Anisotropic excitonic magnetism from discrete ${\mathrm{C}}_4$ symmetry in CeRhIn${}_5$

Abstract

Anisotropy in strongly correlated materials is a central parameter in determining the electronic ground state and is tuned through the local crystalline electric field. This is notably the case in the CeCo${}_x$Rh${}_{1-x}$In${}_5$ system where the ground-state wave function can provide the basis for antiferromagnetism and/or unconventional superconductivity. We develop a methodology to understand the local magnetic anisotropy and experimentally investigate with neutron spectroscopy applied to antiferromagnetic ($T_N$=3.8 K) CeRhIn${}_5$ which is isostructural to $d$-wave superconducting ($T_c$=2.3 K) CeCoIn${}_5$. Through diagonalizing the local crystal field Hamiltonian with discrete tetragonal ${\mathrm{C}}_4$ point group symmetry and coupling these states with the Random Phase Approximation (RPA), we find two distinct modes polarized along the crystallographic $c$ and $a-b$ planes, agreeing with experiment. The anisotropy and bandwidth, underlying the energy scale of these modes, are tuneable with a magnetic field which we use experimentally to separate in energy single and multiparticle excitations thereby demonstrating the instability of excitations polarized within the crystallographic $a-b$ plane in CeRhIn${}_5$. We compare this approach to a $S_{eff}=\frac{1}{2}$ parameterizations and argue for the need to extend conventional SU(2) theories of magnetic excitations to utilize the multi-level nature of the underlying crystal-field basis states constrained by the local point-group ${\mathrm{C}}_4$ symmetry.

(17 pages, 8 figures, to be published in Physical Review B)