Theory of propagating spin wave spectroscopy using inductive antennas: conditions for unidirectional energy flow

Many recent papers report on the interest of spin waves for applications. This paper revisits the propagating spin wave spectroscopy when using inductive transceivers connected to a network analyzer. The spin wave conduit can be made of a non-reciprocal material. The formalism offers a method to understand, design and optimize devices harnessing propagating spin waves, including when a unidirectional energy flow is desired. The concept of the mismatch of helicity between the spin wave and the magnetic field radiated by antennas is first clarified. Owing to the form of the susceptibility tensor reflecting the precession ellipticity, there exists specific orientations of the wavevector for which a perfect helicity mismatch is reached. The spin waves with this orientation and this direction of wavevector are "dark" in the sense that they do not couple with the inductive antenna. This leads to single-sided wavevector generation, that should not to be confused with a unidirectional emission of energy. A method to calculate the antenna-to-antenna transmission parameter is then provided. Analytical approximations are then applied on situations that illustrate the respective role of the direction of the spin wave wavevector versus that of the group velocity. The often-encountered cases of spin waves possessing either a V-shaped or a flat dispersion relation are revisited. These reciprocal dispersion relations lead to amplitude non-reciprocity because of the helicity mismatch phenomenon. Conversely, for spin waves with a line-shaped dispersion relation, a quasi-unidirectional emission of spin waves occurs. This situation can be obtained when using the acoustical spin waves of synthetic antiferromagnets when the wavevector is close to parallel to the applied field. We finally show that this configuration can be harnessed to design reconfigurable frequency filters

Gilbert damping of high anisotropy Co/Pt multilayers

Using broadband ferromagnetic resonance, we measure the damping parameter of [Co(5 \r{A})/Pt(3 \r{A})]${\times 6}$ multilayers whose growth was optimized to maximize the perpendicular anisotropy. Structural characterizations indicate abrupt interfaces essentially free of intermixing despite the miscible character of Co and Pt. Gilbert damping parameters as low as 0.021 can be obtained despite a magneto-crystalline anisotropy as large as $10^6~\textrm{J/m}^3$. The inhomogeneous broadening accounts for part of the ferromagnetic resonance linewidth, indicating some structural disorder leading to a equivalent 20 mT of inhomogenity of the effective field. The unexpectedly relatively low damping factor indicates that the presence of the Pt heavy metal within the multilayer may not be detrimental to the damping provided that intermixing is avoided at the Co/Pt interfaces

Spin wave emission by spin-orbit torque antennas

We study the generation of propagating spin waves in Ta/CoFeB waveguides by spin-orbit torque antennas and compare them to conventional inductive antennas. The spin-orbit torque was generated by a transverse microwave current across the magnetic waveguide. The detected spin wave signals for an in-plane magnetization across the waveguide (Damon-Eshbach configuration) exhibited the expected phase rotation and amplitude decay upon propagation when the current spreading was taken into account. Wavevectors up to about 6 rad/$\mu$m could be excited by the spin-orbit torque antennas despite the current spreading, presumably due to the non-uniformity of the microwave current. The relative magnitude of generated anti-damping spin-Hall and Oersted fields was calculated within an analytic model and it was found that they contribute approximately equally to the total effective field generated by the spin-orbit torque antenna. Due to the ellipticity of the precession in the ultrathin waveguide and the different orientation of the anti-damping spin-Hall and Oersted fields, the torque was however still dominated by the Oersted field. The prospects for obtaining a pure spin-orbit torque response are discussed, as are the energy efficiency and the scaling properties of spin-orbit torque antennas.Comment: 20 pages, 5 figure