Spin Configurations in the Rectangular Lattice

DOI: 10.4236/wjcmp.2013.34030   PDF   HTML     2,648 Downloads   4,497 Views   Citations


Using matrix method, the possible spin configurations have been determined for four sublattices in rectangular lattice taking into account only nearest-neighbor exchange interactions. We obtain collinear and non-collinear spin configurations in the ground and the first excited states for the three different propagation vectors. When k = 0, depending on the sign of exchange parameters, we find a ferromagnetic mode and three antiferromagnetic modes. When k = [1, 1] and [1.5, 1.5], we find non-collinear (canted) spin configurations. Moreover, we observe that spins of some sublattices in the excited state change their orientations.

Share and Cite:

Mert, G. and Mert, H. (2013) Spin Configurations in the Rectangular Lattice. World Journal of Condensed Matter Physics, 3, 184-188. doi: 10.4236/wjcmp.2013.34030.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] E. F. Bertaut, “Configurations de Spin et Théorie des Groups,” Journal de Physique et le Radium, Vol. 22, No. 5, 1961, pp. 321-322.
[2] E. F. Bertaut, “Lattice Theory of Spin Configuration,” Journal of Applied Physics, Vol. 33, No. 3, 1962, pp. 1138-1143. http://dx.doi.org/10.1063/1.1728635
[3] A. Kallel, H. Boller and E. F. Bertaut, “Helimagnetism in MnP-Type Compounds: MnP, FeP, CrAs and CrAs1-xSbx Mixed Crystals,” Journal of Physics and Chemistry of Solids, Vol. 35, No. 9, 1974, pp. 1139-1152.
[4] J. Villain, “La Structure des Substances Magnetiques,” Journal of Physics and Chemistry of Solids, Vol. 11, No. 3-4, 1959, pp. 303-309.
[5] M. G. Townsend, G. Longworth and E. Roudaut, “Triangular-Spin, Kagome Plane in Jarosites,” Physical Review B, Vol. 33, No. 7, 1986, pp. 4919-4926.
[6] H. S. Darendelioglu and H. Yüksel, “Spin Configuration of Two-Dimensional Orthorhombic Lattice,” Journal of Physics and Chemistry of Solids, Vol. 54, No. 11, 1993, pp. 1599-1602.
[7] E. Belorizky, “Exact Ground State Spin Configurations for 2D and 3D Lattices with Nearest Neighbor Bilinear Exchange,” Solid State Communications, Vol. 96, No. 11, 1995, pp. 853-858.
[8] M. H. Yu and Z. D. Zhang, “Spin Configurations in the Absence of an External Magnetic Bilayer with in-Plane Cubic or Uniaxial Anisotropies,” Journal of Magnetism and Magnetic Materials, Vol. 195, No. 2, 1999, pp. 514-519. http://dx.doi.org/10.1016/S0304-8853(99)00101-8
[9] J. K. Yakinthos, P. A. Kotsanidis, W. Schafer, W. Kockelmann, G. Will and W. Reimers, “The Two-Component Non-Collinear Antiferromagnetic Structures of DyNiC2 and HoNiC2,” Journal of Magnetism and Magnetic Materials, Vol. 136, No. 3, 1994, pp. 327-334.
[10] A. Stroppa and M. Peressi, “Non-Collinear Magnetic States of Mn5Ge3 Compound,” Physica Status Solidi (a), Vol. 204, No. 1, 2007, pp. 44-52.
[11] K. Horigane, T. Uchida, H. Hiraka, K. Yamada and J. Akimitsu, “Charge and Spin Ordering in La2-xSrxCoO4 (0.4 < x < 0.6),” Nuclear Instruments and Methods in Physics Research A, Vol. 600, No. 1, 2009, pp. 243-245.
[12] S. Kurian and N. S. Gajbhiye, “Non-Collinear Spin Structure of E-FexN (2 < x < 3) Observed by Mossbauer Spectroscopy,” Chemical Physics Letters, Vol. 489, No. 4, 2010, pp. 195-197.
[13] E. Belorizky, R. Caslegno and J. Sivardiare, “Configurations of a Simple Cubic Lattice of Pseudo-Spins S = 1/2 with Anisotropic Exchange,” Journal of Magnetism and Magnetic Materials, Vol. 15-18, 1980, pp. 309-310.

comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.