The theory of anomalous Hall effect for the heat transfer in a paramagnetic dielectric, discovered experimentally in [1], is developed. The appearance of the phonon heat flux normal to both the temperature gradient and the magnetic field is connected with the interaction of magnetic ions with the crystal field oscillations. In crystals with an arbitrary phonon spectrum this interaction creates the elliptical polarization of phonons. The kinetics related to phonon scattering induced by the spin-phonon interaction determines an origin of the off-diagonal phonon density matrix. The combination of the both factors is decisive for the phenomenon under consideration. PACS numbers: 66.70.+f, 72.15.Gd, 72.20.Pa A novel interesting phenomenon is found experimentally in recent paper [1]. The matter concerns an analog of the anomalous Hall effect (AHE) for the heat conductivity of an ionic paramagnetic dielectric. In fact, applying magnetic field B in the direction normal to heat flow j, the authors have discovered an appearance of the heat transfer in the direction normal to B and j. For the complete lack of free charged carriers and negligible role of the spin-spin coupling at the parameters concerned, the transverse flow is naturally associated with the evolution of the phonon system. However, the magnetic field does not directly act on phonons and only polarizes paramagnetic ions. It is the coupling between phonons and subsystem of isolated ions carrying magnetic moment M that determines the formation of the picture observed. Note in this aspect that the phenomenon concerned is an analog of the AHE in the paramagnetic phase of a ferromagnetic above the Curie point, discovered a long time ago [2]. An existence of the effect found in [1] has been confirmed in work [3]. In both [1] and [3] the choice of terbium gallium garnet (TbGG) was not accidental. In this compound for T < 10K the heat conductivity due to spin-phonon coupling (SPC) proves to be about two orders of the magnitude smaller as compared with gadolinium garnet [4] of the identical structure.As it is known, in most of ion dielectrics the spinphonon relaxation is determined by the two-phonon processes, see, e.g., [5] and [6]. Usually this supposes the presence of the Kramers doublet in the ground state and the transitions via virtual excitation of higher Kramers doublets. Trivalent ion T b 3+ has the even number of felectrons and the Kramers degeneration is absent. However, for rare earth ions with the even number of felectrons, an appearance of the quasi-doublet structure is typical for splitting the multiplet in the crystalline field with the level spacing ε 12 of about several Kelvins in the ground state. TbGG is a striking example of the similar compound, see, e.g., [7]. From the general symmetry reasons and the direct analysis [8, 9, 10] one can conclude that the SPC under conditions concerned reduces to a scalar production of magnetic moment M and the orbital moment related to the motion of surrounding ions. At low temperatures when the long wave acou...
In terms of linearized Gross-Pitaevskii equation we have studied the process of sound emission arises from a supersonic particle motion in a Bose-condensed gas. By analogy with the method used for description of Vavilov-Cherenkov phenomenon, we have found a friction work created by the particle generated condensate polarization. For comparison we have found radiation intensity of excitations. Both methods gives the same result.
We discuss the tunneling of phonon excitations across a potential barrier separating two condensates. It is shown that a strong barrier proves to be transparent for the excitations at low energy epsilon. Moreover, the transmission is reduced with increasing epsilon in contrast to the standard dependence. This anomalous behavior is due to the existence of a quasiresonance interaction. The origin of this interaction is a result of the formation of a special well determined by the density distribution of the condensate in the vicinity of a high barrier.
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