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Phenomenological Theories of Magnetic Order
Symmetry and Its Consequences
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absorption approximation assumed atomic axis band structure Bloch functions Brillouin zone calculation coefficients components consider constant contribution coordinates crystal cubic defined degeneracy denoted density dependence described determined diagonal diagrams dielectric dielectric function discussion effective mass eigenvalues electric field energy band evaluated expression external field factor Fermi energy Fermi surface ferromagnetic Fourier frequency given Green's function Hamiltonian Hartree-Fock impurity integral interaction introduce ions irreducible representations magnetic field matrix element metal momentum normal obtained operator orbit orthogonal oscillations parameter particle perturbation theory phonon Phys plane waves point group potential problem procedure pseudopotential quantity quantum reciprocal lattice vector relation result scattering Schrodinger equation Section single single-particle solid solution space group specific heat spherical spin wave substituted superconducting suppose symmetry temperature term theorem thermal tion transformation transition unit cell values vanishes Wannier functions wave function wave vector zero