title: Ð­Ð½ÐµÑÐ³ÐµÑÐ¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ¿ÐµÐºÑÑ ÑÐ²Ð¾Ð±Ð¾Ð´Ð½ÑÑ Ð½Ð¾ÑÐ¸ÑÐµÐ»ÐµÐ¹ Ð² ÑÐ°Ð·Ð±Ð°Ð²Ð»ÐµÐ½Ð½Ð¾Ð¼ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð¼ Ð¿Ð¾Ð»ÑÐ¿ÑÐ¾Ð²Ð¾Ð´Ð½Ð¸ÐºÐµ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: The energy spectrum of free carriers in a dilute magnetic semiconductor
Creators: name: ÐÑÑÐºÐ¸Ð½, ÐÐµÐ¾ÑÐ³Ð¸Ð¹
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2024
Subjects: ÑÐ°Ð·Ð±Ð°Ð²Ð»ÐµÐ½Ð½ÑÐµ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½ÑÐµ Ð¿Ð¾Ð»ÑÐ¿ÑÐ¾Ð²Ð¾Ð´Ð½Ð¸ÐºÐ¸
ÑÐ½ÐµÑÐ³ÐµÑÐ¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ¿ÐµÐºÑÑ
Ð¾Ð±Ð¼ÐµÐ½Ð½Ð¾Ðµ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ðµ
Ð¼Ð¾Ð´ÐµÐ»Ñ ÐÐµÐ¹Ð·ÐµÐ½Ð±ÐµÑÐ³Ð°
Ð¿ÑÐ¸Ð±Ð»Ð¸Ð¶ÐµÐ½Ð¸Ðµ ÑÑÐµÐ´Ð½ÐµÐ³Ð¾ Ð¿Ð¾Ð»Ñ
Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ðµ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½ÑÑ Ð¼Ð¾Ð¼ÐµÐ½ÑÐ¾Ð²
ÑÑÑÐµÐºÑ ÐÐµÐµÐ¼Ð°Ð½Ð°
Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð°Ñ Ð¿ÑÐ¸Ð¼ÐµÑÑ
diluted magnetic semiconductors
energy spectrum
exchange interaction
Heisenberg model
Mean-field theory
interaction of magnetic moments
Zeeman effect
magnetic impurity

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description: The given work is devoted to the study of the energy spectrum of free carriers (electrons) in dilute magnetic semiconductors in an external permanent magnetic field. The paper describes a microscopic model of the exchange interaction of an electron of the conduction band with a certain number of atoms of a magnetic impurity. The model is obtained by reducing the complete Hamiltonian of a system of N atoms of a magnetic impurity and a free electron, the interaction between which is described by the Heisenberg exchange Hamiltonian, to the spin Hamiltonian using the virtual crystal approximation. For the specific case of N = 4 and intrinsic moment j=1/2, the problem of finding the eigenvalues of the energy and eigenfunctions of the full spin Hamiltonian is precisely solved. Using the obtained spectrum and Gibbs distribution, exact expressions were then obtained for the average values of the projections of the spin of the electron and the intrinsic moment of the impurity atom in the direction of the magnetic field. Approximate expressions are obtained for the case of an arbitrary number N and an arbitrary intrinsic moment of impurity atoms. It is shown that the expressions used in the theory of the mean field are the limits of the obtained approximate expressions of the model at large N. The purpose of the microscopic model study was to clarify the origin of the effective parameters in the formulas of the mean field model used to describe experimental dependencies. The comparison of exact and approximate expressions with the expression of the mean field model suggests that the appearance of effective parameters can be caused by neglecting the non-diagonal elements of the spin Hamiltonian.