Spin-Wave Analysis of the Sublattice Magnetization Behavior of Antiferromagnetic and Ferromagnetic CrCl3

Abstract

The temperature and magnetic-field dependences of the sublattice magnetization in the hexagonal layertype compound Cr${\mathrm{Cl}}_3$ ($T_N=16.8\mathrm{}°$K) have been deduced from the ${}_{}{}^{53}{}_{}{}^{}\mathrm{Cr}$ nuclear magnetic resonance (NMR) for $0.4\le T\le 8.1°$K and $0\le H\le 10$ kOe. The observed zero-field data can be accounted for over the whole temperature range by a renormalized spin-wave model based on isotropic ferromagnetic ($J_T$) intralayer and antiferromagnetic ($J_L$) interlayer exchange interactions in the presence of a weak effective anisotropy field ($H_A$). Appropriate renormalized spin-wave dispersion relations are given for the four-sublattice antiferromagnetic (weak-field) and two-sublattice ferromagnetic (strong-field) equilibrium spin configurations. The validity of the two-dimensional approximation to these states is examined in detail for $k_{B}T>\mathrm{}2\left|J_L\right|z_{L}S$ and $\left|J_L\right|\ll J_T$. It is shown that under these conditions the sublattice magnetizations for $J_L<0\mathrm{}$ and $J_L>0\mathrm{}$ are identical. The three-dimensional zero-field spin-wave fit gives $\frac{J_T}{k_B}=5.25\mathrm{}°$K, $H_A\mathrm{}\left(0\right)=650\mathrm{}$ Oe and a 0°K, zero-field ${}_{}{}^{53}{}_{}{}^{}\mathrm{Cr}$ frequency $\nu \mathrm{}\left(0\right)=63.318\mathrm{}$ Mc/sec. Parallel magnetic susceptibilities calculated with these parameters in the range $0.4<T\le 8.1°$K are in quantitative agreement with experimental values based on measured splittings of the ${}_{}{}^{53}{}_{}{}^{}\mathrm{Cr}$ NMR in weak fields ($H\le 100$ Oe). The interlayer constant, $\frac{J_L}{k_B}=-0.018\mathrm{}°$K, used in the spin-wave calculations was obtained from single-crystal bulk magnetization measurements (${\chi }_{\perp }=9.9\mathrm{}$ emu/mole for $T\le 4°$K), corrected for demagnetizing effects. These measurements show that the net anisotropy in the ferromagnetic state (i.e., $H\ge 1.68$ kOe) is zero, presumably because of a cancellation of dipolar and single-ion contributions. The sublattice magnetization...