Dimerization of ferrimagnets on chains and square lattices

Abstract

A linear spin wave analysis of dimerization of alternating Heisenberg system with spins s 1 and s 2 on linear chain as well as square lattice is presented. Among the several possible dimerized configurations considered in two dimensions the plaquette configuration is found to be energetically the most favored one. Inclusion of a variable nearest neighbor exchange coupling J(a) = J a leads to a uniform power law behavior: that is to say, the same δ-dependence is found (i) in chains as well as in square lattices; (ii) in systems consisting of different pairs of spins s 1 and s 2 ; (iii) for the magnetic energy gain, the energy gap, the energy of the gapped magnetic excitation mode as well as for the sublattice magnetization; (iv) for all the configurations of the square lattice; and (v) in the entire range of δ : (0 ≤ δ < 1). The variable exchange coupling also allows the energy of the gapped excitation spectrum to be δ-dependent even in the linear spin wave theory.

Ferro- and Antiferromagnetic Aspects of Alternating Spin Systems

“…This decrease is faster for higher  , and scales with T as . At the critical value of frustration, 2 T , c  the free energy become imaginary and our LSW theory fails to go beyond this value of frustration. It was reported earlier [2,20] that at T = 0.0 the ground states energy increases with frustration parameter and then starts to decrease for values of frustration close to c  .…”

“…At T = 0 it shows the ground state energy of the system. It was founded that dimerization at T = 0 reduces ground state energy [2,14], it does the same with free energy. We found that the decrease of the free energy goes as .…”

“…The effect of frustration in ferrimagnetic systems was investigated [2,20] at zero temperature. Several characterization of the frustration parameter were reported; mainly, c  which marks the complete destruction of the long range order in the system and *  marks the onset of spiral phase transition.…”

“…The procedure of working out the physical quantities was discussed in detail in Ref. [2]. After that all the thermal quantities defined above are reproducible for the case of 2D.…”

“…This stimulated also several attempts to investigate the quantum behavior of chains consisting of two types of spins. An integrable model of this type was constructed by De Vega and Woynarovich [1], which allows us to guess the essential consequences of chains with spins of different length S. Recently [2], several authors discussed in detail such a bimetallic chain with spins s = 1 and 1/2 as the simplest case.…”