Solid State Communications, Vol. 44, No. 8, pp. 1247-1251, 1982. Printed in Great Britain. 0038-10981821441247-05503.00]0 Pergamon Press Ltd. DOMAIN-LIKE MAGNETIC STRUCTURE IN SUPERCONDUCTORS OF ErRh4B4 AND HoMo6S8 TYPE L.N. Bulaevskii, A.I. Buzdin and S.V. Panyukov P.N. Lebedev Physical Institute, Moscow, U.S.S.R. and M.L. Kuli6 Institute of Physics, P.O. Box 57, 11011 Beograd, Yugoslavia (Received 7 December 1981;in revised form 18 January 1982 by B. MOhlschlegel) The problem of the coexistence of superconductivity and magnetic order is studied by taking into account the indirect exchange interaction, magnetic dipolar interaction and magnetic anisotropy. It is shown that the domain-like magnetic structure should be realized in the superconducting phases of ErRh4B4 and HoMo6S8 at the temperatures Tm= 1.4 and 0.7 K respectively. The transition from superconducting domain-like phase (DS) to the normal ferromagnetic (FN) state is described. THE INTEREST in the problem of the coexistence of superconductivity and magnetic order is due to their antagonistic character. Anderson and Suhl [1] have shown that the competition of these two forms of order gives rise to a new effect; if the indirect exchange inter- action in the absence of superconductivity gives a ferro- magnetic order below temperature 0c, then the presence of superconductivity induces a nonuniform magnetic order below temperature Tm which is close to 0e. Later, Krey [2a], Blount and Varma and others (see [2b] and references therein) arrived to the similar conclusion by assuming that the interaction between superconducting electrons and magnetic moments is realized via the magnetic field generated by the moments. Recent experiments on neutron scattering confirm that the nonuniform magnetic order, with the wave- vector Q ~ 0.06 A -l, appears in the superconducting state of ErRh4B4 below T m = 1.4 K. The superconduct- ing critical temperature of ErRh4B4 is Tel = 8.7 K. At the temperature To ~ 0.9 K a transition to the normal ferromagnetic (FN) state takes place [3]. Similar behaviour has been observed also in HoMo6Ss with Tot ~ 1.8 K, T m ~ 0.7 K, Q ~ 0.03 A -1 and To2 ~ 0.65 K [4]. Complete theoretical treatment of compounds ErRh4B4 and HoMo6Sa must take into account the exchange (EX) and electromagnetic (EM) interaction between the superconducting electrons and localized magnetic moments, as well as the magnetic anisotropy (MA) of the system. However, recently models were studied with either neglect the EX interaction [2], or take into account only the EX and EM interactions neglecting MA [5]. In this paper we will treat the problem of the coexistence of magnetism and superconductivity includ- ing EX, EM and MA. In [5] it is shown that in the absence of MA, the helical order of magnetic moments and superconductivity could coexist. Here we will show that MA transforms the helical order into a domain-like structure, and that this structure is determined mainly by EX and MA terms for realistic values of parameters. We shall also evaluate the parameters of this structure and compare them with the experimental data available at the present time. We shall consider the system of superconducting electrons (BCS model) and the localized magnetic moments (LM) regularly distributed on a crystal lattice. Magnetic moments, at sites {rl}, are treated in the mean- field approximation, i.e. the operator of magnetic moment Si is replaced by the mean value Si = (S~), where 0 ~< I<Si>l ~< 1. The Hamiltonian of the system is given by + A(r) $÷(r) ioy$÷(r) + A*(r) if(r) ior$(r ) +--IAI2+ B2(r) + ~ ](r -- ri) ff+(r)oO(r) Si g i + ~ [--/aSgB(ri) + DS~ + DS?z], (I) i where if(r) is the spinor operator,a are Pauli matrices, B is the magnetic induction, A(r) is the superconduct- ing order parameter, g is the parameter of the 1247