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

Abstract

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.

Bayesian optimization package: PHYSBO

“…By searching for (J 1 , J 2 , J 3 ) so that ∆ becomes minimum, we can estimate the model parameters that describe the target magnetization curve. In an actual problem involving model parameter estimation [28], the target property to be fitted is mainly the experimental result. Here, however, since the aim is to investigate the efficiency of PHYSBO for model estimation, we set the target magnetization curve as calculated using the Hamiltonian with (J 1 , J 2 , J 3 ) = (1.0, 0.5, 0.3); that is, these values are the solution to the model estimation problem.…”

Global‐Oriented Strategy for Searching Ultrastrength Martensitic Stainless Steels

“…However, the experiments are very expensive owning to hundreds of iterations involved. [29][30][31] On the contrary, only a few valuable data may be acquired by choosing the best predicted objectives. [16,32,33] In short, adaptive design can indeed provide new opportunities for discovering new materials owning to its powerful ability in extrapolating search.…”