Physica 108B (1981] 1239-1240 SF 14 North-Holland Publishing Company THE INFLUENCE OF THE DISORDERED FERROMAGNETISM ON THE SUPERCONDUCTIVITY Mircea Crisan, Alexandru Anghel, and Szolt Gulacsi Department of Physics, University of Cluj 3400 Cluj-Napoca, Romania The influence of the disordered ferromagnet on superconductivity is studied in the molecular field approximation. The disordered ferromagnet is obtained, from spin- spin interaction of the quenched randomly distributed impurities. The equation for the magnetic susceptibility and the critical temperature is obtained. 1. INTRODUCTION The coexistence of the magnetic order and super- conductivity has been recently reconsidered in connection with the new experimental results ob- tained by Roth [i], Fischer [2], Lynn et al. [3], and Willis et al. [4]. These results support the hypothesis of the co- existence between superconductivity and short range magnetic order which is supposed to be the spin-glass state. In the theory of the spin- glass state, Sherrington and Kirkpatrick [5] pointed out the existence of two regions in the phase diagram: the pure spin-glass state and the disordered ferromagnet state. The pure spin-glass state is described by q ~ 0 (q is the Edwards-Anderson parameter) but in the dis- ordered ferromagnet state the magnetization and the parameter q are at the same time different from zero. The influence of the pure spln-glass state on the superconductivity has been recently treated by Soukoulis and Grest [6] in the Born approxi- mation. It is the purpose of this paper to treat the influence of the disordered ferromag- netic state on the superconductivity in the molecular field approximation. In order to overcome the difficulties connected with the description of the spin-glass state we adopted for the impurity spins the random co- linear structure proposed by Medvedev and Zaborov [7]. This model is equivalent with the infinite-range model proposed in [5] , and which is described by the Hamiltonian H = ~ Jij<siZ>sj z cos ~iJ - ~B gH ~j Sj cos Oj s i J (i) where Ji" is the exchange integral between the Ni 3 impurities in the lattice and <'''> is the thermal average. In the Hamiltonian (i) it is assumed that each spin has its own local quantization axis which is determined by the equilibrium orientation of the molecular field at the site+"i". The unit vector of the molecu- lar field e. at the site "J" is defined by the 3 projections on the laboratory coordinate system as 5. = (sin @. cos e sin 8. sin ej, cos 8j) 3 3 J' 3 and cos~ ij = +ei.e j .+ The total Hamiltonian which describes the superconducting alloy con- taining magnetic impurities is H = HBC S + Hs_ d + H s + H z (2) where HBC S is the Bardeen-Cooper-Schrieffer Hamiltonlan, H is the spin-spin interaction Hamlltonian (i)~ i r ÷÷ %÷ ÷ Hs-d = - 2-N [i J d~ l(r-R i) ~ (r)O~8~8(r) (3) Hz =-~Bg lj ~jHj - --N- [i dr ~ ~a (r)O~8~B(r)6(r-Ri) (4) J where I is the s-d interaction, H the external magnetic field, o B the Pauli matrices, ~a (r), ~8(r) the creation, respectively, anni- hilation operators for the electrons. If we consider l(r-R i) = 16(r-R i) the Hamiltonian (3) becomes I [i SiMi (5) Hs_ d = - where M i = ~e (r)OaS~8 (r)" Now, we have to re- mark that in this model the impurity spin ~i as well as the magnetic moment M. are random variables and we consider the I two cases SiM i (6) 2. ~i~i = SiN i cos @i For the magnetic moment of the electrons local- ized on the impurity site we will use M i E Mi z = [ exp i~i(~-I')(C~÷Ck÷- C~$Ck+) i,k,k' (7) 0378-4363/81/0000-0000/$02.50 © North-Holland Publishing Company 1239