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

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

OF LOCAL MAGNETIC MOMENTS

K. Bennemann, J. Garland

To cite this version:

K. Bennemann, J. Garland. THEORY FOR THE EFFECT OF THE LOCAL ATOMIC ENVI- RONMENT ON THE FORMATION OF LOCAL MAGNETIC MOMENTS. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-750-C1-752. �10.1051/jphyscol:19711260�. �jpa-00214091�

JOURNAL DE PHYSIQUE Colloque C I , supplkment au no 2-3, Tome 32, Fe'vrier-Mars 1971, page C 1 - 750

THEORY FOR THE EFFECT OF THE LOCAL ATOMIC ENVIRONlWENT ON THE FORMATION OF LOCAL MAGNETIC MOMENTS (*)

K. H. BENNEMANN and J. W. GARLAND

University of Rochester, Rochester, New York and Argonne National Laboratory, Argonne, Illinois

Rbumb. - On presente une theorie qui donne les effets du voisinage atomique sur la stabilite des moments localis6s, sur la temperature a laquelle ils apparaissent dans un amas d'atomes magnetiques, sur celle A laquelle ils s'ordonnent, et celle a laquelle les moments des differents amas s'ordonnent. On trouve que la separation covalente des etats d'electrons d provoque l'apparition et le blocage des moments dans les alliages Cu : Ni et Au : V. La persistance des moments au- dessus de la temperature de Curie dans Cu : Ni, predite ici, est confirmee par les mesures de resistivite et d'dmission photo- Clectrique.

Abstract. - 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 appea- rance 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 fre- quently the stability of local magnetic moments depends sensitively on the surrounding atomic envi- ronment. 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 interest- ing 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 func- tion 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:

+

+

Here, E: denotes the unperturbed energy of the d-states assumed to be degenerate, U , and J, denote the intra-atomic Coulomb- and 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 t o recognize that this is an adequate approximation only for very dilute concen- trations 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.,,

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 poten-

tial approximation is presently performed with the (1 - c) ~ C U a ~ C C I t6i ^a + ^{( C} - nccl) ^{t ~a i}= 0 . ( 6 ) helo of an electronic comouter.

we

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 magne- tic 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

A,,, (mi, = 0) .

Eq. (8) can also be put into the form

m, = (U,

+

+

+

1'

where denotes the unenhanced static susceptibility due to the d-states at the atomic site I.

The Curie temperature of a cluster of magnetic moments is approximately given by

where ~ i y ' d e n o t e s the Gibbs free-energy for 2 nearest neighbor atoms 1 and I' with spin o and of. F;" can be determined from G,,,. Using the Heisenberg Hamilto- nian one finds that the spins of a cluster of magnetic atoms begin to align at Tc ⁼ 4 ^zl JS(S

+

A detailed numerical evaluation of the above outlined theory for atomic environment effects on

summarize now some preli&inary results and the main physical features of our theory. According to m,(E,)

151, which (for J, = 0 ) is symmetric with respect to El = U,/2 and zero at E, x 0 and El x U,, we expect that the magnetic moment of an isolated Ni-atom in Cu : Ni alloys is quenched since ( U ,

+

+

+

I I f > and I I 4 > farther below EF. It follows from an approximate evaluation of eq. (1) and eq. (2) using T,,. = 0.15 eV that for a spherically symmetric cluster of Ni-atoms the central Ni-atom possesses a magnetic moment for 2, 2 6. Since

and TNiNi < TNiFe one finds for TNiF, x 0.2 eV that p1 increases by about 30 % if the central Ni-atom is replaced by a Fe impurity. The observed stability of the magnetic moments in Au : V alloys is explained by assuming for one isolated V-atom that El x U,/2, (U,

+

Since the covalent splitting decreases rapidly with increasing distance between two V-atoms, it follows then from eq. (9) that

and hence that two V-atoms which are not nearest neighbors strengthen mutually their magnetic moments. Calculating approximately TM(l) from eq. (1) one finds that TM(I) 2 T ,

and approximately T , x 2 Tc for 2, w 12.

Consequently, we expect that around the Curie temperature of a cluster of magnetic moments the electrical resistivity p,, resulting from the conduction electron scattering by the clusters of magnetic moments should approximately change by

where c,, denotes the concentration of the clusters of magnetic moments with aveiage total spin Scl and consisting of n atoms with average spin S. This predic- tion is supported by the anomalous electrical resistivity observed for Cu : Ni alloys [3]. Also T M ( l ) > T, implies a splitting BE, 2 U, ml of the d-states 1 1

t

and I I J > at the atomic site I which explains, for

example, for Ni the absence of a shift at T , of the optical density of states Nd(E) deduced from photo-

C 1

-

emission. A shift of N,(E) should be observed at Consequently, the low temperature specific-heat of TM. It follows from recent susceptibility measurements Cu : Ni alloys resulting from spin clusters cannot be that the average spin excitation energy E of the spin explained by using the equipartition theorem as has clusters in Cu : Ni is E NN 6 > kB T a t T 2 1 OK. been done previously.

References

[I] ROBBINS (C. G . ) , CLAUS (H.), and BECK (P. A.), Phys. [4] KOUVEL (J. S.) and COMLY (J. B.), Phys. Rev. Letters,

Rev. Letters, 1969, 22, 1307. 1970, 24, 598.

[2] CLAUS (H.), SINHA (A. K.) and BECK (P. A.), Phys. [S] ANDERSON (P. W.), Phys. Rev., 1961, 124,41.

Letters, 1967, 26A, 38. [6] KIM (D. J.), Phys. Rev., 1970, B 1 , 3725.

[33 HOUGHTON (R. W.), SARACHIK (M. P.) and Kou- [7] SOVEN (P.), Phys. Rev., 1969, 178, 1136.

VEL (J. S.), Phys. Rev. Letters, 1970, 25, 238.