Nuclear specific heat of bccHe3near the magnetic ordering transitions

Precise specific-heat measurements were made on low-density samples of bcc ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ in the vicinity of the various magnetic ordering transitions. The data obtained for magnetic fields of 0, 6, and 10 kOe span the temperature range 0.6–10 mK. At H=0, the data exhibit an extremely sharp peak indicative of a first-order transition. Below $T_N$ the specific heat is proportional to $T^3$ and yields a spin-wave velocity ($v_{\mathrm{spin}}$) in excellent agreement with a previous determination. Above $T_N$, the results show no anomalous satellite peaks as seen in other experiments and as suggested by theoretical calculations. Within the precision of the measurements, the effect of changing the density is only to rescale the temperature. The data obtained at 6 and 10 kOe, when plotted as a function of T/$T_c$, nearly fall on a universal curve with a shape characteristic of a λ-type transition. A detailed analysis of the density distribution in the solid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ samples supports the claim that this transition is second order. At 10 kOe, $T_c$ is found to be proportional to $V^{8.7}$, where V is the molar volume. It is demonstrated, however, that this dependence is consistent with the exchange energies being proportional to $V^{17}$, in agreement with other experiments. As a function of increasing field, $v_{\mathrm{spin}}$ decreases for H<4 kOe and increases at higher fields. Above 4 kOe, $v_{\mathrm{spin}}$ is proportional to $T_c$. The field-induced increase in the paramagnetic-phase specific heat can be described well by the free-spin expression with an effective magnetic moment equal to 0.83${\mu }_B$. Magnetization results inferred from the specific-heat data are in excellent agreement with direct measurements. The H-T phase diagram which is thermodynamically consistent with the new data is presented. Also included are results for the field-dependent boundary resistance between solid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and silver.