Pressure-dependent magnetic properties of geometrically frustrated ${\mathrm{ZnCr}}_2{\mathrm{O}}_4$

${\mathrm{ZnCr}}_2{\mathrm{O}}_4$ is a geometrically frustrated antiferromagnet with a first-order transition at $T_N=12.5\mathrm{K}$, where it also undergoes a structural transition from cubic to tetragonal structures. Our pressure- and field-dependent magnetization measurements and our subsequent analysis using a quantum tetrahedral mean field theory are found to be consistent with theories based on spin-lattice coupling. We also found that there is a weak, but unquestionable, field-induced transition around 2.5 T, at which our magnetization shows a subtle anomaly and, at the same time, both the Néel point and the estimated gap energy exhibit a sharp increase. Another finding is that our high pressure data imply that there may well be a pressure-induced splitting in the ordering temperatures of the bond and spin order parameters.

Figure 1

Magnetic susceptibility taken at ambient pressure and 9.5 kbar. Solid lines are for the fitting results using the QTMFT model (see the text).

Figure 2

An enlarged picture of the magnetic susceptibility taken at (a) ambient pressure and (b) 9.5 kbar near the transition temperature. The arrows in (a) and (b) indicate the direction of increasing fields from 0.2 to 5 T. The two insets show how we estimated the gap energy ${\Delta }_E$, using a plot of $\ln [\chi \left(T\right)-{\chi }_0]$ vs $1∕T$, where $\chi \left(T\right)$ is the susceptibility measured at $T$ and ${\chi }_0$ the magnetic susceptibility estimated at $T=0\mathrm{K}$. The lines in the insets represent the fitting results with the gap value shown in the figures (see the text). Temperature derivatives of the susceptibility, $d\chi ∕d\mathrm{T}$, for the data taken at (c) five pressures with $H=0.4\mathrm{T}$ and (d) four representative fields with 3.5 kbar. The arrows in (c) and (d) indicate the determined transition temperatures.

Figure 3

Field and pressure dependence of (a) the transition temperature and (b) the gap energy, ${\Delta }_E$. We used the same symbols in both figures. The vertical dashed line indicates where the magnetization shows a field-induced anomaly as shown in Fig. 4.

Figure 4

Field dependence of magnetization at (a) ambient pressure and (b) 9.5 kbar. The insets are for the field derivative of magnetization, $dM∕dH$, at several temperatures. We used the same symbols in the insets for each temperature as in the main figures. (c) Field derivative of the magnetization taken at 5 K for four pressures. The arrow indicates where the metamagnetic transition occurs at 1 bar.

Figure 5

Pressure and field dependence of (a) $J_1$, (b) $J_2$, and (c) $J_{eff}(=J_1+3J_2)$ for 1 bar (filled square), 3.5 kbar (open circle), 7.0 kbar (filled triangle), and 9.5 kbar (open down triangle). $J_1$ and $J_2$ were obtained from fitting the data given in Fig. 1 using the QTMFT[13] (see the text).