# A neutron scattering measurement of crystalline-electric fields in magnesium rare-earth selenide spinels

## TL;DR

This study uses inelastic neutron scattering to determine the crystal electric field excitations in magnesium rare-earth selenide spinels, revealing their ground state properties and magnetic behaviors relevant to frustrated magnetism.

## Contribution

The paper provides the first detailed CEF analysis for MgRE$_2$Se$_4$ spinels, experimentally confirming ground state characteristics and magnetic anisotropies for multiple rare-earth variants.

## Key findings

- MgTm$_2$Se$_4$ has a non-magnetic ground state
- MgYb$_2$Se$_4$ exhibits effective $S=1/2$ spins with specific g-factors
- MgHo$_2$Se$_4$ has a ground state doublet with Ising spins and accessible low-lying CEF levels

## Abstract

The symmetry of local moments plays a defining role in the nature of exotic grounds states stabilized in frustrated magnetic materials. We present inelastic neutron scattering (INS) measurements of the crystal electric field (CEF) excitations in the family of compounds MgRE$_2$Se$_4$ (RE $\in$ $\{$Ho, Tm, Er and Yb$\}$). These compounds form in the spinel structure, with the rare earth ions comprising a highly frustrated pyrochlore sublattice. Within the symmetry constraints of this lattice, we fit both the energies and intensities of observed modes in the INS spectra to determine the most likely CEF Hamiltonian for each material and comment on the ground state wavefunctions in the local electron picture. In this way, we experimentally confirm MgTm$_2$Se$_4$ has a non-magnetic ground state, and MgYb$_2$Se$_4$ has effective $S=\frac{1}{2}$ spins with $g_\parallel = 5.188(79)$ and $g_\perp = 0.923(85)~\mu_B$. The spectrum of MgHo$_2$Se$_4$ indicates a ground state doublet containing Ising spins with $g_\parallel = 2.72(46)$, though low-lying CEF levels are also seen at thermally accessible energies $\delta_E = 0.591(36)$, 0.945(30) and 2.88(7)~meV, which can complicate interpretation. These results are used to comment on measured magnetization data of all compounds, and are compared to published results on the material MgEr$_2$Se$_4$.