Classical Ground State Spin Ordering of the Antiferromagnetic $J_1$–$J_2$ Model
Ren-Gui Zhu**
College of Physics and Electronic Information, Anhui Normal University, Wuhu 241000
Abstract ：The classical frustrated antiferromagnetic $J_1$–$J_2$ model is considered in a description of the classical spin wave for a vector spin system. Its ground state (GS) spin ordering is analyzed by minimizing its energy. Our analytical derivations show that all the spins in the GS phase must lie in planes that are parallel to each other. When applying the derived formulations to concrete lattices such as the square and simple cubic lattices, we find that in the large $J_2$ region, a large continuous GS degeneracy concluded by a qualitative analysis is lifted, and collinear striped ordering is selected as the GS phase.
收稿日期: 2018-12-11
出版日期: 2019-05-18
:
75.10.Jm
(Quantized spin models, including quantum spin frustration)
75.30.Et
(Exchange and superexchange interactions)
75.10.Hk
(Classical spin models)
[1] Diep H T 2013 Frustrated Spin Systems 2nd edn (Singapore: World Scientific) [2] Lacroix C, Mendels P and Mila F 2011 Introduction to Frustrated Magnetism (Materials, Experiments, Theory) (Berlin: Springer) [3] Villain J, Bidaux R, Carton J P and Conte R 1980 J. Phys. France 41 1263 [4] Shender E F 1982 Sov. Phys. JETP 56 178 [5] Henley C L 1989 Phys. Rev. Lett. 62 2056 [6] Kubo K and Kishi T 1991 J. Phys. Soc. Jpn. 60 567 [7] Dagotto E and Moreo A 1989 Phys. Rev. Lett. 63 2148 [8] Oguchi T and Kitatani H 1990 J. Phys. Soc. Jpn. 59 3322 [9] Farnell D J J, G?tze O and Richter J 2016 Phys. Rev. B 93 235123 [10] Oitmaa J 2017 Phys. Rev. B 95 014427 [11] Majumdar K and Datta T 2009 J. Phys.: Condens. Matter 21 406004 [12] Sun N N and Wang H Y 2018 J. Magn. Magn. Mater. 454 176 [13] Schmidt B and Thalmeier P 2017 Phys. Rep. 703 1 [14] Jiang W, Wang Z, Guo A B, Wang K and Wang Y N 2015 Physica E 73 250 [15] Wang L, Gu Z C, Verstraete F and Wen X G 2016 Phys. Rev. B 94 075143 [16] Wang J M, Jiang W, Zhou C L, Shi Z and Wu C 2017 Superlattices Microstruct. 102 359 [17] Blundell S 2011 Magnetism in Condensed Matter (New York: Oxford University Press Inc) [18] Dmitriev D V and Krivnov V Y 2010 Phys. Rev. B 81 054408 [19] Zhu R G 2011 Chin. Phys. Lett. 28 097501
[1]
.
[2]
.
[3]
.
[4]
.
[5]
.
[6]
.
[7]
.
[8]
.
[9]
.
[10]
.
[11]
.
[12]
.
[13]
.
[14]
.
[15]
.
2019, Vol. 36 
