063/1.329688 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/52/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Magnetic susceptibility studies of the spin-glass and Verwey transitions in magnetite nanoparticles J. Appl. Phys. 113, 17E132 (2013); 10.1063/1.4797628 The spinglass transition in three dimensions: Is it understood? J. Appl. Phys. 61, 4228 (1987); 10.1063/1.338483 Further evidence for a spinglass phase transition in amorphous FeMnPBAl alloys J. Appl. Phys. 53, 2217 (1982); 10.1063/1.330776 Origin of anisotropy in transition metal spin glass alloys (invited) J. Appl. Phys. 53, 2168 (1982); 10.1063/1.330770 Neutron scattering studies of spinglass alloys J. Appl. Phys. 49, 1604 (1978); 10.1063/1.324922

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Origin of magnetic anistropy in transition metal spin-glass alloys

P. M. Levy

Department of Physics, New York University, New York, New York ]0003

A.Fert

Laboratoire de Physique des Solides, Universite Paris-Sud, 91405 Orsay, France

In order to interpret the magnetic anisotropy of spin-glass alloys, we calculate the anisotropic terms arising in the RKKY interaction between transition metal impurities when spin-orbit coupling is taken into account. We find pseudo-dipole and single ion anisotropy terms in the pair interaction and Dzyaloshinsky-Moriya terms when triangles of impurities are considered. Applying our results to ~Fe alloys we find that, although the pseudo-dipole interactions are 40 times stronger than the magnetic dipole-dipole, the Dzyaloshinsky­Moriya interactions are even stronger and are sufficient to explain the magnetic anisotropy observed in ~Fe spin-glass alloys.

PACS numbers: 7S.30.Gw, 7S.S0.Kj

INTRODuCTION

Several recent experimental studies of spin glasses have given new insight into the anisotropy fields maintaining the remanent magnetization in the direction of the initial applied field. These studies include NMR(1,2), EPR(3), hysteresis 100ps(4) and transverse suscep!ibility(2) measurements. The anisotropy field HA is introduced in these studies as ~ fictitious field holding the remanent magnetization ur in a fixed direction. In the most widely studied system CuMn the value of HA determined by NMR(1,2) is in approximate agreement with those determined from EPR(3) and transverse susceptibility measurements (2) , but is always larger than the value of HA estimated from the negative field Hr at which the remanent magnetization undergoes a sharp reversal of direction. For example, in CuMn 1.35 at, % at T « Tg the freezing/glass temperature, and for the maximum remanent magnetization the following values of HA have been obtained. HA = 445 gauss from ESR(3), HA = 375 gauss from NMR(l) while HA = 170 gauss from the analysis of the hysteresis 100p(4). The most striking result in the CuMn system is that the anisotropy is greatly enhanced by the introduction of non-magnetic impurities with strong spin-orbit coupling. For example, HA increases at a linear rate of 34 x 103 gauss per at. % of Pt(4). This marked increase in anisotropy has been accounted for by the presence of Dzyaloshinsky-Moriya interactions between Mn spins induced by the spin-orbit scattering of conduc­tion electrons by non-magnetic impurities (5).

In contrast to the weak anisotropy fields measured in pure CuMn alloys, one finds a large field HA = 50 kG for AuFe~.7 at, %(2). This field is at least three orde;; of magnitude larger than the field estimated by using the magnetic dipole-dipole interaction between Fe impurities. While Mn is a good S-state ion in Cu,Fe in Au has a small orbital contribution to the magnetic moment due to spin-orbit coupling. We have considered the effects of the orbital character of the iron impurities on Fe pair interactions and find both pseudo-dipole interactions and single-ion anisotropy. In addition, we should also consider triangles of iron impurities to determine, as described below, the magnitude of the Dzyaloshinsky-Moriya interactions between a pair of Fe spins. Additional anisotropy comes from the spin-orbit coupled host (Au) band structure, but we leave the discussion of this contribution to a future publication.

CALCl.iLATION To calculate the anisotropy due to the spin-orbit

coupling of the d electrons on the Fe impurities we follow the resonance-resonance picture used by Caroli(6) and based on the Friedel-Anderson model of local moments in transition metal alloys. When we calculate toe pair interaction by using this model and by taking into account the spin-orbit coupling, we find that, in addition to the isotrop~c RKKY interaction Eiso there exists an anisotropic interaction Eaniso of pseudo-dipole and single-ion anisotropy form. The general expression of this interaction is fairly complicated and will be given elsewhere. In the case of Fe impurities in Au we find after calculating the ~= 2 spin up and spin down phase shifts nZ+ and n2- and estimating the magnitude of the several terms in Eaniso, that the leadinp, term is written as

Eaniso = -(25/4n)EF(A/~)2sin4nz_

x {C 2(~a) + C02(~b)}(1 o

cos2(kFR + ni-) (kFR) 3

+ ~:.'.·~b),

where A is the spin-orbit coupling constant of the

(1)

3d electrons, ~ is the half width of the virtual bound states and R is the distance between impurities. In the same way, the leading term of Eiso is written as(6)

The first term in the last parenthesis in Eq. (1) leads to single ion anisotropy

2 A A A

Co (u)= 1/2[3(u'Rab) - 1), (3)

and the second term can be written as a combination of pseudo-dipole and dipole-octupole terms

[C02(~a) + C02(~b»)~a'~b = 2/S[3(ua·Rab) (ub·Rab) A A A A 2. A A 2 (4)

-ua'ub)-'V2I/5{(C3(u,,)xubl)o + [ualxC3 (ub»)o}

where u is a unit vector in the direction of the iron magnetic moment and Rab is a unit vector pointing along the pair axis. The last term in square bracket represents the dipolar coupling of a unit octupole moment C3(~) to a dipole moment ~.

1718 J. Appl. Phys. 52 (3), March 1981 0021-8979/81/031718-02$1.10 © 1981 American Institute of Physics 1718

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RESULTS

For Fe in Au we have derived the phase shifts from the number of 3d electrons and the impurity spin by using the following relations

and

(5/n) (n2+ - n2-) = Z+ - Z_ = 2S = 2.2

where Z+ is the number of 3d electrons with spin up and down and S = 1.1 (7). When we use the atomic value for A = 0.05 eV and EF = 5.55 eV we find the pseudo-dipole interaction is 40 times larger than the magnetic dipole interaction. By using a method to estimate the macroscopic anisotropy energy which is similar to the one used for the CuMn system(5) we find a value of HA for AuFe 3.7 at. % whlch is too small to explain the experimental value. The calculation of the single-ion contribution to HA yields the same order of magnitude; therefore we cannot explain the observed anisotropy fields as solely arising from orbital contributions to the pair interactions between the spins.

Thus we have considered the Dzyaloshinsky­Moriya component of the RKKY interaction between a pair of Fe spins induced by spin-orbit scattering from a third Fe ion. We find an expression of the form pr~sly obtained by us (Eqs. 5 and 6 in Ref. 5) with the only change that the factor sin[(n/lO)Zdl is replaced by

(1/2) [sin{ (n/S)Z+)+ sin{ (n/5)Z_}}

It is difficult to evaluate, for a given pair of Fe spins, the contribution to the anisotropy from all the triads coming from neighboring Fe ions. However for the concentrations used in spin-glass systems the Fe spins are sufficiently dilute so that we can assume the contributions from the triads are randomly distributed. By estimating the ~croscopic anisotropy energy Ea as in Ref. 5, we find the maximum value possible for the anisotropy field in AuFe 3.7 at.% is

1719 J. Appl. Phys., Vol. 52, No.3, March 1981

This is amply sufficient to explain the observed anisotropy field(2)

HI, '" SOkG.

CONCLUSION

We conclude that, while most people have invoked the magnetic dipole interaction to account for magnetic anisotropy effects in transition metal spin glass alloys, the RKKY interaction between these spins contains much stronger anisotropic couplings. While pseudo-dipole interactions are about 40 times larger than the magnetic dipole interactions in AuFe, we have found to our surprise that the Dzyaloshinsky­Moriya interaction is even larger. It is certainly at the origin of the magnetic anisotropy of the Cu MnxTy systems(5), while for AuFe there is the possibility of additional anisotropy coming from the spin-orbit coupled host (Au) band st.ucture.

We would like to thank Dr. C.M. Pond for very helpful discussions and comments. This work was supported in part by the National Science Foundation and the Centre National de la Recherche Scientifique under the United States - France Program of Scientific Cooperation (DMR 78-25008).

REFERENCES

1) H. Alloul, J. App1. Phys. 50 (11), 7330 (1979). 2) H. Alloul and F. Hippert, to be published. 3) P. Monod and Y. Berthier, J. Magn. and Magn. Mat.

15-18, 149 (1980). 4) ~ Monod, J.J. Prejean and B. Tissier, J. Appl.

Phys. 50 (11) 7324 (1979). 5) A. Fert and P.M. Levy, Phys. Rev. Letters 44, 1538

(1980) . 6) B. Caroli, J. Phys. Chem. Solids 28, 1427 (1967). 7) J.L. Tholence and R. Tournier, J.-Phys. (Paris)

C 1, 211 (1971).

Magnetism & Magnetic Materials-1980 1719

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