Application of compressional cooling to the study of nuclear ordering in solid helium three
"A powerful cooling technique for He3 has been used to observe ordering of the nuclear spins in solid He3 He3 atoms in the solid are localized at lattice sites. Interactions between neighboring atoms, due to zero point motion, are relatively small until temperatures in the low I millidegree Kelvin range are reached. Liquid He 3 is a Fermi liquid. Due to the Pauli exclusion principle, the nuclear spins in the liquid begin ordering at much higher temperatures. This difference in ordering temperatures leads to an interesting region between about 0.5 mOK and 0.32°K in which the solid has a higher entropy than the liquid. In this temperature range, isentropic conversion of liquid to solid He 3 will produce cooling. Starting at temperatures above 20 m oK, cooling to below 3 mOK has been obtained. At the lower end of this temperature range, appreciable ordering of the nuclear spins in the solid has been observed. A flexible walled cell has been developed for compressing a two phase, liquid-solid, mixture of He 3 at temperatures below the minimum in the melting curve. The cell was precooled to about 20 mOK using a continuous dilution refrigerator. Compression was accomplished using liquid He as a pressurizing fluid. Along the melting curve, the pressure and temperature were measured using, respectively, a beryllium copper capacitor and a cerium magnesium nitrate (CIv.IN) powder thermometer. The solid entropy has been determined using the Clapeyron equation for a first order phase transition; [equation] where S ,V and S ,V are the molar entropy and volume of solid and s s 1· 1. liquid He3 on the melting curve, respectively. The use of this equation involved a calculation of S based on the 27.0 atm heat capacity measure- "" . ments of Abel, Anderson, Black, and Wheatley. Also, the values of V"" - Vs measured by Scribner, Panczyk, and Adams were used. The . * C:MN thermometer calibration, ,assuming the magnetic temperature T equal to the Kelvin temperature T, was self consistently done so the nneasured and calculated values of dP /dT agreed in the 20 to 38 mO K tennperature range. In this tennperature range, S is still essentially s R In 2, the entropy of a connpletely disordered system of spin ~ particles. However, at lower tennperatures appreciable nuclear ordering was observed. For exannple, at T * = 3.4 nnoK the measurennents gave S = 0.58 R = 0.83 R In 2. Using the effective spin Hamiltonian s [equation] where the sunn is only over nearest neighbors, with the high tennperature expansion for the free energy of a bec Heisenberg antiferronnagnet given by Baker, Gilbert, Eve, and Rushbrooke, the low temperature data suggest J /k = -( 1.7 +/- 0.3) mOK. This value is in reasonable agreement with values of J deduced from higher temperature measurements."
compressional cooling, nuclear ordering, solid helium-3
University of Illinois - Urbana-Champaign
Networked Digital Library of Theses and Dissertations