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arXiv:2408.00841 · Physical review. B./Physical review. B

Altermagnetism on the Shastry-Sutherland lattice

Francesco Ferrari, Roser Valentí

Published Nov 19, 2024• 32 citations
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Abstract

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 $d$-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).

DOI
10.1103/physrevb.110.205140

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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).
We investigate the metal-insulator transition driven by the onsite repulsive interaction UUU in an altermagnetic Hubbard model defined on a Lieb lattice. Using the slave-rotor approach at half-filling, we find that the system exhibits a cascade of interaction-driven phase transitions. As UUU increases, the system evolves from a normal metal to an altermagnetic metal, then to an altermagnetic insulator, and eventually to an altermagnetic Mott insulator characterized by the complete suppression of the quasiparticle weight. These phases are supported by the calculation of the electronic spectral function, which features spin-split bands in both the metallic and insulating regimes. However, the spin splitting becomes substantially suppressed in the Mott-insulating phase. Our results suggest that the observation of spin splitting in the spectral function of ddd-wave altermagnets with a Lieb-lattice-like structure may be limited to the weak-to-moderate correlation regime.
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 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.
We propose the projected BCS wave function as the ground state for the doped Mott insulator SrCu2(BO3)2 on the Shastry-Sutherland lattice. At half filling this wave function yields the exact ground state. Adding mobile charge carriers, we find a strong asymmetry between electron and hole doping. Upon electron doping an unusual metal with strong valence bond correlations forms. Hole doped systems are d-wave resonating valence bond superconductors in which superconductivity is strongly enhanced by the emergence of spatially varying plaquette bond order.
Altermagnets - collinear, zero-net-moment magnets with momentum-odd spin splitting protected by crystalline symmetries - offer a tunable route to suppress long-range antiferromagnetism while preserving strong short-range spin fluctuations. We show that this environment robustly stabilizes unconventional superconductivity and naturally produces mixed-symmetry pairing. Through a strong-coupling analysis of a spin-anisotropic Hubbard model, we derive an anisotropic t-J model where exchange interactions cooperatively enhance singlet d-wave pairing and promote triplet p-wave pairing. Our mean-field analysis reveals a pairing evolution driven by altermagnetic anisotropy: for small spin anisotropy, the d-wave channel is enhanced, closely resembling the dominant pairing symmetry in cuprate superconductors, which suggests that weak spin anisotropy may be an essential ingredient in realistic models of these materials. Constrained-path quantum Monte Carlo simulations confirm this picture, showing a regime where dominant d-wave correlations coexist with an emergent p-wave component near optimal doping. As spin anisotropy increases, strong C2 anisotropy and spin splitting activate the triplet channel, leading to a stable d+p mixed-pairing state. This synergistic state exhibits significantly enhanced overall pairing strength, suggesting the possibility of a higher superconducting transition temperature.
Altermagnetism and bond-nematicity in the spin-1/21/21/2 square lattice J1−J2−δJ_1-J_2-δJ1​−J2​−δ model
We study appearance of bond-nematicity in insulating altermagnetic materials induced by increased frustration and quantum-fluctuations driven melting of the altermagnetic order. Using novel machine learning approach that combines symmetry enhanced neural network architectures and variational Monte Carlo we consider the spin-1/21/21/2 square lattice J1−J2−δJ_1-J_2-δJ1​−J2​−δ model known to have altermagnetic ordering in the regime of small geometric frustration and a gapless spin liquid phase in the regime of strong frustration and small exchange interaction modulation parameter δδδ. In the regime where exchange modulation is relatively large, resulting in the significant splitting of the magnon modes with different chiralities in the altermagnetic regime, we find that melting of the altermagnetic order by increased frustration leads to an intriguing phase that hosts coexisting symmetry protected topological valence bond solid and bond-nematic orders. The phase is characterized by condensation of magnon pairs that results in bond-nematicity, breaking of U(1) spin rotation and Z2\mathbb{Z}_2Z2​ spin inversion symmetries and chiral splitting of the triplon-like energy levels in the excitation spectrum. Whilst numerous recent studies address non-trivial impact of altermagnetic moments on various properties in altermagnetic materials, like electronic band structure and superconductivity, influence of strong quantum fluctuations and phases that can result from melting of the altermagnetic order are much less explored. Our study therefore presents an important step in identifying exotic phases of matter that can emerge in vicinity of the altermagnetic order.