Paramagnetic and Diamagnetic Susceptibility of Infinite Quantum Well

Adam Badra Cahaya

Abstract


Paramagnetism and diamagnetism of a material characterized by its magnetic susceptibility. When a material is exposed to an external magnetic field, magnetic susceptibility is defined as the ratio of the induced magnetization and the magnetic field. A paramagnetic material has magnetic susceptibility with positive sign. On the other hand, a diamagnetic material has magnetic susceptibility with negative sign. Atomically, paramagnetic materials consist of atoms that has orbital with unpaired electrons. Theoretical study of paramagnetic susceptibility and diamagnetic susceptibility are well described by Pauli paramagnetism and Landau diamagnetism, respectively. Although paramagnetism and diamagnetism are among the simplest magnetic properties of material that are studied in basic physics, theoretical derivations of Pauli paramagnetic and Landau diamagnetic susceptibility require second quantization formalism of quantum mechanics. We aim to discuss the paramagnetic and diamagnetic susceptibilities for simple three-dimensional quantum well using first quantization formalism.

Keywords


Magnetic susceptibility, Pauli paramagnetism, Landau diamagnetism, quantum well, first quantization

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References


D. Halliday, R. Resnick, and J. Walker, Fundamentals of physics. John Wiley & Sons, 2013.

C. Kittel, Introduction to solid state physics. John Wiley & Sons, 1986.

N. W. Ashcroft and N. D. Mermin, Solid State Physics. Brooks/Cole,Belmont, 1976.

E. G. Batyev, “Pauli paramagnetism and Landau diamagnetism,” Physics-Uspekhi, vol. 52, no. 12, pp. 1245–1246, Dec. 2009.

W. Nolting and A. Ramakanth, Quantum theory of magnetism. Springer Science & Business Media, 2009.

S. Doniach and E. Sondheimer, Green’s functions for solid state physicists. World Scientific, 1998.

D. J. Kim, New perspectives in magnetism of metals. Springer Science & Business Media, 1999.

M. A. Ruderman and C. Kittel, “Indirect Exchange Coupling of Nuclear Magnetic Moments by Conduction Electrons,” Phys. Rev., vol. 96, no. 1, pp. 99–102, 1954.

T. Kasuya, “A Theory of Metallic Ferro- and Antiferromagnetism on Zener’s Model,” Prog. Theor. Phys., vol. 16, p. 45, 1956.

K. Yosida, “Magnetic Properties of Cu-Mn Alloys,” Phys. Rev., vol. 106, no. 5, pp. 893–898, 1957.

G. M. Genkin, “Dynamic Ruderman-Kittel-Kasuya-Yosida indirect interaction,” Phys. Rev. B, vol. 55, no. 9, pp. 5631–5633, Mar. 1997.

A. O. Leon, J. d’Albuquerque e Castro, J. C. Retamal, A. B. Cahaya, and D. Altbir, “Manipulation of the RKKY exchange by voltages,” Phys. Rev. B, vol. 100, no. 1, p. 14403, Jul. 2019.

L. Landau, “Diamagnetismus der Metalle,” Zeitschrift für Phys., vol. 64, no. 9, pp. 629–637, 1930.

R. Peierls, “Zur Theorie des Diamagnetismus von Leitungselektronen,” Zeitschrift für Phys., vol. 80, no. 11, pp. 763–791, 1933.

F. A. Buot and J. W. McClure, “Theory of Diamagnetism of Bismuth,” Phys. Rev. B, vol. 6, no. 12, pp. 4525–4533, Dec. 1972.

A. B. Cahaya, A. O. Leon, M. R. Aliabad, and G. E. W. Bauer, “Equilibrium current vortices in rare-earth-doped simple metals.” 2020.

S. Gasiorowicz, Quantum physics. John Wiley & Sons, 2007.

F. Bloch, “Quantum mechanics of electrons in crystal lattices,” Z. Phys, vol. 52, pp. 555–600, 1928.

B. R. Nag, Physics of quantum well devices, vol. 7. Springer Science & Business Media, 2001.

L. D. Hicks and M. S. Dresselhaus, “Effect of quantum-well structures on the thermoelectric figure of merit,” Phys. Rev. B, vol. 47, no. 19, pp. 12727–12731, 1993.

Y. Aharonov and D. Bohm, “Significance of Electromagnetic Potentials in the Quantum Theory,” Phys. Rev., vol. 115, no. 3, pp. 485–491, Aug. 1959.

R. Gurtler and D. Hestenes, “Consistency in the formulation of the Dirac, Pauli, and Schrödinger theories,” J. Math. Phys., vol. 16, no. 3, pp. 573–584, 1975.

E. Saitoh, “Introduction,” in Spin Current, S. Maekawa, E. Saitoh, S.Valenzuela, and Y. Kimura, Eds. Oxford University Press, 2012, pp. 3–14.




DOI: https://doi.org/10.15408/fiziya.v3i2.18119 Abstract - 0 PDF - 0

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