The magnitude of the magnetic exchange interaction in the heavy fermion antiferromagnet CeRhIn$_{5}$*

The family of heavy fermion compounds Ce$T$In$_{5}$ ($T$ = Co, Rh, Ir) has been a fertile ground to explore and understand the interplay between magnetism, unconventional superconductivity and quantum criticality due to their tunability by pressure, substitution and magnetic field. CeRhIn$_{5}$ is a heavy fermion antiferromagent which can be tuned to quantum criticality under pressure. The strength of the magnetic exchange interaction, which is a key parameter to understand its complex properties, however remained unknown. We have used high-resolution neutron spectroscopy to determine the complete spin wave spectrum in CeRhIn$_{5}$. The spin wave dispersion can be quantitatively reproduced with a simple frustrated $J_1-J_2$ model that also naturally explains the magnetic spin-spiral ground state of CeRhIn$_{5}$ and yields a dominant in-plane nearest-neighbor magnetic exchange constant $J_0 = 0.74(3)$ meV. Our results pave the way to a quantitative understanding of the rich low-temperature phase diagram of the prominent Ce$T$In$_{5}$ class of heavy fermion materials.