Magnetic and Thermodynamic Properties of the Cylindrical DMS Quantum Dot

被引:0
|
作者
Babanli, A. M. [1 ]
Balci, M. [2 ]
Sabyrov, V. [3 ,4 ]
Saparguliyev, R. [3 ]
Shamuhammedov, Sh. [3 ]
Kakalyyev, A. [3 ]
机构
[1] Suleyman Demirel Univ, Dept Phys, TR-32260 Isparta, Turkiye
[2] Isparta Univ Appl Sci, TR-32260 Isparta, Turkiye
[3] Inst Engn Tech & Transport Commun Turkmenistan, Ashkhabad 74400, Turkmenistan
[4] Suleyman Demirel Univ, Inst Nat Sci, TR-32260 Isparta, Turkiye
关键词
Magnetic susceptibility; Quantum dot; Diluted magnetic semiconductors; SPIN-ORBIT INTERACTION; HYDROGENIC IMPURITY; ELECTRON; FIELD; HEAT;
D O I
10.1007/s10909-024-03222-x
中图分类号
O59 [应用物理学];
学科分类号
摘要
In this work, the magnetic and thermodynamic properties of dilute magnetic semiconductor quantum dots of cylindrical geometry are investigated. The eigenvalue of the quantum system we are considering is obtained by solving the one-electron Schr & ouml;dinger equation within the framework of the effective mass approach. Then, taking into account the energy spectrum, expressions for thermodynamic quantities and magnetic susceptibility are obtained. The behavior of these expressions depending on temperature is studied using the parameters B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B$$\end{document}, x\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x$$\end{document}, R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{0}$$\end{document} and L0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{0}$$\end{document}. Based on the results obtained, it is established that the average energy, free energy, heat capacity, entropy and magnetic susceptibility at low temperatures depend on the parameter x\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x$$\end{document}. Also at low temperatures, when x=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x = 0$$\end{document}, the average energy and free energy exhibit a linear relationship. With increasing temperature, this dependence becomes nonlinear. For x not equal 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x \ne 0$$\end{document}, the dependence of the average energy and free energy on temperature is a rapidly increasing nonlinear function. In addition, when x not equal 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x \ne 0$$\end{document}, magnetic susceptibility reaches a maximum at low temperatures. The peak height increases with x\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x$$\end{document} and disappears when x=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x = 0$$\end{document}. The peak of magnetic susceptibility decreases as the magnetic field increases when x not equal 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x \ne 0$$\end{document} and shifts toward higher temperatures. The specific heat forms a Schottky peak at low temperatures and asymptotically approaches Cv=3kB\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{v} = 3k_{B}$$\end{document} at high temperatures.
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页码:584 / 597
页数:14
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