Some properties of paramagnetic salts at very low temperatures

The susceptibilities and specific heats of various paramagnetic substances have been measured at temperatures between 20°K and 0.006°K, and the results compared with theoretical predictions. In some cases the agreement between theory and experiment was found to be very good.
Susceptibilities were measured by an a.c. method from the change of mutual inductance of a pair of coils surrounding the specimen, using a Hartshorn bridge. This involved the construction of an accurate decade inductometer which is described in full detail.
Magnetic specific heats above 1°K were measured in terms of the adiabatic and isothermal susceptibilities, from the ratio of which the specific heat at constant magnetisation can be calculated thermodynamically. These susceptibilities can be measured with the Hartshorn bridge using suitable audio frequencies. The method depends on the mechanism of spin lattice relaxation by means of which the magnetic ions can exchange energy with their surroundings. If the relaxation time is sufficiently long, then the susceptibility measured in the presence of a large field using the audio frequency method is equal to the adiabatic susceptibility. The isothermic susceptibility is equal to the susceptibility in zero external field for all measuring frequencies. The method measures only the specific heat of the assembly of paramagnetic ions and is independent of the lattice specific heat of the substance.
Below 1°K entropies and hence specific heats were measured by the method of adiabatic demagnetization in terms of the magnetic temperature T°. This is defined as T° = λ/χ where χ is the susceptibility, and λ is determined from measurements in the helium range. The dependence of T° on the shape of the specimen is discussed.
The susceptibility or oxygen trapped in a "clathrate" enclosure compound of β quinol was measured and the temperature variation between 20°K and 1°K compared with that of an assembly of free oxygen molecules as calculated from spectroscopic data. Almost perfect agreement was found down to 2°K, indicating that the molecules are free to rotate within the cage of quinol. However, below about 2°K a discrepancy was observed suggesting a "freezing in" of the rotation. fThis conclusion was supported by a second experiment on oxygen enrichced in O16O18. The susceptibility of this "gas" at very low temperatures would be expected to differ from that of normal oxygen on the basis of free rotation, but no appreciable difference was found in the range 1-5°K.
The magnetic specific heat of Cerium Magnesium Nitrate was measured at 1°K by the relaxation method and between 1°K and 0.006°K by the method of adiabatic demagnetization. It was found that the specific heat is very small, being given in this range of temperatures by CM = 7.3 x 10-6 R/T2, and that it can be accounted for almost entirely by magnetic dipole-dipole interaction. The uses of the salt for work below 1°K are discussed.
Specific heat measurements by the relaxation method were also made on four other substances:-
Cerium zinc nitrate. This was found to have very nearly the same properties as the magnesium salt, its susceptibility being exactly the same and its specific heat being given by CM = 6.4 x 10-5 r/t2.
Neodymium magnesium nitrate. The specific heat of this salt was measured at 1°K and found to be given by CM = 8.73 x 10-4 R/T2, in good agreement with the value calculated on the basis of magnetic dipole-dipole interaction plus the effect of hyperfine splittings. In view of the good agreement between theory and experiment at 1°K, the theory will almost certainly hold down to temperatures of the order of 0.01°K where the interaction energy becomes comparable with kT. An expression for the deviation from Curie's law in the the temperature range 1°K to 0.05°K is derived and the uses of the salt for work below 1°K are discussed.
Chromic methylamine alum. The value of the specific heat near 1°K was found to be CM = 0.0192 R/T2 in excellent agreement with the values derived from adiabatic demagnetization data. However, when compared with the value calculated from dipole-dipole interaction plus the effect of the Stark splittings it was found that there was a 12% discrepancy. Possible explanations are discussed but the discrepancy remains unresolved.
Ferric Rubidium alum. The value of the specific heat near 1°K was found to be CM = 8.2 x 10-3 R/T2. This is compared with the value 10.0 x 10-3 R/T2 deduced from demagnetization experiments, and the value 5.8 x 10-3 R/T2 calculated from the splittings and the dipole-dipole interactions. Possible explanations for the discrepancy with the theoretical value are discussed.
Finally a new method of relating magnetic temperatures below 1°K to absolute temperatures is described. Cerium magnesium nitrate, which is known to obey Curie's law down to 0.006°K was used as a thermometer since its very anisotropic susceptibility can be measured in the presence of another isotropic paramagnetic substance. The design and construction of a system of mutual inductance coils to measure susceptibilities in two directions at right angles is discussed in detail. The method has been used to determine the T-T° relation for manganous ammonium sulphate from its Curie point to 1°K. The temperature of the Curie point of was identified as 0.127°K±0.003. The advantages of this method over the conventional thermo- dynamic method are discussed with special reference to measurements in the Curie point region.