Double exchange in a magnetically frustrated system

This work examines the magnetic order and spin dynamics of a double-exchange model with competing ferromagnetic and antiferromagnetic Heisenberg interactions between the local moments. The Heisenberg interactions are periodically arranged in a Villain configuration in two dimensions with nearest-neighbour, ferromagnetic coupling J and antiferromagnetic coupling -ηJ. This model is solved at zero temperature by performing a 1/√S expansion in the rotated reference frame of each local moment. When η exceeds a critical value, the ground state is a magnetically frustrated, canted antiferromagnet. With increasing hopping energy t or magnetic field B, the local moments become aligned and the ferromagnetic phase is stabilized above critical values of t or B. In the canted phase, a charge-density wave forms because the electrons prefer to sit on lines of sites that are coupled ferromagnetically. Due to a change in the topology of the Fermi surface from closed to open, phase separation occurs in a narrow range of parameters in the canted phase. In zero field, the long-wavelength spin waves are Isotropic in the region of phase separation. Whereas the average spin-wave stiffness in the canted phase increases with t or η, it exhibits a more complicated dependence on field. This work strongly suggests that the jump in the spin-wave stiffness observed in Pr_1-xCa_xMnO₃ with 0.3 ≤ x ≤ 0.4 at a field of 3 T is caused by the delocalization of the electrons rather than by the alignment of the antiferromagnetic regions.