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Perpendicular Magnetic Anisotropy in Magnetic Thin Films
Published in Sam Zhang, Dongliang Zhao, Advances in Magnetic Materials, 2017
Prabhanjan D. Kulkarni, Somnath Bhattacharyya, Prasanta Chowdhury
Spin–orbit coupling is the origin of several types of magnetic anisotropies: magnetocrystalline, magnetoelastic, and Néel’s anisotropy. The Dirac equation, which defines the electron relativistically, reduces to the Pauli equation in limit of low velocities as () HPauli=p22m−eΦ−p48m3c2+eℏ28m2c2divE+eℏ4m2c2σ·(E×p),
Instability of magnetosonic waves in magnetized degenerate half-spin-polarized quantum plasma
Published in Waves in Random and Complex Media, 2023
W. F. El-Taibany, P. K. Karmakar, A. A. Beshara, M. A. El-Borie, S. A. Gwaily, A. Atteya
When applying a strong magnetic field on a spin-1/2 quantum plasma, the spin magnetization current of the electron and the magnetic dipole force will be significant. Over the last few decades, the field of research in magnetized spin-1/2 quantum plasma has experienced a remarkable interest in understanding the electrostatic disturbances in various plasma environments via applying the Quantum Magneto Hydrodynamic Model (QMHD) model. Marklund and Brodin [16] highlighted the concept of spin magnetohydrodynamics, where they derived the multi-fluid equations for spin-1/2 quantum plasmas, starting with the Pauli equation. In recent times, Kumar and Ahmad [17] treated the surface plasma waves on a metal-vacuum interface in semiconductor quantum plasma by taking into account the effects of Coulomb's exchange interaction, the quantum Bohm force, and the polarization due to spin. Furthermore, the effect of spatially varying magnetic fields on the excitations of the nonlinear waves in a dissipative quantum plasma have been discussed by Roy and Sahu [18]. As well, Zhu et al. [19] studied the behavior of extraordinary and upper-hybrid waves associated with spin quantum magneto-plasmas with vacuum polarization effect. additionally, Andreev [20] extended the QHDM to include pressure and pressure flux third-order tensor evolution equations and investigated the Langmuir and the spin-electron acoustic waves.
Helium II phase: superfluid, supersolid, liquid crystal or spin ice?
Published in Molecular Physics, 2022
It should be noted that the Hamiltonian Equation (4) ignores so important relativistic corrections as retarded potentials for electromagnetic interactions within the intra- and interatomic bonds [43], but the proper treatment of the corresponding problem needs special relativistic approach based on Pauli equation with spinor basis. However, here we shall restrict our consideration to the non-relativistic problem of the helium–helium interatomic interactions, taken into account spin contribution only through parity and degeneration of the four-spin system on the helium–helium interatomic bond. The relativistic corrections will be taken into account as perturbation using spatial matrix elements calculated with the ground state wave function of the non-relativistic problem (see Section 3.2.3).