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The fluctuation theory of concentration and thermodynamic magnetic phase transitions in chiral helicoidal ferromagnetic binary and quasi-binary alloys with the Dzyaloshinsky-Moriya interaction is being developed. The ground state is described based on the LDA+U+SO approximation with additional allowance for concentration fluctuations associated with the difference in the potentials of intra-atomic Hubbard interaction at the sites. The functional of free energy of electronic and magnetic subsystems with thermodynamic and concentration spin fluctuations is constructed. The equations of magnetic state obtained from the conditions of the saddle point allow us to consider the conditions for the realization of the phases of the helicoidal long-range and short-range orders with right and left magnetic chirality. Solutions of the equations of magnetic state are considered on the example of quasi-binary alloys Fe1-xCoxSi, which are the main prototypes of materials of modern spintronics. h-T diagrams of spin phases arising due to the concentration shift of the chemical potential and concentration magnetic fluctuations with a change in the concentration x were constructed. It was found that, in the concentration range 0.05

MMM 2020

Phase transitions induced by concentration and thermodynamic magnetic fluctuations in chiral ferromagnets Fe1-xCoxSi

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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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Spin Orbit Torque (SOT) is an efficient way to electrically manipulate nanoscale magnetic objects for high-speed, high-density and low power spintronic devices1. However, the high critical current density, jc, required to switch the magnetization of a film is a major bottleneck that limits the practical application of SOT in memory devices2. In this work, we achieve an order of magnitude reduction in jc by irradiating magnetic thin films using a focused helium ion beam. These films consist of Pt(2.0)/Co(1.0)/W(1.5) sandwiches (numbers in nm), chosen to have heavy metals with opposite spin Hall angles (Pt, W)3, and they are sufficiently thin to exhibit perpendicular magnetic anisotropy. The critical current required to switch the magnetic state (±Mz) depends on several parameters including saturation magnetization and magnetic anisotropy, all of which are interface dependent, and can be altered using He+ irradiation4. Our key advance is in-situ monitoring of the evolution of the out-of-plane magnetization under local ion irradiation using the anomalous Hall effect (Fig. 1a). In principle, this allows both precise control of the anisotropy and <~10 nm spatial resolution, while avoiding additional lithography steps needed for patterned broad-beam irradiation. The reduction of the jc is determined via Sot switching experiments (Fig. 1b). This work demonstrates a promising and practical approach for the reduced power consumption in SOT-based spintronic devices which opens the prospect of preferential current driven magnetization switching of predetermined sample areas, limited by the resolution of the ion beam microscope, down to the nanometer scale, while preserving the flat topography of the initial magnetic stack.References: 1 I.M. Miron, K. Garello and G. Gaudin, Nature 476, 189 (2011). 2 R. Ramaswamy, J.M. Lee and K. Cai, Appl. Phys. Rev. 5, 031107 (2018). 3 S. Woo, M. Mann and A.J. Tan, Appl. Phys. Lett. 105, 212404 (2014). 4 C. Chappert, H. Bernas and J. Ferré, Science 280, 1919 (1998).

Helium Ion Microscopy for Reduced Spin Orbit Torque Switching Currents

Recently ferromagnets with antisymmetric exchange (e.g. DMI) interactions have been actively investigated, in part because of the nonreciprocal propagation of spin waves where the frequency for positive and negative wavevectors, i.e. +k or -k, is not the same. This occurs because the DMI interaction leads to an effective field which is proportional to the wavevector k. In contrast, we study a system without DMI, but where the exchange interaction varies linearly as a function of position as shown in Fig. 1. Such a structure could be created by nonuniform lateral doping of Cu into Permalloy for example. [1] We also find an effective field which is linear in k, but the directions of the effective field are different from those found in the DMI systems. Using a simple one-dimensional model and a set of coupled Landau-Lifshitz equations, we set the exchange on the right side to be the value for iron, and it is decreased linearly by a factor of three at the left side. A field of 100 mT is applied perpendicular to the chain. The length of the system is 1 micron, but larger lengths give similar results. We demonstrate a number of interesting features: (1) The eigenstates are strongly asymmetric and can be localized on one side of the sample or the other [2]; (2) Depending on the frequency of excitation, there can be a huge asymmetry in propagation amplitudes for waves going in opposite directions as seen in Fig. 2, and (3) If a wave is excited at the center of a sample, there is a large asymmetry in propagation speed for waves travelling in different directions, where waves travelling in the region where the exchange is larger propagate at a higher speed than waves travelling where the exchange is smaller. We compare our results with analytic calculations, with reasonable agreement. We discuss the potential for applications such as isolators at the end.References: [1] N. Sorensen, R. E. Camley, and Z. Celinski, J. Magn and Magn. Mat. Vol. 477, p 344 (2019) [2] K L Livesey, D C Crew, R L Stamps, Phys. Rev. B Vol. 73, p. 184432 (2006)

Nonreciprocal Behavior in Ferromagnets with Spatially Varying Exchange

Spin waves (or magnons) in a micrometer-sized disk magnetized in the vortex state offer an ideal playground to investigate nonlinear magnetization dynamics. In the past, we demonstrated that the radial spin waves in a vortex, once excited above their instability threshold decay into secondary azimuthal modes due to highly efficient spontaneous three-magnon splitting in a rich variety of scattering channels [1]. Here, we present a combined numerical, theoretical and experimental study on nonlocal stimulated splitting in a magnetic vortex disk. We show that three-magnon splitting can be triggered below the threshold of spontaneous splitting by coupling the magnetic vortex to magnons propagating in an adjacent waveguide. Furthermore, using nonlinear spin-wave theory and time-resolved Brillouin-light-scattering experiments we demonstrate that stimulated scattering can be used to manipulate the time scales of nonlinear magnetization dynamics. We believe that the possibility to actively control three-magnon splitting in confined magnetic elements could provide a way to use magnon-based nonlinear networks as hardware e.g. for neuromorphic computing. Financial support by the Deutsche Forschungsgemeinschaft within programmes SCHU 2922/1-1 and KA 5069/1-1 is gratefully acknowledged.References: [1] K. Schultheiss, et al. PRL 122, 097202 (2019) [2] L. Körber, et al. arXiv:2005.12663 (submitted)

Nonlocal stimulation of three-magnon splitting in a magnetic vortex

Spin waves can be excited by a radio-frequency (rf) real magnetic field or an effective one generated e.g. by a surface acoustic wave (SAW) using magneto-elasticity [1,2]. Thanks to their low attenuation, SAWs in the GHz frequency range are an ideal tool to address remotely magnetic structures and generate or actuate on spin waves quasi-resonantly, which could be implemented in magnonic devices. Although the dynamic strain created by the SAW remains weak (10-5-10-3), non-linear magnetization dynamics is acoustically induced even in moderately magnetostrictive ferromagnetic layers. In order to become of technological interest these non-linearities must be carefully characterized and modeled. Using a time- and spatially-resolved magneto-optical Kerr setup with laser detection synchronized to the SAW rf bursts [3], we evidence clear non-linear effects (frequency and wavevector doubling: f/2f and k/2k components, respectively) in the magnetization dynamics of a GaMnAs ferromagnetic layer [4]. Tuning the spin-wave frequency close to the SAW frequency by magnetic field and temperature the resonance behavior of both the f and 2f dynamical components are obtained. The dependence on these components on the strain amplitude reveals two regimes. In the low-strain regime the f (2f) component has a linear (quadratic) behavior with the SAW amplitude. We show that this regime is well accounted for by an all-analytical perturbative model of two coupled parametric oscillators [5] with SAW-dependent frequency, damping, coupling and force terms while the intrinsic magnetic non-linearities of the Landau-Lifschitz-Gilbert equation can be neglected. With increasing SAW amplitude, the f-component becomes sublinear and the peak of the SAW-induced ferromagnetic resonance curve shifts to lower magnetic field, which are signatures of the rising importance of intrinsic magnetic nonlinearities as shown by our numerical simulations. We thus reach a comprehensive description of the acoustically-driven magnetization dynamics, enabling further development of this magnon-phonon coupling.References: [1] L. Dreher, M. Weiler, M. Pernpeintner et al., Phys. Rev. B 86, 134415 (2012). [2] L. Thevenard, C. Gourdon et al., Phys. Rev. B 90, 094401 (2014). [3] P. Kuszewski, J.-Y. Duquesne, L. Becerra et. al., Phys. Rev. Appl. 10, 034036 (2018). [4] M. Kraimia, P. Kuszewski, J.-Y. Duquesne et al., Phys. Rev. B 101, 144425 (2020). [5] C. L. Chang, A. M. Lomonosov, J. Janusonis et al., Phys. Rev. B 95, 060409 (2017).

Non-linearities Induced by Surface Acoustic Waves in Magnetization Dynamics

Optical frequency combs are powerful tools used for synchronization, stabilization and frequency conversion in both fundamental science and technical applications. In this work, we present experimental observations on the generation of a spin wave frequency comb in a low damping Co25Fe75 conduit measured using Brillouin light scattering microscopy. By driving the magnetization to large precession angles, nonlinear interactions such as four magnon scattering can be observed. When applying two RF signals with independently tunable frequencies and amplitudes to our microstructure, we can actively control the final states that will be populated by these scattering processes. Our results show the generation of a frequency comb, consisting of several spin waves with adjustable frequency spacing and amplitude. We demonstrate that the known effect of frequency mixing for k=0 modes [1] can be extended towards propagating spin waves. This enables simultaneous information transport and processing. This behaviour is studied for different sample geometries, which allow mixing of co-propagating as well as counter-propagating spin waves. Our observations are in qualitative agreement with micro magnetic simulations. The presented data encourage a deeper understanding of the interaction of propagating spin waves in the nonlinear regime and propose utilization of spin wave frequency combs as broadband tunable clocks for information processing. The authors acknowledge financial support from the Deutsche Forschungsgemeinschaft within programs SCHU 2922/1-1, WE5386/4-1 and WE5386/5-1. K. S. acknowledges funding within the Helmholtz Postdoc Programme.References: [1] Marsh, J., & Camley, R. E., Physical Review B - Condensed Matter and Materials Physics, 86(22), 224405 (2012)

Generation and tuning of a spin wave frequency comb

Recently, the formation of a magnon Bose-Einstein Condensate (BEC) triggered by the rapid cooling of magnonic nano-structures was reported [1]. A rapid decrease in the phonon temperature achieved by the application of DC pulses to a nano-sized YIG/Pt sample leads to a non-equilibrium between the phononic and the magnonic system. This results in a redistribution of magnons to the lowest frequencies of the spectrum. Here we report on the application of such a non-equilibrium, showing the possibiltiy to amplify coherently excited spin waves. The structures under investigation (see Fig. 1) consist of a 34 nm thin and 2 µm broad YIG-waveguide. A 3 µm long area is covered with a 7 nm thin layer of platinum, and an antenna allows for the excitation of a propagating spin-wave packet. The magnetization dynamics is investigated using time-resolved micro-focussed Brillouin light scattering spectroscopy. After the applied DC pulse is switched off, a spin wave pulse excited by the antenna is propagating in the waveguide region below the Pt covered area during rapid cooling. Depending on the time-delay between the DC-pulse and the spin-wave package, an amplification of the propagating spin wave is observed (see Fig. 2). This research does not only show the applicability of the phenomenon of rapid cooling to compensate the intrinsic damping in spintronic devices [2], but also gives insight to new physics, namely the interaction of a prepared coherent state with the rapid cooling induced quantum state of the magnon BEC. This research has been supported by ERC StG 678309 MagnonCircuits, ERC ADG 694709 SuperMagnonics and DFU Grant DU 1427/2-1.References: [1] M. Schneider, T. Brächer, D. Breitbach, et. al., Bose-Einstein Condensation of Quasi-Particles by Rapid Cooling, Nat. Nanotechnol. 15, 457–461 (2020) [2] Q. Wang, M. Kewenig, M. Schneider, et. al., Realization of a nanoscale magnonic directional coupler for all-magnon circuits, arXiv:1905.12353

Amplification of Propagating Spin Waves by Rapid Cooling

Magnonic computing (MC) architectures based on spin waves are increasingly of interest for special-purpose computing applications [1]. MC offers advantages over conventional charge-based computing [2-5], including low power dissipation (magnon propagation does not require charge transfer), and incorporation of phase information in addition to amplitude, reducing the component count needed for certain logic operations [6]. One of the challenges in the realization of most MC concepts is that they require an efficient means for routing magnons in complex networks. In particular, a scalable, nonvolatile, and reconfigurable mechanism to do so is currently lacking [6,7]. Here we address this challenge by utilizing a Néel skyrmion as a programmable scattering center to route magnons. The skyrmion is stabilized by the interfacial Dzyaloshinskii-Moriya Interaction (DMI) and perpendicular magnetic anisotropy (PMA), which itself can be controlled by electric fields via the voltage-controlled magnetic anisotropy (VCMA) effect, making the magnon-skyrmion interaction tunable by voltage. We investigate the interaction of exchange spin waves with wavelength of 26 to 190 nm, with skyrmions having diameters from 9 to 74 nm. Our micromagnetic simulations show that the propagation, scattering angle, and energy transmission of spin waves can be effectively controlled by tuning the ratio of magnon wavelength to the skyrmion diameter, which depends strongly on PMA and DMI. Based on this approach, we propose a new skyrmionic magnon switch (SMS) device, which provides voltage-controlled routing of spin waves in a magnetic wire and can be applied to build basic logic circuits. We simulate the SMS performance using typical material parameters for thin ferromagnetic films supporting skyrmions, and assess the requirements for its experimental realization.References: [1]. Khalili P, Wang K L. IEEE Spectrum, Vol.52(7), p.30-56(2015) [2]. Wang, K.L. and P. Khalili Amiri, SPIN, Vol.02(02), p.1250009(2012) [3]. Khitun, A., D.E. Nikonov, and K.L. Wang, Journal of Applied Physics, Vol.106(12), p.123909(2009) [4]. Dutta, S., et al., Scientific Reports, Vol.5, p.9861(2015) [5]. Cherepov, S., et al., Applied Physics Letters, Vol.104(8), p.082403(2014) [6]. Shabadi, P., et al., SPIN, Vol.02(03), p.1240006(2012) [7]. Vogt, K., et al., Applied Physics Letters, Vol.101(4), p.042410(2012)

Investigation of spin wave - skyrmion interactions for magnonic information processing

The spin Seebeck effect (SSE) is defined as the generation of a pure spin current (Js) when a magnetised material is subjected to a temperature gradient .[1] To detect Js, a thin non-magnetic [NM] layer such as Pt, is deposited on top of the material of interest. This converts Js into an observable thermoelectric voltage (VSSE) by way of the Inverse Spin Hall Effect (ISHE). It is of interest for thermoelectric and spintronic applications where it could be used to harvest electricity, or produce a pure spin current, respectively. The spin Seebeck effect can be phonon or magnon driven, therefore investigating the thermomagnetic voltage VSSE as a function of temperature can enable separation of these contributions – particularly in non-insulating materials such as Fe3O4 which undergoes a semiconductor-insulator phase transition at approximately 120 K.[2],[3] We have developed a measurement of VSSE as a function of temperature using the heat flux method [4][5], which enables accurate measurement of thin film samples. We will show how this technique can be used to investigate subtle changes in the SSE as a function of temperature and correlate this with measurement of the magnon dispersion in single crystal Fe3O4 using time of flight (TOF) inelastic neutron scattering (INS). We find an upper limit of the magnon diffusion length (MDL) of 34 ± 7 nm determined from bulk INS (Figure 1). Corresponding SSE measurements of Fe3O4 thin films as a function of thickness indicate an MDL of 19 ± 2 nm, which does not change significantly between 300 and 50 K.[6] We also find that the low energy magnon modes are steeper than previously reported[7] and broaden with increasing temperature (Figure 2).References: [1] K. Uchida et al., Nature, 455, 778 (2008) [2] A. Caruana et al., Phys. Status Solidi: RRL, 10, 613-617 (2016) [3] E. J. W. Verwey, Nature, 144, 327 (1939) [4] A. Sola et al., Sci. Rep. 7 46752 (2017) [5] G. Venkat et al., arXiv:2003.07925, submitted to Rev. Sci. Instrum. [6] G. Venkat et al., arXiv:2001.03738, accepted to Phys. Rev. Mat. (2020) [7] R. J. McQueeney et al., Phys. Rev. B 73 174409 (2006)

Magnon Diffusion Lengths in Bulk and Thin Film Fe3O4 for Spin Seebeck Applications

The individual spins associated with nitrogen-vacancy (NV) centers in diamond can serve as exquisite nanoscale magnetic field sensors, enabling (among other things) the measurement of stray fields near YIG [1] and Py [2] films influenced by spin transfer torques. This presentation provides an overview of our latest efforts to (i) reliably fabricate high-quality Py/Pt nanowires on a single-crystal diamond substrate while maintaining the performance of NVs implanted 10's of nanometers below the surface, (ii) develop a Bayesian protocol for optimal estimation of NV spin relaxation, and (iii) estimate thermal time scales in these (and other) nanocircuits while calibrating the applied microwave current. Time permitting, I will also discuss preliminary measurements (microwave transport and NV magnetometry) of driven and thermally populated spin wave modes controlled by spin Hall torques.References: [1] C. Du, T. van der Sar, et al., Science, 357, 195-198 (2017) [2] A. Solyom, Z. Flansberry, et al., Nano Lett., 18, 6494-6499 (2018)

Sensing Stray Fields from Spin-Hall-Controlled Magnetic Nanowires with Nitrogen-Vacancy Centers in Diamond INVITED

Magnetic materials with perpendicular magnetic anisotropy, such as thin films based on CoFeB alloys, are gaining interest and have accelerated the development of high-density non-volatile memories. The requirement of high memory bandwidth for next-generation computing systems moved the attention to the development of devices that can combine storage and logic capabilities. The High Bandwidth Memory interface for 3D-stacks DRAM chips is just one example. Domain wall-based spintronic devices intrinsically combine both these requirements making them suitable both for non-volatile storage and computation. Among all the proposed logics, perpendicular nanomagnetic logic (pNML) takes advantage of magnetic dipole coupling to propagate and elaborate information. The materials explored in literature for its realization such as Co/Pt and Co/Ni were the technology drivers [1], but for power constraints and depinning fields, novel CoFeB/MgO layers are investigated for low power and high-density computing devices. Ta/CoFeB/MgO ultrathin films show significantly lower coercivities, even with high perpendicular anisotropy (PMA) [2], thus becoming very promising candidates for low power pNML devices. In this paper, we investigate different Ta/CoFeB/MgO stacks at the simulation and experimental level, to show their potential for the next generation of magnetic logic devices. The micromagnetic simulations are used to support the experiments. We focus, first, on the magnetostatic analysis of magnetic islands quantifying the stray field that can be achieved with different layout topologies. Then, at the experimental level, we measure the coercivity of films with different thicknesses, Ms from SQUID measurements to estimate the coupling strength achievable between neighboring magnetic islands and measure the domain wall speed on magnetic nanowires. Our results show that the achieved coupling is strong enough to realize logic computation with magnetic islands, moving a step forward in the direction of low power perpendicularly magnetized logic devices.References: [1] S. Breitkreutz et al., in IEEE Transactions on Magnetics, vol. 49, no. 7, pp. 4464-4467 (2013) [2] T Devolder et al. , Journal of Applied Physics, 113(20):203912, (2013).

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