Nonunitary triplet superconductivity tuned by field-controlled magnetization: URhGe, UCoGe, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>UTe</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>
Kazushige Machida
Abstract
We report on a theoretical study on ferromagnetic superconductors URhGe and UCoGe and identify the pairing state as a nonunitary spin-triplet one with time-reversal symmetry broken, analogous to the superfluid $^{3}\mathrm{He}\ensuremath{-}A$ phase. A recently found superconductor ${\mathrm{UTe}}_{2}$ with almost ferromagnetism is analyzed by the same manner. Through investigating their peculiar upper critical field ${H}_{\mathrm{c}2}$ shapes, it is shown that the pairing symmetry realized in all three compounds can be tuned by their magnetization curves under applied fields. This leads to the reentrant ${H}_{\mathrm{c}2}$ in URhGe, an S-shaped in UCoGe and an L-shaped ${H}_{\mathrm{c}2}$ in ${\mathrm{UTe}}_{2}$ observed for the magnetic hard $b$-axis direction. The identification with double chiral form $\mathbf{d}(k)=(\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{b}+i\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{c})({k}_{b}+i{k}_{c})$ in ${\mathrm{UTe}}_{2}$ naturally enables us to understand (1) multiple phases with ${A}_{1}, {A}_{2}$, and ${A}_{0}$ phases observed under pressure, (2) the enhanced reentrant ${H}_{\mathrm{c}2}$ for the off-axis direction associated with first-order metamagnetic transition, and (3) Weyl point nodes oriented along the magnetic easy $a$ axis. All three compounds are found to be topologically rich solid-state materials worth further investigation.