Spontaneous emergence of altermagnetism in the single-orbital extended Hubbard model

TL;DR

This paper demonstrates that altermagnetism can spontaneously emerge in a simple single-orbital extended Hubbard model on a 2D square lattice, without spin-orbit coupling or multi-orbital effects, broadening potential material candidates.

Contribution

It reveals a new mechanism for altermagnetism emergence in a minimal single-orbital model, expanding the understanding of magnetic order origins.

Findings

d-wave altermagnetism can spontaneously form without spin-orbit coupling.

The phase diagram shows stable altermagnetic phases away from half-filling.

Coexistence of antiferromagnetic and complex d-wave spin bond orders is key.

Abstract

Altermagnetism (AM), the recently discovered third class of collinear magnetic order, is characterized by non-relativistic momentum-dependent spin-split electronic structure with compensated zero net magnetization. It can arise from the conventional antiferromagnetism by introducing local anisotropy on the two opposite-spin sublattices, either through structural changes in local crystallographic symmetry or spontaneous emergence of local staggered orbital order from electron correlations in multi-orbital systems. Here, we demonstrate on the two-dimensional square lattice that a $d$-wave AM can emerge spontaneously in the single-orbital extended Hubbard model, without invoking the spin-orbital coupling and multi-orbital physics. We carry out mean-field studies on the concrete single-orbital $t$-$U$-$V$ model with $U$ and $V$ the onsite and nearest-neighbor Coulomb interactions, obtaining the ground states, analyzing their properties, and determining the phase diagram in the $U$-$V$ plane. The $d$-wave AM with novel spin-transport behavior is found to be stabilized in a wide region of the phase diagram when the system is doped away from half-filling, actualized by the coexistence of onsite antiferromagnetic order and complex $d$-wave nearest-neighbor spin bond orders. Our findings provide an alternative route to achieve AM and substantially expand the range of candidate AM materials.