RKKY-dipolar Interactions and 3D Spin Supersolid on Stacked Triangular Lattice

TL;DR

This study combines electronic structure analysis, effective spin modeling, and Monte Carlo simulations to reveal a novel mechanism for 3D spin supersolidity in a metallic antiferromagnet on a stacked triangular lattice, inspired by recent experimental discoveries.

Contribution

It introduces a minimal spin model derived from first-principles that explains the emergence of 3D spin supersolidity through RKKY and dipolar interactions, matching experimental thermodynamics.

Findings

Identification of a 3D spin supersolid ground state

Detailed phase diagram with multiple magnetic phases

Explanation of supersolid transitions in EuCo₂Al₉

Abstract

Inspired by the recent discovery of metallic spin supersolidity and its giant magnetocaloric effect in the rare-earth alloy EuCo$_2$Al$_9$ [Nature 651, 61 (2026)], we perform a combined study through electronic structure analysis, effective spin model, and Monte Carlo simulations on a stacked triangular lattice, and reveal a novel mechanism for the emergence of 3D spin supersolid in a metallic antiferromagnet. From first-principles inputs, we derive a minimal spin model on a stacked triangular lattice (STL), which arises from the interplay between Ruderman-Kittel-Kasuya-Yosida (RKKY) and dipolar interactions and accurately reproduces the experimental thermodynamics. Based on the STL model, we identify a ground state that simultaneously breaks discrete lattice translational symmetry and continuous spin-rotational symmetry -- the hallmark of a spin supersolid. Furthermore, we present the field-temperature phase diagram of the 3D STL model and discuss the various magnetic phases and associated phase transitions. Under zero field, the spin supersolid Y order establishes in two steps: an upper transition at $T_{N1}$, where an emergent U(1) symmetry appears and the system enters a fluctuating collinear regime, followed by a lower transition at $T_{N2}$ into the spin supersolid Y phase. In contrast, the supersolid V phase undergoes a single phase transition at $T_N^V$. Our results not only provide a comprehensive theoretical understanding of the metallic spin supersolid reported for EuCo$_2$Al$_9$ but also pave the way for further experimental investigations into its supersolid transitions and universality class.