Understanding Geometrical Frustration in Complex Magnetic Materials

Geometrical frustration -- the inability of a system to satisfy all its pairwise interactions simultaneously because of geometrical constraints -- can generate exotic states in magnetic materials, such as spin ices and quantum spin liquids [1]. The traditional route towards such states typically considers only magnetic interactions between nearest-neighbor and (sometimes) next-nearest-neighbor spins. Surprisingly, however, recent work has revealed that exotic spin-liquid states may be hosted in materials with complex exchange interactions [2,3]. In my talk, I will present neutron-scattering data and modeling results on two such materials, MgCr$_2$O$_4$ [4] and LiGaCr$_4$S$_8$ [5], and discuss the origin of the unexpected spin-liquid behavior in each case. In both materials, Cr$^{3+}$ magnetic ions occupy a frustrated lattice of corner-sharing tetrahedra, and the temperature of conventional magnetic ordering or spin freezing is strongly suppressed. I will show how the magnetic diffuse scattering observed in neutron-scattering experiments can be analyzed to determine the further-neighbor exchange interactions in these materials, providing a foundation for understanding both their spin dynamics and their magnetic ground states [4]. Finally, I will present a new open-source computer program for the refinement of spin Hamiltonians to magnetic diffuse-scattering data, to facilitate this type of analysis for a wide range of topical magnetic materials. [1] R. Moessner \& A. P. Ramirez, \emph{Physics Today} \textbf{15}, 24 (2006); [2] C. Balz \emph{et al.}, \emph{Nature Physics} \textbf{12}, 942 (2016); [3] P. Henelius \emph{et al.}, \emph{Phys. Rev. B} \textbf{93}, 024402 (2016); [4] X. Bai \emph{et al.}, \emph{Phys. Rev. Lett.} \textbf{122}, 097201 (2019); [5] G. Pokharel \emph{et al.}, \emph{Phys. Rev. B} \textbf{97}, 134117 (2018).