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Skyrmions in antiferromagnetic (AFM) materials with the Dzyaloshinskii-Moriya (DM) interaction are expected to exist for essentially the same reasons as in DM ferromagnets (FM). On the other hand, the dynamics of solitons in AFM is substantially different [1,2]. We give the fundamental formula and a corresponding argument to show that traveling solitary waves (such as skyrmions) are possible in an AFM in contrast to the dynamics observed in FM. The formula shows that the skyrmion number, known to be linked to the dynamics of topological solitons in FM, is, here, unrelated to the dynamical behavior. We calculate numerically the configuration of skyrmions in chiral antiferromagnets that are traveling as solitary waves. They are found to be elongated and they expand in size with the velocity (Fig. 1). The velocity takes values from zero up to a maximum value, which depends on a scaled DM parameter λ. The maximum skyrmion velocity is found analytically as a function of λ. The formula is based on a strong theoretical argument that links the breakdown of a traveling skyrmion with the DM parameter value λ=2/π for the transition from the uniform to the spiral state. The energy and the linear momentum of an AFM skyrmion lead to a proper definition of its mass. We give the details of the energy-momentum dispersion of traveling skyrmions and explore their particle-like character based on exact relations. The traveling skyrmion behaves as a Newtonian particle for small velocities, while it presents relativistic behavior for velocities close to the critical. It is notable that the energy-momentum formula differs from the standard relativistic one by a constant shift of the energy. The solitonic and particle-like behavior of skyrmions in AFM is in stark contrast to the dynamical behavior of their FM counterparts [3]. We acknowledge support by the project ThunderSKY, funded by HFRI and GSRT, under Grant No. 871.References: [1] E. G. Galkina and B. A. Ivanov, Low Temp. Phys. 44, 618 (2018) [2] H. Velkov, O. Gomonay, M. Beens, et al, New J. Phys. 18, 075016 (2016) [3] S. Komineas and N. Papanicolaou, SciPost Phys. 8, 086 (2020)

MMM 2020

Traveling Skyrmions in Chiral Antiferromagnets

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

Recently, there have been reports on observation of electrical polarization and/or giant magnetoelectric effect in epitaxial rare-earth iron garnet (RIG) films [1–5] but the mechanism behind it is still in dispute. First-principles methods are employed to understand the existence of such polarization in RIGs. In contrast with previous beliefs, it is found that its occurrence can be explained if the system adopts magnetic multidomains and does neither require local magnetic moments of the rare-earth ions nor non-collinear magnetism. Table I reports the predicted polarization of a studied RIG multidomains (with R=Gd) with DW in the middle of supercells when we consider or not f-electrons of the Gadolinium (G) ions as valence electrons, which we denote as the “with-f” versus the “without-f” cases, respectively. Within each supercell, the two magnetic domains have a magnetic configuration that is reversed with respect to each other. As one can see, domain walls (DW) in GIG gives rise to a polarization even without f-electrons. This is further confirmed by the prediction of polarization in Yttrium (IG) and Lutetium (IG) iron garnet systems having multidomains as well. Furthermore, we found that the microscopic mechanism responsible for this DW-induced-polarization originates from a magnetoelectric effect arising from ferromagnetic interactions between octahedral and tetrahedral Fe ions at the domain walls (note that this interaction is antiferromagnetic in bulk RIG). More precisely, this mechanism is a symmetric exchange-striction mechanism, which, for the electrical polarization, takes the analytical form of Ρ=∑ Pesij Si●Sj, where the summation is over all the spin pairs and Pesij is the polarization coefficient vector associated with the spin pair. Acknowledgments This work is supported by the Department of Energy, Office of Basic Energy Sciences, under Award No. DE-SC0002220References: [1] A. S. Logginov, G. A. Meshkov, A. V. Nikolaev, and A. P. Pyatakov, JETP Lett. 86, 115 (2007). [2] G. V. Arzamastseva, A. M. Balbashov, F. V. Lisovskii, E. G. Mansvetova, A. G. Temiryazev, and M. P. Temiryazeva, J. Exp. Theor. Phys. 120, 687 (2015). [3] A. P. Pyatakov, A. K. Zvezdin, A. M. Vlasov, A. S. Sergeev, D. A. Sechin, E. P. Nikolaeva, A. V. Nikolaev, H. Chou, S. J. Sun, and L. E. Calvet, in Ferroelectrics ( Taylor & Francis Group , 2012), pp. 79–88. [4] V. Koronovskyy and Y. Vakyla, Electron. Mater. Lett. 11, 1028 (2015). [5] I. S. Veshchunov, S. V. Mironov, W. Magrini, V. S. Stolyarov, A. N. Rossolenko, V. A. Skidanov, J. B. Trebbia, A. I. Buzdin, P. Tamarat, and B. Lounis, Phys. Rev. Lett. 115, (2015).

Magnetic-domain-wall-induced electrical polarization in rare-earth iron garnet systems: A first-principle study

In the present work, we show that the in situ growth of oriented nanometric aggregates of cobalt oxide can be explored to alter and tune magnetocrystaline anisotropy. As such, the impact of interparticle interaction on magnetic properties of the aggregates is studied. Mono-dispersed cobalt oxide (CoO) nanostructures were prepared through decomposition of metal-organic compound of cobalt (II) in an alcoholic solution under controlled microwave irradiation, below 150 ⁰C. CoO nanostructures were effectively synthesized without the use of any surfactant. The structures were found to be inert to oxidation in ambient air for several months. We attribute the stability of CoO nanospheres to their dense packing, the driving force being, minimization of surface area and surface energy [1]. X-ray diffractometry (XRD) measurements indicate the formation of well crystallized CoO nanoparticles, without the need for post-synthesis annealing. Deconvolution of the active modes in Raman spectra obtained at room temperature reveals the Oh symmetry in rock-salt CoO, induced by microwave-assisted synthesis route [2]. Its effect on magnetic characteristics of CoO is analyzed here. Field-dependent magnetization (MH) and temperature-dependent magnetization (MT) measurements show a phase transition from paramagnetic to superparamagnetic interactions in CoO nanostructures at around 10 K, at which the average particle size was estimated to be 9 nm. The nanostructures however do not exhibit a distinct antiferromagnetic transition around 300 K as the bulk sample [3], but instead show a hysteresis below a blocking temperature of ~10 K (Figure 1). This finding reveals the magnetic behavior of CoO nanostructures that opens new opportunities for future applications as anisotropy source for magnetic recording.References: [1] M. Ibrahim Dar, S. Sampath and S. A. Shivashankar, Journal of Materials Chemistry., Vol. 22, p.22418 (2012) [2] A. V. Ravindra, B. C. Behera and W. Prellier, Journal of Applied Physics, Vol. 116, p.33912 (2014) [3] C.N.R. Rao and B. Raveau, Transition metal oxides, Wiley., (1995)

Tuning the magnetic anisotropy and phase transition in superparamagnetic cobalt oxide nanostructures synthesized through novel solution-growth technique

Magnetization switching using spin orbit torque (SOT) [1] has been investigated intensively to realize the low power and high endurance magnetic memory. For the in-plane magnetization switching, fabrication of spin valves is generally required because the anomalous Hall effect is not applicable. Such an additional fabrication procedures impede the rapid development of material search for the materials that exhibit a large SOT. In this study we demonstrated SOT induced in-plane magnetization switching of a single Ni80Fe20 layer on platinum layer by using spin rectification effect (SRE). Under the microwave irradiation, dc voltage via SRE appears near the ferromagnetic resonance field, well known as the spin-torque FMR[2]. In contrast, non-zero dc voltage also appears around zero magnetic field due to the non-resonant SRE (nrSRE), whose voltage level corresponds to the magnetization direction [3]. We found that the nrSRE was drastically enhanced under the irradiation of microwave with a frequency lower than FMR condition. By using the enhanced nrSRE, we demonstrated a highly sensitive detection of in-plane magnetization switching even for a 100 nm-in-width Ni80Fe20 electrode. Figure 1 shows a schematic of the fabricated device. Firstly, a large magnetic field was applied along +y direction to initialize the magnetization direction. After removing the magnetic field, a low frequency microwave was applied to measure the initial DC voltage generated by the nrSRE. After stopping the microwave irradiation, a pulse current was applied into the Pt layer. Then, dc voltage induced by nrSRE was measured again to detect the magnetization reversal. Figure 2 shows the voltage difference between before and after application of the pulse current as a function of the pulse-current density. Clear voltage differences were obtained above 2.5×107 A/cm2, indicating successful magnetization switching. In the presentation, we will discuss the origin of the enhanced nrSRE.References: [1] L. Liu, C. -F. Pai, Y. Li, H. W. Tseng, D. C. Ralph and R. A. Buhrman, Science, Vol. 336, p.555 (2012) [2] L. Liu, T. Moriyama, D. C. Ralph and R. A. Buhrman, Phys. Rev. Lett., Vol. 106, p. 036601 (2011) [3] X. F. Zhu, M. Harder, J. Tayler, A. Wirthmann, B. Zhang, W. Li, Y. S. Gui and C. -M. Hu, Phys. Rev. B, vol. 83, p.140402 (2011)

Detection of in-plane magnetization switching of Ni80Fe20 layer by spin rectification effect

The electrical detection of ferromagnetic resonance through the spin rectification (SR) effect has inspired great interest to investigate the magnetization dynamics in the last two decades. Furthermore, a comprehensive understanding of SR is essential to study the spin pumping and spin Hall effects. Recently, the single crystalline Co0.5Fe0.5 (001) alloy film has attracted attention due to the giant damping anisotropy and current-orientation effect of anisotropic magnetoresistance [Phys. Rev. Lett. 122, 117203 (2019)]. In this experimental work, we studied the SR dependence on the magnetization and current orientations in the single crystalline Co0.5Fe0.5 (001) alloy film. We present the experimental evidence that the magnetization-orientation dependence of the SR signal in Co0.5Fe0.5 strongly differs from those reported in the polycrystalline films. The strong anisotropy ratio of the damping constant up to 520% is determined, which can induce the strong anisotropy of the resonant susceptibility driven by the microwave field. By considering the current-orientation dependent anisotropic magnetoresistance and the anisotropic susceptibility in single crystalline Co0.5Fe0.5, we explain such unusual angular dependent SR signal by the SR theory. Our measurements show the amplitude of the SR signal could have 13 times difference for the devices along the <110> and <100> directions, which introduces the crystalline symmetry as a new approach to engineer the microwave characteristics in microwave spintronics.

Role of crystalline and damping anisotropy to the angular dependences of spin rectification effect in single crystal CoFe film

Hybrid magnonic systems have recently attracted wide attentions due to due to rich potential applications in coherent information processing. One particularly interesting platform is the thin-film-based magnon-magnon hybrid system, which has been recently explored in magnetic bilayers [1-4]. Because magnon excitations are confined within the magnetic media, it is convenient to build up more compact hybrid platforms in micron scale compared with millimeter-scale microwave circuits. Furthermore, the abundant spintronic properties, such as spin-torque manipulation and spin pumping, can be used to control and engineer the hybrid dynamics especially for magnetic thin-film devices. In this work, we demonstrate electrical detection of strongly coupled magnon-magnon hybrid system in yttrium iron garnet/permalloy (YIG/Py) bilayer devices. Direct microwave current injection through the conductive Py layer drives the hybrid dynamics consisting of the uniform mode of Py and the first standing spin wave (n=1) mode of YIG, which are strongly coupled via interfacial exchange coupling. The hybrid dynamics is detected via the spin rectification signal from Py, which provides phase resolution of the coupled dynamics. For the Py-dominated mode we measure a constant phase evolution. For the YIG-dominated mode a π phase shift is measured across the avoided crossing, which agrees with theoretical prediction. In addition, the characterization of nonlocal devices consisting two Py devices on a YIG base device shows that the two Py devices are coupled by inductive coupling, allowing spin rectification measurements of the nonlocal Py device. Our results provide a new device platform for exploring hybrid magnonic dynamics and probing their phases, which are crucial for implementing coherent information processing with magnon excitations. Sample preparation and measurements were supported by the US Department of Energy, Basic Energy Sciences, Materials Science and Engineering Division. Use of the Center for Nanoscale Materials, an Office of Science user facility, was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357.References: [1] S. Klingler, et al., Phys. Rev. Lett. 120, 127201 (2018). [2] J. Chen, et al., Phys. Rev. Lett. 120, 217202 (2018). [3] H. Qin, et al., Sci. Rep. 8, 5755 (2018). [4] Y. Li, et al., Phys. Rev. Lett. 124, 117202 (2020)

Phase-resolved electrical detection of strongly coupled magnon-magnon hybrid device

Reducing energy dissipation while increasing speed in computation and memory is a long-standing challenge for spintronics research [1]. In the last 20 years, femtosecond lasers have emerged as a tool to control the magnetization in specific magnetic materials at the picosecond timescale [2]. However, the use of ultra-fast optics in integrated circuits and memories would require a major paradigm shift. An ultrafast electrical control of the magnetization [3] is far preferable for integrated systems. Here we demonstrate reliable and deterministic control of the out-of-plane magnetization of a 1 nm-thick Co layer with single 6 ps-wide electrical pulses that induce spin orbit torques on the magnetization. We can monitor the ultrafast magnetization dynamics due to the spin orbit torques with sub-picosecond resolution, thus far accessible only by numerical simulations. Due to the short duration of our pulses, we enter a counter-intuitive regime of switching where heat dissipation assists the reversal. Moreover, we estimate a low energy cost to switch the magnetization, below 50 pJ for our micrometer sized device. These experiments show that spintronic phenomena can be exploited on picosecond time-scales for full magnetic control and should launch a new regime of ultrafast spin torque studies and applications.References: [1] Åkerman, J. Toward a universal memory. Science. 308, 508–510 (2005). [2] Kirilyuk, A., Kimel, A. V & Rasing, T. Ultrafast optical manipulation of magnetic order. Rev. Mod. Phys. 82, (2010). [3] Garello, K. et al. Ultrafast magnetization switching by spin-orbit torques. Appl. Phys. Lett. 105, 1–12 (2014).

Picosecond Spin Orbit Torque Switching

Vortex-based magnetic tunnel junctions (MTJs) are a rich dynamic system with a variety of different resonant modes, spanning a wide frequency spectrum from hundreds of MHz to tens of GHz [1, 2]. The diverse spectral properties of vortex-based MTJs makes them potential candidates for high frequency signal detectors [3, 4], with a dc rectification ‘spin-diode’ effect resulting when one of the resonant modes are excited with an rf current passing across the MTJ. In this study, we investigate the spin-wave modes present in a vortex-based MTJ, by analysis of the spin-diode rectification effect and by comparison with Fourier analysis of micromagnetic simulations. We demonstrate that the nature of the spin wave mode is strongly related to the position of the vortex core, varying from a pure azimuthal mode when the core is located at the centre of the MTJ, to a more standing wave edge mode when the core is strongly displaced to the edge. Furthermore, we demonstrate that the dominant excitation mechanism also changes depending upon core position, with the azimuthal mode being more sensitive to the field-like spin torque effect, and with the edge mode being more susceptible to the radial Oersted field. In addition to analysing the nature and the excitation scheme of these modes, we also show how their resonant excitation can lead to the modification of the critical current of the steady state excitation of the gyrotropic mode. The ability to control the gyrotropic mode via excitation of the higher order mode gives rise to a frequency down converter which can demodulate a signal with a carrier signal at 7.7 GHz with a modulation rate of 1 MHz. By harnessing the higher order spin wave modes present in vortex-based MTJs, new radio-frequency technologies such as signal detection and demodulation, which target GHz frequency bands can be envisaged. VC and PB acknowledge the ANR project “SPINNET” ANR-18-CE24-0012.References: [1] K. Y. Guslienko, A. N. Slavin, V. Tiberkevich, and S. K. Kim, “Dynamic origin of azimuthal modes splitting in vortex-state magnetic dots,” Phys. Rev. Lett., 101, 24, 1–4, 2008. [2] M. Kammerer et al., “Magnetic vortex core reversal by excitation of spin waves,” Nat. Commun., 2, 1, 279, 2011. [3] - A. S Jenkins et al., “Wideband High-Resolution Frequency-to-Resistance Converter Based on Nonhomogeneous Magnetic-State Transitions”, Phys. Rev. Applied 13, 014046, (2020) [4] - A. S Jenkins et al., “Spin-torque resonant expulsion of the vortex core for an efficient radiofrequency detection scheme”, Nature Nanotechnology volume 11, 360–364, (2016)

Controlling the gyrotropic critical current by resonant excitation of the higher order spin wave modes in vortex-based magnetic tunnel junctions

Recently, the Co8Zn8Mn4 alloy was found to host the skyrmion crystal phase at room temperature [1,2]. Understanding the GHz spin dynamics and magnonic eigenmodes of this phase is key for developing room temperature applications in spintronics and magnonics. Here, we report the broadband microwave absorption spectroscopy measurement of bulk Co8Zn8Mn4 crystal, mounted onto a coplanar waveguide (CPW). We have determined the resonance frequencies of the eigen-excitations of the various magnetic phases in Co8Zn8Mn4 - at room temperature - including the helical, skyrmion crystal, conical and fully polarized magnetic order (Fig. 1 and Fig. 2). In particular, we found that the clockwise, counter-clockwise and breathing modes of the skyrmion crystal magnetic configuration resides between ~0.8 and 2.5(2) GHz. The frequencies of the modes depend on the orientation of the applied field with respect to the CPW and the long axis of the crystal. We account for the frequency variations by means of magnetic anisotropies. Furthermore, we augment our results with single crystal x-ray diffraction measurements and temperature-dependent magnetic susceptometry. We thank S. Watanabe, P. R. Baral and I. Zukovic for experimental support. The research was financially supported by the SNSF (grant no. 171003 - sinergia project Nanoskyrmionics) and the EPSRC (grant no. EP/M020517/1).References: 1. Y. Tokunaga, X. Z. Yu, J. S. White, et al. Nature Communication, Vol. 6 p. 7638 (2015) 2. K. Karube, J. S. White, N. Reynolds, et al. Nature Materials, Vol. 15, p. 4752 (2016)

Magnetization Dynamics of Helical and Skyrmion Phases in Bulk Co8Zn8Mn4 at Room Temperature

The finding of skyrmions at room temperature has boosted the potentiality of skyrmionic devices. From the theoretical point of view, the temperature in micromagnetic systems has been taken into account either using stochastic spin dynamics, the stochastic Landau-Lifshitz equation, or the Landau-Lifshitz-Block equation. Also, the rigid model has been used to describe the skyrmion dynamics taking into account thermal effects, using the stochastic Thiele equation [1]. Here we present a deterministic method to study the skyrmion dynamics [2], an approach in which the temporal motion of skyrmions can be studied without relying on repetition of stochastic simulations, but on solving once the associated deterministic Fokker-Planck equation. This is a substantial advance, since by finding and solving a single partial differential equation, one could obtain all the relevant probabilistic information of the system. Indeed, within the rigid approximation, the probability density for the presence of skyrmions under any external potential can be found at any time and position, and as a function of the temperature. This allows one to evaluate the probability of presence/survival trapping/escaping ... of skyrmions in many practical situations, which is a key information to ensure the viability of applications. In particular, the probability of trapping/escaping of a skyrmion that encounters a pinning site, and the probability of survival of a skyrmion along a track are presented as a function of temperature.References: [1] D. Pinna, F. Abreu Araujo, J. Grollier, Phys. Rev. Applied., Vol. 9, (2018) [2] J. Castell-Queralt, L. González-Gómez, C. Navau. Phys. Rev. B 101, 140404 (R) (2020)

Deterministic Approach to Skyrmionic Dynamics at Nonzero Temperatures: Pinning Sites and Racetracks

Electron-correlated oxide materials display a plethora of physics phenomena due to their multiples degrees of freedom. Transition-metal oxides, in particular, exhibit coincidental structural, magnetic, and metal-insulator transitions among others. When combined in proximity with single-metallic-ferromagnets, it is possible to enhance the magnetic control at the nanoscale [1]. Understanding the magnetic dynamics in such systems provides the means to untangle the underlying physical phenomena which govern these strongly correlated materials. Here we will present two examples of such systems studied by angular-dependent Ferromagnetic resonance as a function of temperature. In both cases, the magnetic dynamics is governed by the proximity of an oxide undergoing a structural transition with a ferromagnet, as in the case of VOx/Ni heterostructures [2], or in the case of La-Pr-Ca-Mn-O thin films, by their complex magnetic-electronic phase transitions [3]. FMR and micromagnetic simulations allowed us to trace back the details of the phase transitions and to map the changes in anisotropy and the magnetic domain reorganization. Work done in collaboration with Christian Wolowiec, Diego Carranza, Ali Basaran, Amlan Biswas, Michael Fitzsimmons, Arantxa Fraile Rodríguez, Javier Rodriguez-Alvarez, Amílcar Labarta, Xavier Batlle, and Ivan K. Schuller. Funded by the US DoE, Office of Basic Energy Sciences, under Award FG02-87ER-45332 and Colciencias under contract 137-2016. Spanish MINECO projects MAT2015-68772-P and PGC2018-097789-B-I00 and European Union FEDER funds.References: [1] I. Valmianski, et al., in preparation. [2] J. G. Ramirez, et al., Phys. Rev. B 93, 1 (2016). [3] D. Carranza-Celis, et al., in preparation.

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Traveling Skyrmions in Chiral Antiferromagnets

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Magnetic-domain-wall-induced electrical polarization in rare-earth iron garnet systems: A first-principle study

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