Zero-temperature configurations of short odd-numbered classical spin chains with bilinear and biquadratic exchange interactions

Abstract

The lowest energy configurations of short odd open chains with classical spins are determined for antiferromagnetic bilinear and biquadratic nearest-neighbor exchange interactions. The zero field residual magnetization generates differences with the magnetic behavior of even chains, as the odd chain is like a small magnet for weak magnetic fields. The lowest energy configuration is calculated as a function of the total magnetization M , even for M less than the zero field residual magnetization. Analytic expressions and their proofs are provided for the threshold magnetic field needed to drive the system away from the antiferromagnetic configuration and the spin polar angles in its vicinity, when the biquadratic interaction is relatively weak. They are also given for the saturation magnetic field and the spin polar angles close to it. Finally, an analytic expression along with its proof is given for the maximum magnetization in zero magnetic field for stronger biquadratic interaction, where the lowest energy configuration is highly degenerate.

Influence of the biquadratic exchange interaction in the classical ground state magnetic response of the antiferromagnetic icosahedron

“…NM and Nχ give the total number of magnetization and susceptibility discontinuities right after discontinuities appear or disappear. The saturation magnetic field is hsat = (5 + √ 5)(cosω + 2sinω) [27,53]. …”

“…The classical lowest energy configurations of the icosahedron are degenerate, and whenever they are presented it is for one of the degenerate configurations, or colorings, while all the colorings can be decomposed according to I h [26,52]. The saturation magnetic field is given by [27,53].…”

“…The line in Fig. 2(a) shows the nearest-neighbor correlation − 1 2tanω of an open odd chain for comparison [27]. For ω=arctan …”

Zero-temperature magnetic response of small fullerene molecules at the classical and full quantum limit

“…As the dodecahedron has been shown to have enriched magnetic response in the presence of intermolecular interactions without having zero-field magnetization [13], it would be of interest to examine the behavior of interacting collections of fullerene molecules with Mg N = 0. Their magnetization could demonstrate even-odd effects, as is the case with an open spin chain [51,52], but here in the number of molecules and on top of the isolated molecule properties.…”

Discontinuous classical ground state magnetic response as an even–odd effect in higher order rotationally invariant exchange interactions

“…It was also investigated in higher dimensions [31][32][33], and for the magnetism of iron-based supeconductors [34,35]. The classical ground state magnetic response with bilinear and biquadratic exchange has been calculated for short odd-numbered chains [36], while in the case of the icosahedron it has been shown to generate many magnetization discontinuities [12]. A similar Hamiltonian in two-dimensional spin space includes the standard bilinear exchange and generalized nematic interactions [37][38][39][40][41].…”