Emergent magnetic anisotropy in cubic CeIn$_3$

Metals containing cerium exhibit a diverse range of fascinating phenomena including heavy fermion behavior, quantum criticality, and novel states of matter such as unconventional superconductivity. Because spin-orbit coupling and crystal field energy scales are large relative to the energy scales of the associated phenomena it is generally believed to be safe to assume that the interactions between the f-electrons are spherically symmetric in spin space. By using magnetic fields with strengths comparable to the crystal field energy scale we illustrate the breakdown of the spherical approximation in the prototypical cubic heavy fermion material CeIn$_3$, which also displays unconventional superconductivity near a quantum critical point under applied pressure. Above 40 T, the H-T phase diagram develops a surprising anisotropy. This work illustrates that magnetic fields can tune the effective hybridization and exchange interactions potentially leading to new exotic field tuned effects in f-based materials.