Saturation magnetization and heat capacity of ferromagnetics
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KLYUKANOV, Alexandr, NIKA, Denis. Saturation magnetization and heat capacity of ferromagnetics. In: Materials Science and Condensed Matter Physics, Ed. 8-th Edition, 12-16 septembrie 2016, Chişinău. Chişinău: Institutul de Fizică Aplicată, 2016, Editia 8, p. 75. ISBN 978-9975-9787-1-2.
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Materials Science and Condensed Matter Physics
Editia 8, 2016
Conferința "International Conference on Materials Science and Condensed Matter Physics"
8-th Edition, Chişinău, Moldova, 12-16 septembrie 2016

Saturation magnetization and heat capacity of ferromagnetics


Pag. 75-75

Klyukanov Alexandr, Nika Denis
 
Moldova State University
 
Proiecte:
 
Disponibil în IBN: 19 iulie 2019


Rezumat

In the physics of magnetism Heisenberg model and its modifications play an important role, since 1928 up to the present time. Heisenberg effective spin-Hamiltonian in which the non-relativistic exchange interaction is expressed as a spin-spin interaction allowed explaining many experimental results. The temperature dependence of the heat capacity and the saturation magnetization of the ferromagnetics cannot be understood without involvement into the consideration of the concept of spin waves. But most exhaustively Heisenberg model is manifested in the case of the HolsteinPrimakoff transformation that allow to introduce the magnons operators.   This work is devoted to the calculation of the saturation magnetization and heat capacity of the ferromagnetics near the temperature T = 0 K, from the first principles. Comparison of the obtained results and known results of model theory of magnons are performed.     Magnetization in thermal equilibrium is represented as a series in powers of fluctuations 0 - VV . In the zero approximation the magnetic moment is given by the expression NS M B  2)0 ( (here we take into account the complete quenching of the orbital angular momentum). In the first order perturbation theory we use the Schrödinger equation in the mean field Hartree - Fock approximation. The energy spectrum of electrons is determined by the diagonalization of the Hamiltonian matrix, which depends both on the direct Coulomb interaction and the exchange interaction. If we restrict our consideration with the second order perturbation theory, Coulomb interaction gives the contribution into charge-charge correlator, diverging at 0 -q . To avoid Coulomb divergence one may use the fluctuation-dissipation theorem. It is shown that electrons interact with quasiparticles, which spectrum is determined by the poles of the retarded Green's charge-charge function. This response function is developed taking into consideration the spin-orbit interaction. It determines also the longitudinal dielectric function without the external magnetic field. Correlation, in addition to the screening, allows one to take into account the polaron energy spectrum renormalization.   It was shown that a non-zero contribution of the temperature correction to the saturation magnetization ) ()0()( T MMTM - is determined by the transitions with spin flip due to the spinorbit coupling. A constant of the spin-orbit interaction satisfies inequality 2/1 F E mc  . In the limit 0  when the detuning of the resonance between the excitation frequency and the transition frequency is due to the spin-orbit interaction, in the expression for M arises the uncertainty 0 /0 caused by the interaction with magnons. Any other interactions do not contribute to M in the limit of 0  . It was demonstrated that magnons are the excitations whose frequencies are lower than the electron transfer frequency from the local level state in to the band state  l . It was established, that magnon dispersion law is determined by the electron energy dispersion in the band state  l .     Finally, the calculated temperature correction M  (Bloch 2 /3T law) of the magnon dispersion law and the heat capacity of ferromagnetics are in agreement with the Heisenberg model. The latter reflects the resonance character of the transitions due to the spin-orbit coupling.