Magnetism and superconductivity in bilayer nickelate

TL;DR

This paper introduces a minimal theoretical model for bilayer nickelates that unifies high-temperature superconductivity with spin-density-wave order, highlighting the role of interlayer interactions and Hund's coupling.

Contribution

The study proposes a bilayer type-II t-J model incorporating Hund's coupling, explaining the coexistence of magnetism and superconductivity in bilayer nickelates.

Findings

Competition between ferromagnetism and superexchange leads to stripe SDW order.

Increasing interlayer exchange suppresses magnetic order and promotes s-wave superconductivity.

The model captures key features of magnetism and superconductivity in bilayer nickelates.

Abstract

The discovery of high-temperature superconductivity in bilayer nickelate La$_{3}$Ni$_{2}$O$_{7}$ necessitates a minimal theoretical model that unifies the superconducting phase with the spin-density-wave (SDW) phase without external pressure or strain. We propose a model where half-filled $d_{z^{2}}$ local moments interact with itinerant $d_{x^{2}-y^{2}}$ electrons via strong Hund's coupling $J_H$, which reduces to a bilayer type-II t-J model in the large $J_H$ limit. Using iDMRG calculations on an $L_y=4, L_z=2$ cylinder, we demonstrate that the competition between double-exchange ferromagnetism and in-plane superexchange generates period-4 stripe-like SDW order-a feature absent in one-orbital t-J model with only $d_{x^2-y^2}$ orbital. Furthermore, increasing the interlayer exchange coupling suppresses magnetic order and stabilizes interlayer s-wave superconductivity. These results identify the type-II t-J model as a minimal framework for capturing the interplay of magnetism and superconductivity in bilayer nickelates.