Investigation of Nuclear Effects in Paramagnetic Single Crystals at Very Low Temperatures

Abstract

The hyperfine structure coupling of the magnetic moment of the nucleus with the magnetic moment of the electronic cloud of a paramagnetic ion gives rise to a Schottky specific heat anomaly at an appropriate temperature. For the cobaltous ion in a single crystal of cobalt ammonium sulfate this temperature is about 0.1\ifmmode^\circ\else\textdegree\fi{}K. In the region where the specific heat goes as $\frac{A}{{T}^{2}}$ and where the Curie law $\ensuremath{\chi}=\frac{C}{T}$ holds, one can make measurements of $A$ by means of an ac mutual inductance bridge which measures the susceptibility of the paramagnetic salt. The method of measurement consists in superposing a dc magnetic field on the salt already in the ac field of the bridge. This dc field depresses the susceptibility an amount depending on the parameter $\frac{C}{A}$ which is therefore a constant of the material being investigated. If one knows the Curie constant, then one has $A$ immediately. This measured $A$, however, is made up of two contributions: (a) that arising from the nuclear-electronic coupling and (b) that arising from the dipole interaction of neighboring paramagnetic ions. The (b) contribution is a function of concentration of the ions, so that by making measurements of $A$ at various dilutions and plotting $A$ as a function of dilution, one obtains an intercept by extrapolation to infinite dilution which is the part of $A$ due to nuclear specific heat. The thermodynamic measurements made thus give a nuclear specific heat of ${C}_{v}{T}^{2}=16.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}R$, where $R$ is the gas constant, which is in excellent agreement with ${C}_{v}{T}^{2}=16\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}R$ calculated from microwave data. It is observed that pure cobalt ammonium sulfate has a Curie point at \ensuremath{\sim}0.125\ifmmode^\circ\else\textdegree\fi{}K, while the diluted salts do not possess one in the same temperature region.