Data-driven determination of the spin Hamiltonian parameters and their uncertainties: The case of the zigzag-chain compound KCu4 P3 O12

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±0.51meV, J2=-2.67±1.13meV, J3=-3.90±0.15meV, and J4=6.24±0.95meV, 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.