Abstract
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.
Highlights
Bertaut’s matrix method enables possible magnetic modes associated with a given propagation vector in magnetic systems [1,2,3]
Macroscopic and microscopic methods were applied to the two-dimensional orthorhombic lattice with four spins by Darendelioğlu et al and they determined that the four collinear modes are along the z-axis and the non-collinear modes are in the xy-plane of the two-dimensional orthorhombic lattice [6]
We consider the four magnetic ions localized rectangular lattice displayed in Figure 1 in which one shows the corresponding exchange integrals
Summary
Bertaut’s matrix method enables possible magnetic modes associated with a given propagation vector in magnetic systems [1,2,3]. Method is valid for magnetic cells different from the chemical cells. The greatest advantage of this method is to consider fundamental interaction being isotropic classical Heisenberg and is applicable when the chemical and magnetic cells are not identical. Isotropic terms as well as anisotropic terms can be expressed by a Hamiltonian of a second order and problem can be reduced to an eigenvalue problem. Solving this eigenvalue equation, one is able to find all possible magnetic configurations. Townsend et al dealt with triangular-spin structure by the application of this method and predicted triangular-spin magnetic ordering for KFe3(OH)6(SO4) and KFe3(OH)6(CrO4)2 [5]. Belorizky performed a systematic research of the bilinear exchange Hamiltonian pro-
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