Spin-lattice coupling from first principles

The hexagonal manganites are a class of multiferroic materials that are simultaneously ferroelectric and antiferromagnetic, in which many physically interesting and potentially technologically relevant manifestations of spin-lattice coupling have been observed. Chromium spinels such as ZnCr$_2$O$_4$ and CdCr$_2$S$_4$ are antiferromagnetic and ferromagnetic insulators respectively, each displaying a differrent manifestation of a spin-lattice effect. In ZnCr$_2$O$_4$ a large magnetically induced phonon anisotropy has been observed while mode-dependant phonon anomalies have been measured in CdCr$_2$S$_4$. With the continuing advances in theoretical algorithms such as the LSDA+U method and in computational power it is now possible to study structurally and magnetically complex solids such as these using density-functional first-principles methods. Here, I describe a first-principles approach to study the influence of magnetic order on the phonons and dielectric properties of YMnO$_3$, ZnCr$_2$O$_4$, and CdCr$_2$S$_4$, our ongoing investigation of the coupling between the magnetic order and polarization in hexagonal manganites, and the search for ferroelectric behaviour in the simple ferromagnet CdCr$_2$S$_4$.