Metamagnetism and crystal-field splitting in pseudohexagonal CeRh3Si2

${\mathrm{CeRh}}_{3}{\mathrm{Si}}_{2}$ has been reported to exhibit metamagnetic transitions below 5 K, a giant crystal field splitting, and anisotropic magnetic properties from single crystal magnetization and heat capacity measurements. Here we report results of neutron and x-ray scattering studies of the magnetic structure and crystal-field excitations to further understand the magnetism of this compound. Inelastic neutron scattering and resonant inelastic x-ray scattering reveal a ${J}_{z}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}1/2$ ground state for Ce when considering the crystallographic $a$ direction as quantization axis, thus explaining the anisotropy of the static susceptibility. Furthermore, we find a total splitting of 78 meV for the $J=5/2$ multiplet. The neutron diffraction study in zero field reveals that, on cooling from the paramagnetic state, the system first orders at ${T}_{{\text{N}}_{1}}=4.7\phantom{\rule{4pt}{0ex}}\mathrm{K}$ in a longitudinal spin density wave with ordered Ce moments along the $b$ axis (i.e., the [0 1 0] crystal direction) and an incommensurate propagation vector $\mathbf{k}=(0,0.43,0$). Below the lower-temperature transition ${T}_{{\text{N}}_{2}}=4.48\phantom{\rule{4pt}{0ex}}\mathrm{K}$, the propagation vector locks to the commensurate value $\mathbf{k}=(0,0.5,0)$, with a so-called lock-in transition. Our neutron diffraction study in applied magnetic field $H\ensuremath{\parallel}b$ axis shows a change in the commensurate propagation vector and development of a ferromagnetic component at $H=3\phantom{\rule{4pt}{0ex}}\mathrm{kOe}$, followed by a series of transitions before the fully field-induced ferromagnetic phase is reached at $H=7\phantom{\rule{4pt}{0ex}}\mathrm{kOe}$. This explains the nature of the steps previously reported in field-dependent magnetization measurements. A very similar behavior is also observed for the $H\ensuremath{\parallel}$ [0 1 1] crystal direction.