Abstract
We study the possibility of collective spin excitations in 2D paramagnetic crystal with the dipole-dipole interaction and without the exchange interaction. The crystal is under uniform constant magnetic field. All the magnetic moments are oriented along the magnetic field at the saturation. Using the Holstein–Primakoff transformation, we describe the properties of paramagnetic in terms of the spin waves at the low-temperature limit. We obtain the dispersion relations for spin waves at the square and hexagonal flat lattices. It is shown the wavelength of the collective excitations and their bandwidth are determined by the external magnetic field direction. The long-wave perturbations have the lowest energy when the magnetic field is orthogonal to the lattice plane, and the short-wave perturbations are the most preferable when the field is parallel to the lattice. We provide the direct numerical simulation of the group of interacting magnetic moments under the constant external field with different orientation to the lattice. The total transversal spin and dipole energy evolution in time and their Fourier-spectrum are considered. The numerical results match the analytical calculation in spin-wave approach. Received 22.08.2016; accepted 31 .0 8 .2016
Highlights
We study the possibility of collective spin excitations in 2D paramagnetic crystal with the dipoledipole interaction and without the exchange interaction
Using the Holstein–Primakoff transformation, we describe the properties of paramagnetic in terms of the spin waves at the low-temperature limit
The square and hexagonal flat lattices. It is shown the wavelength of the collective excitations and their bandwidth are determined by the external magnetic field direction
Summary
Исследование магнитных и тепловых характеристик спиновых систем обладает большой значимостью для дальнейшего развития теории магнитных резонансов и релаксации [1,2,3]. Учёт дипольного взаимодействия важен при описании свойств парамагнитных диэлектриков в твёрдой фазе, например, H и O в чистом виде [12, 13], или внедрённых в кристаллы диамагнетиков [14, 15], солей редкоземельных элементов, в которых расстояние между магнитными атомами столь велико, что обменное взаимодействие практически исчезает [4, 16]. Что дипольное взаимодействие имеет низкую интенсивность и становится значимым только при температурах
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