Thermal-Expansion Anomaly of MnCL2 · 4H2O near its Néel Point

We have observed a λ anomaly in the thermal expansion of ${\mathrm{MnCl}}_2\text{\hspace{0.17em}·\hspace{0.17em}4}{\mathrm{H}}_2\mathrm{O}$ due to antiferromagnetic ordering at 1.622°K. The linear thermal expansion coefficient, $\alpha$ , was measured along three mutually perpendicular directions between 0.4° and 4.2°K. The length of the sample determined the plate spacing of a capacitor, so that length changes of 0.05 Å could be measured using a capacitance bridge. Temperature resolution was about three microdegrees, with points taken at 40 μ°K intervals near the transition. The expansion coefficient along the $a$ axis. ${\alpha }_a$ , is negative, while ${\alpha }_b$ and ${\alpha }_{\mathrm{c\prime }}$ , are positive. The temperature dependences of ${\alpha }_a$ , ${\alpha }_b$ , ${\alpha }_{\mathrm{c\prime }}$ , and the specific heat are similar but not identical, in agreement with theoretical expectations. Near the transition, for ${10}^{\text{−4}}{\text{<\hspace{0.17em}|\hspace{0.17em}1\hspace{0.17em}−\hspace{0.17em}T/T}}_N{\text{\hspace{0.17em}|\hspace{0.17em}<10}}^{\text{−1}}$ , the singularity in $\alpha$ appears to be logarithmic for ${\mathrm{T\hspace{0.17em}<\hspace{0.17em}T}}_{\mathrm{N}}$ , and of the form ${\text{|\hspace{0.17em}1−\hspace{0.17em}T/T}}_{\mathrm{N}}{\mathrm{\hspace{0.17em}|}}^{\mathrm{-p}}$ with $\text{p≃0.35}$ for ${\mathrm{T>\hspace{0.17em}T}}_{\mathrm{N}}$ .