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Microscopic origin of the spin-reorientation transition in the kagome topological magnet TbMn$$_{6}$$Sn$$_{6}$$

カゴメ格子トポロジカル磁性体TbMn$$_{6}$$Sn$$_{6}$$におけるスピン再配列転移の微視的起源

Huang, Z.*; Wang, W.*; Ye, H.*; Bao, S.*; Shangguan, Y.*; Liao, J.*; Cao, S.*; 梶本 亮一  ; 池内 和彦*; Deng, G.*; Smidman, M.*; Song, Y.*; Yu, S.-L.*; Li, J.-X.*; Wen, J.*

Huang, Z.*; Wang, W.*; Ye, H.*; Bao, S.*; Shangguan, Y.*; Liao, J.*; Cao, S.*; Kajimoto, Ryoichi; Ikeuchi, Kazuhiko*; Deng, G.*; Smidman, M.*; Song, Y.*; Yu, S.-L.*; Li, J.-X.*; Wen, J.*

TbMn$$_{6}$$Sn$$_{6}$$ is a correlated topological magnet with a Mn-based kagome lattice, in which a Chern gap opens at the Dirac point at low temperatures. The magnetic moment direction of the ferrimagnetic order changes from in the kagome plane to the out-of-plane upon cooling, which is essential for generating the Chern gap, but the underlying mechanism for the spin reorientation remains elusive. Here, we investigate the spin-reorientation transition in TbMn$$_{6}$$Sn$$_{6}$$ using neutron scattering. We provide direct evidence for the spin-reorientation transition and unveil the coexistence of two Tb modes at 200 K. To account for these results, we put forward a model based on SU(N) spin-wave theory, in which there is a temperature evolution of the ground state Tb $$4f$$ orbitals, driven by the crystalline electric field, single-ion anisotropy, and exchange interactions between Tb and Mn ions. Our findings shed light on the complex magnetism of TbMn$$_{6}$$Sn$$_{6}$$, despite its relatively simple ground state magnetic structure, and provide insights into the mechanisms for tuning magnetic topological materials.

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