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Magnetoelastic Hamiltonian

Starting point is the Taylor expansion of the magnetic exchange parameters with respect to the components of the strain tensor e, leading to the so-called magnetoelastic Hamiltonian. [Pg.313]

All other representations require higher multipolar (/ = 4,6) operators. The are not to be confused with the individual OJ operators in the CEF potential [eq. (1)]. The latter are in general not cubic representations. However, the O can be expressed as linear combinations of the O . The magnetoelastic Hamiltonian has to be invariant under the relevant point group. To first order in the local strains this leads to (Callen and Callen 1963)... [Pg.237]

Inserting this into eq. (9) and retaining only quadrupolar terms one obtains the magnetoelastic Hamiltonian... [Pg.237]

In PrSb the C44 mode exhibits a minimum at T = 25 K, whereas the calculated quadrupolar strain susceptibility has a minimum at 60 K. With the addition of terms of the order of in the magnetoelastic Hamiltonian one obtains better agreement with the experiment (fig. 13). [Pg.254]

Following Callen and Callen (1963) one can generalize the magnetoelastic Hamiltonian [eqs. (8), (9)] by including terms with 1 = 4. [Pg.254]

Here ri9 ) the coupling in the magnetoelastic Hamiltonian, eq. (14). At the crossing point q = qp the mixed modes show a splitting... [Pg.275]

The electron-phonon Hamiltonian used for the explanation of magnetoelastic effects, eq. (14), has to be generalized for RAI2 because of the strain-optic-phonon couphng mentioned above. This leads to an additional mixed term in the lattice potential... [Pg.249]

As a framework for the discussion of the magnetization, magnetic anisotropy and magnetostriction we consider a hamiltonian which comprises the following isotropic exchange, effective single-ion anisotropy, elastic, magnetoelastic and Zeeman terms ... [Pg.415]

Bi = coefficients of operator equivalents in crystal field hamiltonian S = magnetoelastic coupling constant Bj(x) = Brillouin function B(q) = function entering spin-wave energy [see eq. (7.100)] e = (kT)- p = gmeHIkT c = c-axis lattice constant c = reciprical lattice constant C = basal plane elastic constant C] , C,-, = creation and annihilation operators for state m> on site 1 X = bulk susceptibility X, = atomic susceptibility x(d) - generalized wave number-dependent susceptibility function of conduction electrons... [Pg.489]

Expansion of the function Bj in a Fourier series in q R-,) and applications of the Bloch theorem to the sum over i in eq. (7.24) leads to peaks in x whenever qm is a sub-multiple of a c-axis reciprocal lattice vector. The same argument can be made in the case of a spiral structure. The reasons for the incommensurate-to-commensurate q transition are to be found in (a) the single-ion anisotropy terms in the hamiltonian, including magnetoelastic effects. For CAM-type structures the axial anisotropy favors maximum ordered moment at each site which can only develop in a commensurate structure. For spiral-type structures the basal plane anisotropy will also favor a commensurate structure, as will the nagnetoelastic anisotropy (b) the exchange will also favor a maximum ordered... [Pg.504]

Upon rotating the magnetic field in the (011) plane of a single crystal of LaS doped with 2000 ppm Er, Bloch et al. (1982) found an angular-dependent linewidth. They assumed a T7 ground state of Er followed by a Tg excited state. Internal strains of Fs type are coupled to the lanthanide ions via magnetoelastic effects. The spin Hamiltonian... [Pg.261]

In Nd pnictides which have a Fg ground state, quadrupole-quadrupole interactions appear to be dominant. For NdSb the tetragonal distortion below the N6el point (Levy, 1969) due to the magnetoelastic effect has been interpreted with a Hamiltonian including crystal field, Weiss molecular field and a magnetoelastic term (Bak and Lindgdrd, 1973 Furrer et al., 1976 Wakabayashi and Furrer, 1976)... [Pg.190]

The change of the interatomic distance caused by a shear soxmd wave is of the second order compared with a longitudinal wave. The main contribution to the attenuation arises in this case firom the single-ion magnetoelastic interaction. The Hamiltonian of this interaction can be expressed in the form proposed by Callen and Callen (1965) and is linear in strain and squared in spin variables ... [Pg.125]


See other pages where Magnetoelastic Hamiltonian is mentioned: [Pg.309]    [Pg.254]    [Pg.262]    [Pg.270]    [Pg.271]    [Pg.412]    [Pg.416]    [Pg.490]    [Pg.126]    [Pg.309]    [Pg.254]    [Pg.262]    [Pg.270]    [Pg.271]    [Pg.412]    [Pg.416]    [Pg.490]    [Pg.126]    [Pg.312]    [Pg.315]    [Pg.112]    [Pg.231]    [Pg.272]    [Pg.280]    [Pg.495]    [Pg.505]    [Pg.576]    [Pg.329]    [Pg.337]    [Pg.340]    [Pg.341]    [Pg.360]    [Pg.199]    [Pg.83]    [Pg.127]    [Pg.146]    [Pg.156]    [Pg.223]    [Pg.526]   
See also in sourсe #XX -- [ Pg.416 , Pg.461 ]




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