Excitonic Magnetism in Ruthenium Pyrochlores

Abstract

Strong spin-orbit coupling in $d^4$ systems is expected to stabilize a nonmagnetic $J=0$ singlet ground state, yet many ruthenium pyrochlores exhibit robust long-range magnetic order. Motivated by this apparent contradiction, we develop a microscopic theory of Van Vleck excitonic magnetism on the pyrochlore lattice. Starting from a multi-orbital Hubbard model with spin-orbit coupling, we derive the effective superexchange interactions within the low-energy singlet--triplet manifold of Ru$^{4+}$ ions. We analyze the resulting excitonic Hamiltonian using both the spectrum of triplon excitations and a variational treatment of the condensed phase. We identify the instability of the nonmagnetic singlet state toward triplon condensation and determine the resulting magnetic phase diagram as a function of the microscopic hopping parameters. The phase diagram reproduces the magnetic orders known from conventional pyrochlore models while also predicting an additional magnetic phase unique to the singlet--triplet description. Finally, we apply the theory to the pyrochlore ruthenates, with particular emphasis on Nd$_2$Ru$_2$O$_7$, and show that it lies in close proximity to the excitonic quantum critical point. Our results establish a microscopic framework for understanding excitonic magnetism in pyrochlore ruthenates and their magnetic excitation spectrum, providing direct connections to spectroscopic probes, including Raman scattering.