Determination of the Range of Magnetic Interactions from the Relations between Magnon Eigenvalues at High-Symmetry Points
-
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 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. -
-
References
[1] Stöhr J and Siegmann H 2006 Magnetism from Fundamentals to Nanoscale Dynamics Berlin: Springer[2] Buschow K H J, Boer F R et al.. 2003 Physics of Magnetism and Magnetic Materials Berlin: Springer[3] White R M 2007 Quantum Theory of Magnetism: Magnetic Properties of Materials Berlin: Springer-Verlag[4] Lichtenstein A I, Anisimov V I, and Katsnelson M I 2003 Electronic Structure and Magnetism of Correlated Systems: Beyond LDA Berlin: Springer[5] Prabhakar A and Stancil D D 2009 Spin Waves: Theory and Applications Berlin: Springer vol 5[6] Krawczyk M and Grundler D 2014 J. Phys.: Condens. Matter 26 123202 doi: 10.1088/0953-8984/26/12/123202[7] Kosevich A M, Ivanov B, and Kovalev A 1990 Phys. Rep. 194 117 doi: 10.1016/0370-15739090130-T[8] Fogedby H C 1980 J. Phys. A 13 1467 doi: 10.1088/0305-4470/13/4/035[9] Giamarchi T, Rüegg C, and Tchernyshyov O 2008 Nat. Phys. 4 198 doi: 10.1038/nphys893[10] Nikuni T, Oshikawa M, Oosawa A, and Tanaka H 2000 Phys. Rev. Lett. 84 5868 doi: 10.1103/PhysRevLett.84.5868[11] Demokritov S, Demidov V, Dzyapko O, Melkov G, Serga A, Hillebrands B, and Slavin A 2006 Nature 443 430 doi: 10.1038/nature05117[12] Onose Y, Ideue T, Katsura H, Shiomi Y, Nagaosa N, and Tokura Y 2010 Science 329 297 doi: 10.1126/science.1188260[13] Chisnell R, Helton J S, Freedman D E, Singh D, Bewley R, Nocera D G, and Lee Y S 2015 Phys. Rev. Lett. 115 147201 doi: 10.1103/PhysRevLett.115.147201[14] Kondo H, Akagi Y, and Katsura H 2019 Phys. Rev. B 99 041110 doi: 10.1103/PhysRevB.99.041110[15] Mook A, Henk J, and Mertig I 2014 Phys. Rev. B 90 024412 doi: 10.1103/PhysRevB.90.024412[16] Zhang L, Ren J, Wang J S, and Li B 2013 Phys. Rev. B 87 144101 doi: 10.1103/PhysRevB.87.144101[17] Fransson J, Black-Schaffer A M, and Balatsky A V 2016 Phys. Rev. B 94 075401 doi: 10.1103/PhysRevB.94.075401[18] Owerre S A 2017 J. Phys. Commun. 1 025007 doi: 10.1088/2399-6528/aa86d1[19] Okuma N 2017 Phys. Rev. Lett. 119 107205 doi: 10.1103/PhysRevLett.119.107205[20] Yao W, Li C, Wang L, Xue S, Dan Y, Iida K, Kamazawa K, Li K, Fang C, and Li Y 2018 Nat. Phys. 14 1011 doi: 10.1038/s41567-018-0213-x[21] Bao S, Wang J, Wang W, Cai Z, Li S, Ma Z, Wang D, Ran K, Dong Z Y, Abernathy D L, Yu S L, Wan X, Li J X, and Wen J 2018 Nat. Commun. 9 2591 doi: 10.1038/s41467-018-05054-2[22] Li F Y, Li Y D, Kim Y B, Balents L, Yu Y, and Chen G 2016 Nat. Commun. 7 12691 doi: 10.1038/ncomms12691[23] Mook A, Henk J, and Mertig I 2016 Phys. Rev. Lett. 117 157204 doi: 10.1103/PhysRevLett.117.157204[24] Su Y, Wang X S, and Wang X R 2017 Phys. Rev. B 95 224403 doi: 10.1103/PhysRevB.95.224403[25] Serga A, Chumak A, and Hillebrands B 2010 J. Phys. D 43 264002 doi: 10.1088/0022-3727/43/26/264002[26] Kruglyak V, Demokritov S, and Grundler D 2010 J. Phys. D 43 264001 doi: 10.1088/0022-3727/43/26/264001[27] Chumak A, Vasyuchka V, Serga A, and Hillebrands B 2015 Nat. Phys. 11 453 doi: 10.1038/nphys3347[28] Nikitov S A, Kalyabin D V, Lisenkov I V, Slavin A, Barabanenkov Y N, Osokin S A, Sadovnikov A V, Beginin E N, Morozova M A, Filimonov Y A et al.. 2015 Phys.-Usp. 58 1002 doi: 10.3367/UFNe.0185.201510m.1099[29] Lenk B, Ulrichs H, Garbs F, and Münzenberg M 2011 Phys. Rep. 507 107 doi: 10.1016/j.physrep.2011.06.003[30] Xiang H, Lee C, Koo H J, Gong X, and Whangbo M H 2013 Dalton Trans. 42 823 doi: 10.1039/C2DT31662E[31] Liechtenstein A I, Katsnelson M I, Antropov V P, and Gubanov V A 1987 J. Magn. Magn. Mater. 67 65 doi: 10.1016/0304-88538790721-9[32] Bruno P 2003 Phys. Rev. Lett. 90 087205 doi: 10.1103/PhysRevLett.90.087205[33] Wan X, Yin Q, and Savrasov S Y 2006 Phys. Rev. Lett. 97 266403 doi: 10.1103/PhysRevLett.97.266403[34] Ebert H, Koedderitzsch D, and Minar J 2011 Rep. Prog. Phys. 74 096501 doi: 10.1088/0034-4885/74/9/096501[35] Secchi A, Lichtenstein A I, and Katsnelson M I 2015 Ann. Phys. 360 61 doi: 10.1016/j.aop.2015.05.002[36] Rosengaard N M and Johansson B 1997 Phys. Rev. B 55 14975 doi: 10.1103/PhysRevB.55.14975[37] Halilov S, Eschrig H, Perlov A, and Oppeneer P 1998 Phys. Rev. B 58 293 doi: 10.1103/PhysRevB.58.293[38] Paddison J A M 2020 Phys. Rev. Lett. 125 247202 doi: 10.1103/PhysRevLett.125.247202[39] Anisimov V, Aryasetiawan F, and Lichtenstein A 1997 J. Phys.: Condens. Matter 9 767 doi: 10.1088/0953-8984/9/4/002[40] Kotliar G, Savrasov S Y, Haule K, Oudovenko V S, Parcollet O, and Marianetti C A 2006 Rev. Mod. Phys. 78 865 doi: 10.1103/RevModPhys.78.865[41] Hohenberg P C and Brinkman W F 1974 Phys. Rev. B 10 128 doi: 10.1103/PhysRevB.10.128[42] Kitaev A 2006 Ann. Phys. 321 2 doi: 10.1016/j.aop.2005.10.005[43] Gardner J S, Gingras M J, and Greedan J E 2010 Rev. Mod. Phys. 82 53 doi: 10.1103/RevModPhys.82.53[44] Dzyaloshinsky I 1958 J. Phys. Chem. Solids 4 241 doi: 10.1016/0022-36975890076-3[45] Moriya T 1960 Phys. Rev. 120 91 doi: 10.1103/PhysRev.120.91[46] Kotliar G and Sompolinsky H 1984 Phys. Rev. Lett. 53 1751 doi: 10.1103/PhysRevLett.53.1751[47] Nagaosa N and Tokura Y 2013 Nat. Nanotechnol. 8 899 doi: 10.1038/nnano.2013.243[48] Winter S M, Tsirlin A A, Daghofer M, van den Brink J, Singh Y, Gegenwart P, and Valentı́ R 2017 J. Phys.: Condens. Matter 29 493002 doi: 10.1088/1361-648X/aa8cf5[49] Santini P, Carretta S, Amoretti G, Caciuffo R, Magnani N, and Lander G H 2009 Rev. Mod. Phys. 81 807 doi: 10.1103/RevModPhys.81.807[50] Kugel K and Khomskii D 1982 Sov. Phys. Usp. 25 231 doi: 10.1070/PU1982v025n04ABEH004537 -
Related Articles
[1] X. F. Liu, Y. F. Fu, W. Q. Yu, J. F. Yu, Z. Y. Xie. Variational Corner Transfer Matrix Renormalization Group Method for Classical Statistical Models [J]. Chin. Phys. Lett., 2022, 39(6): 067502. doi: 10.1088/0256-307X/39/6/067502 [2] TU Tao, WANG Lin-Jun, HAO Xiao-Jie, GUO Guang-Can, GUO Guo-Ping. Renormalization Group Method for Soliton Evolution in a Perturbed KdV Equation [J]. Chin. Phys. Lett., 2009, 26(6): 060501. doi: 10.1088/0256-307X/26/6/060501 [3] LIU Zheng-Feng, WANG Xiao-Hong. Derivation of a Nonlinear Reynolds Stress Model Using Renormalization Group Analysis and Two-Scale Expansion Technique [J]. Chin. Phys. Lett., 2008, 25(2): 604-607. [4] LIN Ming-Xi, QI Sheng-Wen, LIU Yu-Liang. Influence of Gauge Fluctuation on Electron Pairing Order Parameter and Correlation Functions of a Two-Dimensional System [J]. Chin. Phys. Lett., 2006, 23(11): 3076-3079. [5] WU Xin-Tian. Two-Dimensional Saddle Point Equation of Ginzburg--Landau Hamiltonian for the Diluted Ising Model [J]. Chin. Phys. Lett., 2006, 23(2): 305-308. [6] SONG Bo, WANG Yu-Peng. The Green Function Approach to the Two-Dimensional t-J model [J]. Chin. Phys. Lett., 2003, 20(2): 287-289. [7] SUN Gang, CHU Qian-Jin. Phase Diagram of the 2-Dimensional Ising Model with DipolarInteraction [J]. Chin. Phys. Lett., 2001, 18(4): 491-494. [8] YAN Xiao-hong, ZHANG Li-de, DUAN Zhu-ping, YANG Qi-bin. Renormalization Group Approach on Nanostructured Systems [J]. Chin. Phys. Lett., 1997, 14(4): 291-294. [9] YAN Xiaohong, YOU Jianqiang, YAN Jiaren, ZHONG Jianxin. Renormalization Group on the Aperiodic Hamiltonian [J]. Chin. Phys. Lett., 1992, 9(11): 623-625. [10] TAN Weichao, YANG Chuliang. RENORMALIZATION GROUP METHOD FOR CALCULATING THE LOCALIZATION LENGTH OF COUPLED DISORDERED CHAINS [J]. Chin. Phys. Lett., 1989, 6(5): 213-216.
DownLoad: