Specific Heat of Praseodymium and Neodymium Metals Between 0.4 and 4°K

Abstract

The specific heat $C_p$ of praseodymium and neodymium metals has been measured between 0.4 and 4°K in a ${\mathrm{He}}^3$ cryostat. After assuming, on the basis of earlier research, $C_L=0.554\mathrm{}{T}^3$ (specific heat always given in mJ/mole °K) and $C_E=10.5T$ for the lattice and electronic specific heats of praseodymium, the remaining $C_p$ was analyzed into a nuclear contribution $C_N=20.9\mathrm{}{T}^{-2\mathrm{}}$ and into a magnetic contribution $C_M$. If compared with Bleaney's calculations based on fully magnetized electronic states in the metal, our experimental $C_N$ shows that 2.0% of the sample was in a cooperative state, probably ferromagnetic, the rest of the metal being paramagnetic. $C_M$ was further separated into a Schottky contribution with an excited electronic level at 28°K (ions in hcp surroundings corresponding to 50% of the sample) and into a smeared-out cooperative peak with a maximum at 3.2°K. The entropy under the latter curve is 95 mJ/mole °K as compared with the value $0.020\times R\ln 2=115$ mJ/mole°K which would be expected as a result of magnetic ordering in 2.0% of the sample. Both $C_N$ and $C_M$ thus suggest that 2% of the sample enters a cooperative phase below 3.2°K. This mechanism to explain $C_N$ and $C_M$ must be considered as preliminary. Our value of $C_N$ is rather different from earlier results. A sample-dependent $C_N$ is consistent with the picture of ferromagnetic domains. Below 2°K the specific heat of praseodymium can be written, with 1% accuracy, $C_p=4.53\mathrm{}{T}^3+24.4T+20.9\mathrm{}{T}^{-2\mathrm{}}$. At higher temperatures $C_p$ cannot be represented by a simple power series. The magnetic contribution to the specific heat of neodymium is huge due to cooperative peaks at 7 and 19°K; even at 1°K $C_M$ represents 88% of the total $C_p$. Below 7°K neodymium is antiferromagnetic. After adopting $C_L=0.502\mathrm{}{T}^3$ and $C_E=10.5T$ an analysis gave $C_N=(7\mathrm{}\pm 0.7)T^{-2\mathrm{}}$. This value is about 50% smaller than that calculated by Bleaney if full electronic magnetization is assumed. However, the splitting of the electronic levels is rather large in neodymium and one cannot assume that $〈J_z〉$ in a cooperative state tends to $J=\frac{9}{2}$, but rather reaches a lower limiting value at $T=0\mathrm{}°$K. This explains the smaller experimental $C_N$. Between 0.4 and 1°K the specific heat of neodymium may be written with 1% accuracy $C_p=125.7\mathrm{}{T}^3+22.5T+6.4\mathrm{}{T}^{-2\mathrm{}}$. The accuracy of these measurements is estimated as 1.5% at 0.4°K and as 0.5% between 1 and 4°K. While checking the performance of our cryostat the specific heat of copper was found to be $C_p=0.0510\mathrm{}{T}^3+0.698T$.