Revisiting spin Hamiltonian parameters in a Kitaev material via Bayesian optimization of magnetization curves
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arXiv
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| Natura: | Preprint |
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2026
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| _version_ | 1866917528819728384 |
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| author | Misawa, Takahiro Tamura, Ryo Yoshimi, Kazuyoshi Yamaji, Youhei |
| author_facet | Misawa, Takahiro Tamura, Ryo Yoshimi, Kazuyoshi Yamaji, Youhei |
| contents | Determining the spin Hamiltonian of a magnetic compound is crucial for understanding its magnetic properties. A standard approach is to derive model parameters from $ab$ $initio$ calculations based on the crystal structure. However, the resulting Hamiltonian can depend sensitively on methodological details of the $ab$ $initio$ procedure. This issue is particularly evident in $α$-RuCl$_3$, a candidate Kitaev material. Here, we present an alternative, data-driven approach to determine the spin Hamiltonian parameters of $α$-RuCl$_3$ by Bayesian optimization of experimental magnetization curves along the $b$- and $c$-axis directions. We optimize five parameters, namely the Kitaev interaction $K$, off-diagonal interactions $Γ$ and $Γ'$, the Heisenberg interaction $J$, and the $c$-axis $g$-factor $g_c$. The parameter set that minimizes the cost function is $(K,Γ,Γ',J,g_c)=(-6.0,\,7.5,\,-0.3,\,-1.75,\,2.3)$, where the exchange couplings are in meV. We find that the cost function is insensitive to the absolute value of the Kitaev coupling $K$. Thus, the magnetization data alone do not determine its energy scale. The cost function also depends only weakly on $Γ'$ and $J$, while the optimization favors a large positive $Γ$. By computing the static spin structure factor, magnetic susceptibility, and specific heat, we show that these quantities favor the large-$Γ$ scenario over the small-$g_c$ scenario and that the parameter set that minimizes the cost function yields good agreement with experiment. The combination of Bayesian optimization and accurate low-energy solvers provides an effective approach for determining parameters of spin Hamiltonians. This methodology opens a systematic route to determining spin Hamiltonians in quantum magnets from experimental data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24857 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Revisiting spin Hamiltonian parameters in a Kitaev material via Bayesian optimization of magnetization curves Misawa, Takahiro Tamura, Ryo Yoshimi, Kazuyoshi Yamaji, Youhei Strongly Correlated Electrons Materials Science Determining the spin Hamiltonian of a magnetic compound is crucial for understanding its magnetic properties. A standard approach is to derive model parameters from $ab$ $initio$ calculations based on the crystal structure. However, the resulting Hamiltonian can depend sensitively on methodological details of the $ab$ $initio$ procedure. This issue is particularly evident in $α$-RuCl$_3$, a candidate Kitaev material. Here, we present an alternative, data-driven approach to determine the spin Hamiltonian parameters of $α$-RuCl$_3$ by Bayesian optimization of experimental magnetization curves along the $b$- and $c$-axis directions. We optimize five parameters, namely the Kitaev interaction $K$, off-diagonal interactions $Γ$ and $Γ'$, the Heisenberg interaction $J$, and the $c$-axis $g$-factor $g_c$. The parameter set that minimizes the cost function is $(K,Γ,Γ',J,g_c)=(-6.0,\,7.5,\,-0.3,\,-1.75,\,2.3)$, where the exchange couplings are in meV. We find that the cost function is insensitive to the absolute value of the Kitaev coupling $K$. Thus, the magnetization data alone do not determine its energy scale. The cost function also depends only weakly on $Γ'$ and $J$, while the optimization favors a large positive $Γ$. By computing the static spin structure factor, magnetic susceptibility, and specific heat, we show that these quantities favor the large-$Γ$ scenario over the small-$g_c$ scenario and that the parameter set that minimizes the cost function yields good agreement with experiment. The combination of Bayesian optimization and accurate low-energy solvers provides an effective approach for determining parameters of spin Hamiltonians. This methodology opens a systematic route to determining spin Hamiltonians in quantum magnets from experimental data. |
| title | Revisiting spin Hamiltonian parameters in a Kitaev material via Bayesian optimization of magnetization curves |
| topic | Strongly Correlated Electrons Materials Science |
| url | https://arxiv.org/abs/2605.24857 |