Critical-Region Thermal Expansion in Mn${\mathrm{Cl}}_2$·4${\mathrm{H}}_2$O and Mn${\mathrm{Br}}_2$·4${\mathrm{H}}_2$O

The Néel-point anomaly in the linear thermal-expansion coefficients along three mutually perpendicular directions in Mn${\mathrm{Cl}}_2$·4${\mathrm{H}}_2$O and Mn${\mathrm{Br}}_2$·4${\mathrm{H}}_2$O has been observed. Using the three-terminal capacitance technique, length changes were measured between 0.4 and 4.2 K with a resolution of approximately 0.02 Å under the best conditions. Temperature resolution was about 4μK, with points taken at 40-μK intervals near the transition. In Mn${\mathrm{Cl}}_2$·4${\mathrm{H}}_2$O, the linear expansion coefficient along the $a$ axis, ${\alpha }_a$, is negative, while ${\alpha }_b$ and ${\alpha }_{c^{\prime }}$ are positive. All three linear expansion coefficients are negative in Mn${\mathrm{Br}}_2$·4${\mathrm{H}}_2$O. The temperature dependences of the thermal-expansion coefficients for a given salt are similar but not identical, in agreement with theoretical expectations. On a reduced temperature scale, the temperature dependences of the thermal-expansion coefficients for the two salts are also similar. Near the transition ($\frac{|T-T_N|}{T_N}<0.1\mathrm{}$), the results can be fitted by the relations: $\alpha =A_{-}+B_{-}\ln (1-\frac{T}{T_N},), T<\mathrm{}{T}_N$ and $\alpha =A_{+}+B_{+}{(\frac{T}{T_N}-1)}^{-p}, T>\mathrm{}{T}_N$ where $p=0.30\mathrm{}\pm 0.06$ in Mn${\mathrm{Cl}}_2$·4${\mathrm{H}}_2$O and $p=0.42\mathrm{}\pm 0.08$ in Mn${\mathrm{Br}}_2$·4${\mathrm{H}}_2$O. Using recent high-resolution critical-region specific-heat results for Mn${\mathrm{Cl}}_2$·4${\mathrm{H}}_2$O, we calculate the dependence of the transition temperature on applied stress for this salt.