Materials containing non-Kramers magnetic ions can show unusual quantum excitations because of the exact mapping of the two-singlet crystal-field ground state to a quantum model of Ising spins in a transverse magnetic field. Here, we model the magnetic excitation spectrum of garnet-structured Ho3Ga5O12, which has a two-singlet crystal-field ground state. We use a reaction-field approximation to explain published inelastic neutron-scattering data [Zhou et al., Phys. Rev. B 78, 140406(R) (2008)] using a three-parameter model containing the magnetic dipolar interaction, the two-singlet crystal-field splitting, and the nuclear hyperfine coupling. Our study clarifies the magnetic Hamiltonian of Ho3Ga5O12, reveals that the nuclear hyperfine interaction drives magnetic ordering in this system, and provides a framework for quantitative analysis of magnetic excitation spectra of materials with singlet crystal-field ground states.
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