Chlorine-Nuclear-Magnetic-Resonance Study of the Ferromagnet Gadolinium Trichloride

Abstract

We have utilized chlorine nuclear magnetic resonance to measure the magnetization as a function of temperature (0.032-4.2 K) and applied field (0-10 kOe) in the ferromagnet Gd${\mathrm{Cl}}_{3}$. Above the Curie temperature, 2.214 K, there is only one $^{35}\mathrm{Cl}$ pure-quadupole-resonance transition at 5314 kHz. Below the Curie temperature the internal field at the chlorine site splits the single transition line into three temperature-dependent transition lines. This observation is consistent with an internal field parallel to the symmetry axis ${C}_{3}$. Analysis based on the method of energy moments yields a quadrupole asymmetry parameter of 0.4265 \ifmmode\pm\else\textpm\fi{} 0.0001. The quadrupole Hamiltonian is diagonalized to give transition frequencies as a function of the pure-quadrupole-resonance transition frequency, the asymmetry parameter, and the magnitude of the internal field. A least-squares analysis is used to determine the magnitude of the internal field as a function of temperature. With an external magnetic field applied parallel to the direction of the magnetization for a spherical sample, the critical point at the field ${\stackrel{\ensuremath{\rightarrow}}{H}}_{\mathrm{int}}={\stackrel{\ensuremath{\rightarrow}}{H}}_{A}\ensuremath{-}\stackrel{}{\mathrm{D}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{M}(T)=0$ is used to measure the relationship between the internal field and the bulk magnetization. They are found to be simply proportional to within 0.5%, indicating a temperature-independent transferred hyperfine interaction. The transferred hyperfine field at the chlorine site is found to be antiparallel to the magnetization and equal to 1644 G at saturation. The $zz$ component of the transferred hyperfine interaction tensor is 685 kHz for the $^{35}\mathrm{Cl}$ nucleus. The zero-point magnetization defect $\frac{\ensuremath{\Delta}{M}_{0}}{{M}_{0}}$ is estimated at (1.31 \ifmmode\pm\else\textpm\fi{} 0.49)%. For $T<0.5$ K the measurements show that the magnetization decreases faster than the predictions of Marquard and Stinchcombe and Cottam, based on the measured exchange constants. In the range $0.5<T<1.0$ K the internal field follows the equation $B(T)=4956.9\ensuremath{-}868.1{T}^{\frac{3}{2}}{e}^{\ensuremath{-}\frac{{E}_{min}}{\mathrm{kT}}}$, where $\frac{{E}_{min}}{k}=0.3586\ifmmode\pm\else\textpm\fi{}0.0026$ K. Near the Curie temperature the critical exponent $\ensuremath{\beta}$ is found to be 0.3904 \ifmmode\pm\else\textpm\fi{} 0.0060 with ${T}_{C}=2.2140\ifmmode\pm\else\textpm\fi{}0.0016$ K. The Green's-function predictions in the random-phase-approximation are compared to the magnetization measurements in zero and applied fields. The zero-field susceptibility is also calculated from the measurements.