THEORY FOR THE EFFECT OF THE LOCAL ATOMIC ENVIRONMENT ON THE FORMATION OF LOCAL MAGNETIC MOMENTS

A theory is presented for the effects of the atomic environment on the stability of localized magnetic moments, on the temperature at which the spins of a cluster of magnetic atoms appear, order, and at which magnetic order among different magnetic clusters occurs. It is argued that the covalent splitting of the d-electron states causes the appearance and quenching of the magnetic moments in Cu : Ni and Au : V alloys. The predicted persistance of magnetic moments above the Curie temperature in Cu : Ni is supported by the electrical resistivity and photo-emission. Recently, many experiments have shown that frequently the stability of local magnetic moments depends sensitively on the surrounding atomic environment. For example, in Cu : Ni alloys Ni-atoms help each other to acquire a local magnetic moment [I] and in Au : V alloys nearest neighbor V-atoms help each other to quench their magnetic moments while V-atoms which are not nearest neighbors strengthen their magnetic moments [2]. For Cu : Ni alloys one observes an anomalous electrical resistivity which disappears at a temperature corresponding to the Curie temperature of Ni [3], spin order among different clusters of magnetic Ni-atoms [4], and that Fe impurities increase considerably the giant magnetic moments existing in Cu : Ni alloys. In the following we attempt to explain these interesting experimental observations by using the Anderson theory for the formation of local magnetic moments [ 5 ] . The magnetic moment m, of the I-th impurity is given by where the Green's function G,,(o) for the d-electrons with energy o and spin a at the atomic site 1 is given by Here, T,,, denotes the hopping integral describing the electronic transitions between the localized d-states at the atomic sites I and 1', and A, denotes the width of (*) Supported in part by the U. S. Office of Naval Research and in part by the U. S. Atomic Energy Commission. the d-states at the atomic site I which results from their hybridization with the conduction electron states [5]. The admixture potential T,, describes the electronic transitions between the localized d-states and the states of the conduction electrons which Green's function is denoted by Gk,(o). Gr,,(o) is the off-diagonal Green's function involving the atomic sites I and I" [S], and U 2 U , E , = E: + --' N , + (U, J,) N , a m1 2 5 Here, E: denotes the unperturbed energy of the d-states assumed to be degenerate, U, and J, denote the intra-atomic Coulomband Hund's rule exchange integral of the I-th atom with d-electrons, and J , , denotes the interatomic exchange integral. In all previous theoretical studies [6] of atomic environment effects on local magnetic moments eq. (2) has been used with G,.,, put equal to zero. how eve^, it is important to recognize that this is an adequate approximation only for very dilute concentrations of magnetically active impurities and for weak hybridization of the localized magnetic impurity d-states with the host d-band. If this is not the case, then G , , need be determined by G,,,, = G.,, where Here, the Green's function G,,,, is determined by the coherent potential approximation [7] Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711260 THEORY FOR THE EFFECT OF THE LOCAL ATOMIC ENVIRONMENT C 1 751 and magnetic moment formation using the coherent potential approximation is presently performed with the (1 c) ~ C U a ~ C C I t6i a + ( C nccl) t ~ i a = 0 . (6) helo of an electronic comouter. we would like to The t-matrix tl, = v,(l v,, G;,)-l describes the multiple electron scattering by v,, r El, ~, . t , '~ , refers to the Ni-atoms having a magnetic moment. C and C,, are the concentration of Ni and magnetic Ni clusters. For the treatment of a cluster of n magnetic atoms in alloys we propose to rewrite eq. (2) as where I' sums over all atomic sites I' which scattering t-matrices change if we change the average atomic composition around the atomic site I by replacing atoms of type B, which effect on GI,, is already included in GI,,,, by atoms of type A. Hence, if I' refers to an atomic site where an atom of type B has been replaced by one of type A, then ti,, arises from If I' refers to an atomic site which magnetic moment changes form m , to mi, upon changing the average atomic composition in its vicinity, then t;,, results from u;,, E Elt,(m;,) El,,(mr). Substituting now eq. (2) or eq. (7) into eq. (I), one finds the general result The appearance of magnetic moments m,(T,(l)) at the temperature TM(l) within a cluster consisting of I magnetically active atoms is then calculated from the 1 linear equations obtained from eq. (8) for