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Assessment of local magnetization in 3D objects is indispensable to performance estimation of magnetic recording processes and electric power devices. It was shown that an elementary Stoner-Wohlfarth-like hysteresis operator may be constructed using two-node Hopfield neural network (HNN) having internal positive feedback [1]. The approach was further utilized to simulate vector hysteresis in arbitrary 2D geometries ([2, 3]). This paper presents an approach using which local magnetization in 3D objects exhibiting hysteresis may be assessed. It utilizes a four-node tetrahedron-shaped HNN (Fig. 1.a) with activation functions “f” constructed using a weighted superposition of a step and sigmoidal functions in accordance with the M-H curve squareness. Vector orientation of the activation function a neuron is assumed to be along the unit vector ev initiated from the tetrahedron center point to the vertex corresponding to that neuron (Fig. 1.b). Feedback kij between any two neurons is given by: Kij=kcopl (evi . evj), where kcopl is a constant identified by the material coercivity. Given an applied field H orientated along the unit vector eH, activation function outputs of the tetrahedron HNN implicitly settles in accordance with the minimum of the energy E: E=- ∑i= 1 to 4 (HeH . f evi + ½ ∑j=1 to 4, j≠i kij fi fj ). (1) Overall vector magnetization of the tetrahedron M eM is given by: M eM = ∑i = 1 to 4 fi evi . (2) Geometrical (shape) configuration of the tetrahedron affects the internal mutual node feedback factors and consequently the overall vector magnetization components. To demonstrate the applicability of the approach, an ellipsoid whose diameters were in the ratio of 2:1:1 was constructed using 120 tetrahedra. Main M-H curve of the material was assumed and corresponding activation function specifics and kcopl factor were consequently set (Figs. 1 and 2). More theoretical and computational details are given in the paper.References: [1] A.A. Adly and S.K. Abd-El-Hafiz, Journal of Advanced Research, Vol. 4, p. 403 (2013). [2] A.A. Adly and S.K. Abd-El-Hafiz, Journal of the Applied Computational Electromagnetics Society, Vol. 31, p. 765 (2016). [3] A.A. Adly and S.K. Abd-El-Hafiz, Journal of Magnetism and Magnetic Materials, Vol. 434, p. 151 (2017).

MMM 2020

Utilizing Four-Node Tetrahedra-Shaped Hopfield Neural Network Configurations in the Local Magnetization Assessment of 3D Objects Exhibiting Hysteresis

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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poster

Chiral magnetic structures induced by Dzyaloshinskii-Moriya interaction (DMI) [1] have been proposed as the cornerstone of new technology applications such as high-density data storage devices or neuromorphic computing [2], due their room temperature stability and efficient current induced motion. Recent studies of the amplitude of magnetic satellites of a crystal Bragg peak by Zhang et al. [3] showed that x-ray resonant magnetic scattering (XRMS) is a powerful tool to access to the relevant topological parameters of these magnetic structures. In this work, we use small angle reflectivity XRMS to reveal directly the chiral properties of FM multilayers with tailored magnetic chiralities driven by spin-orbit-related effects at interfaces [4,5]. We show that it can straightforwardly and unambiguously determine the main characteristics of chiral magnetic distributions in perpendicularly magnetized multilayers [4]: its chiral nature, the quantitative winding sense (clockwise or counterclockwise), and its type, i.e. Néel (cycloidal) or Bloch (helical). Moreover we prove that this approach combined with micromagnetic simulations reveals hybrid chiral spin texture in multilayers [5]. Finally, we studied the in plane field dependence intensity of the dichroism and the appearance of second order diffraction peaks, usually forbidden on these systems. An asymmetric change of the intensity of the magnetic asymmetry lobes and a hysteretic behavior of these ones with the external field suggest a complex interplay between the hybrid domain wall state existing in these systems and DMI fields. European Union Grant FLAG-ERA SoGraph (ANR-15-GRFL-0005), French ANR grant TOPSKY (ANR-17-CE24-0025), DARPA TEE program grant (MIPR#HR0011831554) and EU grant SKYTOP (H2020 FET Proactive 824123) are acknowledged for their financial support.References: References [1] I. Dzyaloshinskii, J. of Phys. and Chem. of Solids 4, 241 (1958), T. Moriya, Phys. Rev. 120, 91 (1960) [2] A. Fert, N. Reyren and V. Cros, Nat. Rev. Mat. 2, 17031 (2017) [3] S. L. Zhang, G. van der Laan, and T. Hesjedal, Nat. Commun. 8, 14619 (2017) [4] J.-Y. Chauleau et al., Phys. Rev. Lett. 120, 037202 (2018) [5] W. Legrand et al., Sci. Adv. 4, eaat45 (2018)

Field dependence chirality in ferromagnetic multilayers probed by dichroism in x-ray resonant magnetic scattering

Complex oxides offer possibilities to engineer and control spin textures via their many degrees of freedom and sensitivity to epitaxial strain, and have been proposed for use in energy efficient magneto-electric spin-orbit logic architectures.1 Additionally, recent interest in antiferromagnetic spintronics has surged due to the possibility of obtaining ultrafast magnetization dynamics with no stray field2. However, lack of stray field makes imaging of antiferromagnetic domain structure difficult though conventional magnetic imaging techniques. This talk will discuss the use of X-ray photoemission electron microscopy (PEEM) with both x-ray linear and circular dichroism to spatially and chemically resolve the shape and voltage-controlled ferroic order in heterostructures containing antiferromagnetic (AFM), ferroelectric(FE), and ferromagnetic (FM) layers of including (La,Sr)FeO33,4, Ni/CoFeB/PMN-PT5, and CoFe/(La,Bi)FeO36. Dimensional confinement can be used to tailor the easy axis spin orientation in (La,Sr)FeO3, as edge-induced anisotropy in microstructures can induce nearly-single domain structures in wires,3 and in the limit of few unit-cell thick layers, the antiferromagnetic spin axis lies in the plane of the film in contrast to thicker layers where the spin axis cants out of plane.4 By changing the ratio of Ni to CoFeB in artificial multiferroic heterostructures, the ground state domain configuration and magneto-electric coupling behavior are strongly modified, and this coupling can be visualized in situ with PEEM.5 Furthermore, we show that the energy barrier for magneto-electric switching energy density can be scaled through careful engineering in a BiFeO3-based system towards 10 µJ cm-2 at a switching field of 200 mV.6 Thus, coupling at these interfaces allows for mutual control of the domain structure via a variety of pathways, including shape anisotropy and magneto-electric interactions, and thus offers additional degrees of freedom towards low-energy AFM-based spintronics.References: 1. S. Manipatruni et al, Nature 565 35 (2018). 2. V. Baltz et al, Rev. Mod. Phys 90, 015005 (2018). 3. A. D. Bang, RVC et al, Appl. Phys. Lett 115 112403 (2019). 4. M.S. Lee, RVC et al, J. Appl. Phys 127, 203901 (2020). 5. Z. Xiao, RVC et al, ACS Appl. Mat. 12, 6752 (2020). 6. B. Prasad, RVC et al, Adv. Mat. 2001943 (2020).

Imaging Shape and Voltage Control of Spin Textures in Ferroic Heterostructures

Although it is well documented that the vortex core in a micromagnet can switch polarisation in response to magnetic field pulses[1], the temperature dependence of this process has not yet been addressed by experiments. Using scanning transmission x-ray microscopy, we investigate the magnetic vortex dynamics in a La0.7Sr0.3MnO3 microplatelet at temperatures ranging from 150 K up to TC at 350 K[2]. The time-resolved images reveal qualitatively different dynamic regimes as function of temperature and applied field, as the relative strengths of the micromagnetic energy terms strongly vary over this temperature range. By explicitly accounting for the temperature dependence of the magnetic parameters in our micromagnetic simulations[3], we found an excellent agreement with the experiments over the full measurement range. In line with previous models, the simulations reveal that the vortex core switches polarisation when it reaches a critical velocity[4] that mainly depends on the strength of the exchange interaction. It is therefore strongly temperature dependent, thus explaining our observation of the different dynamical regimesReferences: [1] B. Van Waeyenberge, A. Puzic, H. Stoll, et al., Nature Vol. 444, p.461 (2006). [2] E. Digernes, J. Leliaert, M. Weigand, et al., submitted manuscript [3] A. Vansteenkiste, J. Leliaert, M. Dvornik, et al., AIP Adv. Vol.4, p.107133 (2014). [4] K. Y. Guslienko, K.-S. Lee, and S.-K. Kim, Phys. Rev. Lett. Vol. 100, p. 027203 (2008)

Direct Observation of Temperature Dependent Vortex Dynamics in a La0.7Sr0.3MnO3 Micromagnet

Fluorescent defects in diamond present a versatile platform for compact quantum magnetometers, [1] and optical fiber technology enables in situ laser excitation and signal collection from these sensors. [2-4] The advent of microstructured fibers has allowed novel analytical techniques employing differential magnetic field measurements, common-mode noise rejection, [5] and high-resolution magnetic field imaging [6] to be used in environments without easy optical access. In this work, we demonstrate a microresolution stereomagnetometer probe by attaching a high nitrogen–vacancy (NV) concentration microdiamond to the tip of a dual-core photonic-crystal fiber (PCF) and simultaneously interrogate two regions of the diamond separated by the 6 μm core-to-core distance (Fig. 1 (a)). This probe was then used to characterize the magnetic field emanating from a 40 μm diameter current carrying wire in the presence of a large static bias solenoid by extracting the center wavelength of each peak in the optically detected magnetic resonance (ODMR) spectrum of the diamond fluorescence recollected by the PCF. [5] The magnitude and direction of the inhomogeneous wire field source was discriminated from a homogeneous background bias field with a magnitude more than 1000 fold larger than the localized wire field (Fig. 1 (b)). This stereomagnetometer was found to have a shot-noise limited sensitivity of 2 nT/√Hz and a 6 μm spatial resolution while imaging the vector field around the wire. [5]References: [1] L. Bougas, A. Wilzewski, Y. Dumeige, et al., Micromachines 9 (6), 276 (2018) [2] Y. Ruan, D. A. Simpson, J. Jeske, et al., Scientific Reports 8 (1), 1268 (2018) [3] S. M. Blakley, I. V. Fedotov, S. Ya. Kilin, et al., Optics Letters 40, 3727-3730 (2015) [4] S. M. Blakley, I. V. Fedotov, L. V. Amitonova, et al., Optics Letters 41, 2057-2060 (2016) [5] S. M. Blakley, I. V. Fedotov, J. Becker, et al., Applied Physics Letters 113 (1), 011112 (2018) [6] I. V. Fedotov, S. M. Blakley, E. E. Serebryannikov, et al., Optics Letters 41, 472-475 (2016)

Fiber-Optic Magnetic Vector Gradient Imaging with Fluorescent Defects in Diamond

Increasingly impressive demonstrations of voltage-controlled magnetism have been achieved recently, highlighting the potential for low-power data processing and storage devices. Magnetoionic approaches appear particularly promising, electrolyte- and ionic-conductor-based devices being shown capable of on/off voltage control of ferromagnetism and voltage tuning of magnetic anisotropy [1-3]. A clear limitation, however, is that such demonstrations involve either electrically tuning a known ferromagnet, or electrically inducing ferromagnetism from another magnetic state, e.g., antiferromagnetic. In this work, we report proof-of-principle that ferromagnetism can be voltage-induced even from a diamagnetic, i.e., zero-spin state, suggesting that useful magnetic phases could be electrically-induced in “non-magnetic” materials [4]. We use ionic-liquid-gated diamagnetic semiconducting FeS2 as a model system, showing that as little as +1 V gate bias induces a highly reversible insulator-metal transition, driven by electrostatic inversion of the surface from a p-type semiconductor to an n-type metal. Anomalous Hall effect measurements then reveal the onset of robust electrically-tunable surface ferromagnetism at Curie temperatures up to 25 K, with intriguing high temperature spin correlations. Density-functional-theory-based modelling explains the induced magnetism in terms of Stoner-type ferromagnetism induced solely via filling of a narrow Fe eg band. Work supported primarily by the NSF MRSEC.References: [1] Navarro-Senent, Quintana, Menendez, Pellicer, Sort, APL Mater. 7, 030701 (2019) [2] Molinari, Hahn, Kruk, Adv. Mater. 31, 1806662 (2019) [3] Leighton, Nat. Mater. 18, 13, (2019) [4] Walter, Voigt, Day-Roberts, Heltemes, Fernandes, Birol and Leighton, in press (2020)

Voltage-induced Ferromagnetism in Diamagnetic FeS2

Manipulating magnetization of ferromagnetic material with small amount of energy is of contemporary interest in field of Spintronics.There are various ways in which manipulation of magnetization can be done such as,1) Using spin polarized current [1] 2) Electric field controlled [2] 3) SAW based technique [3],4) Heat current controlled [4],among all currently available techniques Electric Field controlled is ultra-low power [5].All the effects in nature also have a reciprocal effect based on the Onsager reciprocity e.g. the inverse of spin transfer torque effect viz. spin pumping can be used for converting magnetization oscillations into spin current.Here we have experimentally demonstrated the Inverse of VCMA effect by which magnetization oscillations produce charge voltage. To demonstrate the inverse-VCMA effect [6],we fabricated a two port device as shown schematically in Fig.1 We deposited stack on Si/SiO2 substrate: Ta(5)/Ru(5)/Ta(5)/Ru(5)/Ta(9)/COFEB(1)/CoFe(0.2)/Ir(0.1)/MgO(2.4)/Ta(5)/Ru(7). We then fabricated tunnel junctions of dimension 3umx80um with contacts. A CPW was fabricated on the top,which was electrically insulated from the bottom pillar. The patterning of the device was done by e-beam lithography and Ar-ion milling. We measured the S-parameters of the device using a (VNA). The magnetic field was swept along different directions by varying θ and φ. The measurement of S21 signal corresponds to the direct VCMA effect.Applying signal to port 1 oscillates magnetization of FM by the VCMA effect and signal is induced in the port 2 by induction.The measurement of S12 corresponds to the inverse of VCMA effect as shown in Fig.2. On applying oscillating voltage to port 2,creates oscillating field on the FM.The oscillation of the magnetization of the FM induces voltage in the port 1 by the inverse-VCMA effect.Both the S12 & S21 signal are largest at the FMR frequency.We observed that the Onsager reciprocity relation S12(B)=S21(-B) is satisfied.The angular dependence of the S-parameters confirmed that the signals arise from inverse VCMA effect. We would like to thank IIT Bombay NanoFabrication facility for supportReferences: [1] J.C.Slonczewski JMMM volume 159, Issues 1–2 (1996). [2] T. Maruyama, et.al., Nat. Nanotechnology. 2008, 406(2009). [3] Swapnil Bhuktare et.al., Appl. Phys.Lett. 114, 052402 (2019). [4] Arnab Bose et.al, PhysRevB.98.184412 (2018). [5] T. Nozaki et.al., Nat. Physics. 2298 (2012). [6] Ambika Shanker Shukla et.al. Science Advances (accepted) 2020.

Inverse of Voltage Controlled Magnetic Anisotropy (VCMA) effect

Recently, we experimentally demonstrated that the nucleation and annihilation of µm-sized skyrmions in Pt/Co/AlOx trilayers can be controlled by tuning the perpendicular magnetic anisotropy with electric field gating [1]. Here, we show our present efforts to extend this concept to smaller skyrmions, down to 50 nm lateral size. Two trilayer systems, in which sub-100 nm skyrmions were observed at room temperature, were studied: Pt/Co/MgO [2] and Pt/Co/TbOx. The stacks were patterned by electron beam lithography and ion beam etching into stripes (1 – 50 µm width) then covered with a 10 nm thick ZrO2 dielectric layer and a 6 nm thick Pt top electrode to form capacitor-like structures, Fig (a). Using Magnetic Force Microscopy, Fig (b-c), we show that in both stacks, starting from a stable skyrmion network, a positive electric field (EF) leads to the increase of the PMA and to the annihilation of the skyrmion phase. We attribute this to the EF-induced migration of oxygen towards the top Co interface. This result is confirmed by the variation of the hysteresis loops taken with polar Magneto-Optical Kerr Effect, Fig (d). This new state persists after removing the EF i.e. EF-gating leads to a non-volatile effect. In the Pt/Co/MgO trilayer, the application of a negative EF shows no effect on the magnetic anisotropy, preventing us to renucleate the skyrmions. This irreversible process is probably due to the stabilization of the stochiometric MgO phase induced by oxygen ion migration towards the Co/MgO interface when a positive gating is applied. On the contrary, for Pt/Co/TbOx trilayers, the application of a negative EF triggered the oxygen ion migration away from the top Co interface. This allows us to tune reversibly the magnetic anisotropy, and therefore to reproducibly nucleate and annihilate 50 nm size skyrmions. This is an easily integrable and energetically efficient solution that might ease the use of magnetic skyrmions as information carriers in future spintronic devices.References: [1] Schott et al., Nano Lett 17, 3006 (2017) [2] Boulle et al., Nat Nano 11, 449 (2016)

Tuning magnetic anisotropy and skyrmion stability with electric field

Magneto-ionics has emerged as a promising approach to manipulate magnetic properties in magnetic heterostructures, energy-efficiently. While this has led to exciting magneto-ionically controlled functionalities in primarily oxygen-based systems, such as perpendicular magnetic anisotropy, magnetization, exchange interaction, and superconductivity, there are challenges in oxygen-based magneto-ionics, in terms of switching speed and reversibility [1-3]. There have been keen interests in exploring other ionic systems which may overcome these issues [4]. Here we explore the use of α-Co(OH)2 for hydroxide-based magneto-ionics, which undergoes a reversible paramagnet to ferromagnet transition under electrolyte gating. The α-Co(OH)2 films are grown by electrochemical methods. Grazing incidence x-ray diffraction (XRD) confirmed the formation of α-Co(OH)2 without traces of any other hydroxide or oxide phase. After voltage application in an electrolyte-gating configuration, a ferromagnetic signal can be induced in the paramagnetic as-grown sample under negative voltage due to the reduction of α-Co(OH)2 into metallic Co (Fig. 1). Magneto-electric experiments revealed that the turn-on voltage, i.e. minimum voltage needed to generate the ferromagnetic response, is as low as -2V, among the lowest turns-on voltages reported for propylene carbonate gated experiments [5]. Its paramagnetic character can be fully recovered by reversing the applied voltage polarity. This reversible transition is due to the ionic diffusion of hydroxyl groups into the employed electrolyte. By tuning the voltage magnitude and sample area we demonstrate that the speed of the induced ionic effect can be drastically boosted, up to a factor 60 at -8V (Fig. 2). This work opens new avenues in exploring the benefits of layered materials and hydroxyl groups towards fast magneto-ionic processes. This work has been supported in part by the SRC/NIST SMART Center, the NSF (ECCS-1933527), NSF-REU (DMR-1659532) and NSF-MRI (DMR-1828420).References: [1] U. Bauer et al., Nat. Mater., 14, 174 (2015). [2] D. A. Gilbert et al., Nat Commun 7, 12264, (2016). [3] P. D. Murray et al., ACS Appl. Mater. Interfaces 12, 4741 (2020). [4] A. J. Tan et al., Nat. Mater. 18, 35 (2019). [5] C. Navarro-Senent et al., APL Mater. 7, 030701 (2019).

Hydroxide-based Magneto-Ionics: paramagnetic-to-ferromagnetic transition in electrolyte-gated α-Co(OH)2

Unlike the common expectation that superconducting spintronics and long-range triplet (LRT) proximity effects require complex ferromagnetic multilayers, relying on noncollinear/spiral magnetization or half-metals, we propose a new platform compatible with commercial spintronics. Recently, we have experimentally demonstrated that interfacial spin-orbit coupling (SOC) and symmetry-filtering in all-epitaxial V/MgO/Fe junctions, cooled below the critical temperature of vanadium, provide a thousand-fold increase in tunneling anisotropic magnetoresistance, supporting the LRT formation [1]. Here we report the converse effect: transformation of the magnetocrystalline anisotropy of a Fe(001) layer driven by the superconductivity of an underlying V layer through a spin-orbit coupled MgO interface [2]. We attribute this to an additional contribution to the free energy of the ferromagnet arising from the controlled generation of triplet Cooper pairs, which depends on the relative angle between the exchange field of the ferromagnet and the spin-orbit field. This observation offers the ability to fundamentally tune magnetic anisotropies using superconductivity - a key step in designing future cryogenic magnetic memories.References: [1] I. Martínez et al; Phys. Rev. Appl. 13, 014030 (2020). [2] C. González-Ruano et al; accepted for publication as Rapid Communication in Phys. Rev. B, Cond Mat. ArXiv https://arxiv.org/abs/2006.02118

Superconductivity-induced change in magnetic anisotropy in epitaxial ferromagnet-superconductor hybrids with spin-orbit interaction

Atomistic simulations play a huge part in our understanding of static and dynamic magnetic states in current state-of-the-art research. Motivated by the recent interest in magnetic Heusler alloys, a model based on the LLG equation was developed for investigating magnetisation dynamics in near-compensated ferrimagnets. These materials, including Mn2RuxGa (MRG), are predicted and often experimentally verified to possess key properties, including THz resonance frequencies and high spin-polarisation at the Fermi level [1, 2]. Another hot topic of study are magnetic skyrmions, topological defects in the spin texture of non-centrosymmetric crystals with chiral interactions. There is much interest in the dynamics of skyrmions, with fast skyrmionic magnetic storage one potential application [3, 4]. In this work, the stability of skyrmion states in a 1D ferrimagnet was investigated as a function of material parameters such as anisotropy and Dzyaloshinskii-Moriya interaction (DMI), see Fig. 1. Additionally, skyrmion propagation speed and breathing mode frequency [5] are investigated under the influence of an external magnetic field and/or spin-polarised current. The model has also been applied as a computationally efficient method to obtain magnon frequency dispersions. By applying a perturbing field pulse and taking the Fourier Transform of the resulting dynamics, the entire magnon dispersion can be obtained. A simple example for a 1D ferrimagnetic chain with Heisenberg exchange, DMI and uniaxial anisotropy is shown in Fig. 2. MRG shows compensation of its ferrimagnetic moment at room temperature and as a result is predicted to support sustained spin oscillations in the THz region [6]. Our simple model, once adjusted to accommodate the symmetry and dimensionality of the real material, will represent an efficient method to theoretically investigate the existence of such oscillations and of potential chiral ground states.References: [1] H. Van Leuken and R.A. De Groot, Physical review letters., Vol. 74(7), p.1171 (1995) [2] S. Lenne et al., arXiv preprint arXiv:1903.04432. (2019) [3] W. Legrand et al., Nano letters., Vol. 17(4), pp.2703-2712 (2017) [4] A. Fert, N. Reyren and V. Cros, Nature Reviews Materials., Vol. 2(7), p.17031 (2017) [5] Y. Onose et al., Physical review letters., Vol. 109(3), p.037603 (2012) [6] R. E. Troncoso et al., Physical Review B., Vol. 99(5), p.054433 (2019)

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Utilizing Four-Node Tetrahedra-Shaped Hopfield Neural Network Configurations in the Local Magnetization Assessment of 3D Objects Exhibiting Hysteresis

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Field dependence chirality in ferromagnetic multilayers probed by dichroism in x-ray resonant magnetic scattering

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