Magnetic instabilities and phase diagram of the double-exchange model in infinite dimensions

Abstract

Dynamical mean-field theory is used to study the magnetic instabilities and phase diagram of the double-exchange (DE) model with Hund's coupling JH > 0 in infinite dimensions. In addition to ferromagnetic (FM) and antiferromagnetic (AF) phases, the DE model also supports a broad class of short-range ordered (SRO) states with extensive entropy and short-range magnetic order. For any site on the Bethe lattice, the correlation parameter q of an SRO state is given by the average q = ⟨ sin2 (θi/2)⟩, where θi is the angle between any spin and its neighbours. Unlike the FM (q = 0) and AF (q = 1) transitions, the transition temperature of an SRO state with 0 < q < 1 cannot be obtained from the magnetic susceptibility. But a solution of the coupled Green's functions in the weak-coupling limit indicates that an SRO state always has a higher transition temperature than the AF for all fillings p below 1 and even has a higher transition temperature than the FM for 0.26 ⩽ p ⩽ 0.39. For 0.39 < p < 0.73, where both the FM and AF phases are unstable for small JH, an SRO phase has a nonzero transition temperature except close to p = 0.5. As JH increases, the SRO transition temperature eventually vanishes and the FM phase dominates the phase diagram. For small JH, the T = 0 phase diagram of the DE model is greatly simplified by the presence of the SRO phase. An SRO phase is found to have lower energy than either the FM or AF phases for 0.26 ⩽ p < 1. Phase separation (PS) disappears as JH → 0 but appears for any nonzero coupling. For fillings near p = 1, PS occurs between an AF with p = 1 and either an SRO or a FM phase. The stability of an SRO state at T = 0 can be understood by examining the interacting density-of-states, which is gapped for any nonzero JH in an AF but only when JH exceeds a critical value in an SRO state.