Theory of the ordered phase in A-site antiferromagnetic spinels

Insulating spinel materials, with the chemical formula AB₂X₄, behave as diamond lattice antiferromagnets when only the A-site atom is magnetic. Many exhibit classic signatures of frustration, induced not geometrically but by competing first- and second-neighbor exchange interactions. In this paper, we further develop a theory [ D. Bergman et al. Nat. Phys. 3 487 (2007)] of the magnetism of these materials, focusing on the physics observable within the ordered state. We derive a phenomenological Landau theory that predicts the orientation of the spins within incommensurate spiral ordered states. It also describes how the spins reorient in a magnetic field and how they may undergo a low-temperature “lock-in” transition to a commensurate state. We discuss microscopic mechanisms for these magnetic-anisotropy effects. The reduction in the ordered moment by quantum fluctuations is shown to be enhanced due to frustration. Our results are compared to experiments on MnSc₂S₄, the best characterized of such A-site spinels, and more general implications are discussed. One prediction is that magnetically induced ferroelectricity is generic in these materials, and a detailed description of the relation of the electric polarization to the magnetism is given.