Tripartite coupling between phonons, magnons, and photons in a periodic array of elliptical magnetostrictive nanomagnets delineated on a piezoelectric substrate to form a 2D two‐phase multiferroic crystal is investigated. Surface acoustic waves (SAW) (phonons) of 5–35 GHz frequency launched into the substrate cause the magnetizations of the nanomagnets to precess at the frequency of the wave, giving rise to confined spin‐wave modes (magnons) within the nanomagnets. The spin waves, in turn, radiate electromagnetic waves (photons) into the surrounding space at the SAW frequency. Here, the phonons couple into magnons, which then couple into photons. This tripartite phonon‐magnon‐photon coupling is thus exploited to implement an extreme sub‐wavelength electromagnetic antenna whose measured radiation efficiency and antenna gain exceed the approximate theoretical limits for traditional antennas of the same dimensions by more than two orders of magnitude at some frequencies. Micro‐magnetic simulations are in excellent agreement with experimental observations and provide insight into the spin‐wave modes that couple into radiating electromagnetic modes to implement the antenna.
We derive the reflection and refraction laws for an electron spin incident from a quasi-two-dimensional semiconductor region (with no spin–orbit interaction) on the metallic surface of a topological insulator (TI) when the two media are in contact edge to edge. For a given incident angle, there can generally be two different refraction angles for refraction into the two spin eigenstates in the TI surface, resulting in two different ‘spin refractive indices’ (birefringence) and the possibility of two different critical angles for total internal reflection. We derive expressions for the spin refractive indices and the critical angles, which depend on the incident electron’s energy for given effective masses in the two regions and a given potential discontinuity at the TI/semiconductor interface. For some incident electron energies, there is only one critical angle, in which case 100% spin polarized injection can occur into the TI surface from the semiconductor if the angle of incidence exceeds that critical angle. The amplitudes of reflection of the incident spin with and without spin flip at the interface, as well as the refraction (transmission) amplitudes into the two spin eigenstates in the TI, are derived as functions of the angle of incidence.
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