Effect of Biquadratic Exchange on Two Magnon States of Heisenberg Ferromagnets: Other Neighbor Exchange

1975 ◽  
Vol 53 (6) ◽  
pp. 637-647 ◽  
Author(s):  
D. A. Pink ◽  
Vijay Sachdeva
Keyword(s):  
Ground State ◽  
Nearest Neighbor ◽  
Ferromagnetic State ◽  
Localized States ◽  
Heisenberg Ferromagnet ◽  
Green Functions ◽  
Localized Modes ◽  
One Dimensional ◽  
Localized State ◽  
Biquadratic Exchange

We have investigated the two magnon localized states of a one dimensional Heisenberg ferromagnet the Hamiltonian of which is made up of nearest neighbor and next nearest neighbor isotropic bilinear and biquadratic exchange terms, and a single ion anisotropy term. We have restricted our choice of parameters so that the ground state at T = 0 is the fully aligned ferromagnetic state and we have used the thermodynamic Green functions where the averages have been evaluated in the ground state so that our results are good for [Formula: see text]. We have evaluated the probabilities of finding two spin deviations a distance n apart when the system is in a localized state described by total wave vector q. We have (a) compared the effects of ferromagnetic and antiferromagnetic next nearest neighbor exchange, (b) found that localized modes can lie below or above the two free magnon band depending upon the sign and magnitude of the biquadratic exchange, (c) found that in certain cases two spin deviations appear to behave like objects interacting only via a soft core, and (d) found that modes can have a large single ion component when the single ion anisotropy is zero.

Modified spin-wave theory applied to one-dimensional Heisenberg ferromagnet with the nearest-neighbor and next-nearest-neighbor exchange anisotropies

2019 ◽  
Vol 33 (11) ◽  
pp. 1950106
Author(s):  
Yun Liao ◽  
Yuan Chen ◽  
Ji Pei Chen ◽  
Wen An Li
Keyword(s):  
Low Temperature ◽  
Specific Heat ◽  
Spin Wave ◽  
Nearest Neighbor ◽  
Wave Theory ◽  
Heisenberg Ferromagnet ◽  
Thermodynamic Quantities ◽  
One Dimensional ◽  
Spin Wave Theory ◽  
The One

The modified spin-wave theory is used to investigate the one-dimensional Heisenberg ferromagnet with the nearest-neighbor (NN) and next-nearest-neighbor (NNN) exchange anisotropies. The ground-state and low-temperature properties of the system are studied within the self-consistent method. It is found that the effect of the NN anisotropy on the thermodynamic quantities is stronger than that of the NNN anisotropy in the low-temperature region. The anisotropy dependence behaviors (such as the power, exponential and linear laws) are obtained for the position and the height of the maximum of the specific heat and its coefficient, as well as the susceptibility coefficient. The specific heat and its coefficient both display the low-temperature double maxima which are induced by the anisotropies and the NNN interaction. In the very low temperatures the specific heat and the susceptibility behave severally as T[Formula: see text] and T[Formula: see text] at the critical point J2/J1 = −0.25, where J1 and J2 are the NN and NNN interactions, respectively.

scholarly journals Ripples in Graphene: A Variational Approach

2020 ◽  
Vol 379 (3) ◽  
pp. 915-954
Author(s):  
Manuel Friedrich ◽  
Ulisse Stefanelli
Keyword(s):  
Ground State ◽  
Energy Minimization ◽  
Variational Approach ◽  
Nearest Neighbor ◽  
Interaction Energies ◽  
Dimensional Problem ◽  
Neighbor Interaction ◽  
Configurational Energy ◽  
One Dimensional ◽  
Math Phys

Abstract Suspended graphene samples are observed to be gently rippled rather than being flat. In Friedrich et al. (Z Angew Math Phys 69:70, 2018), we have checked that this nonplanarity can be rigorously described within the classical molecular-mechanical frame of configurational-energy minimization. There, we have identified all ground-state configurations with graphene topology with respect to classes of next-to-nearest neighbor interaction energies and classified their fine nonflat geometries. In this second paper on graphene nonflatness, we refine the analysis further and prove the emergence of wave patterning. Moving within the frame of Friedrich et al. (2018), rippling formation in graphene is reduced to a two-dimensional problem for one-dimensional chains. Specifically, we show that almost minimizers of the configurational energy develop waves with specific wavelength, independently of the size of the sample. This corresponds remarkably to experiments and simulations.

STATES OF A FEW HOLES IN A t-J MODEL

1991 ◽  
Vol 05 (09) ◽  
pp. 1401-1417 ◽  
Author(s):  
DANIEL C. MATTIS ◽  
HUA CHEN
Keyword(s):  
Ground State ◽  
Green Functions ◽  
Constant Energy ◽  
One Dimensional ◽  
Energy Surfaces

The interaction of a few holes with the magnons and with each other in the t-J model, is formulated in k-space. At small J/t, each hole is accompanied by a cloud of <n> ≈ 1.4(t/J)1/3 magnons (spin reversals), on average. We obtain, and in some cases, solve formal expressions for the ground state eigenfunctions, eigenvalues, and Green functions. The constant energy surfaces are quasi-one-dimensional.

scholarly journals Two Types of Localized States in a Photonic Crystal Bounded by an Epsilon Near Zero Nanocomposite

2018 ◽  
Author(s):  
Rashid G. Bikbaev ◽  
Stepan Ya. Vetrov ◽  
Ivan V. Timofeev
Keyword(s):  
Photonic Crystal ◽  
Defect Mode ◽  
Localized States ◽  
Simultaneous Formation ◽  
One Dimensional ◽  
Nanocomposite Layer ◽  
Localized State ◽  
Plasmon Polariton ◽  
Field Localization ◽  
First Time

The spectral properties of a one-dimensional photonic crystal bounded by a resonant absorbing nanocomposite layer with the near-zero permittivity have been studied. The problem of calculating the transmittance, reflectance, and absorptance spectra of such structures at the normal and oblique incidence of light has been solved. It is shown that, depending on the permittivity sign near zero, the nanocomposite is characterized by either metallic or dielectric properties. For the first time, the possibility of simultaneous formation of the Tamm plasmon polariton at the photonic crystal/metallic nanocomposite interface and the localized state similar to the defect mode with the field intensity maximum inside the dielectric nanocomposite layer is demonstrated. Specific features of field localization at the Tamm plasmon polariton and defect mode frequencies are analyzed.

A Heisenberg Ferromagnet With Biquadratic and Dipol-octupol Interactions

1981 ◽  
Vol 36 (8) ◽  
pp. 797-801 ◽  
Author(s):  
Z. Ba̮k
Keyword(s):  
Free Energy ◽  
Ground State ◽  
Collective Excitation ◽  
Field Approximation ◽  
Molecular Field ◽  
Heisenberg Ferromagnet ◽  
Excitation Spectra ◽  
Molecular Field Approximation ◽  
Biquadratic Exchange ◽  
Ferromagnetic Ground State

Abstract A Heisenberg S - 3/2 ferromagnet with isotropic biquadratic exchange and dipole-octupol coupling is discussed. The conditions for the exact ferromagnetic ground state are derived. The thermodynamical behaviour in the molecular field approximation is discussed. Collective excitation spectra and the 1/z correction to the free energy are found.

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