Inelastic neutron scattering studies on the eight-spin zigzag-chain compound ${\mathrm{KCu}}_4{P}_3{O}_{12}$: Confirmation of the validity of a data-driven technique based on machine learning

We performed inelastic neutron scattering (INS) experiments on ${\mathrm{KCu}}_4{P}_3{O}_{12}$ powder and compared the experimental results with those calculated for the spin model (an eight-spin zigzag chain with $S=\frac{1}{2}$) using the data-driven technique based on machine learning. We observed magnetic excitations at approximately 3.0, 4.1, 5.9, and 8.8 meV at 5.5 K and at approximately 3.8 and 5.9 meV at 49 K. The excitations corresponding to 3.0, 4.1, and 8.8 meV were magnetic excitations from the ground state to the first, second, and fourth excited states (2.87, 4.23, and 8.53 meV from the calculations), respectively. The excitations corresponding to 3.8 and 5.9 meV were magnetic excitations from the first excited state to the third and fourth excited states (3.78 and 5.67 meV from the calculations), respectively. An excitation was likely to exist between the first and second excited states at approximately 1.35 meV in the experimental results. The excitation energies obtained from the INS experiments were almost consistent with those calculated from the exchange interaction values via the data-driven technique (data-driven values). The experimental $I\left(Q\right)$ curves could not be reproduced. We found that $I\left(Q\right)$ curves could be changed largely by small changes of exchange-interaction values. Therefore, we expect that exchange-interaction values, which can explain not only the magnetic susceptibility, magnetization curves, and excitation energies but also INS intensity, are in the vicinity of the data-driven values.