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Bulk and Surface Polaritons in PML-type Magnetoelectric Multiferroics and the Resonance Frequency Shift on Carrier-Mediated Multiferroics
Vincensius Gunawan, 2012
The University of Western Australia
Abstract
Polaritons are shown to be influenced by magnetoelectric coupling in a semi-infinite multi-ferroic material. The magnetoelectric coupling is considered as PML-type which allows a small uniform canting in magnetic sub-lattices, resulting in a weak ferromagnetism. In this type of coupling, electric polarisation P, weak ferromagnetism M and antiferromagnetic vector L are perpendicular each other. The case of transverse electric (TE) and transverse magnetic (TM) polarization are obtained when electric polarisation P and weak ferromagnetism M are directed in the plane parallel to the surface while the antiferromagnet vector L is directed out of plane perpendicular to the surface. Using parameters appropriate for BaMnF4, the Maxwell equations are solved to obtained dispersion relation for bulk and surface modes. It is shown that TE surface polaritons are non-reciprocal, such that !(k) 6= !(−k), where ! is frequency and k is propagation vector. It is also shown that the non-reciprocity can be controlled by an applied electric field. The magnetoelectric interaction also gives rise to “leaky” surface modes in the case of TM polarisation, i.e. pseudosurface waves that exist in the pass band, and that dissipate energy into the bulk of material. These pseudosurface mode frequencies and properties can be modified by temperature, and application of external electric or magnetic fields.
In the configuration where the electric polarisation P and antiferromagnetic vector L are in the plane parallel to the surface while the weak ferromagnetism is out of plane perpendicular to the surface, it is found that the surface modes are neither TE nor TM. We term this condition as “un-polarised” modes. Since in this configuration there are two attenuation constant, it is required the superposition of two plane waves to generate the un-polarised surface modes. It is also shown that surface modes are non-reciprocal due to magnetoelectric interaction. The strength of the non-reciprocity depend on the strength of magnetoelectric coupling.
In the multilayer which unit cell is a trilayer comprised of a metallic ferromagnet, ferroelectric and normal metal, it is shown that an applied voltage is able to enhance
the polarization of the ferroelectric, and increases the magnetic moment at one interface through spin polarization and charge transfer. The induced surface magnetism results in shifts of resonance and standing spin wave mode frequencies. A new resonance peak is predicted, associated with a strongly localized surface moment. Estimates are provided using parameters appropriate to the ferroelectric BaTiO3 and four different ferromagnetic metals, including a Heusler alloy (Fe, CrO2, Permalloy and Co2MnGe). The calculations use an entire-cell effective medium approximation that takes into account the polarization profile in the ferroelectric. The metallic ferromagnetic electrode is treated as a real metal, and the depolarization field is included in the determination of polarization in ferroelectric.
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