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arXiv:2312.10151 · Physical Review Letters

Realizing Altermagnetism in Fermi-Hubbard Models with Ultracold Atoms

Purnendu Das, Valentin Leeb, Johannes Knolle, Michael Knap

Published Jun 26, 2024• 83 citations
arXivHTMLPDF

Abstract

Altermagnetism represents a type of collinear magnetism, that is in some aspects distinct from ferromagnetism and from conventional antiferromagnetism. In contrast to the latter, sublattices of opposite spin are related by spatial rotations and not only by translations and inversions. As a result, altermagnets have spin-split bands leading to unique experimental signatures. Here, we show theoretically how a d-wave altermagnetic phase can be realized with ultracold fermionic atoms in optical lattices. We propose an altermagnetic Hubbard model with anisotropic next-nearest neighbor hopping and obtain the Hartree-Fock phase diagram. The altermagnetic phase separates in a metallic and an insulating phase and is robust over a large parameter regime. We show that one of the defining characteristics of altermagnetism, the anisotropic spin transport, can be probed with trap-expansion experiments.

DOI
10.1103/physrevlett.132.263402

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Altermagnetism represents a type of collinear magnetism, that is in some aspects distinct from ferromagnetism and from conventional antiferromagnetism. In contrast to the latter, sublattices of opposite spin are related by spatial rotations and not only by translations and inversions. As a result, altermagnets have spin-split bands leading to unique experimental signatures. Here, we show theoretically how a d-wave altermagnetic phase can be realized with ultracold fermionic atoms in optical lattices. We propose an altermagnetic Hubbard model with anisotropic next-nearest neighbor hopping and obtain the Hartree-Fock phase diagram. The altermagnetic phase separates in a metallic and an insulating phase and is robust over a large parameter regime. We show that one of the defining characteristics of altermagnetism, the anisotropic spin transport, can be probed with trap-expansion experiments.
We study the emergence of altermagnetism from repulsive interactions for electrons on the Lieb lattice as a model of quasi-2D oxychalcogenides with the so-called "anti-CuO_{2}" lattice structure. A comprehensive study of the Lieb lattice Hubbard model, using unrestricted Hartree-Fock and exact diagonalization techniques, establishes the presence of a spin-1/2 altermagnetic Mott insulating ground state for average electron densities of 2 and 4 per unit cell. Both phases show the characteristic spin splitting in the electron bands as well as in the magnon bands, as indicated by solutions of an effective spin-1/2 Heisenberg model that we construct. We also provide evidence for altermagnetic metal formation in the electron- and hole-doped Mott state, giving rise to Fermi surfaces with d_{x^{2}-y^{2}}-wave spin splitting and quasi-one-dimensional characteristics.
Altermagnetism, featuring momentum-dependent spin splitting without net magnetization, has attracted a growing interest for spintronics. We study a Fermi Hubbard model with altermagnetic order arising from the spin-anisotropic hopping near half-filling using constrained-path quantum Monte Carlo. Spin-dependent hopping breaks SU(2) symmetry and disrupts Fermi surface nesting, giving rise to an altermagnetic state with momentum-space spin splitting but no net magnetization. We find that increasing anisotropy suppresses long-range antiferromagnetic order and significantly enhances effective ddd-wave pairing correlations. Our results demonstrate a doping-free route to unconventional superconductivity mediated by short-range spin fluctuations in an altermagnetic background.
We study an extension of the 2D Fermi--Hubbard model, which was recently introduced in [Das et al., Phys. Rev. Lett. 132, 263402 (2024)] and shown to describe altermagnetism that can be studied in cold atom systems. Using an updated Hartree--Fock method that can detect instabilities towards phase separation, we show that the model is in a mixed phase in large parts of the parameter regime at half-filling. We argue that the occurrence of a mixed phase is an indication of exotic physics which, in this model, occurs in parameter regimes accessible in cold atom experiments.
Altermagnetism has recently emerged as a third fundamental branch of magnetism, combining the vanishing net magnetization of antiferromagnets with the high-momentum-dependent spin splitting of ferromagnets. This study provides a comprehensive real- and momentum-space analysis of topological phases in two-dimensional d-wave altermagnets. By employing a tight-binding Hamiltonian, we characterize the topological phase transition occurring at a critical intra-sublattice hopping strength (taCt_a^CtaC​). We examine the emergence of Dirac nodal points and the resulting Berry curvature singularities, supported by a visual analysis of pseudospin texture winding. Crucially, we analize spin splitting, effective altermagnetic strength, and investigate the transport implications of these phases, uncovering giant conductivity anisotropy and spin-dependent ``steering'' effects driven by group velocity distribution across the Fermi surface. Beyond bulk properties, we analyze the edge state topology in ribbon geometries through the lens of information-theoretic markers like fidelity-susceptibility and inverse participation ratio, offering a robust alternative to traditional Chern number calculations, without relying on translational symmetry. Our results demonstrate that the hybridization of edge states in ultra-narrow nanoribbons opens a controllable energy gap, a feature we exploit to propose a novel topological altermagnetic field-effect transistor design where ballistic and spatially spin-polarized transport can be electrostatically gated. This work establishes a theoretical and information-theoretic framework for ``edgetronics'' in altermagnetic materials, paving the way for next-generation, high-speed spintronic and ``spin-splitter'' logic devices and architectures.
Altermagnetism is an unconventional form of magnetic order characterized by spin-split electronic bands and zero net magnetization. Here, the authors utilize a variational Monte Carlo approach to reveal the emergence of ddd-wave altermagnetism in the Hubbard model on the Shastry-Sutherland lattice and demonstrate how strong electronic correlations manifest in the metal-insulator transition. The calculation of photoemission spectral functions highlights the presence of altermagnetic Zeeman splitting, also in the Mott insulating phase (and upon doping).
The Fermi-Hubbard model is a key concept in condensed matter physics and provides crucial insights into electronic and magnetic properties of materials. Yet, the intricate nature of Fermi systems poses a barrier to answering important questions concerning d-wave superconductivity and quantum magnetism. Recently, it has become possible to experimentally realize the Fermi-Hubbard model using a fermionic quantum gas loaded into an optical lattice. In this atomic approach to the Fermi-Hubbard model, the Hamiltonian is a direct result of the optical lattice potential created by interfering laser fields and short-ranged ultracold collisions. It provides a route to simulate the physics of the Hamiltonian and to address open questions and novel challenges of the underlying many-body system. This review gives an overview of the current efforts in understanding and realizing experiments with fermionic atoms in optical lattices and discusses key experiments in the metallic, band-insulating, superfluid, and Mott-insulating regimes.