Local and long-range order and the influence of applied magnetic field on single-crystalline ${\mathrm{NiSb}}_2{\mathrm{O}}_6$

The magnetic and thermal properties of single-crystalline ${\mathrm{NiSb}}_2{\mathrm{O}}_6$ are reported. The ${\mathrm{Ni}}^{2+}$ ions exhibit local magnetic order below $\sim 50$ K followed by long-range antiferromagnetic order below $T_N=6.7$ K. Analysis of the magnetic susceptibility data using the one-dimensional Heisenberg model with spin $\mathbb{S}=1$ results in a magnetic exchange coupling $J_{\left|\right|}/k_B\sim 26.0\left(1\right)$ K. $T_N$ is observed to either increase or decrease depending on whether field is applied perpendicular or parallel to the magnetic moment axis. A two-sublattice magnetic structure, with the axis of alignment alternating by $90{}^{\circ }$ between neighboring layers along the crystallographic $c$ axis, is argued to result in two magnetic transition temperatures for certain magnetic field directions, which agrees well with theory. This leads to a highly anisotropic magnetocaloric effect.

Figure 1

Magnetic susceptibility for ${\mathrm{NiSb}}_2{\mathrm{O}}_6$ with $H=0.2$ T for the indicated field directions. The long-dashed line is a fit to ${\chi }_{H\perp \left[001\right]}$ using the phenomenological expression obtained by Law et al. [23]. The short-dashed lines are $d\chi /dT$ (right scale), which elucidate the transition at $T_N=6.7\left(1\right)$ K.

Figure 2

Magnetic susceptibility for ${\mathrm{NiSb}}_2{\mathrm{O}}_6$ with (a) $H\parallel \left[001\right]$ and (b) $H\parallel \left[110\right]$ for applied fields of 0.2, 2, 4, 6, and 8 T. Inset: Magnetic moment versus applied field at $T=2$ K. A spin-flop transition is observed at 8.125(5) T for field along either [110] or $\left[1\overline{1}0\right]$.

Figure 3

(a) Specific heat for ${\mathrm{NiSb}}_2{\mathrm{O}}_6$ at magnetic field $H=0$ and 8 T for the indicated field directions. The inset shows ${\mathrm{NiSb}}_2{\mathrm{O}}_6$ and ${\mathrm{ZnSb}}_2{\mathrm{O}}_6$ at $H=0$. (b) Magnetic contribution to the heat capacity $\delta C_P$ obtained by subtracting $C_P$ of ${\mathrm{ZnSb}}_2{\mathrm{O}}_6$. The area under the curve is the magnetic entropy change, $\mathrm{\Delta }S$, plotted in the inset as the solid line along with the maximum theoretical value, $\mathrm{\Delta }S$ = $R\ln (2\mathbb{S}+1)$, shown as the dashed line.

Figure 4

Magnetic field versus temperature for ${\mathrm{NiSb}}_2{\mathrm{O}}_6$. $H\parallel \left[110\right]$ results in a decrease of $T_N$ for the chains whose moments are parallel to $H$, referred to as the easy sublattice (green diamonds), and an increase of $T_N$ for the chains whose moments are perpendicular to $H$, referred to as the hard sublattice (blue triangles). $H\parallel \left[001\right]$ (red circles) is perpendicular to the moments of both sets of chains, resulting in an increase of $T_N$. Dashed black lines show fits using Eqs. (1) and (2).

Figure 5

(a) Linear thermal expansion $\mathrm{\Delta }L/L_{295\mathrm{K}}$ for ${\mathrm{NiSb}}_2{\mathrm{O}}_6$. The insets reveal the region near $T_N=6.7$ K. (b) Thermal expansion coefficient $\mu =d/dT(\mathrm{\Delta }L/L_{295\mathrm{K}})$ for ${\mathrm{NiSb}}_2{\mathrm{O}}_6$ (solid lines) and the nonmagnetic analog ${\mathrm{ZnSb}}_2{\mathrm{O}}_6$ (dashed lines). The inset details the region near $T_N$.

Figure 6

Plot of $C_P^{*}$ and $\lambda \mathrm{\Omega }T$ vs temperature illustrating the overlap of heat capacity and volume thermal expansion coefficient data in the vicinity of $T_N$.

Figure 7

(a) Change in magnetic entropy $\mathrm{\Delta }S$ obtained using Eq. (5) (solid symbols) and Eq. (6) (open symbols) for a maximum field of $H=8$ T. (b) Change in temperature $\mathrm{\Delta }T$ realized through a change in magnetic field of 8 T determined with Eq. (7). The Néel temperatures for $H_{\max }\parallel \left[001\right]$ (red) and $H_{\max }\parallel \left[110\right]$ (purple) are indicated by the arrows.