Magnetic stimulation of an impurity by a vacancy

Volume

45A, number

5

PHYSICS

MAGNETIC

STIMULATION

22 October

LETTERS

OF AN IMPURITY

1973

BY A VACANCY

B.G.S. DOMAN Department

ofApplied

Mathematics,

University of Liverpool,

Received

13 September

P.O. Box 147, Liverpool,

197 3

The Green functions derived in the preceding letter are used to show how a vacancy late a non-magnetic transition metal atom to become magnetic.

In the preceding letter [l] it was shown that the Green function method of Kim and Nagaoka [2] can be used to calculate the interaction energy between a vacancy and a transition metal impurity in a noble metal. In this letter we shall see how this same interaction could lead to the magnetisation of an impurity atom such as Co which by itself would be non-magnetic. We start by expanding eq. (7) of ref. [l] in the way used in the treatment of two almost magnetic impurities [3]

G,, = (D(E) + UUJ’

+ V2 WJ&E) (D(e)+ UC@.

(1)

Following the argument in ref. [3] we have i;O(e + io) = + npi, and &(E f io) = ~ rtp exp(* ik,R)/k,R, where p is the density of states at the Fermi energy, k, is the wave vector of a free electron with energy eandR= iR, -R,l. From (1) we can evaluate u = +((n,+) - (n,_)) ; 8 WEF 2 71~= arctan (x +yu) + ~__

L69 3BX. UK

in a noble me!al could

Here x = (E,: - ed)/A,y

stimu

= u/A. A = nV*p, g(s) =

(s cos s - sin s)/s4 and g(s) = (s sin s + cos s)/s4.

lo see how magnetism might be stimulated let us consider the simplest case when x = 0 and expand the right hand side of (2) in powers of u, mJ =yu ~ fyV... +(16WeF~u/V2)

(1 -~2y2u2...)g(2k$7).

It can be seen that eq. (3) has a real solution than zero provided

(3) other

y >yc = rr/(l + 16We, ~(2k$)/V2).

(4)

For certain separations y, < rr, its value in the absence of the interaction. For such separations it is clear that the vacancy could stimulate the impurity to become magnetic.

References

V*

x (Kx +_YKP -

~a

384

118w~mt2(x tw)a2w)) [(xtyu)* t I] 2

similar expression with -u instead of u.

111K. Masuda, Phys. Lett. 45A (1973) 381. 121 D.J. Kim and Y. Nagaoka, Prog. Theor. Phys. 30 11963)

(2)

743. 131 R.B. Middleton (1971) 611; R.B. Middleton,

and B.G.S. Doman, Ph.D. Thesis,

Phys. Stat. Sol. 45

Liverpool

1973.