High-speed antiferromagnetic domain walls driven by coherent spin waves

Magnonics, a crucial domain in information science and technology, utilizes spin waves in magnets as efficient information carriers. While antiferromagnets have been suggested for versatile magnonic platform because of the coexistence of right- and left-handed spin waves, their energetic degeneracy poses challenges for observation through spectral measurements, limiting their applicability. Recent observations of distinct spin wave handedness within the gigahertz regime have reported but, are yet to be demonstrated in terahertz (THz) frequencies of antiferromagnetic spin waves. Most of all, the coherence of spin waves is a key aspect of quantum information. Here, employing THz time-domain spectroscopy—a direct, precise, and easy probe for monitoring coherent spin wave dynamics—we discern chiral antiferromagnetic spin waves of opposite phase windings in the time domain, noting their handedness reversal across the angular momentum compensation temperature in ferrimagnets. We establish a principle for directly measuring the handedness of coherent antiferromagnetic spin waves in ferrimagnets with net magnetic moment M ≠ 0 but angular momentum L = 0. Our multidimensional access in the time and spectral domain enables the accurate determination of critical temperature and the dynamic observation of coherent chiral spin waves simultaneously in a single experiment, with potential applications in exploring other quantum chiral entities.

: The report describes in detail the technical progress made in studies of strong infrared light scattering from coherent spin waves during the second six months of a three year interdisciplinary research program. Coherent light scattering from coherent microwave spin waves in yttrium iron garnet (YIG) is studied theoretically and experimentally. The method is then used, in conjunction with standard microwave techniques, to probe the propagation of spin waves and magnetoelastic waves, in spatially-and/or-temporally-varying magnetic fields. The dispersion of magnetoelastic waves propagating parallel to saturation magnetization when the latter is in an arbitrary crystallographic direction, first presented by Morgenthaler, is rederived. The report discusses the first direct observation of strong Bragg Scattered infrared light (1150 nm wavelength) from coherent microwave spin waves.

Local perturbations in the relative orientation of the magnetic moments in a continuous magnetic system can propagate in the form of waves. These so-called spin waves represent a promising candidate as an information carrier for spin-based low-power applications. A localized, energy-efficient excitation of coherent and short-wavelength spin waves is a crucial technological requirement, and alternatives to excitation via the Oersted field of an alternating current must be explored. Here, we show how a domain wall pinned at a geometrical constriction in a perpendicularly magnetized thin nanowire emits spin waves when forced to rotate by the application of a low direct current flowing along the wire. Spin waves are excited by the in-plane stray field of the rotating domain wall and propagate at an odd harmonic of the domain wall rotation frequency in the direction of the electron’s flow. The application of an external field, opposing domain wall depinning induced by the current, breaks the symmetry for spin wave propagation in the two domains, allowing emission in both directions but at different frequencies. The results presented define a new approach to manufacture tuneable high-frequency spin wave emitters of easy fabrication and low power consumption.

We theoretically study the interaction of magnons, quanta of spin waves, and a domain wall in a one-dimensional easy-axis antiferromagnet in the presence of an external magnetic field applied along the easy axis. To this end, we begin by obtaining the exact solution for spin waves in the background of a domain wall magnetized by an external field. The finite magnetization inside the domain wall is shown to give rise to reflection of magnons scattering off the domain wall, deviating from the well-known result of reflection-free magnons in the absence of a magnetic field. For practical applications of the predicted reflection of magnons, we show that the magnon reflection contributes to the thermally driven domain-wall motion. Our work leads us to envision that inducing a finite magnetization in antiferromagnetic solitons such as vortices and skyrmions can be used to engender phenomena that do not occur in the absence of magnetization.

IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, SpainWe studied effect of magnetoelastic anisotropy and role of defects on domain wall (DW) dynamics andremagnetization process of magnetically-bistable microwires. We manipulated the magnetoelastic anisotropychanging the ratio between the metallic nucleus diameter and glass coating thickness and applying the tensilestresses. Application of stresses resulted in increase of the switching field and decrease of the DW velocity, v. Therole of defects existing in magnetically bistable microwires is related with nucleation of new reversed domains.Abrupt jumps on v(H) dependences correlate with defects existing in microwires. Annealing allows considerablyincrease DW velocity, enhances the magnetic field range of single DW propagation regime and domain wall mobility.Key words: amorphous microwires, domain wall dynamics, magnetic anisotropy1. IntroductionStudies of domain wall (DW) propagation in thinmagnetic wires prepared by different methods attractedgrowing attention during last few years [1, 2]. Maintechnological interest is related with proposedapplications involving the information storage,magnetic sensors and logics. For aforementionedapplications the DW speed and the ways for the DWdynamics manipulation are essentially relevant.Reported DWs propagation can be driven by themagnetic field as well as by the electric current flowingthrough the sample. The DW velocity is determined bythe magnetic field value as well as by the shape anddimensions of the wires [1, 3-6]. Thus, for amorphousmicrometric wires with circular cross section fastest DWvelocity (exceeding 1000 m/s) have been reported [7,8].Additionally the DW velocity, v, depends on themagnetoelastic anisotropy depending on themagnetostriction constant value as well as on theinternal or applied stress [9]. On the other hand, forcontrolling the DWs dynamics in thin wires (either withrectangular or cylindrical cross-section), fewmechanisms involving the DW injection, creation ofartificial defects and inhomogeneities, controllable DWcollision etc have been reported [9, 10].Studies of glass-coated microwires withferromagnetic nucleus attracted considerable attentionwithin last few years owing to their reduced dimensionsand unusual soft magnetic properties such asspontaneous magnetic bistability, Giantmagnetoimpedance effect and high magneticpermeability. Magnetic bistability is related with largeand single Barkhausen jump observed in amorphousmicrowires with positive magnetostriction constant isparticularly interesting for studies of the DWpropagation within the inner core of microwire [5-7, 11].On the other hand giant magneto-impedance, GMI,effect and extremely soft magnetic properties can beuseful for magnetic sensors applications [12, 13].Abovementioned magnetic bistability observed inamorphous glass-coated microwires with positivemagnetostriction constant is related with fastmagnetization switching of a large single axiallymagnetized domain by fast DW propagation of a singleDW [5-8, 11, 13]. Therefore these microwires are uniquematerial allowing studying the magnetization dynamicsof a single DW in a cylindrical micrometric wire.Appearance of such peculiar domain structureconsisting of a large single axially magnetized domainsurrounded by outer radially magnetized shell isdetermined by the stresses arising during rapidsolidification of composite thin wire [5, 13-17]. Thestrength of these stresses originated from the differencein thermal expansion coefficients of the metal and glassis determined by the volumes of metallic nucleus andglass coating [14-16]. Consequently the magneticsoftness of glass-coated microwires is determined by themagnetoelastic anisotropy originated from thecomposite character being also depending on themetallic nucleus composition and ratio between themetallic nucleus diameter, and total microwirediameter.Consequently fast magnetization switching ofmicrowires is related with the propagation of the singlehead-to head DW along the wire.Recently we reported, that the samplesinhomogeneities, observed through the measurementsof the distribution of the local nucleation fields, H

We study the thermal gradient (TG) induced domain wall (DW) dynamics in a uniaxial nanowire in the framework of the Stochastic-Landau–Lifshitz–Gilbert equation. TG drives the DW in a certain direction, and DW (linear and rotational) velocities increase with TG linearly, which can be explained by the magnonic angular momentum transfer to the DW. Interestingly, from Gilbert damping dependence of DW dynamics for fixed TG, we find that the DW velocity is significantly smaller even for lower damping, and DW velocity increases with damping (for a certain range of damping) and reaches a maximal value for critical damping which is contrary to our usual desire. This can be attributed to the formation of standing spin wave (SSW) modes (from the superposition of the spin waves and their reflection) together with travelling spin wave (TSW) modes. SSW does not carry any net energy/momentum to the DW, while TSW does. Damping α compels the spin current polarization to align with the local spin, which reduces the magnon propagation length and thus α hinders to generate SSWs, and contrarily the number of TSWs increases, which leads to the increment of DW speed with damping. For a similar reason, we observe that DW velocity increases with nanowire length and becomes saturated to maximal value for a certain length. Therefore, these findings may enhance the fundamental understanding as well as provide a way of utilizing the Joule heat in the spintronics (e.g. racetrack memory) devices.

We investigate the inertial domain wall (DW) dynamics driven by spin-polarized current in ferromagnets. The exact solutions reveal an upper limit for DW velocity, given by V ≤ 1 / α τ . This indicates that damping and inertia become the key factors in achieving higher DW speeds. For the case of uniaxial anisotropy, we analyze the effects of inertia and current on DW dynamics. Due to inertia, the DW velocity, width, rotation frequency, and wave number are mutually coupled. When the DW width varies slightly, the velocity decreases rapidly while the magnetization precession frequency increases sharply with the inertia term. However, once the rotation frequency exceeds its maximum value, both the DW velocity and rotation frequency gradually decline. Regarding current-driven dynamics, we identify a critical current j 1c that directly triggers the Walker breakdown. For currents below this threshold j 1 < j 1c, the absolute DW velocity increases with current, whereas it decreases for j 1 > j 1c. During this process, the DW velocity rapidly peaks under current drive, accompanied by the magnetization rotation frequency nearing its maximum and minimal variation in DW width. These results suggest that the DW behaves like a classical rigid body, reaching its maximum velocity as it approaches peak rotational speed. For biaxial anisotropy, we derive analytical solutions. The competition between hard-axis anisotropy and inertia causes the DW magnetization to lose its spiral structure and rotational symmetry. The inertia effect leads to a slow initial decrease followed by a rapid increase in DW width, whereas current modulation gradually widens the DW. The analytical solution also reveals another critical current, j 1 max = α / τ / β , which scales with the square root of the inertia-to-damping ratio and is inversely proportional to the nonadiabatic spin-transfer torque parameter β.

The control of domain walls or spin textures is crucial for spintronic applications of antiferromagnets. Despite many efforts, it has been challenging to directly visualize antiferromagnetic domains or domain walls with nanoscale resolution, especially in magnetic field. Here, we report magnetic imaging of domain walls in several uniaxial antiferromagnets, the topological insulator MnBi2Te4 family, using cryogenic magnetic force microscopy (MFM). Our MFM results reveal higher magnetic susceptibility inside the domain walls than in domains. Domain walls in these antiferromagnets form randomly with strong thermal and magnetic field dependence. The direct visualization of these domain walls and domain structures in the magnetic field will not only facilitate the exploration of intrinsic topological phenomena in antiferromagnetic topological insulators but will also open a new path toward control and manipulation of domain walls or spin textures in functional antiferromagnets.

Coherent spin waves possess immense potential in wave-based information computation, storage, and transmission with high fidelity and ultra-low energy consumption. However, despite their seminal importance for magnonic devices, there is a paucity of both structural prototypes and theoretical frameworks that regulate the spin current transmission and magnon hybridization mediated by coherent spin waves. Here, we demonstrate reconfigurable coherent spin current transmission, as well as magnon–magnon coupling, in a hybrid ferrimagnetic heterostructure comprising epitaxial Gd3Fe5O12 and Y3Fe5O12 insulators. By adjusting the compensated moment in Gd3Fe5O12, magnon–magnon coupling was achieved and engineered with pronounced anticrossings between two Kittel modes, accompanied by divergent dissipative coupling approaching the magnetic compensation temperature of Gd3Fe5O12 (TM,GdIG), which were modeled by coherent spin pumping. Remarkably, we further identified, both experimentally and theoretically, a drastic variation in the coherent spin wave-mediated spin current across TM,GdIG, which manifested as a strong dependence on the relative alignment of magnetic moments. Our findings provide significant fundamental insight into the reconfiguration of coherent spin waves and offer a new route towards constructing artificial magnonic architectures.

Antiferromagnetic (AFM) spintronics is an emerging subject where one tries to exploit the indispensable properties of AFMs for spintronics such as negligible stray fields and terahertz resonance frequencies. Unfavorably, small electric, and magnetic responses make it difficult to write and read the information in AFM spintronic devices. Thus, from the applied perspective, it is crucial to search the AFM materials having manipulable AFM order. Mn3Ge and Mn3Sn are novel functional AFMs that exhibit magnetic responses comparable to FMs1,2. The magnetic states characterized by magnetic cluster octupoles (MCOs) are tunable under a small external magnetic field. Thus, data writing and reading can be realized by inductively using a recording head, likewise FMs. A recent numerical simulation predicts an antiferromagnetic domain wall (AFDW) velocity up to 2 km/s without a walker break down3. A pulse current could drive such AFDW under the threshold current density of 109 A/m2, two or three orders of magnitude smaller than in FMs4. Thus, it could open a new avenue for racetrack memory applications to overcome the shortcomings of low velocity and high energy consumption of ferromagnetic domain walls. Besides, the multistate of MCOs could generate multilevel magnetic responses rather than conventional two-level memory responses. It may provide a new idea for three-dimensional memory without vertical multilayer architecture. Therefore, the understanding of AFDW structure and dynamics in Mn3Sn and Mn3Ge is indispensable for the memory application.We put our focus on Mn3Ge in this study because it has the native advantages of strong chemical stability in air and robustly retaining the MCO structure down to 0.3 K over the Mn3Sn. We grew Mn3Ge single crystal using the bismuth flux method5. The obtained single crystal sample is a perfect hexagonal column, reflecting the hexagonal crystal structure. We performed polar and longitudinal MOKE measurements at room temperature. Figure 1a shows a polar hysteresis loop measured by laser scanning MOKE microscope. The positive and negative signs of the MOKE signal correspond respectively to oppositely aligned MCOs with the order parameters of α±, as shown in the inset of Fig 1a. Figure 1(b) shows the angular dependence of longitudinal MOKE measurement at room temperature. The intensity of decreased from 5.6 mdeg to 0 deg with increasing from 0° to 90°.Domain observation was furtherly performed by using high-resolution CCD MOKE microscope. Firstly, a magnetic field, up to -100 Oe downwards, which is larger than the saturation field according to the MOKE hysteresis loop in Fig. 1b, was applied to reset the magnetization in the crystal. We subtracted the image background at this state; then, we captured MCO domain images continuously while sweeping the magnetic field from -20 Oe down to 30 Oe with a sweep rate of 2.5 Oe/s, as shown in Fig. 2a. The exposure time of the CCD camera was 50 ms. Firstly, the droplet of the tilted MCO domain appears at 2 Oe. Here, the gray at -100 Oe and the white areas at 25 Oe represent the oppositely polarized MCO domains. The droplet occurs at the surface center due to the nearly zero magnetization in Mn3Ge. Noticeably, the color contrast gradually changes from gray to white within a narrow magnetic field range of about 2 Oe. As the grayscale in the CCD camera is proportional to the out-of-plane component of MCO moment Mz. We can obtain the tilting angle φ of the MCO moment where cosφ = Mz/M, as shown in Fig. 2b. In this way, we can understand how the magnetic octupole evolves during the domain nucleation process. The six-fold symmetry in the kagome plane may offer the possibility of a multilevel MCO memory application. The droplet of the switched domain emerges in the magnetic field range from H1 = 1.875 Oe to H2 = 3 Oe, as shown in Fig. 2c. The decrease in magnetic potential energy compensates for the energy consumed by AFDW. Thus, we have:-μ0(MH2-MH1)×ΔV-σ×ΔS=0where M and, σ denote the MCO moment (7 mµB/Mn) and the 180° AFDW energy density, respectively. ΔV is the volume of the switched MCO domain, and ΔS is the area of nucleated AFDW. We estimated the and by assuming the hemi-ellipsoidal MCO domain beneath the surface, as illustrated in Fig. 2c. The obtained σ is 0.0198 erg/cm2.In conclusion, we have obtained the large MOKE signal, including the polar and longitudinal MOKE. The sizeable MOKE signals enable us visualize the MCO domain optically. Thereby, we systematically studied MCO domain evolution and estimated the AFDW propagation in a single crystal Mn3Ge. Our work provides important insights for the study on the exploitation of the AFDW based memory devices. **

Searching for new methods controlling antiferromagnetic (AFM) domain wall is one of the most important issues for AFM spintronic device operation. In this work, we study theoretically the domain wall motion of an AFM nanowire, driven by the axial anisotropy gradient generated by external electric field, allowing the electro control of AFM domain wall motion in the merit of ultra-low energy loss. The domain wall velocity depending on the anisotropy gradient magnitude and intrinsic material properties is simulated based on the Landau-Lifshitz-Gilbert equation and also deduced using the energy dissipation theorem. It is found that the domain wall moves at a nearly constant velocity for small gradient, and accelerates for large gradient due to the enlarged domain wall width. The domain wall mobility is independent of lattice dimension and types of domain wall, while it is enhanced by the Dzyaloshinskii-Moriya interaction. In addition, the physical mechanism for much faster AFM wall dynamics than ferromagnetic wall dynamics is qualitatively explained. This work unveils a promising strategy for controlling the AFM domain walls, benefiting to future AFM spintronic applications.

Spin waves, quantized as magnons, have low energy loss and magnetic damping, which are critical for devices based on spin-wave propagation needed for information processing devices. The organic-based magnet [V(TCNE)x ; TCNE = tetracyanoethylene; x ≈ 2] has shown an extremely low magnetic damping comparable to, for example, yttrium iron garnet (YIG). The excitation, detection, and utilization of coherent and non-coherent spin waves on various modes in V(TCNE)x is demonstrated and show that the angular momentum carried by microwave-excited coherent spin waves in a V(TCNE)x film can be transferred into an adjacent Pt layer via spin pumping and detected using the inverse spin Hall effect. The spin pumping efficiency can be tuned by choosing different excited spin wave modes in the V(TCNE)x film. In addition, it is shown that non-coherent spin waves in a V(TCNE)x film, excited thermally via the spin Seebeck effect, can also be used as spin pumping source that generates an electrical signal in Pt with a sign change in accordance with the magnetization switching of the V(TCNE)x . Combining coherent and non-coherent spin wave detection, the spin pumping efficiency can be thermally controlled, and new insight is gained for the spintronic applications of spin wave modes in organic-based magnets.

Various devices have been proposed which use magnetic domain walls (DWs) in nanosized magnetic structures to perform logic operations or store information. In particular in ‘Racetrack memory’ bits of information represented by DWs are shifted in a magnetic wire to be stored. For these memory and logic devices to be successful, great control of DW motion is of vital importance. In cooperation with IBM’s Almaden research laboratory a pump-probe Kerr magnetooptical scanning microscope has been developed. In order to control DW injection, motion and reset, magnetic fields have to be applied locally on the nanowire. For this a special Damascene CMOS chip has been fabricated at the 200 mm wafer facility at IBM Microelectronics Research Laboratory (MRL). Probing of the local magnetization is done with a focused pulsed laser spot of 400 nm diameter where the polarization rotation caused by the Kerr effect is measured after reflection. In order to achieve optimal focusing a perpendicular incident laser beam is focused with a high numerical aperture objective. Synchronized ‘pumping’ in this scheme is achieved by successively: 1 injecting a DW; 2 propagate the DW down the nanowire with either current through or an applied field pulse over the nanowire; 3 and finally resetting the whole nanowire to its original magnetization by applying a large field together with the injection of an opposite magnetic domain. With this setup field and current induced DW motion is studied in permalloy nanowires ranging in width from 200 to 700 nm and thickness of 20 nm. For control of DWs in Racetrack memory it is important to understand the different mechanism for driving a DW already in motion (dynamic) and driving a DW that is currently at rest (static). The propagation field, the minimum field below which no DW motion takes place, is measured for both dynamic DWs and static DWs. It is found that Static DWs require a much higher field than DWs already in motion. A model is build where this effect is related to the wire roughness, successfully describing the existence of a propagation field, the difference between both propagation fields and a specific effect related to the method of injection. For Racetrack memory to be successful the critical current needs to be small (the current needed to move a DW solely by current) and the DW velocity high. Much of the influence of intrinsic magnetic properties of materials on DW dynamics is unknown. One important property affecting DW velocity and possibly also the critical current is Gilbert damping. Gilbert damping in permalloy can be tuned by doping the nanowires with osmium. This is used to prepare a sample series with increasing Gilbert damping. Measurement of the field induced DW velocity revealed a profile well known that includes the Walker breakdown (a maximum field where further increasing field strength does not further increase the DW velocity). From this profile the dependence of the Walker breakdown, DW mobility and maximum DW velocity on Gilbert damping has been determined. With the same sample series also current induced field assisted DW motion has been measured. Current induced DW motion is known to be driven by two effects: adiabatic and ballistic- spin momentum transfer (SMT) which relative contribution is parameterized by beta in the Landau Lifshitz Gilbert equation (LLG). Measurement of DW velocity depending on current density revealed the relative contribution of the two SMT schemes. Also the influence of Gilbert damping on the relative contribution of both schemes has been explored. A pronounced dependence of the measured spin torque efficiency on osmium concentration was found. This result may be interpreted as a sign that the intensively debated ratio ? / ? is far from constant over the range of ? studied.

Controlling magnon densities in magnetic materials enables driving spin transport in magnonic devices. We demonstrate the creation of large, out-of-equilibrium magnon densities in a thin-film magnetic insulator via microwave excitation of coherent spin waves and subsequent multimagnon scattering. We image both the coherent spin waves and the resulting incoherent magnon gas using scanning-probe magnetometry based on electron spins in diamond. We find that the gas extends unidirectionally over hundreds of micrometers from the excitation stripline. Surprisingly, the gas density far exceeds that expected for a boson system following a Bose–Einstein distribution with a maximum value of the chemical potential. We characterize the momentum distribution of the gas by measuring the nanoscale spatial decay of the magnetic stray fields. Our results show that driving coherent spin waves leads to a strong out-of-equilibrium occupation of the spin-wave band, opening new possibilities for controlling spin transport and magnetic dynamics in target directions.

We investigate domain walls in antiferromagnets focusing on the effect of Dzyaloshinskii–Moriya interactions (DMIs). Using spin model simulations and analytical arguments within a continuum theory, we show that Dzyaloshinskii–Moriya interactions affect static as well as dynamic properties of the domain wall. For certain configurations of the DMI vectors, the DMI can either tilt the easy plane of the domain wall, an effect that leads to a reduced domain wall width, or it can favor a certain chirality of the domain wall. Depending on the DMI configuration, the DMI may lead to an increasing or decreasing domain wall velocity. The asymmetry of the domain wall velocity observed in ferromagnets subject to DMI cannot be found in antiferromagnetic systems.