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arXiv:2410.06955

Quantum dynamics in a spin-1/2 square lattice $J_{1}$-$J_{2}$-$δ$ altermagnet

Yang Liu, Shiqi Shao, Saisai He, Z. Y. Xie, Jia‐Wei Mei, Hong‐Gang Luo, Jize Zhao

Published Oct 9, 2024• 0 citations
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Abstract

A key feature of the newly discovered altermagnet is that its spin degeneracy is lifted, although it has an antiferromagnetic order and zero net magnetization. In this work, we investigate a frustrated spin-1/2 $J_1$-$J_2$-$δ$ Heisenberg model on the square lattice by the tensor network methodin combination with the linear spin-wave theory, with our focus on both the magnon excitations and longitudinal excitations.For a small $J_2$ and a finite range of $δ$ we demonstrate that such a model hosts an altermagnetic ground state. Its magnon spectrum is split into two branches and the largest splitting occurs at $\left(\pmπ/2, \pmπ/2\right)$ in the Brillouin zone. The magnitudes of splitting in the two magnon modes are equal with respect to the case of $δ=0$. Dynamical spin structure factors show that the low-energy peak in the longitudinal spectral weight around $(π/2, π/2)$ is also split, and thus the relative positions of the magnon modes and longitudinal modes in energy may change in the presence of a finite $δ$. These findings demonstrate that the altermagnets harbor more complex quantum dynamics than the conventional collinear antiferromagnets.

DOI
10.48550/arxiv.2410.06955

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Spin excitation spectra of two dimensional S=1/2S=1/2S=1/2 Heisenberg model with checkerboard structures.
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Altermagnets, a newly classified type of collinear magnet, exhibit zero magnetization, akin to antiferromagnets, but have spin-split electronic bands, akin to ferromagnets. Their low-energy excitations are predicted to be magnons, but with linear energy-momentum dispersion, typical of antiferromagnets, and additional chiral splitting analogous to those of electronic bands. However, such predictions are made using linear spin wave theory, which considers infinitely long-lived noninteracting magnons. This study employs nonperturbative quantum many-body calculations, via tensor network algorithms, to find how a chiral magnon will acquire finite lifetime and how the bands will shift due to magnon-magnon interaction. Such corrections to noninteracting magnon bands could be detected by Raman scattering experiments, for which the recipe is provided. Although the same interaction effects are often described in magnetism by nonlinearity of the Landau-Lifshitz-Gilbert equation, direct comparison using altermagnetic magnons as the testbed, shows how such classical methods cannot fully reproduce the results of quantum many-body calculations.