Theory of thermal expansion based on the localized paramagnon model

Many researchers have studied physical properties of U compounds theoretically [1, 2] and experimentally [3]. Moriya, Kawabata, and Takahashi developed the self-consistent renormalization theory of spin fluctuations (the SCR theory) that takes into account mode-mode couplings of spin fluctuations beyond the random phase approximation self-consistently [1]. 5f electrons of U ions in U compounds are more localized than 3d electrons of transition metal compounds and less localized than 4f electrons of Ce compounds. As the first starting point, we use the localized paramagnon model in the SCR theory where the damping constant of spin fluctuations is independent of wave numbers. Konno and Moriya examined specific heats of U compounds based on the localized paramagnon model [2]. This model is valid in UPt3 and UAl2. Their theory explained the specific heat experimental data qualitatively. Although it was experimentally reported that the short range antiferromagnetic correlation was important [3], the localized paramagnon model can consider both the nearly ferromagnetic and nearly antiferromagnetic metals because the damping constant is independent of wave numbers. We feel that thermal expansion in U compounds has not been understood theoretically. We investigate thermal expansion based on the localized paramagnon model. By using Takahashi’s method [1] thermal expansion is obtained. Whether the behavior of the specific heat is consistent with that of the thermal expansion coefficient is discussed. This paper is organized. In the next section the formulation will be provided. In section 3 the numerical results will be shown. In the last section the conclusion will be provided.