Anisotropic excitonic magnetism from discrete C₄ symmetry in CeRhIn₅

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 CeCoₗRh₁-ₗIn₅ 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₍=3. 8 K) CeRhIn₅ which is isostructural to d-wave superconducting (T₂=2. 3 K) CeCoIn₅. Through diagonalizing the local crystal field Hamiltonian with discrete tetragonal C₄ 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 CeRhIn₅. We compare this approach to a S₄₅₅=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 C₄ symmetry.