Theory of the superconductivity of $UGe_2$ revisited

Abstract

We present a unified theory of magnetism and superconductivity of $UGe_2$. To this end, we consider part of $5f$ uranium electrons as mostly itinerant and other ones as mostly localized. The main feature that distinguishes the localized from the itinerant electrons is the effect of the pressure on them. The pressure strongly screens the itinerant electrons while the localized ones are almost unaffected. The screening of itinerant electrons leads to decreasing of their Coulomb repulsion, therefore to formation of doubly occupied and empty states. These states are spin-singlet and the effective spin of itinerant electrons, the zero-temperature magnetization in units of Bohr magneton, decreases. We obtain an effective two-spin Heisenberg model, which explains the magnetization-temperature diagram of $UGe_2$. It is shown that the experimentally observed characteristic temperature $T_x$, is a partial order transition temperature. Below the Curie temperature $(T_x<T_C)$ the system undergoes a transition from high temperature phase, were only localized electrons contribute the magnetization, to the low temperature one, where both itinerant and localized electrons contribute the magnetization. The characteristic temperature decreases when pressure increases. At the quantum partial order point $T_x=0$, the Zeeman splitting of the itinerant electrons is zero. This permits formation of Cooper pairs and an onset of superconductivity induced by the transversal fluctuations of the localized electrons. Small deviation from the quantum partial ordered state leads to suppression of superconductivity. This explains the dome form of the superconducting transition temperature. The very low superconducting critical temperature is a consequence of the Ising ferromagnetism.