Application of high-resolution dilatometry to the study of critical phenomena in antiferromagnetic systems
White, Benjamin Dakotah.
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Thermal expansion is an under-utilized physical property with enormous potential in its application to the study of classical critical phenomena. The Pippard relation scales the coefficient of volume thermal expansion multiplied by temperature with heat capacity in the vicinity of a continuous phase transition. This justifies the study of critical behavior, characterized by critical-exponent a, with the coefficient of volume thermal expansion instead of heat capacity. We evaluate potential advantages and disadvantages and develop strategies uniquely suited to the analysis of critical behavior exhibited by the coefficient of thermal expansion. The most notable disadvantages arise as a result of numerically differentiating thermal-expansion data to obtain its coefficient. In the course of assessing the detrimental effects of this procedure, we developed a critical expression for thermal expansion, with which we quantitatively evaluate the effect numerical differentiation has on the study of critical phenomena. Antiferromagnets are less susceptible than ferromagnets to long-range dipole contributions, which adjust critical behavior away from theoretical predictions. Therefore, three antiferromagnetic materials were selected to test the suitability of studying critical behavior with thermal expansion. Single crystals of CaMn ₂O ₄ and Bi ₂CuO ₄ were grown and characterized by methods described in careful detail. The coefficient of thermal expansion is studied along the principal crystallographic axes of each material demonstrating that the critical behavior exhibited along each axis is the same as that exhibited by the volume. Both transitions belong to the three-dimensional Ising universality class which settles a long-standing question by suggesting that Bi ₂CuO ₄ exhibits easy-axis anisotropy rather than easy-plane anisotropy. The thermal expansion of each material (as opposed to the coefficient of thermal expansion) is studied with our critical expression in order to increase the critical temperature range close to the Neel temperature. The limitations of studying the critical behavior of a polycrystalline sample are demonstrated when we investigate the antiferromagnetic transition of a-Mn. This element has a surprisingly complicated magnetic structure and our results constrain its transition to be in either the three-dimensional Heisenberg or n = 4 universality class.