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Micrometer diameter bilayers of 20 nm Permalloy/20 nm Cobalt Oxide deposited on nanomechanical resonators were used to investigate exchange bias effects. The mechanical compliances of two resonator axes were enhanced by severing one torsion arm, Figure 1, resulting in a unique three-axis resonator that responds resonantly to torques generated by a three-axis RF field [1]. Our technique permits simultaneous measurement of three orthogonal torque components. Measurements of the anisotropies associated with exchange bias effects have been made. First, at cryogenic temperatures, observations of shifted linear hysteresis loops confirm the presence of a positive exchange bias at the Py/CoO interface. A rotating DC bias field was used to probe in-plane anisotropies through the out-of-plane torque, as shown in Figure 2 (open circles). Training effects in both the linear and rotating hysteresis data were observed and show that most of the training occurs during the first half of the first loop, consistent with an athermal training mechanism [2]. The data from the rotating hysteresis loops were fit with parameters from a macrospin solution to the Landau-Lifshitz-Gilbert equation. In order to reproduce our observations standard anisotropy terms, a spin-flop coupling term [3], and a rotatable anisotropy axis [3,4] are introduced to the model. Each parameter of the exchange bias model accounts for specific features of the rotational loop. A unidirectional anisotropy asymmeterizes the extrema magnitudes. The orientation of the rotatable anisotropy axis with respect to the ferromagnetic magnetization introduces a one-fold rotational symmetry that would otherwise be at least two-fold. The spin-flop term influences the angular positions of the peaks in the torque curve.

![](https://assets.underline.io/uploads/markdown_image/1/image/904fce60d2079057eb98db71f95841b7.jpg)

Figure 1: Electron micrograph of a micromechanical device used for demonstration of the three-axis torque measurement technique. The arrows indicate the three orthogonal torsional displacements.

![](https://assets.underline.io/uploads/markdown_image/1/image/a6f1c83647a790b3299d22bf142cc7ae.jpg)

Figure 2: Thermomechanically calibrated experimental data of the z torque component (resonator at liquid nitrogen temperature). Data were recorded during a rotational hysteresis loop. Fits from macrospin solutions to the LLG equation are shown.



2022 Joint MMM-INTERMAG

Three-axis torque investigation of exchange bias in a micromagnetic disk

The 15th Joint MMM-INTERMAG Conference (2022 Joint) is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a plenary session, and an evening session, with about 1500 presentations overall. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

The 2022 Joint Conference will offer both in-person and prerecorded on-demand content.

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Please register for the Joint MMM-Intermag conference to join the event.

technical paper

We study the effect of thermal fluctuations on dipole coupled mesospins, the building blocks of artificial spin ice (ASI), in a micromagnetic framework. Taking into account the internal magnetic texture, we focus specifically on the fluctuations at the edges, which have previously shown to exhibit a temperature dependent switching between two states that are essentially half of a C- or S-state [1]. We study two different systems, the first being a system of two coupled magnets and the second being a fourfold coordinated ASI vertex. For the two mesospin system with parallel magnetization, we find magnonic mode splitting at the edges, which is relatively unaffected by temperature. When the magnetization in the two mesospins is opposite, we find the appearance of an asymmetric potential, which can be quantified through the magnetic texture correlations. The Arrhenius law is used to find the attempt frequency and the energy barriers associated with switching, the latter are found to be inversely proportional to the spacing. We find a logarithmic dependence of the attempt frequency on the energy barrier, which is indicative of entropy-energy compensation at small spacings (large barriers). The temperature dependent edge dynamics for the ASI vertex is evaluated for the four different types (Type I-IV), each displaying their own characteristic dynamics. An example of such dynamics is the collective switching of the handedness associated with the perpendicular edge magnetization in a type IV vertex configuration. These results indicate the presence of rich texture dynamics, even at the level of the individual building blocks of the ASI.

Magnetic Texture Fluctuations in Coupled Mesospin Systems

Artificial spin-ice systems (ASI) have been studied for 15 years, allowing detailed studies to examine the frustration, ordering and monopole transport in a variety of two-dimensional geometries [1]. The nanostructuring of magnetic materials in three-dimensions presents a new paradigm in condensed matter physics and allows access to a wide range of new physical phenomena [2]. With respect to ASI systems, there are several reasons why 3D geometries are interesting. This includes the realisation of a degenerate ice-rule, mimicking of bulk spin-ice geometries and studying the influence of surfaces upon ordering. In this talk, I will outline the realisation of a 3D artificial spin-ice system [3] which takes the geometry of a diamond-bond lattice (Fig. 1), capturing the arrangement of spins in bulk pyrochlore systems. By using magnetic force microscopy (Fig. 2), I will show that the vertex states upon the surface can be determined, and the global switching of the lattice can be measured. We find very different magnetic charge dynamics along two principal directions upon the lattice. For a field applied along the surface termination, local energetics force magnetic charges to nucleate over a larger characteristic distance, reducing their magnetic Coulomb interaction and producing lone, uncorrelated monopoles. In contrast, applying a field transverse to the surface termination yields large numbers of highly correlated monopole-antimonopole pairs. A combination of micromagnetic and Monte-Carlo simulations are used to understand the results. These suggest it is the difference in effective chemical potential that yields the striking differences in monopole transport. We anticipate that our study will inspire a new generation in artificial spin-ice research whereby the ground states in complex 3D frustrated lattices are explored.

![](https://assets.underline.io/uploads/markdown_image/1/image/68e61fe5f53c1aa5f59122b57dafa546.jpg)

Fig 1. Atomic force microscopy image of the 3DASI system. Distinct layers within the system are labelled L1 - L3.

![](https://assets.underline.io/uploads/markdown_image/1/image/6da2b1e596bc9e183b4530846549ee08.jpg)

Fig 2. Magnetic force microscopy of the 3DASI surface, showing a number of ice-rule and monopole states.

Magnetic charge propagation upon a 3D artificial spin-ice

The synthesis of single-crystalline and single-domain ferromagnetic nanowire materials has been an area of intense research,1-3 however the control of geometric parameters (diameter, lengths, tip morphology and uniformity) in nanowire syntheses is mostly empirical. Here, we demonstrate a simple method for precise control of geometric parameters in nanowire synthesis by establishing both steady-state growth conditions and a uniform rate of particle growth through the continuous and controlled additions of precursors. To prepare Co nanowires, we used both the 'LaMer' and 'extended LaMer' processes, which allows us to fine control over diameter, aspect ratio, and morphology uniformity of the nanowires with reproducibility. Meanwhile, the structural property analysis of a series of nanowires revealed both qualitative and quantitative information on the growth kinetics of the nanowires. It has been demonstrated how the precursor flow rate, metal precursor mole ratio and the reducing ability of long-chain amine affect the nanowire morphology. We then show how such fine geometric control affects the magnetic coercivity of nanowire assemblies. Based on the shape anisotropy and orientation of the nanowire assemblies, a record high room-temperature coercivity exceeding 10 kOe has been measured in Co nanowires with a diameter of 8 nm.

![](https://assets.underline.io/uploads/markdown_image/1/image/30b2d410cd16b38f3094e1caeb5b2bd1.jpg)

Fig. 1 Schematic illustration of the effect of (a) flow rate of Co-precursor, (b) mole ratio of RuCl3 to Co-precursor and (c) long-chain amine content on the growth kinetic of Co nanowires. (d-f) The TEM images of Co nanowires prepared through the continuous flow of Co-precursor at various decreasing flow rates.

Effects of growth kinetics on structural and magnetic properties of Co nanowires

Arrays of magnetically soft nanowires and microwires have potential sensor applications [1, 2]. We have reported nanowire array manufactured by electrodeposition of permalloy into polycarbonate membranes [3]. In this paper we report permalloy nanowire and microwire arrays produced using alumina and silicon membranes with hexagonally ordered pores with constant pitch. These membranes allow to optimize the nanowire array properties such as coercivity, apparent permeability and amplification factor. Finite element modelling of nanowire arrays is demanding due to the computational complexity. In [4] we calculated apparent permeability and demagnetization factor of single wire and small wire arrays. We have also proposed simplified 2D equivalent model allowing to calculate properties of wire arrays very efficiently [5] and verified the validity of this model by full 3D simulations and also experimentally on arrays of up to 91 permalloy microwires. In this paper we apply this model to manufactured arrays of 3 mm diameter containing 100 000 to 40 million wires with diameters between 180 nm and 2.5 μm and compare simulation results to measurements by SQUID. Figs. 1 and 2 show examples of the measured hysteresis loops with red line showing the slope corresponding to apparent amplitude permeability. The values calculated by FEM using constant permeability model show significant deviations especially at low density arrays. We will show that this difference is caused by the nonlinear shielding effect: the field in the outermost wires is much stronger and thus they are saturated first. Because of that the saturation process propagates fast from the periphery towards inside array which can be shown on non-linear model.

![](https://assets.underline.io/uploads/markdown_image/1/image/4818309d16f32532f9a688524ccc7d9a.jpg)

Fig. 1 Hysteresis loop of the array of 180 nm diameter 100 μm long wires with 480 nm pitch. Measured apparent amplitude permeability μa = 45, calculated incremental μai = 8.6.

![](https://assets.underline.io/uploads/markdown_image/1/image/7178e6971765f6f4dd7a495b3982dd0b.jpg)

Fig. 2 Hysteresis loop of the array of 2.5 μm diameter 200 μm long wires with 4.2 μm nominal pitch. Measured apparent amplitude permeability μa = 5.5, calculated incremental μai = 3.8.

Apparent permeability of ordered magnetically soft nanowire and microwire arrays

Multi-segmented nanowire (NW) arrays are strong candidates to improve the memory storage capacity due to their lower magnetic bit area [1]. But writing/reading information on such devices is still a challenge. Recently, micromagnetic simulations revealed that the integration of a soft magnetic segment (with lower coercivity) along the racetrack could ease the writing process by using external magnetic fields [2]. Here, we demonstrate the feasibility of using NiCu/FeCo magnetic NWs as in-line writing components in 3D racetrack memory devices. Using template-assisted DC electrodeposition [3-5], 4 samples of NW hexagonal arrays (50 nm-diameter, 100 nm of interwire distance) were produced: i) Ni90Cu10; ii) Fe20Co80; iii) bi-segmented NiCu/FeCo; and iv) multi-segmented NiCu/[FeCo/Au]3. Morphological, chemical and structural characterization revealed the formation of single, bi- and multi-segmented NW arrays with tuned dimensions and uniform compositions (Fig. 1). Magnetic hysteresis loops, ferromagnetic resonance (FMR) measurements and first-order reversal curve (FORC) diagram analysis confirmed the hard and soft magnetic properties of the FeCo and NiCu single arrays, respectively. In the interacting NiCu/FeCo bi- and multi-segmented systems, a significant reduction of the parallel coercivity occurred, while keeping the magnetization easy axis lying parallel to the NWs' axis. FORC diagrams also demonstrated a two-step reversal process in systems (Fig. 2), illustrating a FORC fingerprint typically present in soft/hard magnetic interacting bi-layered NWs [6]. Micromagnetic simulations confirmed such a two-step reversal process, revealing the presence of strong interactions at the soft/hard interface [7]. This work was supported by projects POCI-01-0145-FEDER-028676, POCI-01-0145-FEDER-031302, UIDB/04968/2020, EXPL/IF/00541/2015 and contract IF/01159/2015 from Portuguese FCT and COMPETE 2020 (FEDER); grant 02.2020/0261 from the National Research Foundation of Ukraine; and project PID2020-117024GB-C42 from the Spanish Ministerio de Ciencia e Innovacíon.

![](https://assets.underline.io/uploads/markdown_image/1/image/cd280bc8126f81abd395a71d877c76eb.jpg)

Fig. 1. Scanning electron microscopy images of the electrodeposited multi-segmented NWs.

![](https://assets.underline.io/uploads/markdown_image/1/image/22038b2a0a7bf508db8232151a5ff998.jpg)

Fig. 2. FORC diagram of the multi-segmented sample along the parallel direction.

Feasibility of Using NiCu/FeCo Coupled Bi-segmented Nanowires as In-line Writing Heads for 3D Racetrack Storage Devices

Three-dimensional (3D) magnetic assemblies can accommodate unique topological features and exotic spin textures, along with embedded magnetic frustrations [1]. Recently, we have realized interconnected cobalt nanowire networks using multiple angle ion-tracking and electrodeposition; such networks exhibit new magnetization reversal behaviors, offering an interesting platform for 3D information storage [2]. Here we report magnetoresistance (MR) studies of such interconnected networks, to explore how the magnetic configurations can be correlated with spin transport. When a sizable collection of connected nanowires is measured, typical anisotropic magnetoresistance behavior with sharp minima near the coercive fields is found, suggesting that the current is largely bypassing the high resistance intersections. However, when only a few interconnected nanowires are measured, the MR curve exhibits multiple kinks and local minima, indicative of domain wall pinning by the intersections (Fig. 1). More interestingly, during the positive to negative field sweep, a significant MR minimum is observed at positive field, which is the largest among all the MR minima. These features are not seen in parallel nanowires and are a direct consequence of the intersections. Micromagnetic simulations using an equivalent resistor model based on two intersecting nanowires reproduces the experimental observations, including the multiple kinks and a large MR minimum in positive field. Furthermore, small angle neutron scattering has been used to characterize magnetic correlations in the networks under different applied magnetic field configurations. These results show that the intersections in the networks play an important role in pinning / depinning of domain walls, which may be utilized for 3D magnetic memory and memristive devices. Work supported by the SRC/NIST nCORE SMART center and NSF.

![](https://assets.underline.io/uploads/markdown_image/1/image/33fe181bcbcc9e0f263230fd717c8566.jpg)

Figure 1: Magnetoresistance of a few interconnected Co nanowires showing multiple kinks, indicative of domain wall pinning and depinning during magnetization reversal.

Intersection-Mediated Magnetoresistance in 3D Nanowire Networks

Sparked by the limitations of the Von-Neumann architecture, the burgeoning field of neuromorphic computation aims to develop systems that process information both ‘in-memory’ and in a brain-like manner. Neural networks comprise three types of layers – an input layer, hidden layers and an output layer each connected by numeric weights. Training such networks requires continuous updating of each weight requiring both time and energy. Reservoir computing (RC)1 is a subset of neuromorphic computation where training occurs only on the output layer, reducing time and energy cost significantly compared to traditional neural networks, while competing with traditional approaches for time-series classification / prediction task accuracy. Artificial spin networks comprising patterned nanomagnets serve as promising computational substrates for such applications, information can be stored in a single nanomagnet spin (i.e. a nanomagnetic ‘bit’) or the magnetic configuration (microstate) of the entire network. Strong dipolar coupling enables a highly non-linear history-dependent collective response to external stimuli, a key property for RC1. Artificial spin ice (ASI) is one such network where geometric frustration gives rise to a rich microstate space and emergent collective behaviour2 highly promising for RC3,4. However, in these systems individual nanomagnets are constrained to Ising-like states, severely limiting microstate richness. We have previously shown in simulation that combining Ising-like and vortex states allows powerful reconfigurable functionality5. Modifying a subset of bars6,7 in an ASI such that the Ising and vortex states are bistable gives rise to highly non-linear responses to global- and RF-fields allowing multiple reservoir readouts, detectable by the recently developed ‘spectral fingerprinting’ technique8. Here, we explore ASVI-based RC for forecasting and classifying time-series with varying complexity and assess the strengths and limitations of such systems compared against traditional ASI and competing neuromorphic hardware platforms.

Reservoir computing in an artificial spin-vortex ice

Magnetic nanoparticles are increasingly used in biomedical applications such as drug-delivery, gene delivery, hyperthermia, or contrast agents for MRI. Magnetite (Fe3O4) nanoparticles are good candidates for these applications due to their non-toxicity and long-life in the bloodstream. While the structural and magnetic properties of bulk Fe3O4 has been widely studied [1], knowledge is still lacking regarding the magnetic behaviour of collections of Fe3O4 nanoparticles. In particular, when the particles are small and the assembly is superparamagnetic, it is useful to understand the nature of the magnetic correlations within the assemblies. Here we show how inter-particle magnetic correlations can be probed at the nanoscale via x-ray resonant magnetic scattering (XRMS) [2] as illustrated in Fig.1a. By tuning the energy of the x-rays to resonant edges of Fe and comparing opposite polarization helicities, we extract information about the local inter-particle magnetic orders within the nanoparticle assemblies. We show the dependence on particle size, varying from 5 to 11 nm, suggesting an enhancement of magnetic couplings for bigger particles. [3] Additionally, we show model based on chains of nanoparticles, which we use to fit the XRMS data. The data fitting suggests the occurrence of a mix of antiferromagnetic ordering and randomness near remanence at high temperature and near the coercive region at low temperature, for larger particles. [4] Finally we will show preliminary photon correlation (XPCS) (see Fig.1b) and muon sin resonance data obtained on 5 nm Fe3O4 nanoparticles revealing temperature dependence on the dynamics of magnetic fluctuation. [5,6]

![](https://assets.underline.io/uploads/markdown_image/1/image/423b7b0e23ec43cfb7a4335170291ade.jpg)

Nanoscale magnetic correlations and fluctuations in assemblies of Fe3O4 nanoparticles

When temper-annealed around 650 K in the presence of a magnetic-field, off-stoichiometric Heusler alloys in the form Ni50Mn45X5 (X: Al, Ga, In Sn, Sb) decompose and form 2-5 nm full Heusler precipitates which become embedded in a surrounding NiMn neighborhood. The precipitates are cubic and ferromagnetic (FM) whereas the matrix is tetragonal and antiferromagnetic (AF) with a high anisotropy. This spinodal decomposition progresses according to the reaction 5Ni50Mn45X5 → Ni50Mn25X25 + 4Ni50Mn50. The AF/FM interface becomes so strongly pinned in the applied annealing-field direction that a magnetization reversal is not observed in fields up to 20 T. Such materials are relevant to non-volatile magnetic memory applications. In a similar manner, it is possible to temper anneal other Heusler-based materials to obtain precipitation. We adopt this method to prepare spin-polarized FM Co50Ti25Ge25 precipitates in a Pauli paramagnet (PM) Co50Ti50 matrix. The decomposition progresses according to 5Co50Ti45Ge5 → Co50Ti25Ge25 + 4Co50Ti50. The aim is to understand the influence of the spin polarized state on the magnetic and transport properties at reduced dimensions. For this purpose, we carry out x-ray diffraction (XRD), microprobe analysis, magnetization, and resistivity studies. Time-, field-, and temperature-dependent magnetization studies along with XRD show the presence of decomposition into Co50Ti25Ge25 precipitates becoming embedded in a PM matrix. Field-dependent resistivity measurements show asymmetric field-dependence and suggest the preservation of spin-polarization over macroscopic dimensions.

Magnetic and Transport Properties of Shell-ferromagnetically Precipitated Spin-Polarized Co2TiGe in a CoTi matrix

The interface driven exchange bias effect (EB) is a well-studied phenomenon observed in ferromagnetic (FM)/antiferromagnetic (AFM) thin film systems resulting from the interfacial exchange coupling between the F and AF spins [1]. In numerous studies, asymmetrically shaped hysteresis loops have been reported mainly described by coherent rotation of the magnetic domains on the one hysteresis branch and rapid nucleation and domain wall propagation on the other one [2, 3]. Romanens et al. were able to correlate these asymmetries in perpendicular magnetized thin film systems to higher domain nucleation densities when the applied field is aligned antiparallel to the EB field compared to the parallel orientation [4]. Here the statistics of magnetic domain nucleation during the magnetization reversal process in exchange-biased magnetic nano-stripes is investigated by high-resolution optical Kerr microscopy. In such structures the magnetization dynamics are governed by the exchange bias field, the shape anisotropy and stray field interactions between the stripes. The dependency of the nucleation on these parameters is investigated systematically by variation of the lateral dimensions of the stripes and the orientation of the exchange bias fields relative to the stripe axis. Understanding the nucleation behavior of magnetic domains in nanostructures is an important step in the development of spintronic devices.

![](https://assets.underline.io/uploads/markdown_image/1/image/edc0ef18b758f66d641af727d520c25e.jpg)

Investigation of magnetic domain nucleation in exchange-biased nanostructures

Three-axis torque investigation of exchange bias in a micromagnetic disk

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Three-axis torque investigation of exchange bias in a micromagnetic disk

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Magnetic Texture Fluctuations in Coupled Mesospin Systems

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Nanoscale magnetic correlations and fluctuations in assemblies of Fe3O4 nanoparticles

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