SUSCEPTIBILITY OF SPIN GLASSES

Abstract

The magnetic susceptibility of a spin glass (e. g. Cu with 1-10 % Mn) has a sharp cusp at the local ordering temperature, rapidly rounded off by an external magnetic field. We show how the local molecular field theories can be generalized to account for this effect. One defines a local order parameter which is a collective feature of the whole solid due to the random position of the spins and their long-range, oscillatory interaction (RKKY). The critical temperature for the disappearance of local order is therefore unique, as, for example, the screening length of a perturba- tion in a metal is a unique, collective contribution of all the electrons. 1. The recent discovery by Cannella and Mydosh of a cusp in the magnetic susceptibility as a function of the temperature of several spin glasses at zero external magnetic field (I), presents an immediate theoretical challenge. The problem is to reconcile the existence of the sharp cusp with the absence of long range magnetic order characteristic of the spin glasses (2). More specifically, the idea of each spin being in a molecular field which is a random variable with a broad distribution P(H) appears at first sight to be in contradiction with the sharp ordering tem- perature observed by Cannella and Mydosh. In this paper, we show how a cusp in the magnetic susceptibility can be obtained from a molecular field theory with a distribution P(H) calculated from first principles. The cusp is associated with the disappea- rance of short range order. What makes this short range order a truly collective effect involving all the spins in the alloy is the infinite range of the (Ruder- mann-Kittel-Kasuya-Yosida) interaction J(R) between spins (mean free path effects will be discussed in the conclusion). However, the occurrence of long range order is prevented by the random position of the spins together with the oscillatory nature of their interaction. In the calculation of P(H), a short range order parameter - the local magnetisation - for which a self-consistent equation can be found, occurs natu- rally. As a function of temperature, this order para- meter goes to zero at some ordering temperature To in the standard fashion of mean-field theories, i. e. like (To - T)~. To this sudden disappearance of the local magnetisation there corresponds a cusp in the susceptibility. 2. We calculate the distribution of local molecular field P(H) due to N magnetic impurities located at random from first principles, in an Ising, spin 4 model, for simplicity. Generalisation to a Heisenberg model is straightforward, indeed the Ising distribution P(H) is identical to the distribution in the Heisenberg model of molecular field along an arbitrary z direction P(H,) = 2 n dH, H, P(g)