Effect of the Spin-Spin Interaction on the Coulomb’s Law: Application to Ferromagnetism
- 1 Faculty of Physics, University of Bucharest, Bucharest, Romania
- 2 Aix-Marseille University & IM2NP, Marseille, France
Abstract
In this work we present a model for the determination of the interaction energy for triplet and singlet states in atoms with incomplete filled shells. Our model includes the modification of the Coulomb’s law by the interaction between the magnetic moments of the electrons. We find that the energy of the triplet state is lower than the energy of the singlet state. We calculate the interaction energy between the electrons from the adjacent atoms in fcc lattices and we find that the minimum interaction energy is attained for the triplet state. The result is presented for the interaction between the electrons of the first coordination group and those of the second coordination group. The interaction energy which aligns the spins is used to evaluate the Curie temperature in a mean field model.
- R. B. Laughlin, “Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations,” Physical Review Letters, Vol. 50, No. 11, 1981, pp. 1395-1398. doi:10.1103/PhysRevLett.50.1395
- K. von Klitzing, “The Quantized Hall Effect,” Review of Modern Physics, Vol. 58, No. 2, 1986, pp. 519-531. doi:10.1103/RevModPhys.58.519
- P. Grünberg, R. Schreiber, Y. Pang, M. B. Brodsky and H. Sowers, “Layered Magnetic Structures: Evidence for An- tiferromagnetic Coupling for Fe Layers across Cr Interlayers,” Physical Review Letters, Vol. 57, No. 19, 1986, pp. 2442-2445. doi:10.1103/PhysRevLett.57.2442
- M. N. Baibich, et al., “Giant Magnetoresistance of (001)Fe/(001)Cr Magnetic Superlattices,” Physjcal Review Letters, Vol. 61, No. 19, 1988, pp. 2472-2475. doi:10.1103/PhysRevLett.61.2472
- W. Heitler and F. London, “Interaction of Neutral Atoms and Homopolar Binding in Quantum Mechanics,” Zeitschrift für Physik, Vol. 44, No. 2, 1927, pp. 455-472.
- W. Heisenberg, “On the Theory of Ferromagnetism,” Zeitschrift für Physik, Vol. 49, No. 4, 1926, pp. 619-636.
- E. C. Stoner, “Magnetism and Matter,” Methuen, London, 1934.
- J. Hubbard, “Electron Correlations in Narrow Energy Bands,” Proceedings of the Royal Society of London, Vol. A276, No. 1365, 1963, pp. 238-257. doi:10.1098/rspa.1963.0204
- K. Hüller, “The Spin Wave Excitations and the Temperature Dependence of the Magnetization in Iron, cobalt, Nickel and Their Alloys,” Journal of Magnetism and Magnetic Materials, Vol. 61, No. 3, 1986, pp. 347-358. doi:10.1016/0304-8853(86)90048-X
- V. Dolocan, A. Dolocan and V. O. Dolocan, “Quantum Mechanical Treatment of the Electron-Boson Interaction Viewed as a Coupling through Flux Lines. Polarons,” International Journal of Modern Physics B, Vol. 24, No. 4, 2010, pp. 479-495.
- C. Kittel, “Indirect Exchange Interaction in Metals,” Solid State Physics: Advances in Research and Applications, Vol. 22, 1968, pp. 1-26.
- C. S. Wang, R. E. Prange and V. Korenman, “Magnetism in Iron and Nickel,” Physical Review B, Vol. 25, No. 9, 1982, pp. 5766-5777. doi:10.1103/PhysRevB.25.5766
- M. Pajda, J. Kudmovsky, I. Turek, V. Drchal and P. Bruno, “Ab Initio Calculations of Exchange Interactions, Spin-Wave Stiffness Constants, and Curie Temperatures of Fe, Co, and Ni,” Physical Review B, Vol. 64, No. 5, 2001, Article ID: 174402. doi:10.1103/PhysRevB.64.174402