Comments on Biquadratic Exchange Interactions in the Classical Heisenberg Chain

The ground-state phase diagrams are obtained for the spin-2 Ising model Hamiltonian with bilinear and biquadratic exchange interactions and a single-ion crystal field. The interactions are assumed to be only between nearest-neighbors. Obtained phase diagrams are presented in the (Δ,J), (K,J), (Δ/J,K/J), (Δ/|J|,K/|J|), (Δ/|K|,J/|K|), (H/J,Δ/J), (H/|J|,Δ/|J|), (H/J,K/J), and (H/|J|,K/|J|) planes where J, K, Δ, and H are the bilinear, biquadratic exchange interactions, the single-ion crystal field, and the external magnetic field, respectively. The influence of the external magnetic field on the spin configurations is investigated.

Download Full-text

Обменные взаимодействия в паре ионов Cr-=SUP=-3+-=/SUP=--Cr-=SUP=-3+-=/SUP=- в диамагнитной матрице ABO-=SUB=-3-=/SUB=- (A=Ga, In, Sc)

Физика твердого тела ◽

10.21883/ftt.2020.03.49004.618 ◽

2020 ◽

Vol 62 (3) ◽

pp. 403

Author(s):

А.М. Воротынов ◽

В.В. Руденко ◽

О.В. Воротынова

Keyword(s):

Magnetic Resonance ◽

Ion Pairs ◽

Exchange Interactions ◽

Resonance Technique ◽

Biquadratic Exchange ◽

Magnetic Resonance Technique

Abstract The exchange interactions in the Cr^3+–Cr^3+ ion pairs in the isostructural ABO_3 (A = Ga, In, Sc) diamagnetic compounds have been examined using the magnetic resonance technique. The values of bilinear and biquadratic exchange interactions have been determined. It is shown that the biquadratic exchange in the Cr^3+–Cr^3+ pair in these compounds is caused by the exchange striction.

Download Full-text

Effect of Biquadratic Exchange Upon Ferromagnetic Two-Magnon Bound States. II. Anisotropic Exchange

Canadian Journal of Physics ◽

10.1139/p74-005 ◽

1974 ◽

Vol 52 (1) ◽

pp. 33-39 ◽

Cited By ~ 15

Author(s):

D. A. Pink ◽

R. Ballard

Keyword(s):

Bound States ◽

Exchange Interactions ◽

Bound State ◽

Exchange Term ◽

Zero Temperature ◽

Biquadratic Exchange ◽

Anisotropic Exchange ◽

Bound State Spectrum ◽

Mode Pair ◽

Isotropic Exchange

We have investigated the two-magnon bound state spectrum of a ferromagnetically ordered system for which the Hamiltonian contains an anisotropic bilinear exchange term, an anisotropic biquadratic exchange term, and a single-ion anisotropy term. The bound states, labelled by a wave vector q which we have taken to be in the [111] direction, were calculated by using zero-temperature Green functions. The principal results are: (i) the existence of single-ion bound states in the absence of single-ion anisotropy and conversely, their absence in the presence of such anisotropy, in contrast to the case in which the exchange interactions are isotropic; (ii) the appearance of an S mode for values of q, [Formula: see text]; (iii) the ordering of bound states for isotropic exchange interactions wherein the S0 mode lies below the S1-mode, D-mode pair and where the S1 mode lies below (above) the D mode if they lie below (above) the band, no longer holds.

Download Full-text