# Competing magnetic orders in the superconducting state of Nd-doped CeRhIn$_{5}$ under pressure

## TL;DR

This study reveals that 5% Nd or Gd doping in CeRhIn$_{5}$ induces a magnetic instability within the superconducting phase, likely due to impurity-driven spin exciton condensation, highlighting complex magnetic interactions under pressure.

## Contribution

It demonstrates that magnetic impurities induce a spin-density-wave phase inside the superconducting state of CeRhIn$_{5}$, supported by experimental and model calculations.

## Key findings

- Magnetic impurities induce a zero-field magnetic instability.
- A spin-density-wave phase competes with superconductivity.
- Impurity-driven spin exciton condensation explains the instability.

## Abstract

Applied pressure drives the heavy-fermion antiferromagnet CeRhIn$_{5}$ towards a quantum critical point that becomes hidden by a dome of unconventional superconductivity. Magnetic fields suppress this superconducting dome, unveiling the quantum phase transition of local character. Here, we show that $5\%$ magnetic substitution at the Ce site in CeRhIn$_{5}$, either by Nd or Gd, induces a zero-field magnetic instability inside the superconducting state. This magnetic state not only should have a different ordering vector than the high-field local-moment magnetic state, but it also competes with the latter, suggesting that a spin-density-wave phase is stabilized in zero field by Nd and Gd impurities - similarly to the case of Ce$_{0.95}$Nd$_{0.05}$CoIn$_{5}$. Supported by model calculations, we attribute this spin-density wave instability to a magnetic-impurity driven condensation of the spin excitons that form inside the unconventional superconducting state.