Weak ferromagnetism in the square-lattice Heisenberg J1-J2-J2′ model with easy-axis single-ion anisotropy
Abstract
Motivated by recent experimental realizations of the Heisenberg model and two-dimensional altermagnetism using ultracold atoms in optical lattices, we systematically investigate the magnetic properties of the square-lattice Heisenberg J1-J2-J2′ model in the presence of easy-axis single-ion anisotropy D. Here, J1 (>0) is the nearest-neighbor antiferromagnetic exchange parameter, while J2 and J2′ are two distinct next-nearest-neighbor superexchange parameters that alternate on the lattice. We perform numerical calculations of the sublattice magnetization, net magnetization, and critical temperature. Interestingly, the net magnetization is not identically zero at finite temperatures; its absolute value first increases and then decreases with increasing temperature, revealing a temperature-dependent weak ferromagnetism. We find that J2not=J2′ is the primary factor responsible for weak ferromagnetism at finite temperatures, while D provides the necessary background for two-dimensional long-range magnetic ordering. Moreover, for a fixed J2+J2′, we observe that a larger |J2−J2′| leads to a greater maximum net magnetization and critical temperature, as well as a broader temperature range for weak ferromagnetism. The difference between J2 and J2′ originates from the distinct superexchange pathways between magnetic atoms, with these pathways mediated by two different types of nonmagnetic atoms. This mechanism, which differs from conventional ones such as the Dzyaloshinskii-Moriya interaction, may be detectable in real materials.
Related
- Competition between uniform ferromagnetism and finite-wave-vector instabilities in square-lattice skyrmion crystals
- Establishing Néel order in the square-lattice antiferromagnetic Heisenberg model: a bootstrap proof
- Kitaev-Heisenberg model on the square-hexagon-dodecagon lattice
- Coexistence of liquid-like disordered state and weak ferromagnetism in a s = 1 kagome lattice
- The massive phase of the two-dimensional Heisenberg model is stable under small anisotropy
BibTeX
@misc{mi2026weak,
title = {{Weak ferromagnetism in the square-lattice Heisenberg $J_1$-$J_2$-$J_2^\prime$ model with easy-axis single-ion anisotropy}},
author = {Bin-Zhou Mi and Qiang Gu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16593},
eprint = {2609.16593},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16593},
}
RIS
TY - UNPB
TI - Weak ferromagnetism in the square-lattice Heisenberg J_1-J_2-J_2^′ model with easy-axis single-ion anisotropy
AU - Bin-Zhou Mi
AU - Qiang Gu
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.16593
UR - https://arxiv.org/abs/2609.16593
AB - Motivated by recent experimental realizations of the Heisenberg model and two-dimensional altermagnetism using ultracold atoms in optical lattices, we systematically investigate the magnetic properties of the square-lattice Heisenberg J_1-J_2-J_2^′ model in the presence of easy-axis single-ion anisotropy D. Here, J_1 (>0) is the nearest-neighbor antiferromagnetic exchange parameter, while J_2 and J_2^′ are two distinct next-nearest-neighbor superexchange parameters that alternate on the lattice. We perform numerical calculations of the sublattice magnetization, net magnetization, and critical temperature. Interestingly, the net magnetization is not identically zero at finite temperatures; its absolute value first increases and then decreases with increasing temperature, revealing a temperature-dependent weak ferromagnetism. We find that J_2not=J_2^′ is the primary factor responsible for weak ferromagnetism at finite temperatures, while D provides the necessary background for two-dimensional long-range magnetic ordering. Moreover, for a fixed J_2+J_2^′, we observe that a larger |J_2−J_2^′| leads to a greater maximum net magnetization and critical temperature, as well as a broader temperature range for weak ferromagnetism. The difference between J_2 and J_2^′ originates from the distinct superexchange pathways between magnetic atoms, with these pathways mediated by two different types of nonmagnetic atoms. This mechanism, which differs from conventional ones such as the Dzyaloshinskii-Moriya interaction, may be detectable in real materials.
ER -