Data-driven determination of the spin Hamiltonian parameters and their uncertainties: The case of the zigzag-chain compound KCu$_4$P$_3$O$_{12}$

TL;DR

This paper introduces a data-driven method to estimate spin Hamiltonian parameters and their uncertainties from experimental magnetic data, applied to the compound KCu$_4$P$_3$O$_{12}$, enabling accurate modeling of its magnetic properties.

Contribution

The paper presents a novel technique for determining spin Hamiltonian parameters and uncertainties directly from experimental data, specifically applied to a zigzag-chain compound.

Findings

Effective model with specific exchange parameters and uncertainties was obtained.

The method successfully estimates uncertainties via noise analysis.

The model predicts properties like spin gap and magnetic entropy.

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.