Magnetic spin waves

The chief source of all this confusion and apparent indecision lies in our inability to ascribe a definite form to the magnetic spin wave contribution to the heat capacity. A number of theories were introduced in the early 1950 s, for a review of which reference should be made to Mackintosh and Mbller (1972) or, for a review in brief, one may consult Lounasmaa and Sundstrom (1%6). For the sake of completeness, we present in table 5.1 the temperature dependences of the various models. 

Man] Magnetic measiuements with a fluxmeter Magnetization, spin-wave stiffness coefficient and interaction range... 

Numerous experimental studies have shown that the magnetic hyperfine field of magnetic nanoparticles varies linearly with temperature at low temperatures, in accordance with (6.23). This is in contrast to bulk materials for which the decrease in the hyperfine field with increasing temperature in accordance with spin wave... 

Berger L (1996) Emission of spin waves by a magnetic multilayer traversed by a current. Phys Rev B 54 9353-9358... 

Though the true electron spin operators were employed here as well as in the Breit-Pauli Hamiltonian, the phenomenological Spin Hamiltonian, in which the spin coupling is an exchange effect, is in sharp contrast to the Breit-Pauli Hamiltonian, that is including the (magnetic) spin-spin interactions. Since the exchange effect is an effect introduced by the Pauli principle imposed on the wave function, we may write the electron-electron interaction as an expectation value,... 

In the above calculation of A and B, it was assumed that the wave functions were pure d orbitals, and hence no contribution from the 8(r) term was found, since d orbitals go to zero as r approaches zero. Experimentally, however, it is found that the 8(r) term does contribute a sizeable isotropic term to A and B. Since this contact term contributes only for s electrons, we need to understand how the magnetic spin of the atom acquires this s character. Basically this s character results from the partial unpairing or polarization of the inner s electrons as a result of an interaction with the unpaired d electrons. To see this more directly, consider the polarization of the Is electron spins. The basic wave function for the atom can be... 

Interna] and external magnetic fields also play a special role for the observation of light scattering at magnons, as the quanta of spin waves are called - see Fig. 10. 

From the spin wave (or magnon) model of magnetic systems, the heat capacity versus temperature behavior below the ordering temperature is given192 by the following equation ... 

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