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We investigate the physical origin of nonlinear damping due to mode coupling between several auto-oscillatory modes driven by spin-orbit torque in constricted Py/Pt heterostructures by examining the dependence of auto-oscillation on temperature and applied field angle. We observe a transition in the nonlinear damping of the auto-oscillation modes extracted from the total oscillation power as a function of drive current, which coincides with the onset of power redistribution amongst several modes and the crossover to linewidth broadening of all individual modes, as opposed to linewidth narrowing expected from the larger anti-damping current. This indicates the activation of a new relaxation process by nonlinear magnon-magnon scattering within the modes. We also find that both nonlinear damping and threshold current in the mode interaction damping regime at high drive current after transition are temperature independent, suggesting that the mode coupling occurs dominantly through a non-thermal magnon scattering process via a dipole or exchange interaction rather than thermally excited magnon-mediated scattering.

MMM 2020

Origin of Nonlinear Damping due to Mode Coupling in Auto-Oscillatory Modes Strongly Driven by Spin-Orbit Torque

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

In recent years, a great deal of interest has been attracted by the physics of designer materials called `Artificial Spin Ice' (ASI) systems [1-2]. One of the most promising aspects of ASI system is their high tunability of the array geometry, which has opened new avenues [2]. While most efforts have focused on study of array of artificial spin ice structures [3-4], little work has been done on understanding the switching behavior of individual nanoislands coupled by dipolar interactions in ASI systems [5-6]. These strong shape anisotropic nanomagnets exhibits Ising spin-like behavior and may get affected by the unintentional defects introduced during fabrication. Thus, it is essential to investigate how such defects modify the local magnetic behavior which in turn may play a significant role in the overall switching behavior of the corresponding nanostructures [7]. In this work, we have investigated the magnetization reversal of a special geometry of dipolar coupled system of Ti/Ni80Fe20/Al arranged in double square-ring geometry, which represents the building block of square ASI system. We employed two-dimensional electron gas (2-DEG) based micro-Hall magnetometry technique to measure the nanoislands’ stray field and study their switching behavior. Fig. 1(a) shows the SEM image of fabricated structure on top of GaAs/AlGaAs based Hall sensors. The changes in the Hall voltage reflect the changes in the magnetic state of the dipolarly coupled nanomagnets. We observe that although magnetic force microscopy images exhibit single domain like magnetic states for the nanostructures (shown in Fig. 1(b)), their reversal processes undergo complex behavior. The results suggest that local irregularities may play critical role in defining the exact micromagnetic state of the otherwise single domain nanomagnets leading to complex switching behavior, which is discussed in this work.References: [1] R. Wang, et al., Nature 439, 303 (2006). [2] N. Rougemaille and B. Canals, Eur. Phys. J. B 92, 62 (2019). [3] A. Farhan, et al., Science Adv. 5, eaav6380 (2019). [4] E. Östman, et al., Nature Phys. 14, 375 (2018). [5] F. Montoncello, et al., Phys. Rev. B 97, 014421 (2018). [6] N. Keswani and P. Das, J. Appl. Phys. 126, 214304 (2019). [7] N. Keswani, et al., Appl. Phys. Lett. 116, 102401 (2020).

Magnetization Reversal Studies of Building Blocks of Square Artificial Spin Ice Probed by 2-DEG Based Micro-Hall Magnetometry

Magnetic charge propagation1-3 in the bulk frustrated materials known as spin-ice has yielded a paradigm shift in science, allowing the symmetry between electricity and magnetism to be studied in condensed matter systems. Artificial spin-ice materials4, arrays of frustrated nanostructured magnetic islands, have been produced in a range of sophisticated geometries5. These systems provide a powerful insight into the physics of frustration but do not capture the exact 3D geometry of the spin-ice lattice, meaning it is not possible to explore monopole transport upon the surface, where the lattice symmetry is broken. In this talk we will detail the direct imaging of magnetic charge propagation upon a 3D nanostructured diamond-bond lattice (Fig 1), capturing the geometry of bulk systems. Vastly different magnetic charge dynamics are observed along two principle lattice directions. Applying a field along the [110] direction leads to a small number of distant magnetic charges within the measured area. In contrast, a field along [-110] leads to a larger number of closely spaced monopole-antimonopole pairs. We will discuss these results by referring to detailed Monte-Carlo simulations and calculations which illuminate the importance of the surface coordination in determining the monopole effective chemical potential.References: 1. Castelnovo, C., Moessner, R. & Sondhi, Nature 451, 42-45 (2008) 2. Jaubert, L. D. C. & Holdsworth, P. C. W., Nat Phys 5, 258-261 (2009) 3. Morris, D. et al., Science 326, 411-414 (2009) 4. Wang, R. F. et al., Nature 446, 102-102 (2007) 5. S. H. Skjærvø, C. M., R. L. Stamps and L.J. Heyderman, Nature Physics Reviews 2, 13-28 (2020)

Magnetic Charge Propagation upon a 3D Artificial Spin-ice

Iron-phtalocyanines (FePc) adsorbed onto a Ag(110) substrate self-assemble into different monolayer phases going from rectangular to different oblique phases, with increasing molecular density. We have investigated the oxygen uptake capability of the different phases and their associated magneto-structural changes [1,2,3]. Our study combines scanning tunneling microscopy and spectroscopy (STM/STS), X-ray magnetic circular dichroism (XMCD), and density functional theory (DFT) calculations. STM measurements reveal that the oxygenation reaction of the FePc/Ag(110) generally involves a displacement and a rotation of the molecules, which affects the electronic state of the Fe centers. The oxygen intercalation between FePc and the substrate is greatly obstructed by the steric hindrance in the high-density phases, to the point that a fraction of oblique phase molecules cannot change their position after oxydizing. Depending on the oxidation state and adsorption geometry, the STS spectra evidence clear differences in the Fe local density of states, which are mirrored in the XAS and XMCD experiments. Particularly, XMCD spectra of the oxidized phases reflect the distribution of FePc species (non-oxygenated, oxygenated-rotated and oxygenated-unrotated) in the different cases. Sum rule analysis yields the effective spin and orbital magnetic moments of Fe in the different FePc species. Upon oxygenation, the magnetic moment of FePc molecules increases about an order of magnitude, reaching mTOT ~ 2.2 µB per Fe atom.References: 1: F. Sedona, M. Di Marino, D. Forrer et al., Nature Materials 11, 970 (2012) 2: J. Bartolome, F. Bartolome, F. Sedona, et al., J. Phys. Chem. C 119, 12488 (2015) 3: E. Bartolomé, J. Bartolome, F. Bartolome, et al., J. Phys. Chem. C 124, 13993 (2020)

Structure and Magnetism of FePc/Ag(110) Monolayer Phases under Oxygen Dosing

Interest in micro robotics and swimmers has showed a significant increase lately, especially magnetic micro swimmers. In this study, using an extrusion-based 3D printer, magnetic micro swimmers were synthesized, drop-wise, with different types of incorporated magnetic materials; Fe micro flakes and nanoparticles, and Nd-Fe-B micro flakes. Particles were encapsulated in alginate matrix. Next, these micro swimmers were stirred along a path via the magnetic gradient created by an electromagnetic system. The base of the electromagnetic system was designed using a CAD computer program and 3d printed. Consisting of four independent solenoids, each two controlling the movement on an axis, the system was designed to move the micro swimmers in a certain path as shown in Figure 1. The solenoids were controlled by Arduino microcontroller board. The electrical current applied to the electromagnetic device in all the trials was 2 amperes which generates a magnetic field in between 100 to 485 Gauss throughout the experiment area (Figure 1 B); as a result a magnetic gradient from the center to the pole of the solenoid was established. The magnetic and chemical behavior of these materials were compared based on their magnetic responsiveness and 3d printability. The comparison showed the high responsiveness of iron flakes relatively to the other materials as shown in Figure 2. Applications of magnetic micro swimmers include biomedical robotics and drug delivery.References: This work was supported by BAP.2019-03.11

Synthesis of Magneto-Responsive Micro Swimmers for Biomedical Applications

Additive manufacturing via 3-D printing technologies have become a frontier in materials research, including its application in the development and recycling of permanent magnets[1,2]. In-situ alignment during 3D printing of magnetic materials has opened new horizons for manufacturing of complex permanent magnets[3,4]. Based on our former work[3], we will present a multiphysics model that couples fluid dynamics and electromagnetic interactions, to predict the degree of alignment (DoA) of a polymer bonded magnet printed under applied field. We have developed a mathematical model which predicts the flow of magnetic particles in a viscous fluid through a nozzle under applied magnetic field. A particle-fluid interactive fluid flow simulation is performed to model the flow regime of molten bonded magnet. The interactions between the drag, inertial, and magnetophoretic forces are analyzed to predict the particle trajectory. Torque balance is performed between the drag torque, magnetic torque on particles from the applied field, and torque from particle-particle interactions. The torque balance is coupled with the flow simulation to predict the degree of rotation of magnetic particles during printing. Experimental validation of the DoA predictions (exp = 0.62 and theory = 0.634) was performed using 65vol.% NdFeB+SmFeN in Nylon12 3D printed samples with variable alignment field (Fig.1a). The model is parameterized to predict the impact design and operating parameters including alignment field, magnetic loading fraction, and particle size. The results demonstrate an increasing alignment field with higher loading fraction magnets (Fig.1b). This work is supported by the Critical Materials Institute (CMI), an Energy Innovation Hub funded by the U.S. Department of Energy (DOE), Office of Energy Efficiency and Renewable Energy, Advanced Manufacturing Office. Ames Laboratory is operated for the U.S. Department of Energy by Iowa State University of Science and Technology under Contract No. DE-AC02-07CH11358. Figure 1. a) DoA prediction for 65vol.% NdFeB+SmFeN in Nylon12 before and after printing with 0.15[T] field, and b) DoA vs. field for NdFeB+SmFeN in Nylon12 with different magnetic loading fractions.References: 1 C. Huber, C. Abert, F. Bruckner, M. Groenefeld, O. Muthsam, S. Schuschnigg, K. Sirak, R. Thanhoffer, I. Teliban, C. Vogler, R. Windl, and D. Suess, Appl. Phys. Lett. 109, 162401 (2016). 2 L. Li, B. Post, V. Kunc, A.M. Elliott, and M.P. Paranthaman, Scr. Mater. (2017). 3 A. Sarkar, M.A. Somashekara, M.P. Paranthaman, M. Kramer, C. Haase, and I.C. Nlebedim, Addit. Manuf. 34, 101289 (2020). 4 Y. Kim, H. Yuk, R. Zhao, S.A. Chester, and X. Zhao, Nature 558, 274 (2018).

Alignment of Magnetic Particles in Functionalized Magnetic 3D Printer

When a spin current is injected into an antiferromagnet, above a certain value of current, the Néel order precesses in a circular orbit about an axis oriented at an angle from the spin-polarization direction [1]. But below this value, for moderate values of damping, the motion evolves into chaos (aperiodic long-term behavior) for a small window of current, before settling down to equilibrium. We theoretically study the chaotic dynamics and emphasize its potential application in secure communication. Consider a uniaxial antiferromagnet whose easy axis is along z. Let the spin polarization make an angle ρ from the easy axis in the z-x plane. If at an instant, the Néel order n makes a polar angle θ from z and azimuthal angle φ from x, the equation of motion in the characteristic timescale of antiferromagnet for effective damping β and spin-current drive Γ is [1] θ″ + βθ′ - (φ′2 - 1)sin θ cos θ = -(Γ/2)sin φ sin ρ, φ″ + βφ′ + 2φ′θ′cot θ = (Γ/2)(cos ρ - cot θ cos φ sin ρ). The chaotic dynamics arises from the nonlinear structure of the flow in the four-dimensional phase space (θ, φ, θ′, φ′) from the initial condition (π/2, 0, 0, 0). For ρ = π/4 and β = 0.2 in specific, the steady-state behavior is static for Γ < 0.43, periodic for 0.43 < Γ < 0.44, chaotic for 0.44 < Γ < 0.5 and periodic for Γ > 0.5 as shown in Fig. 1. For other values of ρ and β, the chaos would occur for different values of Γ. The dynamics of Néel order in the antiferromagnet can reciprocally pump spin current into an adjacent conductor, proportional to the angular velocity ω = n x n′ shown in Fig. 2. This phenomenon may be exploited to detect and generate a chaotic electric signal at terahertz frequency, which may be used for communication via synchronized chaos. In this scheme, a louder chaos signal is used to mask the information-bearing signal and transmitted. The decryption utilizes the intended receiver’s ability to reproduce the chaos and subtract it from the mask.References: [1] A. Parthasarathy et al., arXiv:1911.00445 (2019).

Spin-torque-induced chaos in antiferromagnets

Magnetization dynamics induced by spin-polarized currents have enabled a new class of spin-torque nano-oscillators (STNOs) including frequency detectors. Frequency detection in vortex STNOs has been demonstrated using several different mechanisms that include the spin diode effect1, resonant core expulsion2,3 and frequency to resistance transduction4. The DC voltage output generated by an RF current injected in a vortex STNO has been shown to exceed the sensitivities of Schottky diodes5. In this work we propose the possibility of adding non-volatility to the functionalities associated with vortex STNOs and we demonstrate that the frequency detection channel can be changed upon fabrication by means of electrical signals. Figure 1(a) shows the stack used for the measured devices. The experiment starts with an initialization (INIT) step where an in-plane field (Hin) applied by a DC current passing through an integrated field line saturates the free layer. Finally, its removal leads to the vortex renucleation. After, an RF signal with a sweeping frequency is applied to the STNO while the DC voltage is monitored [Fig. 1(b)]. Figure 2 shows two spin diode results, where the difference relies on IDC applied to the STNO during INIT. After INIT, with IDC = +5mA (-5mA), the device operates at a gyrotropic frequency of 58.8MHz (60.2MHz). We discuss the relation of these two modes with the four possible combinations of polarity (out-of-plane vortex magnetization component) and chirality (in-plane vortex magnetization circulation). For Hin = IDC = 0, the different frequencies associated with two different states can only be caused by an intrinsic break of symmetry6 that we attribute to the stray magnetic field produced by an uncompensated SAF. In summary, we present a device that acts as a two-channel vortex-based STNO detector with a full electrical and non-volatile control of the selected channel and demonstrate that vortex STNOs can be used to implement programmable frequency RF detectors with potential interest for a wide range of applications.References: [1] Jenkins, A. S. et al., Appl. Phys. Lett. 105, 172403 (2014). [2] Jenkins, A. S. et al., Nat. Nanotechnol. 11, 360–364 (2016). [3] Menshawy, S. et al., AIP Adv. 7, 056608 (2017). [4] Jenkins, A. S. et al., Phys. Rev. Appl. 13, 014046 (2020). [5] Tsunegi, S. et al., Appl. Phys. Express 11, 053001 (2018). [6] Uhlír, V. et al., Nat. Nanotechnol. 8, 341–346 (2013).

Programmable Two Channel Frequency Detector based on a Vortex Nano-Oscillator

The magnetisation dynamics associated with the free layer of a magnetic tunnel junction (MTJ) have been intensely studied over recent years, giving rise to the idea of a spin-torque nano-oscillator (STNO). Whilst these devices have been shown to have clear technological advantages in terms of tunability, agility, scalability and integration. However, the very advantages that make STNOs exciting in terms of tunability make them unlikely to be integrated with conventional wireless communication paradigms, which operate over very narrow frequency bands. In order for STNOs to have a role to play in data transfer, a new paradigm for the data transmission scheme must be envisaged. In this presentation we focus on using the magnetization dynamics of a vortex-based MTJ specifically as a wideband radio-frequency detector. We will present a thorough investigation of the novel dynamic behaviour in such systems, where the in-plane magnetic field induced by an integrated field line induces the constant nucleation and expulsion of the vortex core. Furthermore, we will show how this behaviour can lead to a strong MTJ resistance dependence on the incoming radio-frequency power and frequency, a behaviour which is well recreated with micromagnetic simulations. The frequency and power dependence of the vortex-based MTJs makes them exciting candidates as wide-band analogue dynamic sensors, which are particularly well suited to the demodulation of information encoded by STNOs. In conclusion we present an STNO-based modulation and demodulation scheme, which can encoded and alphabet of M characters, which has the potential for highly efficient data transfer for use in on-chip communications and autonomous sensor networks.References: A. S. Jenkins et al., “Nanoscale true random bit generator based on magnetic state transitions in magnetic tunnel junctions” Scientific Reports vol. 9, p. 15661 (2019) A. S Jenkins et al., “Wideband High-Resolution Frequency-to-Resistance Converter Based on Nonhomogeneous Magnetic-State Transitions”, Phys. Rev. Applied 13, 014046, (2020) A. S. Jenkins et al., “Digital and analogue modulation and demodulation scheme using vortex-based spin torque nano-oscillators”, Scientific Reports, (Accepted, published July 7th)

Vortex dynamics in magnetic tunnel junctions as the basis of a novel modulation and demodulation transmission scheme

A robotic sense of touch would increase the capabilities of robots in a variety of tasks and applications; in particular, it will permit safe and robust handling of different kinds of objects in several scenarios: industrial manufacturing, precision agriculture, food processing, healthcare, public spaces and challenging environments such as nuclear sites or space missions. In the talk I will present a novel concept for the realization of tactile sensors, based on magentic technology. Using this idea, we have developed different types of tactile sensors with different sensing characteristics, that can be used in different robotic applications, from safe object grasping to texture analysis of fruits. Our early work on tactile robot fingertips [1,2], which at the time of publication had the best performance in terms of sensitivity, initiated a world-wide trend of using magnetics-based sensor solutions for embedded tactile/force sensing. The latest advances include: a multi-curved robot fingertip covered with a soft electronic skin that can measure 3D contact forces on multiple distributed contact points, at high spatial resolution and sensitivity [3], a soft miniaturized electronic cilia (200 microns diameter) that can measure contact forces as small as 333 micronewtons [4], a highly-robust and highly-sensitive flat tactile sensor that can be easily integrated on industrial robotic grippers and has become a commercial product [5].References: [1] L. Jamone, G. Metta, F. Nori and G. Sandini, James: A Humanoid Robot Acting over an Unstructured World. IEEE-RAS International Conference on Humanoid Robots (Humanoids). Genova, Italy., 2006. [2] L. Jamone, L. Natale, G. Metta and G. Sandini, Highly sensitive soft tactile sensors for an anthropomorphic robotic hand. IEEE Sensors Journal 15(8):4226-4233, 2015. [3] T. P. Tomo, S. Schmitz, W. Wong, H. Kristanto, S. Somlor, J. Hwang, L. Jamone and S. Sugano, Covering a Robot Fingertip with uSkin: a Soft Electronic Skin with Distributed 3-axis Force Sensitive Elements for Robot Hands. IEEE Robotics and Automation Letters 3(1):124-131, 2018. [4] P. Ribeiro, M. A. Khan, A. Alfadhel, J. Kosel, F. Franco, S. Cardoso, A. Bernardino, A. Schmitz, J. Santos-Victor and L. Jamone, Bio-inspired ciliary force sensor for robotic platforms. IEEE Robotics and Automation Letters 2(2):971-976, 2017. [5] T. P. Tomo, M. Regoli, A. Schmitz, L. Natale, H. Kristanto, S. Somlor, L. Jamone, G. Metta, S. Sugano, A New Silicone Structure for uSkin-a Soft, Distributed, Digital 3-axis Skin Sensor-and its Integration on the Humanoid Robot iCub, IEEE Robotics and Automation Letters 3(3): 2584-2591, 2018.

Magnetic-based tactile sensors for dexterous robotic manipulation INVITED

Electronic spin degrees of freedom provided by spin ensembles have been efficiently exploited into circuit quantum electrodynamics architectures based on microwave devices and resonators at low temperature. Molecular spins have recently emerged as a new class of quantum systems whose electronic and nuclear spin states and their related quantum features can be tailored synthetically. Different strategies for encoding quantum information with molecular ensembles or single molecules have been developed and experimentally proved. Moreover, the coherent coupling with microwave photons have been recently successfully achieved with transition metal-based oxovanadium(IV) complexes [1,2] as well as with organic radicals [3,2] embedded into planar resonant geometries, paving the way for the integration of molecular spin ensembles into microwave quantum architectures. However, along this line, optimal experimental conditions and protocols (i.e. pulse sequences) to efficiently address the molecular spins still need to be found. In this work we test single crystals and solid dispersions of diluted oxovanadium tetraphenyl porphyrin (VO(TPP)) as prototypical molecular spin ensembles for the storage and retrieval of microwave pulses when embedded into planar superconducting microwave resonators (Fig. 1) at low temperature (2K) [4]. We first measure the (Hahn-echo) memory time and the Rabi Oscillations of the samples. We then test two Dynamical Decoupling sequences: the Carr-Purcell-Meiboom-Gill and the Uhrig Dynamical Decoupling. Both the sequences are found to enhance the memory time of the crystal samples up to three times after the application of a low number (3,4) of π pulses, reaching up to 3 μs. We then successfully store and retrieve into the ensembles trains of up to 5 small pulses and we show that individual control on such excitations can be achieved. Our proof-of-principle results demonstrate the memory capabilities of molecular spins when embedded into quantum circuits [4].References: [1] C. Bonizzoni, A. Ghirri, ... and M. Affronte, Scientific Reports, Vol. 7, p. 13096 (2017). [2] C. Bonizzoni, A. Ghirri and M. Affronte, Advances on Physics X, Vol. 3, p. 435305 (2018). [3] A. Ghirri, C. Bonizzoni, ... and M. Affronte, Physical Review A, Vol. 93, p. 063855 (2016). [4] C. Bonizzoni, A. Ghirri, ... and M. Affronte, NPJ Quantum Information, Vol. 6, p. 68 (2020).

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Origin of Nonlinear Damping due to Mode Coupling in Auto-Oscillatory Modes Strongly Driven by Spin-Orbit Torque

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