Double Exchange in a Magnetically Frustrated System

Abstract

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-neighbor, ferromagnetic coupling $J$ and antiferromagnetic coupling $-\eta J$. This model is solved at zero temperature by performing a $1/\sqrt{S}$ expansion in the rotated reference frame of each local moment. When $\eta$ 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 $\eta$, it exhibits a more complicated dependence on field. This work strongly suggests that the jump in the spin-wave stiffness observed in Pr${}_{1-x}$Ca${}_x$MnO${}_3$ with $0.3\le x\le 0.4$ at a field of 3 T is caused by the delocalization of the electrons rather than by the alignment of the antiferromagnetic regions.

28 pages, 12 figures

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Cited by in corpus (2)

• Spin Rotation Technique for Non-Collinear Magnetic Systems: Application to the Generalized Villain Model
• Spin Dynamics of a Canted Antiferromagnet in a Magnetic Field