Model Selection of NiGa<sub>2</sub>S<sub>4</sub> Triangular Lattice by Bayesian Inference

Takenaka, Hikaru; Nagata, Kenji; Mizokawa, T.; Okada, Masato

doi:10.7566/jpsj.83.124706

Cited by 9 publications

(5 citation statements)

References 14 publications

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“…For comparison, also the values of J n [meV] estimated in previous studies are listed. LDA+U: LDA+U calculation, 9) UHF: unrestricted Hartree-Fock calculation, 11) UHF+B: Bayesian inference from the UHF results, 12) DDCI2: ab-initio cluster calculation, 13) NS: neutron scattering, 3) ESR: electron spin resonance. 8) ninth nearest-neighbors, which are all smaller than at most 1.2 meV.…”

Section: Mapping Onto Classical Heisenberg Modelmentioning

confidence: 99%

“…On the theoretical side, spin exchanges were estimated by a first-principles electronic structure calculation (LDA+U) 9) and unrestricted Hartree-Fock (UHF) calculations combined with x-ray photo-emission spectroscopy (XPS) 10,11) or with Bayesian inference. 12) These are based on the itinerant electron picture. They concluded that the third nearest-neighbor coupling is large, which naturally leads to the magnetic ordering with Q ∼ (1/6, 1/6).…”

Section: Introductionmentioning

confidence: 99%

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Weak-coupling Mean-field Theory of Magnetic Properties of NiGa₂S₄

2020

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We report a mean-field theoretical study of a triangular lattice magnet NiGa 2 S 4 . Specifically, spiral mean-field theory is applied to a 17-band d-p model constructed from the maximally localized Wannier functions. Our itinerant-model approach shows that the most stable spiral magnetic state has an ordering vector near Q = (0.15, 0.15, 0), consistent with neutron scattering experiments, when we assume the Ni-site Coulomb interaction is not so strong (U ≈ 2 eV). To map onto a classical Heisenberg spin model, we estimate spin exchange interactions from the mean-field results, and find that the nearest-neighbor exchange is ferromagnetic and the largest (larger than the third nearest-neighbor exchange, in contrast to early studies). We also calculate the dynamical spin correlation function S(q, ω), using the same model within the randomphase approximation (RPA). Calculated S(q, ω) has a spectral structure quite different from that of conventional spin-wave excitations. *

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Section: Mapping Onto Classical Heisenberg Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Weak-coupling Mean-field Theory of Magnetic Properties of NiGa₂S₄

2020

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“…This is a challenging inverse problem in quantum mechanics, for which previous machine-learning solutions were devised but for 1D problems only, such as those based on multilayered neural networks [31] or the nonparametric Bayesian approximation [32]. Bayesian estimation, in particular, has been applied to other problems in solid state physics [33,34], but this is a method that has some limitations depending on the level of complexity of the problem at hand. For instance, it is typically difficult to cover the whole hypothesis space or guess appropriate priors.…”

Section: Introductionmentioning

confidence: 99%

A method for finding the background potential of quantum devices from scanning gate microscopy data using machine learning

Cunha

Aoki

Ferry

et al. 2022

Mach. Learn.: Sci. Technol.

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The inverse problem of estimating the background potential from measurements of the local density of states (LDOS) is a challenging issue in quantum mechanics. Even harder is doing this estimation using approximate methods such as scanning gate microscopy (SGM). Here we propose a machine-learning-based solution by exploiting adaptive cellular neural networks (CNN). For the paradigmatic setting of a quantum point contact, the training data consist of potential-SGM functional relations represented by image pairs. These are generated by the recursive Green’s function method. We demonstrate that the CNN-based machine learning framework can predict the background potential corresponding to the experimental image data. This is aﬃrmed by analyzing the estimated potential with image processing techniques based on the comparison between the charge densities and those obtained from diﬀerent techniques. Correlation analysis of the images suggests the possibility of estimating diﬀerent contributions to the background potential. In particular, our results indicate that both charge puddles and ﬁxed impurities contribute to the spatial patterns found in the SGM data. Our work represents a timely contribution to the rapidly evolving ﬁeld of exploiting machine learning to solve diﬃcult problems in physics.

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“…Recently, datadriven techniques are becoming indispensable in materials science, because they should accelerate the discovery of novel materials [16][17][18][19][20][21][22][23][24][25][26][27][28] and deepen our understanding of materials [29][30][31][32][33][34][35][36] . From the viewpoint of effective model estimations, data-driven techniques are also efficient to accelerate automatic searches for appropriate model parameters 37 and to extract relevant model parameters [38][39][40] .…”

Section: Introductionmentioning

confidence: 99%

Data-driven determination of the spin Hamiltonian parameters and their uncertainties: The case of the zigzag-chain compound KCu4P3O12

et al. 2020

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We propose a data-driven technique to estimate the spin Hamiltonian, including uncertainty, from multiple physical quantities. Using our technique, an effective model of KCu4P3O12 is determined from the experimentally observed magnetic susceptibility and magnetization curves with various temperatures under high magnetic fields. An effective model, which is the quantum Heisenberg model on a zigzag chain with eight spins having J1 = −8.54 ± 0.51 meV, J2 = −2.67 ± 1.13 meV, J3 = −3.90 ± 0.15 meV, and J4 = 6.24 ± 0.95 meV, describes these measured results well. These uncertainties are successfully determined by the noise estimation. The relations among the estimated magnetic interactions or physical quantities are also discussed. The obtained effective model is useful to predict hard-to-measure properties such as spin gap, spin configuration at the ground state, magnetic specific heat, and magnetic entropy.

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Model Selection of NiGa₂S₄ Triangular Lattice by Bayesian Inference

Cited by 9 publications

References 14 publications

Weak-coupling Mean-field Theory of Magnetic Properties of NiGa₂S₄

Weak-coupling Mean-field Theory of Magnetic Properties of NiGa₂S₄

A method for finding the background potential of quantum devices from scanning gate microscopy data using machine learning

Data-driven determination of the spin Hamiltonian parameters and their uncertainties: The case of the zigzag-chain compound KCu4P3O12

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Model Selection of NiGa2S4 Triangular Lattice by Bayesian Inference

Cited by 9 publications

References 14 publications

Weak-coupling Mean-field Theory of Magnetic Properties of NiGa2S4

Weak-coupling Mean-field Theory of Magnetic Properties of NiGa2S4

A method for finding the background potential of quantum devices from scanning gate microscopy data using machine learning

Data-driven determination of the spin Hamiltonian parameters and their uncertainties: The case of the zigzag-chain compound KCu4P3O12

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Model Selection of NiGa₂S₄ Triangular Lattice by Bayesian Inference

Weak-coupling Mean-field Theory of Magnetic Properties of NiGa₂S₄

Weak-coupling Mean-field Theory of Magnetic Properties of NiGa₂S₄