Neutron-diffraction study of the staggered magnetization of Cu Cl 2 ·2 D 2 O

TLDR: In this paper, the authors used the neutron-scattering technique to measure the staggered magnetization of the antiferromagnet Cu${\mathrm{Cl}}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}2$

Abstract: The neutron-scattering technique has been used to measure the staggered magnetization of the $S=\frac{1}{2}$, $d=3$ antiferromagnet Cu${\mathrm{Cl}}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}2${\mathrm{D}}_{2}$O as a function of temperature and magnetic field. The critical exponents ${\ensuremath{\beta}}_{\ensuremath{\perp}}$, ${\ensuremath{\beta}}_{\ensuremath{\parallel}}$ describing the temperature variation of the order parameter in the regions well above and well below the bicritical point, respectively, were found to be ${\ensuremath{\beta}}_{\ensuremath{\perp}}=0.321\ifmmode\pm\else\textpm\fi{}0.01$ and ${\ensuremath{\beta}}_{\ensuremath{\parallel}}=0.324\ifmmode\pm\else\textpm\fi{}0.013$. These values are within experimental error of the theoretically expected value of 0.325 for the $d=3$ Ising model. At the spin-flop transition the staggered magnetization changed 8% in magnitude, the reduction being due to the anisotropy of the $g$ factor. The magnetic form factor in the spin-flop region was found to be the same as that previously determined in zero field. In addition, with the applied field tilted in the $a\ensuremath{-}b$ plane away from the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{a}}$ axis, the direction of the staggered magnetization was found to rotate continuously from the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{a}}$ to the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{b}}$ direction as is expected theoretically. The observed range in field over which the rotation takes place, however, is narrower than the predictions of mean-field theory.