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THE MAGNETIC SUSCEPTIBILITY
THE MAGNETIC HAMILTONIAN
THE STATIC SUSCEPTIBILITY OF NONINTERACTING
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absorption alloys amplitude angular momentum antiferromagnetic applied field arises associated assume average axis band becomes Chap characterized coefficients components compute conduction electrons contribution coordinates correlation function corresponding Coulomb interaction cross section crystal field defined density matrix determine diamagnetic dipolar discussion distribution effect eigenfunctions eigenvalues energy example exchange interaction excitation expression external field factor Fermi liquid Fermi surface ferromagnetic Fourier transform frequency Green's function Hartree-Fock hyperfine impurity integral involving ionic ions Landau lattice leads Let us consider linear magnetic field magnetic system magnon matrix elements metals Mn2+ modes noninteracting nuclear obtain operator orbital paramagnetic particles perturbation phonons Phys proportional quantity quantization quantum number quasi-particle relation relaxation resonance response result second quantize shown in Fig Slater determinant spectrum spin density spin waves spin-orbit spin-wave static susceptibility symmetry temperature dependence term in Eq theorem theory uniform unit cell Vleck wavefunction wavevector Zeeman