Antiferromagnetic order in the FFLO state

TL;DR

This paper explores the coexistence and characteristics of antiferromagnetic order within the FFLO state of a high-field d-wave superconductor, revealing how AF order is induced and behaves at phase boundaries.

Contribution

It introduces a mean field model demonstrating the nature of AF order in the FFLO state, including phase transition types and the spatial structure of magnetic moments.

Findings

First order transition from normal to FFLO state with finite U and J.

Discontinuous Neel temperature at the AF phase boundary.

AF order in FFLO is induced by localized Andreev bound states.

Abstract

We investigate the antiferromagnetic (AF) order in the d-wave superconducting (SC) state at high magnetic fields. A two-dimensional model with on-site repulsion U, inter-site attractive interaction V and antiferromagnetic exchange interaction J is solved using the mean field theory. For finite values of U and J, a first order transition occurs from the normal state to the FFLO state, while the FFLO-BCS phase transition is second order, consistent with the experimental results in CeCoIn_5. Although the BCS-FFLO transition is continuous, the Ne'el temperature of AF order is discontinuous at the phase boundary because the AF order in the FFLO state is induced by the Andreev bound state localized in the zeros of FFLO order parameter, while the AF order hardly occurs in the uniform BCS state. The spatial structure of the magnetic moment is investigated for the commensurate AF state as well as for the incommensurate AF state. The influence of the spin fluctuations is discussed for both states. Since the fluctuations are enhanced in the normal state for incommensurate AF order, this AF order can be confined in the FFLO state. The experimental results in CeCoIn_5 are discussed.