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During the past few years, the Mo3O8 quantum magnets with kagome layers formed by Mo atoms have attracted a great deal of attention as a new candidate to realise quantum spin liquid states. The magnetic susceptibility of LiZn2Mo3O8 has been experimentally shown to follow a Curie-Weiss law with the low- and high-temperature regimes whose Curie constants are related as CL~1/3CH. Originally, the disappearance of 2/3 of the paramagnetic spins at low temperatures in LiZn2Mo3O8 was attributed to valence bond condensation on the trimerized lattice of the Mo3O13 clusters [1], and several possible scenarios have been proposed to describe this unusual behaviour [2,3]. However, their adequacy was questioned by recently synthesized Li2InMo3O8, that shows a conventional Neel 120° magnetic order, and its counterpart Li2ScMo3O8, where no magnetic order has been observed down to 0.5 K [4]. Motivated by these studies, we combine rigorous first-principles calculations and effective low-energy models to study the microscopic origin of magnetism in LiZn2Mo3O8, Li2InMo3O8, and Li2ScMo3O8. Considering the extended Hubbard model constructed in the basis of Wannier functions for the Mo d states on the anisotropic kagome lattice, we argue that the magnetic properties of these systems can be described by two different regimes of electron localization defined by the competition of kinetic energy and intersite Coulomb interactions. Being in the strong interaction limit, LiZn2Mo3O8 will be proposed to reveal a plaquette charge order due to the correlated collective motion of electrons, where the partial spin pairing decoupling 2/3 of the spin originates from the asymmetry of tunneling processes. On the other hand, Li2InMo3O8 and Li2ScMo3O8 will be shown to fall into a cluster Mott insulator regime with the electrons localized at the Mo3O13 clusters, where the former exhibits long-range antiferromagnetic order and the latter is more likely to reveal short-range order with quantum spin liquid-like excitations.References: [1] J. P. Sheckelton, J. R. Neilson, D. G. Soltan, T. M. McQueen, Nat. Mater., Vol. 11, p. 493 (2012). [2] Rebecca Flint and Patric A. Lee, Phys. Rev. Lett., Vol. 111, p. 217201 (2013). [3] Gang Chen, Hae-Young Kee, and Yong Baek Kim, Phys. Rev. B, Vol. 93, p. 245134 (2016). [4] Yuya Haraguchi, Chishiro Michioka, Masaki Imai et. al, Phys. Rev. B, Vol. 92, p. 014409 (2015). 

MMM 2020

First-principles studies of quantum magnetism in Mo3O8 cluster systems

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

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

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.

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

In modern radar and communication systems it is important to determine the frequency composition of complex external signals on the µs time scale and faster [1]. Common swept-tuned spectrum analyzers (SA) are limited to sweep times of 10-100 ms determined by the characteristic times of macroscopic VCOs and YIG-tuned reference oscillators. In contrast, recent progress in spintronics has led to the development of spin-torque nano-oscillators (STNO) generating in the GHz frequency range, and naturally having time constants of the order of several nanoseconds determined by the intrinsic properties of magnetization dynamics at nano-scale [2]. In [3] it was proposed theoretically and in [4] demonstrated experimentally for a vortex-state configuration that STNOs can be used as a central element of an ultra-fast spectrum analyzer. A fastest sweep rate of 0.67us was achieved for spectral analysis in the range of 25MHz around center frequency of 300MHz. Here we demonstrate that an ultra-fast sweep-tuned spectrum analysis can be performed at a central frequency of 3 GHz using uniform-state STNOs. The obtained SA performances sufficiently exceed the results obtained with a vortex-state STNO with a reduced sweep time of T =0.1µs, sweep range of 400 MHz (limited by the STNO power and not by tuning range capabilities) keeping the RBW (resolution bandwidth) close to the theoretical limit (14 MHz). This GHz-frequency technique of spectrum analysis was implemented as shown in Fig.1. The STNO was used as a local oscillator whose frequency was sweep-tuned by injecting a saw-tooth sweep signal. The STNO output (a) is, then, mixed with the input signal (b), digitized (c), and processed with a matched filter, resulting in a narrow output peak (d) whose temporal position corresponds to the input frequency while the width determines the RBW. Financial support is acknowledged from the EC program ERC MAGICAL 669204, from the NSF of the USA (Grants # EFMA-1641989 and “ECCS-1708982), and by the US AFOSR (MURI grant # FA9550-19-1-0307). The EC program GREAT is acknowledged for provision of perpendicular MTJ devices operating at GHz frequencies.References: [1] Chen, V.C. and Miceli, W.J., “Time-varying spectral analysis for radar imaging of manoeuvring targets”, IEEE Proceedings - Radar, Sonar and Navigation 145, 262-268 (1998). [2] Tingsu Chen, et al., “Spin-Torque and Spin-Hall Nano-Oscillators”, IEEE Proceedings, 104, 1919-1945 (2016). [3] Louis, S. et al., “Ultra-fast wide band spectrum analyzer based on a rapidly tuned spin-torque nano-oscillator”, Applied Physics Letters 113, 112401 (2018). [4] A. Litvinenko, et al., “Experimental demonstration of a rapid sweep-tuned spectrum analyzer with temporal resolution based on a spin-torque nano-oscillator,” arXiv preprint arXiv:2004.03508, (2020).

Ultra-fast Spectrum Analysis at GHz frequencies using Spin-Torque Nano-Oscillators

Physical reservoir computing by magnetic devices is becoming an exciting topic in spintronics [1]. Recent studies on physical reservoir computing reveal that high-computation performance is achieved by physical systems at the edge of chaos [2], which is a boundary between chaos and the other dynamical states. An excitation of chaos in spin-torque oscillator (STO) by the delayed feedback was predicted recently [3,4]. Therefore, it becomes of great interest to perform the physical reservoir computing by STOs with the feedback circuit. Although an enhancement of the computation performance of the STO by the feedback was reported in 2019 [5], chaos in the STO was not identified. Since the intensity of the feedback effect in the experiments was weak, only ordered dynamics, such as self-synchronization, had been reported previously [6,7]. In this work, we investigate the edge of chaos in a vortex-type STO by enhancing feedback efficiency. Figure 1 is a schematic view of the STO with the feedback circuit. Spin-transfer torque by direct current excites an autooscillation of the vortex core. The output signal generated from the STO was gained of 40 dB, and was applied to the STO as microwave field with time delay of 150 ns. The magnitude of the feedback signal was toned by an attenuator. Figure 2 summarizes power spectra of the STO with various attenuation rate rAtt. The number of the peaks increases with decreasing the attenuation, as shown in Figs. 2(a) and 2(b), which was typically found in the feedback system [6]. The linewidth of the main peak in Fig. 2(b) is narrow compared with that in Fig. 2(a), indicating the stabilization of the oscillation by the feedback. A further reduction of rAtt , however, results in a broad linewidth with a low power at the main peak shown in Fig. 2(c), which implies an appearance of chaos [8]. The performance of the reservoir computing at this state will be presented at the meeting. This work was supported by NEDO.References: [1] J. Torrejon et al., Nature 547, 428 (2017). [2] J. Nakayama et al., Opt. Exp. 24, 8679 (2016). [3] J. Williame et al., Appl. Phys. Lett. 114, 232405 (2019). [4] T. Taniguchi et al., Phys. Rev. B. 100, 174425 (2019). [5] M. Riou et al., Phys. Rev. Appl. 12, 024049 (2019). [6] S. Tsunegi et al., Sci. Rep. 6, 26849 (2016). [7] D. Kumar et al., Sci. Rep. 6, 30747 (2016). [8] A. Uchida, “Optical communication with chaotic Lasers: Applications of Nonlinear Dynamics and Synchronization”, Wiley (2012).

Physical Reservoir Computing by Spin-Torque Oscillator at the Edge of Chaos

Structural and magnetic properties of a quasi-one-dimensional spin-1/2 compound NaVOPO4 are explored by x-ray diffraction, magnetic susceptibility, high-field magnetization, specific heat, electron spin resonance, and 31P nuclear magnetic resonance measurements, as well as complementary ab initio calculations. Whereas magnetic susceptibility of NaVOPO4 may be compatible with the gapless uniform spin chain model, a detailed examination of the crystal structure reveals a weak alternation of the exchange couplings with the alternation ratio α ~ 0.98 and the ensuing zero-field spin gap Δ0/kB ~ 2.4 K directly probed by field-dependent magnetization measurements. No long-range order is observed down to 50 mK in zero-field. However, applied fields above the critical field Hc1 ~1.6 T give rise to a magnetic ordering transition with the phase boundary TN ∝ (H − Hc1 )1/φ, where φ ~1.8 is close to the value expected for Bose-Einstein condensation of triplons. With its weak alternation of the exchange couplings and small spin gap, NaVOPO4 lies close to the quantum critical point.References: [1] P. K. Mukharjee et. al., Phys. Rev. B 100, 144433 (2019) [2] S. Sachdev, Nat. Phys. 4, 173 (2008) [3] Mukhopadhyay et. al, Phys. Rev. Lett. 109, 177206 (2012) [4] Zapf et. al., Rev. Mod. Phys. 84, (2014)

First-principles studies of quantum magnetism in Mo3O8 cluster systems

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