Magnetic structure and magnetocalorics of ${\mathrm{GdPO}}_4$

The magnetic ordering structure of ${\mathrm{GdPO}}_4$ is determined at $T=60$ mK by the diffraction of hot neutrons with wavelength $\lambda =0.4696$ Å. It corresponds to a noncollinear antiferromagnetic arrangement of the Gd moments with propagation vector $\mathbf{k}=(1/2,0,1/2)$. This arrangement is found to minimize the dipole-dipole interaction and the crystal-field anisotropy energy, the magnetic superexchange being much smaller. The intensity of the magnetic reflections decreases with increasing temperature and vanishes at $T\approx 0.8$ K, in agreement with the magnetic ordering temperature $T_N=0.77$ K, as reported in previous works based on heat capacity and magnetic susceptibility measurements. The magnetocaloric parameters have been determined from heat capacity data at constant applied fields up to 7 T, as well as from isothermal magnetization data. The magnetocaloric effect, for a field change $\Delta B=0-7\mathrm{T}$, reaches $-\Delta S_T=375.8\mathrm{mJ}/{\mathrm{cm}}^3{\mathrm{K}}^{-1}$ at $T=2.1$ K, largely exceeding the maximum values reported to date for Gd-based magnetic refrigerants.

Figure 1

Variation of the intensity of the strong magnetic reflections $(1.5,0,-1.5)$ and $(0.5,-1,-2.5)$ with temperature. Lines are guide to the eye.

Figure 2

Plot of the observed vs calculated intensities for the $(I>5\sigma )$ magnetic and nuclear reflections.

Figure 3

Nuclear and magnetic structure at $T=60$ mK. Red: O, blue: P, yellow: Gd. Green arrows: moments of Gd.

Figure 4

Top: Heat capacity at applied magnetic field $C_B\left(T\right)$. Dashed line: Calculation of the phonon contribution. Bottom: Entropy $S(T,B)$ deduced from heat capacity. Details in the text. Dotted line: infinite temperature limit for the molar magnetic entropy $S_m/R\left(\infty \right)=ln(2s+1)$ for $s=7/2$.

Figure 5

Top: Isothermal entropy increment $\Delta S_T$ for magnetic field increment, from zero to a given value, as labelled, computed from isothermal magnetization measurements and from heat capacity. Vertical axis reports units in ${\mathrm{Jkg}}^{-1}{\mathrm{K}}^{-1}$ (left) and volumetric ${\mathrm{mJ}/\mathrm{cm}}^3{\mathrm{k}}^{-1}$ (right). Details about the absolute entropy in the text. Bottom: Adiabatic temperature increments, from zero field to a given value, as labeled, computed from heat capacity data. The abscissa is the initial temperature.

Figure 6

Free energy per particle considering anisotropy and dipolar interactions for the $C_x{A}_y{C}_z$ magnetic mode as a function of the azimuthal angle $\varphi$ for different $\theta$ values defining the orientation of the moment at Gd1. The experimentally found magnetic energy is indicated.