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The study of magnetic systems, spin glasses, and their states, is an actively developed field of statistical physics. Spin glass models are studied in various scientific contexts, including experimental physics, condensed matter physics, theoretical physics, mathematical statistical physics and, more recently, probability theory [1 - 3]. The problem of finding the ground states (GS), i.e. states with the lowest energy is a very difficult task due to the macroscopic degeneracy and frustrations that are exist in various realistic spin glass models. In fact, it’s well known that finding the GS, of a spin glass in a three-dimensional lattice is an NP-complete problem, which means that this challenge is at least as difficult as the hardest problems of practical interest. The system of interest is the Edwards-Anderson (EA) spin glass model [4] in two-dimensional (2D) lattice, with bimodal distribution of bonds. In present work, for simulation we used a combination of our Hybrid Multispin Method (HMM) [5] and Long Short-Term Memory (LSTM) - an artificial recurrent neural network (RNN) architecture [6] with Boltzmann distribution. HMM’s advantages are the ability to increase the number of simultaneously gathered statistical-thermodynamic parameters without noticeable speed and efficiency loss, and the ability to search for configurations of the ground and low-energy states. The usage of machine learning in statistical physics began relatively recently but is developing rapidly. Neural networks have become popular tool due to the high speed of their training and accuracy of predictions. LSTM with Boltzmann distribution is useful for certain types of prediction that require the network to retain information for longer periods of time that traditional RNNs encounter. In our research, MC algorithm generated a training data set which is configurations of SG system. The trained predicted system configurations, which are using for the next computing cycle for HMM. Such iterative approach allows us to efficiently simulate the spin-glass systems even in the low-temperature regime, avoiding the critical slowing down that plague of usual MC simulation. This work was supported by the state task of the MSHE of Russia No. 0657-2020-0005.References: [1] A. Callison et al., New J. Phys., Vol. 21, 123022 (2019) [2] B. McNaughton et al., Phys. Rev. E, Vol. 101, 053312 (2020) [3] L. A. Fernandez, E. Marinari, V. Martin-Mayor, I. Paga, and J. J. Ruiz-Lorenzo, Phys. Rev. Vol. 100, 184412 (2019) [4] S. Edwards, P. Anderson, Phys. F: Metal Phys., Vol. 5 (5), p. 965 (1975) [5] A.G. Makarov et al., JETP Letters., Vol. 110 (10), pp. 702-706 (2019) [6] S. Hochreiter, J. Schmidhuber, Neural computation., Vol. 9(8), pp. 1735-1780 (1997)

MMM 2020

Investigation of the spin glass density of states using a combination of Monte Carlo method and neural network

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

It was conjectured more than 30 years ago that frustrated exchange interactions at the F/AF interfaces act as an effective random field h exerted on both F and AF at their interfaces [1], profoundly affecting the magnetic properties of the system. However, until now this hypothesis has not been tested. We utilize magnetoelectronic measurements of anisotropic magnetoresistance in F/AF=Py/CoO bilayers to experimentally confirm and to quantify the predicted random-field effects [2]. Our approach is based on the dependence of the magnetization state on the relationship between the magnetic correlation length lM determined by the thickness t of F, and the correlation length lh of the effective field [Fig. 1]. The response of a magnetic system to external field is thus expected to exhibit a crossover at thickness yielding lM=lh. For uncorrelated field, we determined the thickness-dependent response by using scaling arguments and simulations [Fig.2(a)]. Fitting of the magnetoelectronic data with these relations yields the magnitudes of random field that are nearly independent of t [Fig.2(b)], confirming the uncorrelated random-field hypothesis. The presented approach opens a route for the analysis of effective fields and anisotropies in magnetic heterostructures for memory, sensing and computing applications.References: [1] A. Malozemoff, Phys. Rev. B 37, 7673 (1988). [2] G.X. Chen, D. Collette, S. Urazhdin, Phys. Rev. B 101, 144427 (2020)

Demonstration and characterization of effective random exchange fields in ferromagnet/antiferromagnet bilayers

Exchange-coupled systems employing ferrimagnets (FI) provide high tunability, interfacial exchange interaction, and zero magnetic moment at the compensation temperature [1], which is highly beneficial for many applications such as spin valves [2] and magnetic tunnel junction devices [3]. Micromagnetic simulations showed that a partial domain wall is formed at the FI/ferromagnet(FM) interface layer during the reversal of the FM. The minor loop becomes fully reversible if this domain wall generates a hard-axis field that overcomes the anisotropy field of the FM [4]. In this study, the magnetic reversal process of exchange-coupled bilayer systems, consisting of a FI TbFeCo alloy layer and a FM [Co/Ni/Pt]N multilayer (ML), was investigated [5]. In particular, minor loop studies, probing solely the reversal characteristics of the softer FM layer, reveal two distinct reversal mechanisms, which depend strongly on the thickness of the FM layer. For thick layers (N=9, 10.8 nm), irreversible switching of the macroscopic minor loop is observed. The underlying microscopic origin of this reversal process was studied in detail by high-resolution magnetic force microscopy, showing that the reversal is triggered by in-plane domain walls propagating through the FM layer. In contrast, thin FM layers (N=5, 6.0 nm) show a hysteresis-free reversal, which was already reported in previous work [6] and is nucleation-dominated due to grain-to-grain variations in magnetic anisotropy of the Co/Ni/Pt ML and an inhomogeneous exchange coupling with the magnetically hard TbFeCo layer. The results were confirmed by micromagnetic simulations.References: [1] B. Hebler, S. Böttger, M. Albrecht et al., Phys. Rev. B93, 184423 (2016) [2] F. Radu, R. Abrudan, H. Zabel et al., Nat. Commun. 3, 715 (2012) [3] J. S. Moodera, L. R. Kinder, R. Meservey et al., Phys. Rev. Lett. 74, 3273 (1995) [4] C. Vogler, M. Heigl, D. Suess et al., arXiv:2004.04419 (2020) [5] M. Heigl, C. Vogler, M. Albrecht et al., arXiv:2007.00333 (2020) [6] X. Zhao, A.-O. Mandru, H. J. Hug et al., ACS Appl. Nano Mater. 2, 12, 7478 (2019)

Microscopic Origin of Magnetization Reversal in Exchange-coupled Ferro-/Ferrimagnetic Bilayers

Exchange bias is essential to the operation of magnetic read sensors. Recently it has been discovered that in single grain Co/IrMn3 bilayers the exchange bias is caused by a small statistical imbalance in the number of Mn atoms in each sublattice [1]. In realistic devices the IrMn is split into multiple non interacting grains, each of which contributes separately to the exchange bias. Here, we have developed a model of a multigranular IrMn/CoFe bilayer using an atomistic spin model [2]. The properties of the disordered γ-IrMn3 AFM are modelled including localized magnetocrystalline anisotropies and Heisenberg exchange, reproducing key experimental results including the Néel temperature and magnetic ground state. For an atomically flat interface the polygranular system qualitatively reproduces the experimentally observed temperature and grain size dependence of the exchange bias. A problem in maximising the exchange bias is the training effect. There are two known contributions to training: thermal and athermal. Thermal training arises due to the AFM spins undergoing thermally activated transitions during the magnetization reversal process of the FM layer [3]. However, the origin of athermal training is still a widely disputed problem due to the difficulty in experimentally probing the rearrangement of AFM spins. For an atomically flat interface no athermal training was found as the switching of the interfacial spins was found to be completely reversible. By increasing the intermixing between the ferromagnetic and antiferromagnetic layers at the interface we found the appearance of thermal training due to metastable spin states in the interfacial Mn spins which reorient during the first hysteresis cycle. We find a strong dependence on the amount of training on the interface mixing as shown in Fig. 1. These results represent a significant step towards a full understanding of the exchange bias effect in nanoscale devices.References: [1] S. Jenkins, W. J. Fan, R. Gaina, R. Chantrell, T. Klemmer, and R.F.L. Evans. Uncovering the mystery of delocalised pinned interface spins responsible for exchange bias. arXiv:1610.08236 [2] R. F.L. Evans, et al, J Phys Cond. Matter, 26, (2014) [3] X. P. Qiu et al, Phys. Rev. Lett., 101:147207 (2008).

Atomistic Spin Dynamics simulations of exchange bias in polygranular IrMn/CoFe bilayers and the origin of the athermal training effect

Exchange bias is usually the product of an uncompensated spin plane at the interface between an anti-ferromagnet and a ferromagnet. First discovered in 1956, the effect is one of the most studied phenomena in magnetism. [1] However, in the past ten years, numerous observations have been made of exchange bias at molecule-metal interfaces. [2,3] This is unusual, since van der Waals crystals of organic molecules are not expected to exhibit robust magnetic order or strong exchange interactions. There is not yet a universally accepted mechanism for molecular exchange bias, and debate has raged about whether these effects are truly exchange bias, or simply the result of increased interfacial anisotropy.[4] Furthermore, it is not yet clear whether molecular exchange bias occurs only in anti-ferromagnetic stacks of molecular magnets, or whether hybridization and charge transfer also play a role. Here, we present a detailed study of molecular exchange bias at the interface between Co and the non-magnetic molecule C60.[5] We observe the largest bias field and magnetic hardening ever observed in a hybrid molecular system, and provide density functional theory and micro-magnetic models which strongly suggest an exchange spring like mechanism arising from broken interfacial symmetry. We provide a formalism for a new form of interfacial anisotropy, dubbed π-anisotropy, which we explain as the result of asymmetric p-d hybrid interfacial dipoles. While this effect is still confined to low temperature, we explain a development pathway towards a room temperature manifestation of the effect.References: [1] W H Meiklejohn and C P Bean, Phys. Rev. 102, 1413, 1956. [2] M Gruber et al, Nat Mat, 14, 981-984, 2015. [3] J Jo et al, ACS Nano, 13, 1, 894-903, 2019. [4] S Boukari et al, Nano Lett. 18, 8, 4659 – 4663, 2018. [5] T Moorsom et al, Phys Rev B. 101, 060408(R), 2020.

π – Anisotropy: A Magneto-Electric Explanation for Molecular Exchange Bias

Exchange bias (EB) plays an important role in spintronic devices. It has been thoroughly studied between inorganic anti-ferromagnets and metallic ferromagnetic (FM) layers but rather surprisingly, similar EB effects have been reported between metallic ferromagnets and organic molecular (OM) layers. In this case, EB is considered “spinterface” induced magnetic effect and could play big role in the next generation of environment-friendly electronic devices. Molecular EB effect has been first observed in 2015 [1] between cobalt films and manganese phthalocyanine, then expanded and reproduced with different metal (Zn, Fe, Co) phthalocyanine [2] and metal octa-ethyl porphyrin molecules [3]. However, fundamentals of molecular EB and its origins is still not understood and stays controversial. In this work, we investigate the possibility of molecular EB in cobalt/metal tetra-phenyl porphyrin (M=Zn and Ni) hybrid structures. Careful SQUID magnetometer measurements show the absence of EB in “freshly deposited” hybrid samples. Surprisingly, EB appears within few hours and gradually increases with time. Additionally, new, and similar “freshly deposited” samples kept under ultra-high vacuum (UHV) for the same time span did not show EB when measured directly after removal from the UHV chamber. This indicates that EB effect has its origin from the exposure of samples to air. In the light of these unexpected results, atomic force microscopy and X-ray photoelectron spectroscopy have been performed to identify and understand the reasons of our observations. The experimental evidences strongly suggest that EB in FM/OM systems is not an intrinsic effect and originates from air-driven oxidation of cobalt films transforming part of the metallic cobalt into CoOx that is well known to produce EB effects.References: [1] M. Gruber, F. Ibrahim, S. Boukary et al. Nature Materials., Vol 14, p. 981 (2015). [2] S. Boukary, H. Jabbar, F. Schleicher et al. Nano Letters., Vol 18, p. 4659 (2018). [3] J.Jo, J. Byun, I. Oh et al. ACS Nano., Vol 13, p. 894 (2019).

Is Exchange Bias at the Hybrid Organic/Ferromagnet Interface an Intrinsic Effect?

The exchange bias effect, which manifests itself as a shift of the hysteresis loop of a ferromagnet when it is adjacent to an antiferromagnet, is a key feature used in such technological spheres as magnetic recording and storage as well as magnetic sensorics [1]. However, technological applications require materials whose performance is sustainable in a broad temperature range. A perfect candidate for this role is the antiferromagnetic Ni-Mn, multilayered structures based on which are capable of exhibiting exchange bias up to temperatures of above 700 K [2]. It is also a much more affordable option when compared to currently used Ir-Mn and Pt-Mn, since it doesn’t consist precious metals. Although very promising, formation of the ordered q-NiMn requires post-deposition annealing. In this work we show how the emergence of this phase leads to the emergence of exchange bias, depending on the initial condition of the Ni-Mn layer. Moreover, we show that the irreversible disappearance of exchange bias is associated with structural transformations occurring in the films at higher temperatures. In this work we study magnetron-sputtered Ni-Mn (20 nm) and Ni-Mn (20 nm)/Fe-Ni (40 nm) films with and without a 5 nm thick buffer Fe-Ni layer. Films were deposited on Corning glass substrates; 5 nm thick Ta layers were used as seed and capping layers. The composition of the Ni-Mn layer was varied from 10 to 50 at. % of Ni. Structural and magnetic properties of the films were studied by means of X-ray diffractometry (XRD) and vibrating sample magnetometry, accordingly. XRD measurements included a variety of geometries, such as grazing incidence (GIXRD), θ-2θ, and rocking curves (ω-scans). Structural and magnetic studies were executed in a high-temperature chamber, which allowed in-situ observation of corresponding evolution of structural and magnetic properties of films. This work was financially supported by the Russian Science Foundation, project No. 18-72-10044.References: 1. F. Radu, H. Zabel, Magnetic heterostructures, Springer, 97 (2008). 2. V.O. Vas'kovskiy et al., J. Alloys Compd., 777, 264 (2019).

Emrgence and Disappearance of Exchange Bias in Ni-Mn/Fe-Ni Thin Films Due to Structural Transformations

Rubber bands can be found in many children’s toys. For example, one winds up a rubber band and when released it drives an airplane or a racing car. If instead we wind up a tiny magnetic structure, where the magnetization twists and stores energy, then that energy will be released upon unwinding. In this theoretical work we consider a very soft, low-exchange film (80-400 atomic layers of Cu-doped Permalloy [1]), which is pinned at the bottom and coupled to a high-exchange ferromagnetic film on top. We apply a magnetic field which is rotated in the plane of the film. This generates a slow twisting of the soft material with the high-exchange ferromagnet acting as a handle as is seen in Fig. 1. We use both a local self-consistent mean-field theory [2] as well as a dynamic approach with the Landau-Lifshitz equation, with results matching well for both. With these models we have been able to generate multiple twists (over 10) in these films. At some point an instability occurs that prevents additional twists. Often the instability causes one or more twists to be released from the structure. The tightness of the twists as well as how many twists are formed before snapping depends on the length of the structure, the strength of the applied field, the size of the of the ferromagnetic cap, the exchange coupling strength, and the saturation magnetization. For example, increasing the exchange coupling decreases the number of twists that are stable in a given structure. The number of allowed twists also increases linearly with the length of the sample. Analytic energy minimization calculations, using a constant turn angle approximation, also allow us to estimate how many twists will fit into a given structure, matching reasonably well with numerical outcomes. The more twists in a given structure, the more energy it can hold. Once the twist is released or snapped, the system will unwind with frequencies in the gigahertz range. We study the frequency distribution as a function of the number of twists. Based on energy storage and this frequency generation we discuss potential applications.References: [1] N. Sorensen, R. E. Camley and Z. Celinski, J.Magn Magn Mat, vol. 477, p. 344, (2019). [2] R. E. Camley, Phys Rev B, vol. 35, p. 3608, (1987).

Mini Magnetic Propellers: Stability Considerations in Twisted Magnetic Structures

We analyze in this work the low temperature magnetic behavior of a series of Co/Ag multilayers formed by samples having reduced Co content per period (either one monolayer or half a monolayer) separated by several Ag monolayers (either 8 or 16). The multilayers were grown by molecular beam epitaxy on a clean MgO (001) surface, alternating Ag and Co deposition up to complete either 32 or 64 periods (in order to maintain constant in the series the nominal number of Co atoms per unit surface of the sample) and protected by a 3nm Ag cap layer. The samples were studied by X-ray reflectivity and diffraction, TEM, SQUID magnetometry, and ac susceptometry. From the results of our measurements we identified the following facts: 1) the occurrence in all the samples of stacking sequences corresponding to the nominal ones 2) the spatial discontinuity of the Co layers that corresponded to a quasi-monodisperse in-plane distribution of Co particles embedded in a Ag(001) matrix; 3) the observation of hysteresis at temperatures (always below 20 K) that depended on both the number of Co and Ag monolayers per period; 4) an ac field frequency dependence of the real part of the susceptibility, χ’, maxima temperatures corresponding to a Vogel-Fulcher behavior with a frequency shift parameter of the order in all the samples of 4 x 10-2; 5) the collapse (Figure 1 ), for each sample, of the experimental data corresponding to the ac field frequency, f, and temperature, T, variations of the imaginary part of the ac susceptibility, χ’’, in a single curve, G(x) with x = f[(T/Tg) − 1]−Ζν (where Tg and Ζν are the critical temperature and exponent, respectively), and verifying T χ’’ (f, T) = [(T/Tg) – 1]β G(x) [1]. Taken together, these results allow us to conclude that our three multilayers experience a phase transition (of the paramagnetic to superspin glass type) at the corresponding critical temperature and that the exponent β in the universal dynamic scaling law takes values dependent on the number of Co monolayers per period.References: [1] P. Beauvillain, C. Dupas, J.P. Renard, and P. Veillet, Physical Review B 29 (7), 4086 (1984).

Critical Magnetic Behavior in [Ag8/Co0.5]x64, [Ag16/Co1]x32 and [Ag8/Co1]x32 Epitaxial Multilayers

Exchange bias (EB) was discovered more than 60 years ago by Meiklejohn and Bean [1-2]. The origin of EB is the magnetic interaction between two differently ordered magnetic materials that are in close contact. Its fingerprint is the off-center shift of the hysteresis loop [3-4]. Some features of EB can be explained based on this type of model, but many open questions remain [4-8]. In this talk, we present the discovery of exchange bias (EB) switching, from negative to positive sign, in a dipole-induced coupling system where the antiferromagnet (AFM) and the ferromagnet (FM) are separated by a metallic paramagnetic (PM) spacer (AFM-PM-FM); and the EB enhancement in an AFM/FM bilayer coupling across an ultra-thin diluted spacer layer, as shown in the above figure. The results provide a new approach and exciting findings to design novel interacting heterostructures, control localized spin structures at the nanoscale, and create layered structures with novel spin textures.References: [1] W. P. Meiklejohn and C. P. Bean, Phys. Rev., vol. 102, no. 5, pp. 1413–1414 (1956). [2] W. P. Meiklejohn and C. P. Bean, Phys. Rev., vol. 105, no. 3, pp. 904–913 (1957). [3] J. Nogués and I. K. Schuller, J. Magn. Magn. Mater., 192, 203–232 (1999). [4] J. Nogués, J. Sort, V. Langlais, V. Skumryev, S. Suriñach, J. Muñoz and M. Baró, Phys. Rep., 422, 65–117 (2005). [5] B. Dieny, V. S. Speriosu, S. Metin, S. S. P. Parkin, B. A. Gurney, P. Baumgart and D. R. Wilhoit, J. Appl. Phys., 69, 4774–4779 (1991). [6] B. Negulescu, D. Lacour, F. Montaigne, A. Gerken, J. Paul, V. Spetter, J. Marien, C. Duret and M. Hehn, Appl. Phys. Lett., 95, 112502 (2009). [7] M. Kiwi, J. Magn. Magn. Mater., 234, 584–595 (2001). [8] J. Nogués, D. Lederman, T. Moran and I. K. Schuller, Phys. Rev. Lett.,76, 4624 (1996). [9] F. Torres, R. Morales, Ivan K. Schuller, and M. Kiwi, Nanoscale 9, 17074 (2017). [10] F. Torres, and M. Kiwi, IEEE Transactions on Magnetics, 50, 4 (2014).

Exchange Bias due to Dipolar Interactions in Heterostructures INVITED

Due to non-volatile behavior, stochastic switching for low thermal stability, and lower switching power requirements, spintronic devices are being used as synapses and neurons for energy-efficient neuromorphic computing [1][2]. In this work, we propose a spin-orbit torque-driven neuromorphic device-circuit co-design to implement the Hebbian learning algorithm. Using spike time-dependent plasticity (STDP)-based updating of synaptic weights, 8-bit, dynamic pattern recognition is illustrated. The artificial synapse we propose is based on the steady-state domain-wall motion in the MTJ free layer, driven by spin-orbit torque (SOT). The schematic of the neuromorphic circuit is presented in Fig.1(a). While Fig. 1(b) shows the time evolution of synaptic resistance during the learning phase of the circuit to recognize the pattern “A”. At the end of the training phase, we observe that all synapses connected to pre-neurons corresponding to the pattern (A) have been configured into the lowest MTJ resistance state while background synapses are in the highest resistance state. The leaky-integrate and fire mechanism of post-neuron are computed using Landau-Lifshitz-Gilbert (LLG) equation and shown in Fig. 2(a). Fig. 2(b) shows the neurons resetting by a negative current pulse. Post-neuron output voltage pulse generated by firing and resetting of the neuron is shown in Fig. 2(c). The parameters of 3T-MTJ are optimized such that its critical current is (75-80) % of the total current. This ensures that after the training phase, the neuromorphic circuit easily recognizes the incomplete/noisy images of only those patterns which it has been trained for. In this work, spintronics-based neuromorphic device-circuit co-design is proposed to solve some basic pattern recognition task using the STDP algorithm.References: [1]. Deming Zhang, Weisheng Zhao et. al, “All spin neural networks based on compound spintronic synapses and neurons,” IEEE Advances in Biomedical Circuits and Systems, vol. 10, no.4, August-2016. [2]. Chamika M. Liyanagedera, Kaushik Roy et. al, “Stochastic spiking neural networks enabled by magnetic tunnel junction: From non-telegraphic to telegraphic switching regimes,” Physical Review Applied, 8, 064017,2017.

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Investigation of the spin glass density of states using a combination of Monte Carlo method and neural network

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Demonstration and characterization of effective random exchange fields in ferromagnet/antiferromagnet bilayers

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