A microscopic design rule for spin supersolids in triangular-lattice magnets

Abstract

Spin supersolids emerge as a central topic in frustrated magnetism, motivating the search for realization in quantum materials. To this end, we study the origin of exchange anisotropy, $Δ$, in triangular-lattice cobaltate families $X_2$$Y$Co(PO$_4$)$_2$ and $X_2$Co(SeO$_3$)$_2$ ($X$ = Na, K, Rb, Cs; $Y$ = Mg, Ca, Sr, Ba) by tailoring realistic spin models. We show that $Δ$ is determined by the ratio of trigonal crystal field to spin-orbit coupling strength. This framework explains contrasting anisotropies in these families, predicts systematic trends in $Δ$ across $X/Y$-substitutions, and identifies candidate materials for spin supersolids. Our results establish trigonal field engineering as a microscopic route toward the design of spin supersolids.