Criticality in a disordered quantum antiferromagnet studied by neutron diffraction

Field-induced magnetic ordering in the structurally disordered quantum magnets Ni(Cl${}_{1-x}$Br${}_x$)${}_2$$·$4SC(NH${}_2$)${}_2$, $x=8$% and 13%, is studied by means of neutron diffraction. The order-parameter critical exponent is found to be very close to its value $\beta =0.5$ expected for magnetic Bose-Einstein condensation in the absence of disorder. This result applies to temperatures down to 40 mK, and a 1 T range in magnetic field. The crossover exponent is found to be $\varphi \sim 0.4$ for temperature ranges as small as 300 mK. Possible reasons for a discrepancy with recent numerical simulations and bulk measurements are discussed.

Figure 1

Neutron intensity measured in the $x=8\%$ Ni(Cl${}_{1-x}$Br${}_x$)${}_2$$·$4SC(NH${}_2$)${}_2$ sample at the $(0.5,0.5,0.5)$ Bragg position, vs temperature and magnetic field applied along the $c$ axis.

Figure 2

(a)–(c) Symbols: typical constant-temperature field scans of the magnetic Bragg peak intensity in $x=8\%$ (a) and $x=13$% (b), (c) Ni(Cl${}_{1-x}$Br${}_x$)${}_2$$·$4SC(NH${}_2$)${}_2$ samples. Solid lines are power-law fits, as described in the text. (d),(e) Fitted order-parameter critical exponent $\beta$ (d) and critical field $H_c$ (e) for the data in graphs (b) and (c), plotted as functions of maximum field $H_{\max }$ used in the fitting process. The highlighted symbols illustrate the choice of the narrowest useful fitting range, as described in the text.

Figure 3

Data analysis for the $x=8$% Ni(Cl${}_{1-x}$Br${}_x$)${}_2$$·$4SC(NH${}_2$)${}_2$ sample. (a) Symbols: temperature dependence of the order-parameter exponent $\beta$ obtained in fits to individual fit scans in the range $0<H<H_c+\Delta H$, $\Delta H=1.0$ T. The line represents an average obtained for all data measured at $T\lesssim 0.3$ K. (b) Symbols: temperature dependence of the critical field $H_c$ obtained in fits to individual fit scans in the range $0<H<H_c+\Delta H$, $\Delta H=1.0$ T. The line is a power-law fit in the range $0<T<T_{\max }$, $T_{\max }=0.85$ K, as described in the text. (c) Fitted value of the critical index $\varphi$ as a function of fitting interval. The solid symbol represents the narrowest useful fitting range, as described in the text.