Neutron-Scattering Study of Spin Waves in the Ferrimagnet RbNiF3

RbNi${\mathrm{F}}_3$ is a transparent hexagonal ferrimagnet with $T_c=133\mathrm{}°$K. Below $T_c$ the ${\mathrm{Ni}}^{++}$ magnetic moments are aligned collinearly in ferromagnetic hexagonal sheets with a stacking sequence of these planes $\mathrm{BBABBA}$ such that the $A$ spins are antiparallel to the $B$ spins. This magnetic structure is determined by a 180° antiferromagnetic exchange between nearest-neighbor $A$, $B$ spins and a 90° ferromagnetic exchange between nearest-neighbor $B$ spins. In this paper we report a detailed inelastic-neutron-scattering study of the spin waves in RbNi${\mathrm{F}}_3$ both at low temperatures and through $T_c$. The magnetic unit cell contains six ${\mathrm{Ni}}^{++}$ spins so that there are in general six distinct branches in the spin-wave spectrum. All six branches are observed in the $\Gamma A$ direction ($c$ axis), while only the lowest three are observed in the $\Gamma M$ direction. The measured dispersion curves at 4.2°K may be accurately fitted using simple spin-wave theory with $J_{\mathrm{AB}}=(93.2\mathrm{}\pm 2)°$K, $J_{\mathrm{BB}}=-(21.1\mathrm{}\pm 2)°$K ($\mathcal{H}=\Sigma {i>j}^{}{J}_{\mathrm{ij}}{\overrightarrow{\mathrm{S}}}_i·{\overrightarrow{\mathrm{S}}}_j$, $S=1\mathrm{}$), and with all other exchange constants set to zero. Using these exchange constants we can satisfactorily account for other magnetic properties such as the high-temperature susceptibility, the sublattice magnetizations in a field, and two-magnon Raman scattering. At higher temperatures it is found that the $c$-axis acoustic magnons renormalize like the magnetization, whereas the high-lying optic modes are nearly temperature independent. This leads one to the physical picture in which RbNi${\mathrm{F}}_3$ at high temperatures is viewed as a set of strongly correlated two-dimensional ferrimagnets composed of three successive planes $\mathrm{BAB}$ coupled by the strong exchange field $H_{\mathrm{AB}}\sim 6J_{\mathrm{AB}}$; these $\mathrm{BAB}$ "two-dimensional ferrimagnets" are then coupled together by the much weaker exchange field $H_{\mathrm{BB}}\sim J_{\mathrm{BB}}$.