Systematic extraction of crystal electric-field effects and quantum magnetic model parameters in triangular rare-earth magnets

Abstract

A primary goal at the interface of theoretical and experimental quantum magnetism is the investigation of exotic spin states, mostly notably quantum spin liquids (QSLs) that realize phenomena including quasiparticle fractionalization, long-ranged entanglement, and topological order. Magnetic rare-earth ions go beyond the straightforward paradigm of geometrical frustration in Heisenberg antiferromagnets by introducing competing energy scales, and in particular their strong spin-orbit coupling creates multiple split crystal electric-field (CEF) levels, leading to anisotropic effective spin models with intrinsic frustration. While rare-earth delafossites have a triangular-lattice geometry and thus have gained recent attention as candidates for hosting spin-1/2 QSL physics, the reliable extraction of effective spin models from the initial many-parameter CEF spectrum is a hard problem. Using the example of ${\mathrm{CsYbSe}}_{2}$, we demonstrate the unambiguous extraction of the Stevens operators dictating the full CEF spectrum of ${\mathrm{Yb}}^{3+}$ by translating these into parameters with a direct physical interpretation. Specifically, we combine low-field susceptibility measurements with resonant torsion magnetometry (RTM) experiments in fields up to 60 T to determine a sufficiently large number of physical parameters---effective Zeeman splittings, anisotropic van Vleck coefficients, and magnetotropic coefficients---that the set of Stevens operator coefficients is unique. Our crucial identification of the strong corrections to the Zeeman splitting of Kramers doublets as van Vleck coefficients has direct consequences for the interpretation of all anisotropic magnetic susceptibility measurements. Our results allow us to determine the nature and validity of an effective spin-1/2 model for ${\mathrm{CsYbSe}}_{2}$, to provide input for theoretical studies of such models on the triangular lattice, and to provide additional materials insight into routes for achieving magnetic frustration and candidate QSL systems in rare-earth compounds.