Mobile-Electron Ising Ferromagnets

Abstract

A general mobile-electron Ising model is described and its properties discussed: electrons migrate over a lattice of spin-½ positive ions; when there are k electrons on the bond (i, j), their energy is εk, and they induce an Ising spin coupling between the spins i and j. The mean number of electrons per bond, n, is determined by the condition of electroneutrality. The model is solved exactly in terms of the free energy of the underlying lattice; in three dimensions the magnetization, susceptibility and specific heat exhibit the renormalized1 critical-point exponents2 β=0.33−0.36, γ≃1.43, αs≃−0.14. The behavior of the simplest ferromagnetic model with k=0, 1 or 2, and n≤2 depends, for a fixed mode of electron-ion coupling, only on n and ε=2ε1−(ε0+ε2). When ε→−∞ (n≤1), bonds with k=2 are suppressed and the model becomes equivalent to Syozi's dilute ferromagnet.3 For ε<ε*= E0,0+E0,2−2E0,1 (where E0,k is the ground-state magnetic energy of a k bond) the model remains similar to Syozi's, having a critical concentration for the occurance of ordering nc=pc (determined by the underlying Ising lattice; see Ref. 3). However, when ε>ε* and 2pc>n>p*>pc a lower critical temperature arises, below which the spontaneous magnetization M0(T) again vanishes; this results from self-dilution on cooling owing to loss of k=1 bonds as T→0. When n=2pc this Tc, lower vanishes; for 2>n>2pc there is no lower critical point, but M0(T) at first increases with T. With the addition of direct ion coupling and antiferromagnetic interactions the model exhibits an even greater variety of behavior.