Spin-wave Doppler Shift Research Articles

Handedness filter and Doppler shift of spin waves in ferrimagnetic domain walls

Excitation and propagation of spin waves inside magnetic domain walls (DWs) have received attention because of their potentials in spintronic and communication applications. In addition to wave amplitude and frequency, spin waves have a third character: handedness, whose manipulation is certainly of interest. We propose in this paper that the handedness of low-energy spin-wave excitations can be controlled by tuning the net angular momentum ${\ensuremath{\delta}}_{s}$ in a ferrimagnetic (FiM) DW, attributing to the inequivalent magnetic sublattices. The results indicate that the spin-wave dispersion depends on both ${\ensuremath{\delta}}_{s}$ and wave handedness. For a positive (negative) ${\ensuremath{\delta}}_{s}$, a gapless dispersion is observed for left-handed (right-handed) spin waves, while a frequency gap appears for right-handed (left-handed) spin waves. Thus, a FiM wall could serve as a filter of low-energy spin waves in which only spin waves with a specific handedness can propagate. Furthermore, the energy consumption loss for spin-wave excitation in the wall is much lower than that inside the domain, while the group velocity is much faster too, demonstrating the advantages of DWs serving as spin waveguides. Moreover, the current-induced spin-wave Doppler shift in the FiM wall is also revealed and can be controlled by ${\ensuremath{\delta}}_{s}$. In this paper, we unveil the interesting spin-wave dynamics in FiM DWs, benefiting future spin-wave applications.

Current-Induced Spin-Wave Doppler Shift in Antiferromagnets

We theoretically study the spin dynamics in antiferromagnets (AFs)under the influence of an electric current. We identify two different sources of spin-transfer torques that stem from uniform (${\boldsymbol v}_n$) and staggered (${\boldsymbol v}_\ell$) electron spin densities. While the former is well recognized, the latter is often overlooked. We show that both ${\boldsymbol v}_n$ and ${\boldsymbol v}_\ell$ contribute equally to the spin-wave Doppler shift. Microscopic calculations are presented for electrons on a two-dimensional square lattice with nearest-neighbor ($t$) and next-nearest-neighbor ($t'$) hopping, which interpolate two opposite transport regimes of strongly-coupled AF ($t'/t \ll 1$) and two weakly coupled ferromagnets ($t'/t \gg 1$). In the AF transport regime ($t'/t \ll 1$), ${\boldsymbol v}_n$ and ${\boldsymbol v}_\ell$ have opposite signs, and the sign of the Doppler shift depends on band filling; ${\boldsymbol v}_n$ (${\boldsymbol v}_\ell$) is dominant near the AF gap (near the band bottom or the top). As $t'/t$ is increased, ${\boldsymbol v}_n$ undergoes a sign change whereas ${\boldsymbol v}_\ell$ does not. In the limit of vanishing $t$, ${\boldsymbol v}_n$ and ${\boldsymbol v}_\ell$ coincide and the spin-transfer torque reduces to that of ferromagnets.

Spin-Wave Doppler Shift by Magnon Drag in Magnetic Insulators.

The Doppler shift of the quasiparticle dispersion by charge currents is responsible for the critical supercurrents in superconductors and instabilities of the magnetic ground state of metallic ferromagnets. Here we predict an analogous effect in thin films of magnetic insulators in which microwaves emitted by a proximity stripline generate coherent chiral spin currents that cause a Doppler shift in the magnon dispersion. The spin-wave instability is suppressed by magnon-magnon interactions that limit spin currents to values close to but below the threshold for the instability. The spin current limitations by the backaction of magnon currents on the magnetic order should be considered as design parameters in magnonic devices.

Current-induced spin-wave Doppler shift and attenuation in compensated ferrimagnets

We theoretically and numerically study current-induced modification of ferrimagnetic spin-wave dynamics when an electrical current generates adiabatic and nonadiabatic spin-transfer torques. We find that the sign of the Doppler shift depends on the spin-wave handedness because the sign of spin polarization carried by spin waves depends on the spin-wave handedness. It also depends on the sign of the adiabatic-torque coefficient, originating from unequal contributions from two sublattices. For a positive nonadiabaticity of spin current, the attenuation lengths of both right- and left-handed spin waves increase when electrons move in the same direction with spin-wave propagation. Our result establishes a way to simultaneously measure important material parameters of a ferrimagnet, such as angular momentum compensation point, spin polarization, and nonadiabaticity using current-induced control of ferrimagnetic spin-wave dynamics.

Spin-wave propagation and spin-polarized electron transport in single-crystal iron films

The technique of propagating spin wave spectroscopy is applied to a 20 nm thick Fe/MgO (001) film. The magnetic parameters extracted from the position of the resonance peaks are very close to those tabulated for bulk iron. From the propagating waveforms, a group velocity of 4 km/s and an attenuation length of about 6 micrometers are extracted for 1.6 micrometers-wavelength spin-wave at 18 GHz. From the measured current-induced spin-wave Doppler shift, we also extract a surprisingly high degree of spin-polarization of the current of 83%. This set of results makes single-crystalline iron a promising candidate for building devices utilizing high frequency spin-waves and spin-polarized currents.

Observation of spin-wave Doppler shift in Co90Fe10/Ru micro-strips for evaluating spin polarization

The current-induced spin-wave Doppler shift has been investigated for Co90Fe10 films, with and without under- and overlayers of Ru, aiming to obtain quantitative insights into the value of spin polarization of the diffusive electrical currents flowing in this material. This extends the use of spin-wave Doppler shift spectroscopy beyond the study of permalloy to other soft magnetic materials suitable for use in spintronic applications such as racetrack memories. The Damon-Eshbach spin-wave mode was employed, and a control experiment of permalloy yielded a value of spin polarization of P = 0.44 ± 0.03 for that material. An extended method to properly evaluate spin-wave Doppler shifts is developed that takes account of the non-negligible Oersted fields that are generated by the current density asymmetry caused by conducting under- or overlayers. The values of spin polarization for various Co90Fe10-based structures are found to lie in the range of 0.3–0.35, only slightly less than in permalloy.

Spin-transfer torques in antiferromagnetic textures: Efficiency and quantification method

We formulate a theory of spin-transfer torques in antiferromagnets, which covers the small to large limits of the exchange coupling energy relative to the kinetic energy of the inter-sublattice electron dynamics. Our theory suggests a natural definition of the efficiency of spin-transfer torques in antiferromagnets in terms of well-defined material parameters, revealing that the charge current couples predominantly to the antiferromagnetic order parameter and the sublattice-canting moment in, respectively, the limits of large and small exchange coupling. The effects can be quantified by analyzing the antiferromagnetic spin-wave dispersions in the presence of charge current: in the limit of large exchange coupling the spin-wave Doppler shift always occurs, whereas, in the opposite limit, the only spin-wave modes to react to the charge current are ones that carry a pronounced sublattice-canting moment. The findings offer a framework for understanding and designing spin-transfer torques in antiferromagnets belonging to different classes of sublattice structures such as, e.g., bipartite and layered antiferromagnets.

Nonreciprocal Oersted field contribution to the current-induced frequency shift of magnetostatic surface waves

The influence of an electrical current on the propagation of magnetostatic surface waves is investigated in a relatively thick (40 nm) permalloy film both experimentally and theoretically. Contrary to previously studied thinner films where the dominating effect is the current-induced spin-wave Doppler shift, the magnetic field generated by the current (Oersted field) is found to induce a strong non-reciprocal frequency shift which overcompensates the Doppler shift. The measured current induced frequency shift is in agreement with the developed theory. The theory relates the sign of of the frequency shift to the spin wave modal profiles. The good agreement between the experiment and the theory confirms a recent prediction of a counter-intuitive mode localization for magnetostatic surface waves in the dipole-exchange regime.

Current-induced localized spin wave interference in a ferromagnetic nanowire with a domain wall

Spin wave dispersion relations in a ferromagnetic nanowire with and without a domain wall are investigated by means of micromagnetic simulations. We confirm that the spin wave dispersion relation is shifted due to the spin wave Doppler effects, when the spin-transfer torque is applied. We also investigate the position-dependent ferromagnetic resonance spectra in the nanowire and find strong local spin wave interferences because of the formation of the standing wave due to reflections from a domain wall. It is observed that the spacing between the local spin wave constructive interferences is uniform, and it is revealed that the spacing is related with the spin wave Doppler shift.

Current-induced torques in continuous antiferromagnetic textures

We study the influence of an electric current on a continuous noncollinear antiferromagnetic texture. Despite the lack of a net magnetic moment, we find that the exchange interaction between conduction electrons and local magnetization generally results in current-induced torques that are nonzero and similar in phenomenology to spin-transfer torques in ferromagnets. We present the generalization of the nonlinear sigma model equation of motion for the N\'eel vector that includes these current-induced torques, and briefly discuss the resulting current-induced antiferromagnetic domain wall motion and spin-wave Doppler shift. We give an interpretation of our results using a unifying picture of current-induced torques in ferromagnets and antiferromagnets, in which they are viewed as being due to the current-induced spin polarization resulting from an effective spin-orbit coupling.

Spin-wave transduction at the submicrometer scale: Experiment and modeling

We report a complete study of spin-wave transduction combining microwave measurements performed over a frequency range of [1--15] GHz on Permalloy strips ($\text{thickness}=10--20\text{ }\text{nm}$, $\text{width}=2--8\text{ }\ensuremath{\mu}\text{m}$) and an accurate modeling of the experiment. This technique has been used recently to assess the spin polarization of the electrical current by measuring a current-induced spin-wave Doppler shift. We present here an electromagnetism calculation based on the magnetostatic wave theory combined with the Gilbert form of the damping that can be used directly as an optimization tool for future spin-wave experiments.

Current-Induced Spin-Wave Doppler Shift

Spin transfer appears to be a promising tool for improving spintronics devices. Experiments that quantitatively access the magnitude of the spin transfer are required for a fundamental understanding of this phenomenon. By inductively measuring spin waves propagating along a permalloy strip subjected to a large electrical current, we observed a current-induced spin wave Doppler shift that we relate to the adiabatic spin transfer torque. Because spin waves provide a well-defined system for performing spin transfer, we anticipate that they could be used as an accurate probe of spin-polarized transport in various itinerant ferromagnets.