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Antiferromagnetic (AFM) spin Hall oscillators driven by a sub-threshold spin current produce ultra-short (~ 5 ps) spikes in response to a weak external stimulus and can be used as ultra-fast artificial neurons [1, 2]. One of specific features of AFM oscillators is the effective inertia that originates from exchange coupling between two AFM magnetic sublattices and manifests itself, for instance, in hysteretic behavior of the threshold generation current [3]. Here, we theoretically investigate influence of the exchange inertia on the dynamics of AFM-based artificial neural networks. The exchange inertia leads to delay of the spike generated by an AFM neuron relative to the input stimulus signal. The delay time depends on the coupling strength between AFM neurons and can vary from ~ 10 ps to several 100s ps. This effect can be used to create a tunable periodic spike generator by coupling several AFM neurons in a ring structure, in which output of one neuron serves as an input for the next neuron. The exchange inertia can also be used to create an “inhibitor” neuromorphic circuit, in which propagation of a spike is suppressed in the presence of another (“inhibiting”) signal. The inhibitor works by splitting the signal path in two branches and controlling the delay time in one branch by the inhibiting signal. In the presence of the inhibiting signal, the spikes in two branches arrive at the output neuron at different times and do not induce an output spike. It should be noted, that such “inhibitor” circuit is impossible to realize with inertia-less integrate-and-fire neurons. Combining the inhibitor circuit with a ring structure allows one to realize a controllable neuromorphic memory loop (see example simulations in Fig. 1). These and other examples demonstrate that exchange inertia effects can be utilised to achieve new functionalities of AFM-based artificial neural networks.References: [1] R. Khymyn, I. Lisenkov, J. Voorheis, et al., Sci. Rep. 8, 15727 (2018). [2] O. Sulymenko, O. Prokopenko, I. Lisenkov, et al., J. Appl. Phys. 124, 152115 (2018). [3] R. Khymyn, I. Lisenkov, V. Tiberkevich, et al., Sci. Rep. 7, 43705 (2017).

MMM 2020

Dynamic effects of exchange inertia in artificial neural networks based on antiferromagnetic oscillators

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

Alnico permanent magnets contain a number of major alloying additions such as Fe, Co, and Ni, along with some other minor elemental additions; this alloying convention is similar to the high entropy alloys (HEAs) concept [1]. In this paper, we investigate the hard magnetic properties of FeCoNiAl-based HEAs with additions of Cu/Ti. Additions of both Cu and Ti to an equimolar FeCoNiAl alloy are more effective at enhancing coercivity compared to Cu only, but they also decrease the saturation magnetization and remanence (Figure 1). By changing the Fe/Co amounts, however, we can regain some of these properties. Fe2CoNiAlCu0.4Ti0.4 shows promising hard magnetic properties as an isotropic, cast magnet, with a coercivity (HC) of 1.1 kOe and maximum energy product, (BH)max, of 2.06 MGOe, which is slightly better than the performance of isotropic, cast Alnico 2 magnets [2]. The thermal stability is also sufficient to be used at temperatures over 200 °C. The drastic change in HC might be strongly associated with spinodal decomposition at annealing temperatures of ~650-700 °C for all samples (Figure 2).References: [1] D. B. Miracle and O. N. Senkov, Acta Mater. Vol. 122, p.448 (2017). [2] https://en.wikipedia.org/wiki/Alnico.

Hard magnetic properties of FeCoNiAlCuxTix based high entropy alloys

The coherent transfer of information between different waveform is an important ingredient of information technology as it allows transport of quantum states without loss of frequency or phase. An efficient hybridization, though, requires to reach the strong coupling regime, where the interaction rate between two collective states becomes larger than their relaxation rates. This has revived interest for insulating magnetic garnets with low magnetic and acoustic dampings. It was recently shown that the circularly polarized phonons in dielectric crystals can transfer angular momentum over millimeters due to the strong magnon phonon coupling in a dielectric spin valve system, which is composed of two yittrium iron garnet (YIG) layers on both sides of gadolium gallium garnet substrate [1]. The evidence of this coupling is the emergence of a bright and a dark collective states that can be revealed through an interference pattern in the ferromagnetic resonance signal. In this work, we will focus on the collective behavior when the splitting between two Kittel modes is within the coupling strength. We tune the splitting either i) by varying the polar angle of an external magnetic field or ii) by applying a temperature gradient along the stack direction. We describe their mutual coupling as provided by a dissipative cavity, which represents the nearly degenerate standing acoustic shear wave mode that resonates across the whole crystal thickness. The reactive part of this mutual coupling is responsible for the usual level repulsion between the two modes. The contrast between the bright and dark states enhances as the splitting between two Kittel modes reduces. However, when the zero detuning becomes degenerate with an acoustic resonance, the dissipative part dominates over the reactive part and it leads to partial level attraction between the two collective modes. From the experimentally measured voltage contrast between two frequency tones, we extract a qualitative behavior of the coupling strength as a function of detuning, which reproduces the reactive and dissipative part of the phonon mediated coupling. We show that our results can be explained by three coupled oscillator model.References: [1] K. An, A. N. Litvinenko, R. Kohno et al., Physical Review B 101.6 060407 (2020)

Resonant Coupling between Magnetic Layers by Acoustic Phonons

Non-linear interactions related to magnons are expected to be applied to advanced computing devices [1,2]. Synthetic antiferromagnets (SAFs) are candidate materials to observe non-linear magnon interactions because they have two fundamental magnon modes, that are the acoustic (AC) and optical (OP) modes [3]. However, there are no reports whether the AC and OP mode can interact with each other. Here, we report parametric amplification of the AC mode by the OP mode in SAFs using time-resolved magneto-optical Kerr effect (TRMOKE) technique [4]. SAF films, Si/SiO2 (subs.)/Ta(3)/Co20Fe60B20(3)/Ru(0.4)/Co20Fe60B20(3)/Ta(3) (thickness is in nm), was prepared by a sputtering. Fig. 1(a) shows the TRMOKE data with various pump laser power Ppump at the critical magnetic field angle θH,c . At this angle, 2fAC = fOP is satisfied, where fAC and fOP are the frequency of the AC and OP mode, respectively. ΔθK and Δt are the change in the Kerr rotation angle and the pump-probe delay time, respectively. In case of Ppump > 5 mW, the temporal amplification of the magnetization precession was observed (dashed curves). Fig. 1(b) shows the θH dependence of the peak intensity of the FFT spectrum at the Ppump = 10 mW for the AC and OP mode, respectively. At around θH = 45°~ θH,c , the intensity of the AC mode rapidly enhanced. This indicates the non-linear interaction between the AC and OP modes is allowed for SAFs. The threshold of the OP mode to the amplification will be also discussed. This work was partially supported by KAKENHI (Nos. 26103004 and 19K15430). A.K. thanks to GP-Spin at Tohoku University.References: [1] S. Manipatruni et al., Nat. Phys. 14, 338 (2018). [2] J. Torrejon et al., Nature 547, 428 (2017). [3] A. Kamimaki et al., Appl. Phys. Lett. 115, 132402 (2019). [4] A. Kamimaki et al., Phys. Rev. Appl. 13, 044036 (2020).

Parametric Amplification of Magnons in Synthetic Antiferromagnets

The physics of nonlinear magnon scattering has been exploited in nonlinear microwave devices for wireless and satellite communication applications. The latent state, which is the time delay in the magnon response to a microwave pulse, is required to be reduced for rapid information transfer. We have studied the latent state in time-resolved nonlinear magnon scattering in thin films, in both theory and experiment. The experiment is performed using phase-sensitive time-resolved heterodyne ferromagnetic resonance. The theory is a hybrid time-resolved model which uses an analytical equation of motion based on the Holstein-Primakoff transformation, and realistic micromagnetic simulation. From the experiment in Fig. 1(a), we find the latent state is extraordinarily sensitive to the power. When the power is near the threshold, the lifetime t0 of the latent state is of order ten microseconds. At high powers, t0 decreases sharply to a hundred nanosecond. Our simulation shows consistent behavior of the latent state in the same dynamic power range in Fig. 1(b). From capturing the time-resolved magnon number of all the existing modes, we find that the origin of the latent state is the magnon redistribution: the k=0 mode takes time to scatter into non-uniform magnum modes k≠0. The power controls the scattering rate from k=0 to k≠0, where the rate is time dependent on the magnon number. We thank DARPA, XSEDE, and the SMART center (funded by SRC and NIST) for support of this project.

Latent state in time-resolved nonlinear magnon scattering in thin films

The aim of ab-initio spin dynamics is to go beyond the limitations of standard atomistic spin dynamics, which is based on a mapping of the original electronic Hamiltonian to an effective spin Hamiltonian. This spin Hamiltonian assumes constant magnetic moment lengths and constant interaction parameters and is therefore only valid in the magnetic ground-state configuration. Recent studies [1] have shown that non-collinearity in the magnetic state reduces the spin-spin interaction and gives improved accuracy compared to experiment. However, the proposed method in Ref. [1] is not applicable for the general case and reveals limitations of the above mentioned mapping [2]. In ab-initio spin dynamics the magnetic moment lengths and the quasi-classical torques acting on the atomic magnetic moments are calculated from a quasi-equilibrium electronic ground state within the adiabatic approximation [3], where constraining fields are required to stabilize non-collinear magnetic moment configurations [4]. The constraining field has therefore to cancel the internal effective magnetic field, which is expected to be minus the gradient of the energy with respect to the magnetization. In practical calculations the constraints on the moment directions are often only implemented approximately without constraining fields, which can introduce serious errors [5]. We present surprising numerical results from constrained density functional (cDFT) calculations which demonstrate that the constraining field and the effective field obtained from the energy gradient are not exactly opposite, as would be expected [4]. Furthermore, we provide a theoretical explanation of this discrepancy based on a theorem that relates the constraining field and the energy gradient: the constraining field theorem. We argue that in the case of cDFT the correct effective magnetic field is actually given by the energy gradient and not by the constraining field.References: [1] Szilva et al., Phys. Rev. Lett. 111, 127204 (2013). [2] Szilva et al., Phys. Rev. B 96, 144413 (2017). [3] Antropov et al., Phys. Rev. Lett. 75, 729 (1995). [4] Stocks et al., Philos. Mag. B 78, 665 (1998). [5] Singer et al., Phys. Rev. B 71, 214435 (2005).

Discrepancy Between Constraining and Effective Fields in Ab-Initio Spin Dynamics

Ferromagnetic materials are used in a wide range of electromagnetic applications (energy converters, sensors, inductances …). In this domain, we observed a growing interest in the development of simulation tools reducing the experimental campaigns and improving the knowledge and the performances. Accurate simulation results can only be obtained by coupling precise electromagnetic equations to the exact material laws (hysteresis, saturation, frequency dependence) [1]-[3]. Under the influence of an external magnetic excitation, the local magnetic state through the ferromagnetic specimen is ruled by the combination of both the magnetic domain kinetics and the external magnetic field diffusion. The usual methods for the simulation of the magnetic behavior are all based on the separation of the magnetic contributions, where the microscopic Eddy currents due to the domain wall motions and the macroscopic ones due to the extern magnetic field variations are considered separately [4]. This separation remains artificial, since practically both losses mechanisms occurs simultaneously and interact on each other [5]. In this study, an alternative solution is proposed through the resolution of an anomalous fractional magnetic field diffusion (1, 2 or 3D depending on the experimental situation). The fractional order constitutes an additional degree of freedom in the simulation scheme [6]-[8]. It is identified through comparisons to experimental results. By adjusting precisely this order, very accurate local and global simulation results can be obtained on a very broad frequency bandwidth. It allows to predict precisely the dynamic magnetic behavior of classic ferromagnetic components.References: [1] B. Zhang et al., IEEE Transaction on Magnetics, vol. 54, iss. 11 (2018) [2] B. Zhang et al., IEEE Transaction on Magnetics, Vol. 54, iss. 3, (2017). [3] B. Gupta et al., IEEE Transaction on Magnetics, Vol. 54, Iss. 3, (2018). [4] G. Bertotti, IEEE Transaction on Magnetics, vol. 24, iss. 1, pp. 621-630, (1980). [5] M. A. Raulet et al., IEEE Transactions on Magnetics, Vol. 40, iss 2, pp. 872-875, (2004). [6] B. Ducharne et al., International journal of dynamics and control, vol. 6, pp. 89-96, (2018). [7] B. Ducharne et al., Journal of Applied Physics, vol. 117, iss. 24, (2015). [8] B. Ducharne et al., The European Physical Journal Plus, 135:325, (2020).

Fractional equation for the anomalous magnetic diffusion in ferromagnetic materials

Recently we studied magnetic inhomogeneity effects in magnetocaloric properties of a 7.6 nm La0.7Sr0.3MnO3 (LSMO) thin film to understand the nature of magnetic phases transitions1. We proved this sample has two main magnetic phase transitions: superparamagnetic ferromagnetic and ferromagnetic-paramagnetic phases transitions, at T = 240 K (= TB) and T = 270 K (= TC), respectively. Here we want to understand the spin dynamics and relaxation in this sample. Analysis of the results from our investigations of the temperature dependence of ac susceptibilities (χ/ and χ//) and magnetic viscosity in a 7.6 nm thin film of La0.7Sr0.3MnO3 grown on SrTiO3 (001) substrate are presented. The Curie temperature (TC) of this film is magnetic field (H) dependent varying as: [TC(H)-TC(0)] ~ Hn, n ~ 0.15. Temperature dependence of χ/ and χ// measured at ac frequencies fm in the range of 0.1 to 10 kHz shows a broad peak near 230 K associated with the blocking temperature of spin clusters present in the 1.4 nm surface layer and a frequency dependent peak near 270 K associated with TC (Fig. 1). The mean relaxation time τ determined from the Cole-Cole analysis of and is shown to fit the Vogel-Fulcher law: τ = τ0 exp[ΔE / kB(T-T0)] , with TB = 245 K, ΔE / kB = 270 K = TC, and τ = 1.2 10-9 (s) (Fig. 2). Magnetic viscosity S (measured in H = 0 for a sample cooled in H = 50 Oe) determined from the fit to the magnetization: M (t) = M (0) – S Ln t, with time t up to 2 hours, shows a peak at 230 K above which the M (2 hrs) switches to negative values for temperatures up to TC(0). It is argued that this negative magnetization results from interaction between the superparamagnetic like spin clusters and the ferromagnetic phase.References: 1 N. Mottaghi, R.B. Trappen, S.Y. Sarraf, M.S. Seehra, and M.B. Holcomb, J. Alloys Compd. 154200 (2020).

Spin dynamics and relaxation in thin film La0.7Sr0.3MnO3/SrTiO3: ac magnetic susceptibility and magnetic viscosity investigations.

Iron oxide nanoparticles (NP) are under investigation for many biomedical applications [1], including magnetic hyperthermia. The heating efficiency of magnetic hyperthermia depends on how well the single excitation frequency matches the Néel and Brownian relaxation frequencies of the NPs. We directly measured the magnetostatic interaction induced frequency distribution with a custom-built AC susceptometer [2]. Our results show that both the peak and amplitude of this distribution can be tuned by addition of a small DC field, thus enabling a better match to the AC excitation field frequency. We measured the AC magnetic susceptibility (ACS) of 10.7±1.2 nm Fe3O4 NPs dispersed in eicosane (0.15 vol%). The ZFC-FC curve shows a blocking temperature (TB) of ~ 105 K, and the greatest response of the real (χ’) and imaginary (χ”) parts of the ACS was found between 110 and 150 K. Fig. 1 shows the imaginary component of the ACS as a function of frequency, for HDC = 0, at different temperatures. The imaginary part shows a very broad peak at 110K. At higher temperatures the dispersive peak sharpens and the peak shifts to higher frequencies. Both the breadth of the peak and its shift with temperature show that magnetostatic interactions affect high frequency response even for dilute samples. We extended our ACS measurement at 140 K with additional DC fields, ranging from 0 to 4mT. Fig.2 shows the non-monotonical trend of the imaginary part of the ACS at various DC magnetic fields. Below 1.25 mT the peak frequency decreases and the amplitude increases with increasing DC fields. At and above 1.25 mT these trends reverse. The dissipation at 100 kHz increases by a factor of 3.8 between 0 and 1.25 mT. The peak DC field is comparable to the average magnetostatic interaction field. Applying the DC field overcomes part of the spin freezing and enables a larger fraction of the spins to contribute to the dissipation. This methodology can be extended to polydisperse NPs at higher concentrations at body temperature.References: [1] Q.A. Pankhurst, et al., J. Phys. D Appl. Phys. 36, R167 (2003). [2] E. Riordan, et al., Review of Scientific Instruments 90, 073908 (2019).

Tuning the Dynamics in Fe3O4 Nanoparticles for Hyperthermia Optimization

First-order reversal-curves (FORCs) are a powerful tool, which is increasingly used in material science and nano-magnetism as well as ferroelectricity, geology, archeology, and for spin-transition materials [1-4]. Ideally, it can access microscopic distributions of interaction and coercive fields without the need for lateral resolution [5]. Unfortunately, the reliable data analysis and interpretation poses a major challenge. This is why FORC is often seen as a magnetic fingerprint instead of a measurement method yielding quantitative information. To push past these limitations, we present a fast and user-independent analysis algorithm and possibilities to interpret the resulting FORC diagrams beyond the Preisach model. We present a new evaluation approach which exploits the diversity of Fourier space to not only speed up the calculation by a factor of 1000 but also move away from the conventional smoothing factor towards real field resolution. By comparing the baseline resolution of the new and the old algorithm we are able to deduce an analytical equation which converts the smoothing factor into field resolution making the old and new algorithm comparable. We find excellent agreement not only for various systems of increasing complexity but also over a large range of smoothing factors. The achieved speed up enables us to calculate a large number of first-order reversal-curve diagrams with increasing smoothing factor allowing for an autocorrelation approach to find a hard criterion for the optimum smoothing factor. This previously computational prohibitive evaluation of first-order reversal-curves solves the problem of over- and undersmoothing by increasing general readability and preventing information destruction. However, these measured FORC densities are not always straightforward to interpret, especially if the system is interaction dominated and the Preisach-like interpretation of the FORC density breaks down. To understand additional features arising from the interactions in the system, we purposely designed permalloy microstructures which violate the Mayergoyz criteria [7]. These artificial systems allow us to isolate the origin of an additional interaction peak in the FORC density. Modeling the system as a superposition of dipoles allows us to extract interaction strength parameters from this static simulation. Additionally, we suggest a linear relation between integrated interaction peak volume and interaction strength within the system. The presented correlation could be used to investigate the interaction behavior of samples as a function of structural parameters within a series of FORC measurements. This is an important step towards a more quantitative understanding of FORCs which violate the Mayergoyz criteria and away from a fingerprint interpretation.References: [1] J. Gräfe, Phys. Rev. B, 93 (2016) 014406 [2] F. Groß, Phys. Rev. B, 99 (2019) 064401 [3] C.-I. Dobrota, J. Appl. Phys., 113 (2013) 043928 [4] C. R. Pike, Phys. Rev. B, 71 (2005) 134407 [5] J. Gräfe, Rev. Sci. Instr., 85 (2014) 023901 [6] D. Cimpoesu, J. Appl. Phys., 125 (2019) 023906 [7] I. D. Mayergoyz, Phys. Rev. Lett., 56 (1986) 1518

Modern FORC data analysis and interpretation approaches INVITED

Coherent manipulation of quantum information is pivotal for real quantum computing applications. Promising approaches employ hybrid quantum systems based on coupled superconducting qubits and resonators and magnetic elements [1-6], where strong coupling rates (exceeding 100 MHz) are easily reached. An advantage of magnetic elements is that their resonance frequencies are tunable in a wide range by a bias magnetic field. However, all previous studies in this area focus on quasi-static systems where magnetic resonance frequency is constant during the signal lifetime. Here, we propose a new method of coherent information manipulation in hybrid magnetic/superconducting systems based on dynamic control of the magnetic element at timescales comparable or less than characteristic coherence times. This method opens new possibilities for quantum information transduction, processing, and entanglement generation, that are not possible to realize in static hybrid systems. Fig. 1 shows a simple example of how to coherently transfer information from one superconducting resonator P1 to another P2 using intermediate magnetic resonator Pm, where the resonance frequency is rapidly swept across the resonance frequencies of resonators P1,2 with ramp rate ρ = dωm/dt = 2π×2.5 MHz/ns. As one can see, such “passage” results in almost complete information transfer to the P2 resonator. Notably, the population of the magnetic resonator Pm stays low (< 0.2) during the whole process (see bottom of Fig. 1), which explains the weak sensitivity of this process to magnetic damping. Dynamically changing the resonant magnon frequency can be used for information transfer between disparate systems, creating quantum gates, and realizing quantum data exchange between two elements. This dynamic frequency change may perform information processing and can be used to study fundamental properties of magnons, such as if we do 50% information transfer, thereby generating magnon-mediated quantum entanglement.References: [1] H. Huebl, C. W. Zollitsch, J. Lotze, et al., Phys. Rev. Lett., vol. 111, no. 127003, 2013. [2] Y. Tabuchi, S. Ishino, T. Ishikawa, et al., Phys. Rev. Lett, vol. 113, no. 083603, 2014. [3] X. Zhang, C.-L. Zou, L. Jiang, and H. X. Tang, Phys. Rev. Lett., vol. 113, no. 156401, 2014. [4] Y. Tabuchi, S. Ishino, A. Noguchi, et al., Science, vol. 349, no. 6246, pp. 405-408, 2015. [5] Y. Li, T. Polakovic, Y.-L. Wang, et al., Phys. Rev. Lett., vol. 123, no. 107701, 2019. [6] J. Hou and L. Liu, Phys. Rev. Lett., vol. 123, no. 107702, 2019.

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