Electron spin resonance in a two-dimensional compound with appreciable interplane coupling: NaCrS2

Measurements of the electron-spin-resonance (ESR) linewidth $\Delta H$ in NaCr${\mathrm{S}}_2$ are presented and compared with the theory of Richards and Salamon for ESR in two dimensions (2d). NaCr${\mathrm{S}}_2$ was chosen because it is a layer compound with a ferromagnetic intraplane interaction $J$ and a sizable antiferromagnetic interplane interaction $J^{\prime }$ ($\left|\frac{J^{\prime }}{J}\right|=\frac{1}{6}$). Previously the most detailed study of ESR which paid specific attention to the 2d feature of the spin dynamics was for ${\mathrm{K}}_2$Mn${\mathrm{F}}_4$, which has negligible $J^{\prime }$ and an antiferromagnetic $J$; so it is of interest to compare the two systems. $\Delta H$ in NaCr${\mathrm{S}}_2$ does not have a minimum at $3{cos}^2\theta =1\mathrm{}$ ($\theta =\mathrm{angle}\mathrm{of}\mathrm{field}\mathrm{with}\mathrm{respect}\mathrm{to} c \mathrm{axis}$), in contrast to the situation in ${\mathrm{K}}_2$Mn${\mathrm{F}}_4$. This feature is explained by the effect of interplane coupling. The theory, modified to account for interplane exchange, also correctly gives the high-temperature ratio $\frac{\Delta H(\theta =0)}{\Delta H(\theta =90\mathrm{}°)}=1.6\mathrm{}$. The measured peak-to-peak linewidth at $\theta =0\mathrm{}$ and room temperature, $\Delta H=80\mathrm{}$ Oe, is smaller than the calculated 125 Oe. $\Delta H$ increases continuously as the temperature $T$ is lowered in a manner described reasonably well by theory. Here agreement is much better than in some other planar ferromagnets which possibly have more nondipolar broadening mechanisms than NaCr${\mathrm{S}}_2$. The anisotropy $\frac{\Delta H(\theta =0)}{\Delta H(\theta =90\mathrm{}°)}$ decreases as the temperature is lowered, which is in contradiction to theory for a fixed $\frac{J^{\prime }}{J}$ and to results on other quasi-2d compounds and may be indicative of $\frac{J^{\prime }}{J}$ being temperature dependent.