Two-Electron Heisenberg Exchange Interaction between Neighboring Atoms

We have investigated the effect of single-ion anisotropy of the "easy plane" type on the phase states of a ferrimagnet with S = 1 and σ=1/2 sublattices and non-Heisenberg (bilinear and biquadratic in spins) exchange interaction for the sublattice with S = 1. It is shown that taking into account both the non-Heisenberg exchange interaction and the single-ion anisotropy of the sublattice with S = 1 leads to the realization of a phase with vector order parameters (ferrimagnetic phase) and a phase characterized by both vector and tensor order parameters (quadrupole-ferrimagnetic). It is shown that taking into account single-ion anisotropy changes the type of phase transition in comparison with an isotropic non-Heisenberg ferrimagnet. A phase diagram is constructed, and the condition for the compensation of the sublattice spins is determined.

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Ab InitioCalculation of the Heisenberg Exchange Interaction betweenO2Molecules

Physical Review Letters ◽

10.1103/physrevlett.51.1167 ◽

1983 ◽

Vol 51 (13) ◽

pp. 1167-1170 ◽

Cited By ~ 83

Author(s):

M. C. van Hemert ◽

P. E. S. Wormer ◽

A. van der Avoird

Keyword(s):

Exchange Interaction ◽

Heisenberg Exchange

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QUANTUM ENTANGLEMENT IN THE SYSTEM OF TWO SPIN-1/2 PARTICLES WITH HEISENBERG EXCHANGE INTERACTION IN THE PRESENCE OF A SINGLE-MODE VACUUM FIELD

International Journal of Quantum Information ◽

10.1142/s0219749908003657 ◽

2008 ◽

Vol 06 (03) ◽

pp. 437-446 ◽

Cited By ~ 1

Author(s):

GUO-FENG ZHANG

Keyword(s):

Exchange Interaction ◽

Single Mode ◽

Interaction Constant ◽

Vacuum Field ◽

Single Spin ◽

Spin Field ◽

Field Coupling ◽

Heisenberg Exchange ◽

Nonclassical Properties ◽

Field State

The nonclassical properties of two spin-1/2 particles with Heisenberg exchange interaction in a single-mode vacuum field are investigated. By using the quantum reduced entropy, we demonstrate that the ratio ka between Heisenberg exchange interaction constant difference (J - Jz) and the spin-field coupling constant Ω can affect the feature of the entanglement significantly. It is found that the entanglement of the system evolves periodically with time, the evolvement period of the entanglement between two spin-1/2 particles and the field increases with the increasing ka, which is true for the single spin-field entanglement, but that is contrary for the entanglement between the two spin particles. Our results show that three entangled states of two spins-field, spin–spin, and spin-field can be prepared via two spin-1/2 particles interacting with a single-mode vacuum field. We also characterize the field state by using Mandel's Q parameter, it is proved that the nonclassical properties of the field state will get weaker with the increasing ka and are dramatically different from those in the case of selective measurement for spin.

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