Data-driven determination of the spin Hamiltonian parameters and their uncertainties: The case of the zigzag-chain compound KCu$_4$P$_3$O$_{12}$
This work addresses the challenge of accurately modeling magnetic materials for physicists, providing a method to predict hard-to-measure properties, though it appears incremental as it applies an existing data-driven approach to a specific compound.
The researchers tackled the problem of estimating spin Hamiltonian parameters with uncertainties from experimental data, proposing a data-driven technique that successfully determined an effective model for KCu4P3O12 with specific interaction values like J1 = -8.54 ± 0.51 meV, describing magnetic susceptibility and magnetization curves well.
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.