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It is analyzed the influence of a fixed background that breaks the Lorentz symmetry on the scalar field in the nonrelativistic regime. It is considered a medium with a nonuniform magnetization and the presence of an induced electric field. Then, due to the effects of the Lorentz symmetry violation, it is shown that the interaction of the scalar field with the magnetic field (produced by the nonuniform magnetization) and the induced electric field yields an effective potential analogous to the double anharmonic oscillator. Thereby, a discrete spectrum of energy can stem from the effects of the violation of the Lorentz symmetry on the scalar field.

The behaviour of the interaction of the induced electric dipole moment of an atom with a uniform magnetic field and a non-uniform electric field are investigated in a rotating reference frame. An interesting aspect of this interaction is that it gives rise to an analogue of a spinless particle subject to the doubly anharmonic oscillator. Then, it is shown that analytical solutions to the Schrödinger equation can be obtained. Another point raised is that the quantum effects on the induced electric dipole moment can be observed if the uniform magnetic field possesses a discrete set of values.PACS numbers:

We report an investigation of the dc voltage generated in a normal-metal (NM) layer by spin pumping from an adjacent ferromagnetic (FM) layer under ferromagnetic resonance (FMR) excitation. The spin-current injected across the FM/NM interface by the spin pumping effect generates a charge current along the NM layer by means of the inverse spin Hall effect. Room temperature field scan measurements were made in a series of Ni81Fe19/Pt bilayers with several thicknesses of the FM and Pt layers. By varying the angle of the in-plane magnetization we are able to accurately separate the contributions arising from anisotropic magnetoresistance and from the spin-current pumped into the NM layer by the precessing magnetization of the FM layer. The data for the spin pumping dc voltage is in excellent agreement with a theory incorporating the full dependence on the thicknesses of the FM and NM layers.