Cr multilayers

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Physica B 237-238 (1997) 261-263

Temperature dependence of random local moments and giant magnetoresistance of Fe/Cr multilayers Hideo Hasegawa Department of Physics, Tokyo Gakugei University, KoganeL Tokyo 184, Japan

Abstract

Finite-temperature properties of ( F e ) 3 / ( C r ) 4 multilayers have been discussed by taking into account the effect of spin fluctuations with the use of the static functional integral method. The calculated temperature dependence of local moments of Fe and Cr, which are assumed to be randomly distributed at interfaces, deviates significantly from the Brillouin function. This unusual behavior of local moments is shown to reflect on the temperature dependence of the giant magnetoresistance. Keywords: Multilayers; Local moments; Magnetoresistance; Fe/Cr

Experimental and theoretical studies have been extensively made on finite-temperature properties of magnetic multilayers consisting of transition metals. In a previous paper [1] we calculated the temperature dependence of local magnetic moments of Fe/Cr multilayers by including the effect of spin fluctuations which play a very important role at finite temperatures. In this calculation we adopted an ideal Fe/Cr multilayer in which Fe and Cr interfaces are completely separated. This is, however, not the case in real systems where some Cr atoms exist in Fe interface layers and vice versa. It may be indispensable to take account of the interface randomness for a better understanding of the experimental data. It is the purpose of the present paper to theoretically study the finite-temperature properties of (Fe)3/(Cr)4 multilayer whose interfaces include the randomness. We calculated the temperature dependence of local magnetic moments and also the giant magnetoresistance (GMR) of the multilayer. We employed a finitetemperature band theory based on the static functional integral method developed by Hasegawa [2]. Its is a mean-field theory regarding spin fluctuations as

static, local modes, which are treated by the coherent potential application (CPA); related discussions on its formalism and applications having been given in Ref. [2]. We adopted a (Fe)3/(Cr)4 multilayer, in which each layer is assigned by the index n. We introduced the randomness such that the Cr concentration on layer n, Yn, is Yl = Y3 = tS, Y 2 = 26, Y4 = Y7 = 1 -- 26, and Y5 = Y6 = 1 - 6, with 6 = 0.05. Note that the case of 3 = 0 denotes the multilayer with the perfect interface. A given multilayer is assumed to be described by the Hubbard Hamiltonian in which the parameterized hopping integrals of the canonical band theory were employed to get realistic degenerate d-band [1]. First we discuss local moments of the multilayer. We pursued the antiferromagnetic (AF) and ferromagnetic (F) solutions, in which Fe moments separated by intervening Cr layer are antiparallel and parallel, respectively. The calculated groundstate local moments for the AF and F configurations are shown in Figs. l(a) and 2(a), respectively. We should note that Cr (Fe) atoms at n = l-3 (and n =

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tZ Hasegawa / Physica B 237-238 (1997) 261 263

','/'',"

',;

2

(a) 3

~

(b) '

0

'

r

I

i

I

r

J--

10

5

n

AF

--.I

I

0.0

I

I

O5

1.0¸

TITco

Fig. 1. The calculated local moments, M~, in the AF configuration of (Fe)3/(Cr)4 multilayers at T = 0 K (a) and their temperature dependence (b); • (O), • ([]), • (£~), and • (V) denote ~=Fe (Cr) at n=2,3,4, and 5 (mad their equivalent sites), respectively. Solid (dashed) curves connecting moments of Fe (Cr) atoms are shown for a guide of the eye.

3

~

,

f

I

i

I

[

i

I

I

]

--1

1

Cr

:=:t

.~

~r- o

:-

if

II

I

_Q._

~ ..43... ~ .=o..

..43.--

-13-

.,

'II

It

~1

2

(a)

(b) ,

0

5 n

I0

0.0

l

F l

l

l

l

l

05

~o

~

l

1.0

Fig. 2. The calculated local moments, Mn~, in the F configuration of (Fe)3/(Cr)4 multilayers at T = OK (a) and their temperature dependence (b) (see the caption of Fig. 1).

8 - 10) play a role as an impurity (host), whereas at n = 4 - 7 Fe (Cr) atoms are regarded as an impurity

(host). The calculated temperature dependence o f local moments for the AF and F configurations is

shown in Figs. l(b) and 2(b), respectively, where the temperature scale is normalized by Tco, the Curie temperature o f the (Fe)3/(Cr)4 multilayer with the perfect interface ( 6 = 0 ) . Unfortunately, we could not obtain stable solutions for both AF and F con-

263

H. Hasegawa / Physica B 237 238 (1997) 261-263

2

,\ \,

\

I

0

i

0.0

0.2

0.4 T/Td 0.6

7 co

0.8

1.0

Fig. 3. The temperature dependence of AR/R, GMR ratio of (Fe)3/(Cr)4 multilayer. Circles and squares denote the parallel ([I) and perpendicular (_L) GMR, respectively, calculated using Eqs. (1) and (2) with self-consistently determined Ans; solid curves being shown for a guide of the eye. Dashed (dotted) curves denote the results calculated with yn ~ 0.05 and 0.1, respectively, by employing the assumption adopted in Ref. [3l (see text).

figurations at T/Tco > 0.82, where the presence of many meta-stable states is expected to make the selfconsistent calculation difficult. The moment of the host Fe atom (n = 2), central in a Fe layer, approximately follows the Brillouin function in both AF and F solutions. On the contrary, other moments, particularly those of impurity Cr at n = 2 and impurity Fe at n = 5, show a vary unusual temperature dependence, deviating significantly from the Brillouin function. Next we discuss GMR of our (Fe)3/(Cr)4 multilayer. The conductivities for currents parallel (ll) and perpendicular (_L) to the layer plane are given by [3]

vtt~anm/(Ans+Ams),

a'L = (e/h) 2 ~ s

n

(1)

m

where vII, v± and an,,., are specified by the electronic structure of the multilayer [3]. Since Ans, the imaginary part of the coherent potential of an s-spin electron on layer n, were obtained in course of the calculation of the layer moments, we can easily calculate the parallel and perpendicular GMR ratios, which are shown by circles and squares in

Fig. 3, respectively. The ground-state value of (AR/R) j- is 2.49, which is about four times larger than that of (AR/R) II (=0.61). For a comparison, we also calculated GMR with the assumption adopted in [3] that Fe layers have the same magnitude of local moments whose temperature dependence follows the Brillouin function. Dashed and dotted curves denote the results calculated with yn=0.05 and 0.10, respectively. We realize that GMR, in particular the perpendicular one, shows the significant temperature dependence at low temperatures, which arises from the peculiar temperature dependence of local moments. This effect is expected to become more significant in thinner films. It would be interesting to detect experimentally this unusual temperature dependence of local moments by means of some experimental techniques such as Mrssbauer method. References [1] H. Hasegawa, J. Magn. Magn. Mater. 126 (1993) 384. [2] H. Hasegawa, in: Magnetic Properties of Low Dimensional Systems I1, eds. L.M. Falicov, F. Mejia-Lira and J.L. Moran-Lopez (Springer, Berlin, 1990) pp. 175-187. [3] H. Hasegawa, Phys. Rev. B 47 (1993) 15080; J. Appl. Phys. 79 (1996) 6376.