Heat Capacity of Mn(HCOO)2·2H2O between 1.4 and 20°K

The heat capacity of Mn${\mathrm{}\left(\mathrm{HCOO}\right)\mathrm{}}_2$·2${\mathrm{H}}_2$O has been measured between 1.4 and 20°K. Sharp peaks associated with long-range spin ordering are found at 3.72 and 1.72°K. These anomalies can be correlated with corresponding effects in the magnetic and resonance properties of the salt. The present thermal data account for less than half the expected $R \ln 6$ of magnetic entropy, with little contribution expected above 20°K, suggesting that half the manganese moments remain highly disordered at 1.4°K. The response of the heat capacity to external magnetic fields supports this conclusion. A unit cell of Mn${\mathrm{}\left(\mathrm{HCOO}\right)\mathrm{}}_2$·2${\mathrm{H}}_2$O contains two each of two inequivalent ${\mathrm{Mn}}^{++}$ sites, types $A$ and $B$. Formate groups constitute $AA$ and $AB$ bridges and appear to mediate the dominant superexchange couplings. Analysis of the thermal and susceptibility data yields an antiferromagnetic $AA$ exchange parameter $\frac{J}{k}=0.65\mathrm{}$°K and a ferromagnetic $AB$ coupling $\frac{J^{\prime }}{k}=-0.10\mathrm{}$°K. A simplified molecular-field treatment of Mn${\mathrm{}\left(\mathrm{HCOO}\right)\mathrm{}}_2$·2${\mathrm{H}}_2$O using these parameters provides interpretations of several striking effects. In particular, it shows that below a common transition temperature, $B$ spins order much more slowly than $A$ spins and are nearly "free" at 1°K as seen in both magnetic and thermal data. The model also predicts anomalous behavior below 1°K as a consequence of a sharp temperature dependence of the $B$-spin order parameter at very low temperatures.