Chin. Phys. Lett.  2021, Vol. 38 Issue (11): 117101    DOI: 10.1088/0256-307X/38/11/117101
Determination of the Range of Magnetic Interactions from the Relations between Magnon Eigenvalues at High-Symmetry $k$ Points
Di Wang1,2, Jihai Yu1,2, Feng Tang1,2, Yuan Li3,4, and Xiangang Wan1,2*
1National Laboratory of Solid State Microstructures and School of Physics, Nanjing University, Nanjing 210093, China
2Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
3International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
4Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
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Di Wang, Jihai Yu, Feng Tang et al  2021 Chin. Phys. Lett. 38 117101
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Abstract Magnetic exchange interactions (MEIs) define networks of coupled magnetic moments and lead to a surprisingly rich variety of their magnetic properties. Typically MEIs can be estimated by fitting experimental results. Unfortunately, how many MEIs need to be included in the fitting process for a material is unclear a priori, which limits the results obtained by these conventional methods. Based on linear spin-wave theory but without performing matrix diagonalization, we show that for a general quadratic spin Hamiltonian, there is a simple relation between the Fourier transform of MEIs and the sum of square of magnon energies (SSME). We further show that according to the real-space distance range within which MEIs are considered relevant, one can obtain the corresponding relationships between SSME in momentum space. By directly utilizing these characteristics and the experimental magnon energies at only a few high-symmetry $k$ points in the Brillouin zone, one can obtain strong constraints about the range of exchange path beyond which MEIs can be safely neglected. Our methodology is also generally applicable for other Hamiltonian with quadratic Fermi or Boson operators.
Received: 22 September 2021      Editors' Suggestion Published: 28 October 2021
PACS:  71.70.Gm (Exchange interactions)  
  75.30.Ds (Spin waves)  
Fund: Supported by the National Natural Science Foundation of China (Grant Nos. 11834006, 12004170, and 12104215), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20200326), and the Excellent Programme in Nanjing University. Xiangang Wan also acknowledges the support from the Tencent Foundation through the XPLORER PRIZE.
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Di Wang
Jihai Yu
Feng Tang
Yuan Li
and Xiangang Wan
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