Lattice Ginzburg-Landau Model of a Ferromagnetic p-wave Pairing Phase in Superconducting Materials and an Inhomogeneous Coexisting State

TL;DR

This paper introduces a lattice Ginzburg-Landau model to study the coexistence and interplay of ferromagnetism and p-wave superconductivity in materials like UCoGe, revealing inhomogeneous coexisting states through Monte Carlo simulations.

Contribution

It presents a nonperturbative lattice Ginzburg-Landau model for ferromagnetic p-wave superconductors and explores their phase diagram and inhomogeneous coexistence states.

Findings

Phase diagram resembles that of UCoGe.

Coexisting FM and SC appear near the surface for certain temperature ratios.

Inhomogeneous coexistence states are identified.

Abstract

We study the interplay of the ferromagnetic (FM) state and the p-wave superconducting (SC) state observed in several materials such as UCoGe and URhGe in a totally nonperturbative manner. To this end, we introduce a lattice Ginzburg-Landau model that is a genuine generalization of the phenomenological Ginzburg-Landau theory proposed previously in the continuum and also a counterpart of the lattice gauge-Higgs model for the s-wave SC transition, and study it numerically by Monte-Carlo simulations. The obtained phase diagram has qualitatively the same structure as that of UCoGe in the region where the two transition temperatrures satisfy $T_{\rm FM}>T_{\rm SC}$. For $T_{\rm FM}/T_{\rm SC} < 0.7$, we find that the coexisting region of FM and SC orders appears only near the surface of the lattice, which describes an inhomogeneous FMSC coexisting state.