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${\mathrm{Cl}}_{3}$ (${T}_{N}=16.8\ifmmode^\circ\else\textdegree\fi{}$K) have been deduced from the $^{53}\mathrm{Cr}$ nuclear magnetic resonance (NMR) for $0.4\ensuremath{\le}T\ensuremath{\le}8.1\ifmmode^\circ\else\textdegree\fi{}$K and $0\ensuremath{\le}H\ensuremath{\le}10$ 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 ${k}_{B}T>2|{J}_{L}|{z}_{L}S$ and $|{J}_{L}|\ensuremath{\ll}{J}_{T}$. It is shown that under these conditions the sublattice magnetizations for ${J}_{L}<0$ and ${J}_{L}>0$ are identical. The three-dimensional zero-field spin-wave fit gives $\frac{{J}_{T}}{{k}_{B}}=5.25\ifmmode^\circ\else\textdegree\fi{}$K, ${H}_{A}(0)=650$ Oe and a 0\ifmmode^\circ\else\textdegree\fi{}K, zero-field $^{53}\mathrm{Cr}$ frequency $\ensuremath{\nu}(0)=63.318$ Mc/sec. Parallel magnetic susceptibilities calculated with these parameters in the range $0.4<T\ensuremath{\le}8.1\ifmmode^\circ\else\textdegree\fi{}$K are in quantitative agreement with experimental values based on measured splittings of the $^{53}\mathrm{Cr}$ NMR in weak fields ($H\ensuremath{\le}100$ Oe). The interlayer constant, $\frac{{J}_{L}}{{k}_{B}}=\ensuremath{-}0.018\ifmmode^\circ\else\textdegree\fi{}$K, used in the spin-wave calculations was obtained from single-crystal bulk magnetization measurements (${\ensuremath{\chi}}_{\ensuremath{\perp}}=9.9$ emu/mole for $T\ensuremath{\le}4\ifmmode^\circ\else\textdegree\fi{}$K), corrected for demagnetizing effects. These measurements show that the net anisotropy in the ferromagnetic state (i.e., $H\ensuremath{\ge}1.68$ kOe) is zero, presumably because of a cancellation of dipolar and single-ion contributions. The sublattice magnetization behavior in the ferromagnetic state appears to be strongly influenced by long-range dipolar interactions, as evidenced by significantly lower values of $\frac{M(T, H)}{M(0)}$ for $\mathrm{M}\ensuremath{\parallel}c$ than for $\mathrm{M}\ensuremath{\perp}c$.