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 KCu$_4$P$_3$O$_{12}$ 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 $J_1= -8.54 \pm 0.51 \{\rm meV}$, $J_2 = -2.67 \pm 1.13 \{\rm meV}$, $J_3 = -3.90 \pm 0.15 \{\rm meV}$, and $J_4 = 6.24 \pm 0.95 \{\rm meV}$, 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.
Highlights
An effective model in materials science often explains the origin of physical properties in materials
The flow of our prescription of data-driven approach is as follows. (i) Assume a target effective model and the posterior distribution. This constitutes the difference between the experimental and calculated results obtained by an effective model and the appropriate prior distribution of model parameters. (ii) Determine an appropriate hyperparameter in the prior distribution by the elbow method for the maximum a posterior (MAP) estimation results and estimated model parameters. (iii) Obtain a plausible observation noise to minimize the Bayes free-energy. (iv) Perform Markov chain Monte Carlo (MCMC) samplings using an estimated noise amplitude around the estimated model parameters in (ii)
Parameters with uncertainty. (v) Predict various properties, which cannot be measured in experiments using the estimated effective model
Summary
An effective model in materials science often explains the origin of physical properties in materials. The other is a data-driven approach in which model parameters are determined so as to fit the experimentally measured data in the target material[10,11,12,13,14,15]. The paper estimates a spin Hamiltonian as an effective model of KCu4P3O12 by a data-driven approach. We determine the superexchange interactions between Cu ions with uncertainty in this target model by a data-driven approach in which the experimentally measured susceptibility and magnetization curves are in-. By considering the observation noise, four types of magnetic interactions are estimated with the error bars in a target spin Hamiltonian, and their relationships are discussed from the distributions of sampling data by the Monte Carlo method. From the ESR measurements, the g-factor of Cu ions is determined to be 2.08
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