# Interplay of the spin density wave and a possible Fulde-Ferrell-Larkin-Ovchinnikov state in $\mathrm{CeCoIn_5}$ in rotating magnetic field

## TL;DR

This study investigates the competition between spin-density-wave order and the FFLO superconducting state in CeCoIn_5, revealing that the FFLO state emerges when the magnetic field is aligned near the c axis, supported by experimental thermal conductivity measurements.

## Contribution

The paper presents a model based on experimental data showing the interplay between SDW and FFLO states in CeCoIn_5, and experimentally confirms the existence of the FFLO state with field aligned near the c axis.

## Key findings

- SDW stabilized near the a-b plane
- FFLO state emerges near the c axis
- Thermal conductivity measurements support the FFLO state presence

## Abstract

The $d$-wave superconductor $\mathrm{CeCoIn_5}$ has been proposed as a strong candidate for supporting the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state near the low-temperature boundary of its upper critical field. Neutron diffraction, however, finds spin-density-wave (SDW) order in this part of the phase diagram for field in the $a$-$b$ plane, and evidence for the SDW disappears as the applied field is rotated toward the tetragonal $c$ axis. It is important to understand the interplay between the SDW and a possible FFLO state in $\mathrm{CeCoIn_5}$, as the mere existence of an SDW does not necessary exclude an FFLO state. Here, based on a model constructed on the basis of available experiments, we show that an FFLO state competes with an SDW phase. The SDW state in $\mathrm{CeCoIn_5}$ is stabilized when the field is directed close to the $a$-$b$ plane. When the field is rotated toward the $c$ axis, the FFLO state emerges, and the SDW phase disappears. In the FFLO state, the nodal planes with extra quasiparticles (where the superconducting order parameter is zero) are perpendicular to the field, and in the SDW phase, the quasiparticle density of states is reduced. We test this model prediction by measuring heat transported by normal quasiparticles in the superconducting state. As a function of field, we observe a reduction of thermal conductivity for field close to the $a$-$b$ plane and an enhancement of thermal conductivity when field is close to the $c$ axis, consistent with theoretical expectations. Our modeling and experiments, therefore, indicate the existence of the FFLO state when field is parallel to the $c$ axis.