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Antiferromagnets (AFMs) have become the focus of intense research for potentially novel spintronic applications[1]. AFMs have been theoretically proposed to be ideal candidates to support spatially-coherent textured states, that may transport angular momentum over long distance, often called spin superfluids[2,3,4]. The stability of these states hinges upon the structure of the dispersion for excited spin waves. Here, we introduce the spin hydrodynamic equations for AFMs, modeled as two exchange-coupled spin sublattices[5], each dynamically described by a Landau-Lifshitz (LL) equation in the continuum approximation. We include an external magnetic field, the nearest-neighbor inter-lattice exchange interaction, and an easy-plane anisotropy field. Spin hydrodynamics[6] are exactly represented in terms of the spin densities, the perpendicular magnetization component, and the spin velocities, the azimuthal phase gradients, for each spin sublattice. We have identified two distinct classes of spin textures that can be identified as hydrodynamic states[6]: 1) The phase-locked state in which the spins from the two sublattices maintain a constant π phase difference; this state has previously been referred to as a spin superfluid[2]; 2) The polarization state in which the dynamics are governed by oscillating relative phases. This decomposition in terms of the total and relative phase dynamics has been effective in the study of the coupled two-component Bose-Einstein condensates[7]. For the phase-locked state, we verify that the spin dispersion is a gapped mode spectrum[2] and the state exhibits modulational instability at large enough total spin velocity[2,6]. We further study the stability properties of the polarization state by determining dispersion relations for spin wave propagation. Our results suggest that this newly identified state may be favorably excited in long-range spin transport experiments under appropriate conditions.References: [1] V. Baltz, et al., Reviews of Modern Physics, Vol. 90, No. 1, p.015005 (2018). [2] E. B. Sonin, Physical Review B, Vol. 99, No. 10, p.104423 (2019). [3] S. Takei and Y. Tserkovnyak, Physical review letters, Vol. 112, No. 22, p.227201 (2014). [4] W. Yuan, Wei, et al., Science Advances, Vol. 4, No. 4, p. eaat1098 (2018). [5] V. Puliafito, et al., Physical Review B Vol. 99, No. 2, p.024405 (2019). [6] E. Iacocca, T. J. Silva and M. A. Hoefer, Physical Review Letters, Vol. 118, No. 1, p.017203 (2017). [7] A. M. Kamchatnov, et al., Physical Review A, Vol. 89, No. 3, p.033618 (2014).

MMM 2020

Antiferromagnetic Spin Wave Propagation on Nonuniform Magnetic Backgrounds

The 65th Annual Conference on Magnetism and Magnetic Materials (MMM 2020) was held in a virtual form. The COVID-19 pandemic, with its associated uncertainty about international travel and the ability to gather in large groups, meant that the Steering Committee decided to cancel the face-to-face meeting that had been planned in Palm Beach, Florida November 2-6, 2020.

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technical paper

Skyrmion has, in the last decade, attracted considerable attention for its application to novel devices. To realize the futuristic devices that will be using the skyrmion circuit, the tracks which guide the motion of skyrmions are needed. The tracks patterned with differences in the magnetic-anisotropy energy are well-paved without a potential pocket, whereas the tracks carved out of magnetic films have the potential pockets at corners due to the demagnetizing field[1]. This work aims to identify the forces acting between skyrmions and anisotropy walls of the tracks as a first step studying the dynamics of skyrmions in the tracks. The static force on a skyrmion can be expressed as minus the gradient of the potential energy caused by the magnetic-anisotropy undulation[2]. We find that the forces from the wall Fwall depend not only on the distance from the wall X but also on the shape of skyrmions with their radii R and domain wall widths w in Fig. 1[3]. We have also performed micromagnetic simulations where the Magnus force and the force by the magnetic-anisotropy gradient are taken into account. When these forces are in balance with Fwall, the values of Fwall are determined. The simulation results show good agreement with those calculated from the modeled skyrmions as Fig. 2[4]. The force Fwall has a characteristic X-dependence where a peak locates at the skyrmion radius, since the force stems mostly from the transition part of the magnetization overlapping the potential jump at X=0. The force also acts on the skyrmions that have crossed over the wall to push back them to tracks. The property might be useful to stabilize the skyrmion circuits. Another helpful feature is that the magnetic anisotropy wall does not give rise to additional friction. This research and development work was supported by the Center for Spintronics Research Network (CSRN), the ULVAC. Inc., and the MIC.References: [1] Y. Jibiki et al., arXiv: 1909.10130 (2019) [2] A.A. Thiele, Phys. Rev. Lett. 30, 230 (1973) [3] X.S. Wang, et al., Commun. Phys. 1, 31 (2018) [4] E. Tamura, et al., arXiv: 2005.04860 (2020)

Skyrmion dynamics in tracks patterned with magnetic anisotropy: theory and simulations

Phases of matter are ubiquitous with everyday examples including solids and liquids. In reduced dimensions, particular phases, such as the two-dimensional (2D) hexatic phase and corresponding phase transitions occur (1-4). A particularly exciting example of 2D ordered systems are skyrmion lattices (5), where in contrast to previously studied 2D colloid systems (6), the skyrmion size and density can be tuned by temperature and magnetic field (7). In this work we use a skyrmion lattice to study phase transitions in 2D (8). We first show that we can drive the system from a liquid phase to a hexatic phase as deduced from the analysis of the hexatic order. The presence of a hexatic phase highlights the 2D nature of the system. Using coarse-grained molecular dynamics simulations of soft disks, we determine the skyrmion interaction potentials and we find that the simulations are able to reproduce the full two-dimensional phase behaviour. In particular by comparing the numerical simulations and the experimental results, we understand how the equilibration in the hexatic phase occurs on long timescales. This shows that not only the static behaviour of skyrmions is qualitatively well described in terms of a simple two-dimensional model system but skyrmion lattices are versatile two-dimensional model systems that allow for studying phases and phase transitions in reduced dimensions. Finally, as the next step, we investigate the effect of geometrical confinement and find a strong effect on the dynamics and ordering.References: 1. S. C. Kapfer, W. Krauth, Phys. Rev. Lett. 114, 035702 (2015). 2. Y. Nishikawa, K. Hukushima, W. Krauth, Phys. Rev. B 99, 064435 (2019). 3. M. Engel, J. Anderson, S. Glotzer, et al., Phys. Rev. E 87, 042134 (2013). 4. E. P. Bernard; W. Krauth, Phys. Rev. Lett. 107, 155704 (2011). 5. A. Fert, N. Reyren, V. Cros, Nat. Rev. Mater. 2, 17031 (2017). 6. K. Zahn, R. Lenke, G. Maret, Phys. Rev. Lett. 82, 2721–2724 (1999). 7. K. Everschor-Sitte, J. Masell, R. Reeve, M. Kläui, J. Appl. Phys. 124, 240901 (2018). 8. J. Zázvorka et al., arxiv:2004.09244

Skyrmion Lattice Phases in Thin Film Multilayers

Magnetic skyrmions are localized chiral whirling of magnetization that hold great promise as nanoscale information carrier. Skyrmion racetrack memory and logic devices have recently been proposed where trains of skyrmions in tracks are manipulated by electrical current [1]. These devices require the controlled nucleation and current driven motion of skyrmions in narrow tracks. In particular, the skyrmion Hall effect (i.e. the skyrmion motion towards the track edge), is a critical issue as it can lead to the skyrmion annilation [2–5]. Here, we report on the controlled nucleation and current induced guiding of magnetic skyrmions along tracks defined by local He+ ion irradiation on an ultrathin sputtered magnetic film at room temperature. A He+ focused ion beam was used to define 150 nm wide tracks (red areas, Fig.1a) within a sputtered ultrathin Pt/Co/MgO film patterned into 3-µm-wide tracks [5,6]. Magnetometry and Brillouin Light Scattering measurements show that the He+ ion irradiation results in a decrease of the perpendicular magnetic anisotropy as well as the Dzyaloshinskii-Moriya interaction. Under a small perpendicular magnetic field, this leads to the nucleation of skyrmion racetrack (Fig.1b), whose size and density can be tuned by the field amplitude. Experiments of current induced skyrmion motion, show that the skyrmions move along the He+ ion defined tracks. Thus, the track acts as a local potential well that guides the skyrmion trajectory, which allows to suppress the skyrmion Hall effect. Our results are well substantiated by micromagnetic simulations using experimentally derived magnetic and transport parameters. These results open a new path to nucleate and guide skyrmions in racetrack memory and logic devices.References: [1] A. Fert et al., Nat. Nanotechnol. 8, 152 (2013). [2] J. Sampaio et al., Nat. Nanotechnol. 8, 839 (2013). [3] W. Jiang et al., Nat. Phys. 13, 162 (2017). [4] S. Woo et al., Nat. Mater. 15, 501 (2016). [5] R. Juge et al., Phys. Rev. Appl. 12, 044007 (2019). [6] O. Boulle et al., Nat. Nanotechnol. 11, 449 (2016).

Skyrmion racetracks defined by light-ion irradiation and current induced skyrmion guiding at room temperature

Non-interacting particles exhibiting Brownian motion have been observed in many occasions of sciences, including spin textures in magnetic materials. Skyrmions are particle-like topological spin textures stabilized by the Dzyaloshinskii-Moriya interaction (DMI), with their topological properties being governed by the skyrmion number Q, which can also be thermally activated and behave like Brownian particles. In the present report, the Brownian dynamics of skyrmion is firstly discussed through performing micromagnetic simulation based on stochastic Landau-Lifshitz-Gilbert equation. More interestingly, a topology-dependent gyromotion from being clockwise (Q = +1) to counterclockwise (Q = -1) can be identified, as shown in Figs. 1(a) and 1(b), respectively. We subsequently utilized a polar magneto-optic Kerr effect (MOKE) microscopy to experimentally examine the Brownian motion of a single isolated skyrmion in the Ta/CoFeB/TaOx multilayer. The diffusion coefficient of skyrmion is found to exhibit an exponential dependence on temperature, instead of simple linear temperature dependence as Einstein predicted, as shown in Fig.1(c). Further, a topology-dependent Brownian gyromotion is confirmed by revealing the clockwise and counterclockwise rotations for Q = +1 and Q = -1 skyrmions, as shown in Figs. 2(a) and 2(b), respectively. Average rotation angle 〈θsr〉 is systematically calculated and shown in Fig.2(c), in which a clear difference in the whole temperature range can be seen. The experimental results are consistent with the analytical calculations from the stochastic Thiele equation, suggesting the Brownian gyromotion of a single skyrmion is captured.References: [1] L. Zhao, Z. Wang, X. Zhang, Phys. Rev. Lett., (in press)

Topology-Dependent Brownian Gyromotion of a Single Skyrmion

Although current induced motion of magnetic skyrmions have been extensively studied in recent work [1-3], manipulation of magnetic skyrmions that are fixed in space can also be utilized to implement such devices. We have recently shown that, skyrmion core reversal and switching between ferromagnetic states via an intermediate skyrmion state can be achieved in the free layer of an MTJ using Voltage Control of Magnetic Anisotropy (VCMA) which could result in energy efficient memory devices with smaller footprint [4-5]. In this work, we demonstrate experimental evidence of voltage controlled switching of fixed skyrmions in both continuous film [6] and confined geometry. The continuous heterostructure film stack consists of IrMn/CoFeB/MgO layers. The exchange biased structure allows stabilization of skyrmions without any external magnetic field. Upon application of a voltage pulse, the perpendicular magnetic anisotropy (PMA) changes at the ferromagnet/oxide interface. When the PMA is increased by applying a negative voltage pulse, skyrmions are annihilated. On the other hand, skyrmions can be recreated using a positive voltage pulse. We will also present micromagnetic simulations which reveal the detailed magnetization dynamics of this switching. Next, we will show voltage control of skyrmions in patterned nanodots composed of Ta/CoFeB/MgO multilayers. The geometric confinement is expected to influence the switching dynamics as shown in Fig. 1 [4,5]. To systematically modulate the confinement strength, we fabricated nanodots of varying lateral dimensions. The magnetization configurations are imaged using Magnetic Force Microscopy (MFM). Preliminary result of MFM imaging of skyrmion states under 1300 mV applied voltage in a ~5 µm dot is shown in Fig. 2. We will present detailed analysis of the confinement effect on skyrmion switching using further in-situ MFM imaging and rigorous micromagnetic simulations and compare these observations with the switching in thin films. Acknowledgement: NSF CCF collaborative grants: 1909030 and 1909416.References: [1] A. Fert et al, Skyrmions on the track, Nature Nanotechnology volume 8, pages152–156(2013) [2] K. Everschor-Sitte et al, Perspective: Magnetic skyrmions—Overview of recent progress in an active research field, Journal of Applied Physics 124, 240901 (2018) [3] G. Yu et al, Room-Temperature Skyrmion Shift Device for Memory Application, Nano Lett. 17, 1, 261–268 (2017) [4] D. Bhattacharya et al, Voltage controlled core reversal of fixed magnetic skyrmions without a magnetic field, Sci. Rep. 6, 31272 (2016) [5] D. Bhattacharya et al, Skyrmion-mediated voltage-controlled switching of ferromagnets for reliable and energy-efficient two-terminal memory, Applied Mater. & Interfaces 10 (20), 17455-17462 (2018). [6] D. Bhattacharya et al, Creation and annihilation of non-volatile fixed magnetic skyrmions using voltage control of magnetic anisotropy, Nature Electronics (2020)

Switching fixed magnetic skyrmions in continuous film and patterned nanodots using Voltage Control of Magnetic Anisotropy

Strongly-interacting nanomagnetic systems are pivotal in novel technologies such as reconfigurable magnonics1,2 and neuromorphic computation3. Controlling both magnetisation state and local coupling of neighbouring nanoelements allows vast reconfigurable functionality, a vital part of realising next generation devices. However, the extent of reconfigurability is often limited by a lack of local magnetisation control alongside an inability to redefine active and inactive elements in an array. Furthermore, shaping magnon pathways in two dimensions adds additional complexities in terms of power losses and changes in magnon frequency and phase4. A subset of nanomagnetic elements are circular-shaped nanomagnets (nanodisks) capable of supporting macrospin and vortex states5 [Fig. 1] offering higher a density compared to nanowire-based designs. Macrospin states comprise all spins aligning along a freely rotating macrospin axis resulting in a net magnetisation and large dipolar field enabling strong coupling between neighbouring elements. Whereas vortex states comprise an independent in-plane chirality and out-of-plane polarity characterised by a low dipolar-field leakage due to the chiral flux-closure. Yet, means of complete state control on individual nanodisks in an array are lacking. To address these challenges, we propose a novel nanodisk-based magnonic crystal where leveraging the coupling behaviours of different nanodisk states is employed to attain reprogrammable waveguiding capable of bending and splitting magnons around a 2D network [Fig. 2], amplitude gating and phase-shifting of magnons. We then demonstrate the potential of nanodisk-based magnonics by the design of an all-magnonic interferometer performing XNOR logic functionality. State preparation is achieved through local spin manipulation via a high-moment magnetic force microscopy enabling control of vortex chirality, polarity and macrospin axis across a range of nanodisk dimensions.References: 1. Grundler, D., Nature Physics, 11(6), pp.438-441. (2015) 2. Chumak, A.V., Vasyuchka, V.I., Serga, et. al. Nature Physics, 11(6), pp.453-461. (2015) 3. Grollier, J., Querlioz, D., Camsari, et. al. Nature Electronics, pp.1-11. (2020) 4. Haldar, A., Kumar, D. and Adeyeye, A.O., Nature nanotechnology, 11(5), pp.437-443. (2016) 5. Cowburn, R.P., Koltsov, D.K., Adeyeye, A.O., et. al. Physical Review Letters, 83(5), p.1042. (1999)

Magnonic Bending, Phase Shifting and Interferometry in a 2D Reconfigurable Nanodisk Crystal

We investigate the correlations of magnons inside a nanomagnet and identify an unconventional phase so-called magnon antibunching, i.e., where there is a large probability for occupation of the single-magnon state. This antibunched state is very different from magnons at thermal equilibrium and microwave-driven coherent magnons. We further obtain the steady state analytically and describe the magnon dynamics numerically, and ascertain the stability of such antibunched magnons over a large window of magnetic anisotropy, damping and temperature. This means that the antibunched magnon state is feasible in a wide class of low-damping magnetic nanoparticles. To detect this quantum effect, we propose to transfer the quantum information of magnons to photons by magnon-photon coupling and then measure the correlations of photons to retrieve the magnon correlations. Our findings may provide a promising platform to study quantum-classical transitions and for designing a single magnon source.References: 1. H. Y. Yuan and Rembert A. Duine, arXiv:2005.13637v1. 2. H. Y. Yuan, Peng Yan, Shasha Zheng et al., Phys. Rev. Lett. Vol. 124, p.053602 (2020). 3. H. Y. Yuan, Shasha Zheng, Z. Ficek et al., Phys. Rev. B Vol. 101, p.014419 (2020).

Magnon antibhunching in a nanomagnet

Spin wave (SW) based computing i.e. magnonics relies on propagating SW as information carriers. Being quasiparticles, magnons (the SW quanta) have a fine lifetime characterizing the exponential decay of the magnons population. Consequently, up to now, all magnonic devices operate within a short time-window. Finding a SW amplification paradigm is hence a prerequisite for the development of magnonics as a credible CMOS alternative. Two schemes are envisioned for SW amplification: Parametric pumping1 and spin-orbit-torque (SOT)2. Here we will discuss SOT amplification in BiYIG/Pt bilayer3. By passing current in the Pt layer, the spin accumulation resulting from the spin-Hall effect induces a positive torque that compensate the Gilbert damping of BiYIG. At subcritical values, the current has a linear effect that decreases the losses of the system and leads to a lower effective damping. Once the current in the Pt layer reaches a threshold values, the vanishing effective damping allows for the onset of the auto-oscillation regime4. Coherent propagating spin waves are strongly scattered by auto-oscillations5 leading to a strong decrease of their attenuation length6. Here we propose an amplification mechanism that circumvent this detrimental effect. We show using micro Brillouin light scattering spectroscopy (µ-BLS) on a 500 nm Pt/BiYIG waveguide that the precise timing of the dc current in the Pt layer with respect to the radiofrequency pulse in the strip antenna enables experimental observation of a lossless propagation of spin-waves. We take advantage of the strong BLS signal of BiYIG (nearly two orders of magnitude the one of YIG3) to extensively characterize the auto-oscillations non-linear dynamic regime in the presence of SOT. Work supported by ANR grant CE24-0021(MAESTRO).References: 1 T. Brächer, P. Pirro, and B. Hillebrands, Phys. Rep. 699, 1 (2017) 2 V.E. Demidov, A. Anane, S.O. Demokritov, J. Appl. Phys. 127, 170901 (2020) 3L. Soumah, A. Anane, Nat. Commun. 9, 3355 (2018) 4 M. Collet, G. de Loubens, and O. Klein, Nat. Commun. 7, 10377 (2016) 5 B. Divinskiy. O. Demokritov, and V.E. Demidov, Nat. Commun. 10, 5211 (2019) 6 M. Evelt, V.E. Demidov, M. Collet, Appl. Phys. Lett. 108, 172406 (2016)

Insight on the Time-Resolved Spin Wave Amplification in Nano-Magnonic Devices using Spin-Orbit-Torque

We report the evolution of spin conductivity at the YIG/Pt interface when the Pt is subject to an electrical current annealing. By injecting a large current density (12 ×1011A/m2) into Pt nanostrips and reaching a local temperature of 550 K, we observe a clear increase of the spin density emitted and probed at the YIG interface in three different measurements: spin Hall magnetoresistance, spin pumping and non-local magnon transport. As shown in Fig.1, the amplitude of FMR spectra by spin pumping enhances gradually in applying local Joule heating, leading to double the efficiency of spin transmmision by one-hour annealing. On the other hand the FWHM of the spectra remains the same over the whole annealing process (inset of Fig.1), indicating no farther extra damping at the YIG/Pt interface[1] appearing and relaxation processes occuring mainly in extended YIG films beside the strip. Fig.2 shows the non-local magnon transport signals mostly excited by spin orbit torque (SOT) (corresponding to the 1st hamonic signal in ref. [2] and Σ signal in ref. [3]). The non-local voltage enhances by 3 times by one strip annealing (either the injector or detector) and by 9 times by both strips annealing. Finally we estimated that the spin mixing conductance of evaporated Pt on YIG is increased from 0.8 to 1.9×1018 m−2. To sum up, the local annealing allows achieving spin mixing conductance of evaporated Pt on YIG similar quality to sputtered one and is of particular interest for very thin YIG films where chemical etching of the interface has to be avoided.References: [1]: O. Mosendz, V. Vlaminck, J. Pearson, et. al., Physical Review B 82, 214403 (2010). [2]: L. Cornelissen, J. Liu, R. Duine,et. al., Nature Physics 11, 1022 (2015). [3]: N. Thiery, A. Draveny, V. Naletov, et. al., Physical Review B 97, 060409 (2018)

Enhancement of the spin mixing conductance at YIG/Pt interfaces by electrical annealing

Spin waves represent a promising avenue for implementing unconventional wave-based computing platforms. However, combining controlled generation, manipulation and long-distance propagation of submicrometric wavelength spin waves is an outstanding challenge. Recently, nanoscale spin textures such as structured domains, domain walls and vortices, have raised interest as versatile active components in magnonic devices. In this framework, we demonstrated that nanopatterning spin textures via thermally assisted magnetic scanning probe lithography (tam-SPL) [1] allows the stabilization, in exchange bias systems, of 2D domains with arbitrary shape and spin configuration, 1D domain walls and 0D magnetic solitons such as vortices with tailored topology and position [2]. Here, first we show the channeling and steering of spin-waves in arbitrarily shaped nanomagnonic waveguides based on straight and curved domain walls, and a prototypic nanomagnonic circuit comprising two converging waveguides, allowing for the tunable spatial superposition and interference of confined spin-wave modes [3]. Then, we present an optically inspired platform for controlling the generation, propagation, and interference of short-wavelength spin waves, using nanopatterned spin textures in synthetic antiferromagnets, at remanence [4]. We demonstrate the spatial engineering of spin-wave wavefronts, the directional emission and focusing of spin-wave beams, and the generation of robust interference patterns which span multiple times the wavelength. Furthermore, we show that SAF allows to combine concepts borrowed from optics, with phenomena naturally arising from the nonreciprocal spin wave dispersion, such as resilience to spurious back reflections. The ability to control magnons via nanopatterned spin-textures at remanence opens up a range of new possibilities for developing energy-efficient unconventional computing concepts.References: [1] E. Albisetti, D. Petti, M. Pancaldi et al., Nat. Nanotechnol. Vol. 11, p. 545 (2016). [2] E. Albisetti, A. Calò, M. Spieser et al., Appl. Phys. Lett. Vol. 113, p. 162401 (2018). [3] E. Albisetti, D. Petti, G. Sala et al., Commun. Phys. Vol. 1, p. 56 (2018). [4] E. Albisetti, S. Tacchi, R. Silvani et al., Adv. Mater. Vol. 32, p. 1906439 (2020).

Antiferromagnetic Spin Wave Propagation on Nonuniform Magnetic Backgrounds

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Skyrmion dynamics in tracks patterned with magnetic anisotropy: theory and simulations

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