Improved modelling of magnetic splitting in a chrome alum below 300 mK

Abstract

Chrome-Caesium Alum (CCA) is a paramagnetic salt that can be used to achieve ultra-low temperature refrigeration through adiabatic demagnetization. Cooling capacity measurements of CCA show a significant reduction below the isolated paramagnetic spin model for temperatures below 100 mK. A more complete understanding of the thermodynamic properties of CCA could improve model accuracy, vital for meeting cooling requirements at subKelvin temperatures. Modelling effort was undertaken to understand the physical origin of this reduction in heat and refrigeration capacity, and measurements from two separate CCA salt pills between 50 mK and 300 mK were used for model validation. Both the model and the experimental design and results are discussed in this work. The model uses exact eigenvalues for the Cr3+ ions from the spin Hamiltonian. Two interactions of interest are the zero-field splitting and hyperfine splitting, as these are not standard in presently used models.We found that, though hyperfine interactions were not significant at temperatures above 50 mK, the inclusion of the zero-field splitting interaction resulted in qualitative agreement with the data. We optimized this model using a nonlinear least square regression to find the best fit to the two experimental data sets with two independent fitting parameters. Measured data at 50 mK still show a significant reduction below the fitted model prediction. Conductance measurements and thermal relaxation times were used to characterize addenda heat capacity and entropy loss due to non-adiabatic effects, which were not found to be significant. Accordingly, cooling capacity reduction below 50 mK cannot be accounted for by these effects. CCA is in the same chemical family as Chrome-Potassium Alum (CPA) which used widely in adiabatic demagnetization refrigerators. Thus, this modelling work described here is applicable to CPA. New measurements are planned to understand if the remaining discrepancy between the model and data is a systematic effect or a more fundamental feature of the salt.