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Collective dynamics in lithographically-defined artificial spin ices offer insights into emergent correlations and phase transitions of geometrically-frustrated Ising spin systems. Their temporal and spatial evolution observed in experiments are also often simulated using kinetic Monte Carlo (kMC) simulations. As we recently showed, simplified models that describe the switching barriers, which are necessary to obtain predictive simulations results, overlooked a chiral contribution that leads to a splitting of barrier energies and results in faster relaxation [1,2].&lt;br/&gt;&lt;br/&gt;As consequence of the chiral barrier splitting, the relaxation pathways are modified. In this work, we study the evolution from the field-saturated state to the ground-state order of artificial square ice with kMC simulations; and compare the effect of commonly-used mean-field barriers to the chiral split-barrier description at different interaction strengths and temperatures.&lt;br/&gt;&lt;br/&gt;We assess general measures that describe the dynamic evolution, such as vertex populations and net magnetisation as well as spatial correlations. By taking into account the chiral barrier splitting we observe faster and more efficient evolution to the ground state. Compared to the mean-field barrier model, for which the demagnetisation is mainly dominated by the nucleation and propagation of ground-state strings (for strong interactions) or random events (for weak interactions), the chiral barrier splitting promotes a richer diversity of switching events. This leads to a variety of behaviours, such as breaking up strings without the generation of charged defect vertices, the formation of coral-like domain walls, and efficient annihilation of domain walls in the later stages of the evolution to the ground state.&lt;br/&gt;&lt;br/&gt;Our results demonstrate that the rich demagnetisation dynamics of artificial square ice, as is also observed experimentally, can be partially explained even in the absence of additional disorder.

2022 Joint MMM-INTERMAG

Role of Chiral Switching Barriers on Relaxation Kinetics in Artificial Square Ice

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.

For tickets to the event, please register at the following link: https://magnetism.org/register

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

This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

Collective dynamics in lithographically-defined artificial spin ices offer insights into emergent correlations and phase transitions of geometrically-frustrated Ising spin systems. Their temporal and spatial evolution observed in experiments are also often simulated using kinetic Monte Carlo (kMC) simulations. As we recently showed, simplified models that describe the switching barriers, which are necessary to obtain predictive simulations results, overlooked a chiral contribution that leads to a splitting of barrier energies and results in faster relaxation [1,2]. As consequence of the chiral barrier splitting, the relaxation pathways are modified. In this work, we study the evolution from the field-saturated state to the ground-state order of artificial square ice with kMC simulations; and compare the effect of commonly-used mean-field barriers to the chiral split-barrier description at different interaction strengths and temperatures. We assess general measures that describe the dynamic evolution, such as vertex populations and net magnetisation as well as spatial correlations. By taking into account the chiral barrier splitting we observe faster and more efficient evolution to the ground state. Compared to the mean-field barrier model, for which the demagnetisation is mainly dominated by the nucleation and propagation of ground-state strings (for strong interactions) or random events (for weak interactions), the chiral barrier splitting promotes a richer diversity of switching events. This leads to a variety of behaviours, such as breaking up strings without the generation of charged defect vertices, the formation of coral-like domain walls, and efficient annihilation of domain walls in the later stages of the evolution to the ground state. Our results demonstrate that the rich demagnetisation dynamics of artificial square ice, as is also observed experimentally, can be partially explained even in the absence of additional disorder.

technical paper

Interfacial phenomena in magnetic thin film systems are key to future spintronic applications. For materials close to the Stoner criterion, such as Pt, electronic hybridisation at the interface with a magnetic material results in a proximity induced moment (PIM), with debate ongoing regarding the role of the induced moment with regards to interfacial spin transport [1,2]. Recently, rare-earth:transition metal (RE:TM) ferrimagnetic alloys have shown promise in spintronic applications, due to the net zero magnetisation at the compensation point of the two competing magnetic sub-lattices. This compensation, which occurs as a function of both temperature and alloy composition, enhances domain wall motion [3], thermal switching [4] and leads to vanishing skyrmion Hall angles [5]. However, in multilayered systems, it has not been experimentally shown whether the induced moment in a Pt at the interface with a RE:TM ferrimagnet will align with the net moment, or one of the magnetic sublattices. Here we present the results of a recently published study [6] investigating the magnetic moments in ferrimagnetic / Pt systems, using Co77Gd23 and (Co50Fe50)77Gd23 ferrimagnetic alloys to vary the dominant magnetic sublattice. Temperature dependent SQUID measurements, combined with element specific resonant x-ray measurements at the APS, Argonne Lab on the Pt and Gd L3 edges, allowed for the determination of the alignment of the Gd moments and induced Pt moments on either side of the compensation transition. In both cases, the PIM was found to be parallel to the TM sublattice rather than the RE or the net moment. Our results highlight the prominence of the d−d mediated interactions between the Pt and the constituents of the ferrimagnetic RE:TM alloys over the net macroscopic moment.

![](https://assets.underline.io/uploads/markdown_image/1/image/4ff3a1ca1079ff9c262e75f9fde1108a.jpg)

Fig 1: Element specific hysteresis loops taken at the Pt and Gd L3 edges for CoGd/Pt (Gd dominated) and CoFeGd/Pt (CoFe dominated)

Proximity induced magnetism in Pt layered with rare-earth:transition metal ferrimagnetic alloys

Combining perpendicular magnetic anisotropy (PMA) with half-metallicity (HM) in thin-film geometry may provide additional functionalities for spintronic devices. However, such combination may be a challenging task, since HM is usually destroyed in thin-film geometry (e.g., due to the emergence of surface states), while PMA is most pronounced in reduced geometry, because of the contribution from surface anisotropy. Here, we explore the nature of PMA in thin-film full Heusler alloy Co2MnSi. This material is one of the first compounds for which half-metallic electronic structure was experimentally confirmed. In addition, it has been reported that this alloy may exhibit PMA in thin-film geometry. Here, by analyzing site-projected magnetocrystalline anisotropy energy (MAE), we confirm that both PMA and surface half-metallicity are very sensitive to the termination surface and mechanical strain. In particular, while MnSi-termination under compressive strain may retain both 100% spin-polarization and out-of-plane magnetization orientation, Co-termination has a detrimental impact on both. These results may serve as a guide for practical nano-device applications in the field of spintronics. This research is supported by the National Science Foundation (NSF) under Grant Numbers 2003828 and 2003856 via DMR and EPSCoR.

First principles study of perpendicular magnetic anisotropy in thin-film Co2MnSi

In the race for the miniaturization of electronic devices, modern science reached the ultimate level of monoatomic layers. Whereas, magnetic tunnel junctions with perpendicular magnetic anisotropy reached the limit of about twenty atomic monolayers [1]. In our work, we systematically study the magnetic anisotropy of Fe and FeCo thin films of size from one to twenty atomic monolayers. Theoretical studies are based on calculations using the full-potential local-orbital electronic structure code FPLO [2] and generalized gradient approximation (GGA). The chemical disorder in FeCo layers was modeled using virtual crystal approximation (VCA). A set of layers with different thicknesses formed based on the bcc structure was subjected to full geometry optimization. The set of equilibrium structures was then recalculated using a fully relativistic approach for two orthogonal magnetization directions (in-plane and out-of-plane). The results of calculations allow the interpretation of parallel experimental studies in which FeCo layers on Au substrate are analyzed. The result of ab-initio calculations is a series of dependences of structural and magnetic parameters on layer thickness. Fig. 1 shows an example of the dependence of the optimized lattice constant on the Fe layer thickness. For few-atom-thick Fe layers there is a large reduction of the lattice parameter with respect to the value for bulk bcc Fe, to which the parameters determined for thicker layers converge. Fig. 2 presents the dependence of the magnetocrystalline anisotropy energy (MAE) on the Fe layer thickness. Positive values denote perpendicular magnetic anisotropy, negative values denote anisotropy in-plane. The calculated value of MAE for Fe monolayer equal to 0.58 meV/atom is in good agreement with the previous GGA result equal to 0.50 meV/atom [3]. These results were compared with measurements of the ratio of orbital to spin magnetic moment using VNA-FMR. We found that the contribution of surface anisotropy to the effective anisotropy is strong enough to overcome the shape anisotropy in Au/CoFe/Au systems.

![](https://assets.underline.io/uploads/markdown_image/1/image/0cc0613d2960ba04eae25216e4150cf3.jpg)

Fig.1 Dependence of the lattice parameter on the Fe layer thickness.


![](https://assets.underline.io/uploads/markdown_image/1/image/05159cf1c9b8516a3e45b8cc11e76092.jpg)

Fig.2 Dependence of MAE on Fe layer thickness.

Magnetocrystalline Anisotropy of Fe and FeCo Thin Films

Motivated by immense scientific interest in Co-based Heusler compounds [1 - 3] Co2FeSi and Co2TiSi as promising candidates for spintronics applications, 100 nm thick Co2Fe0.5Ti0.5Si (CFTS) thin films were grown on Si(100) substrates at substrate temperatures (TS) ranging from 200°C to 550°C by ultra-high vacuum magnetron sputtering. The deposited films were annealed in-situ at TS for 30 min. Energy-dispersive X-ray absorption spectroscopy yielded the actual alloy composition as Co2.01Fe0.51Ti0.24Si1.24. X-ray diffraction (XRD) patterns, shown in figure 1, reveal no Bragg peaks for TS200 film, broad fundamental peak (220) for TS350 film, and three sharp peaks (111), (220), and (422) for the remaining films. Thus, the crystalline structure gradually evolves from amorphous to ordered L21 structure as the TS increases; the TS500 film has the highest L21 order. Ferromagnetic resonance (FMR) spectra were recorded at various polar (‘out-of-plane’, OP) field angles, θH, at a fixed frequency of 9.45 GHz. A typical FMR spectrum, taken at θH = 0 for the TS500 film, shown in figure 2(a), demonstrates that besides the uniform precession q = 0 spin wave (SW) mode, the SW modes with q ≠ 0 exist. A detailed analysis [4 - 6] of the resonance field, Hres, versus θH plots (see Fig.2(a) inset) reveals a dominant OP uniaxial anisotropy. Fig.2(b) bears out that the frequency (f) vs. Hres plots, obtained using the broad-band (3–17 GHz) FMR setup, are well described by the Kittel resonance condition [7] (the curves through the data points):f=γ/2π[(Hr+Hk)×(Hr+HK+4πMeff)]1/2, where γ=(2πgµB)/h is the gyromagnetic ratio, Meff, effective magnetization while HK, g, and µB are the in-plane (IP) anisotropy field, Lande g-factor and Bohr magneton. We find that the IP anisotropy is very weak, and g has the minimum value of 2.02 for the TS500 film with the highest L21 order. The Gilbert damping constant (α) is determined from the linear fits (straight lines) to the frequency-dependent `peak-to-peak’ FMR linewidth (ΔH) data (symbols), shown in Fig.2(b) inset, based on the relation [8] ΔH=ΔHinhomo+(2/√3)2παf/γ. The TS500 film has the lowest value of α = 0.0032.

![](https://assets.underline.io/uploads/markdown_image/1/image/9533bfba1a7a0a2925e327fb6b2a7807.jpg)

Fig.1:XRD patterns.

![](https://assets.underline.io/uploads/markdown_image/1/image/def68b16a566ae375f2c4e18bf05d2ba.jpg)

Fig.2(a) FMR spectrum; inset: Hres(θH). (b) f(Hres); inset: ΔH(f).

Effect of site disorder on the resonant microwave absorption in Co2Fe0.5Ti0.5Si Heusler alloy thin films

Buckminsterfullerene (C60) can exhibit ferromagnetism at the interface (called as a spinterface) when it is placed next to a ferromagnet (FM). The formation of spinterface can influence the domain size and dynamics of the organic/ferromagnetic heterostructure [1-3]. Perpendicular magnetic anisotropic (PMA) systems are the most suitable candidates for data storage devices due to their high intrinsic anisotropy [4]. It has been demonstrated that with increasing thickness of the OSC layer on a Co ultrathin film one can tune the anisotropy of the system from in-plane to out-of-plane geometry [5]. However, FM-OSC systems with PMA have not been studied extensively. In this context, we have studied the tunability of magnetization relaxation and domain structure for Pt/Co/C60/Pt system with perpendicular anisotropy. We have prepared thin films of Pt/Co/Pt [sample 1] and Pt/Co/C60/Pt [sample 2]. Fig.1 show the hysteresis loops and domain images measured using polar MOKE for both the samples. It has been observed that the size of the bubbles shrinks for sample 2 in comparison to sample 1. The possible explanation may be the formation of spinterface at Co-C60 interface, which increases the overall anisotropy of the system and decreases the domain size. However, the overall shape of the bubble domains remains same to its parent Pt/Co/Pt thin film. To calculate the relaxation time of a system we have performed magnetic relaxation measurements at different sub-coercive fields (0.93, 0.95, 097 Hc). For both the samples relaxation time decrease with increasing the applied magnetic field, which is expected. However, for Pt/Co/C60/Pt (sample 2) the relaxation time is reduced by ~ 50% as compared to Pt/Co/Pt (sample 1). Therefore, it is inferred that by introducing a C60 layer the switching speed of a system can be tuned which is a promising way to build device applications. Further, we have performed DFT calculation to understand the underneath mechanism of the Co/C60 spinterface.

![](https://assets.underline.io/uploads/markdown_image/1/image/aa68447e1fc66264cd907063616e005f.jpg)

Figure 1: (A) Hysteresis loops for sample 1(red) and 2 (blue). (a–c) and (d–f) are the domain images at different field marked in (A) for samples 1 and 2, respectively.

Effect of Fullerence on magnetization relaxation and domain wall dynamics in a perpendicularly magnetized Pt/Co/C60/Pt system

Though nano-hetero-structured (NHS) magnetic materials preparation using sputtering, electron beam lithography/ evaporation (EBL/EBE) have inspired a wealth of experimental results, to date, there is a very limited experimental understanding of preparing in situ NHS magnetic material using electrodeposition technique and the elucidation of their magnetic behavior. Towards this end, using pulse reverse [1] electrodeposition technique with a modified and stable acidic bath chemistry at room temperature, we have prepared in situ NHS magnetic cobalt phosphorus (CoP) thin film and investigated its characteristics structurally and magnetically combined with micromagnetic simulation utilizing MuMax3 [2]. Despite the availability of various techniques, the electrodeposition technique [1,3–5] has been chosen due to its relatively higher deposition rate and low cost. Here, CoP thin films with ultralow coercivity to moderate coercivity have been prepared from a single starting material from the same bath. The crossover from the ultralow coercivity to a comparatively higher coercivity has been demonstrated by the manipulation of the time width of the current (shown in FIG. 1) in a single amorphous system of CoP nanomagnetic thin film. We have characterized the developed smooth, stress-free, and shiny electroplated samples structurally by SEM, TEM, and magnetically by the hysteresis loop tracer (ShB Instruments, USA). The SEM micrographs confirm the fine-grain surface morphology of the cobalt phosphorous nanomagnetic thin films. The elemental analysis by energy dispersive X-Ray (EDX) yields the stoichiometry of the electrodeposited cobalt phosphorous. This pulse reverse plating technique could be an ideal option to tune the spin configuration with respect to the multi-nano layer thicknesses to obtain an optimum exchange coupling. The static in-plane magnetic measurement by the hysteresis loop tracer is shown in FIG. 2(c)-(d) reveals different hysteresis loops of electrodeposited CoP thin film.

![](https://assets.underline.io/uploads/markdown_image/1/image/354a83ea035e65fd21569e8d324cea3e.jpg)

Waveform and timing diagram for PR electroplating to develop nanomaterials from a single bath.

![](https://assets.underline.io/uploads/markdown_image/1/image/2597ecc569fa0fdcb4c80560a976b20e.jpg)

(a) An SEM and (b) a cross-sectional TEM image of CoP thin film. Hysteresis loop of (c) ultralow CoP, and (d) comparatively higher CoP

Structural and Magnetic Study of Single Nano-Hetero-Structured Co-Rich CoP Magnetic Thin Films

One of the main goals of quantum computing is to find stable quantum bit realizations. Magnetic chains on superconducting surfaces manifest topologically protected Majorana quasiparticles as zero-energy modes located at the ends of the chain makeing them possible candidates for such fault-tolerant quantum computing. The rapid development of scanning tunneling microscopy measurements in the past decade provided an effective way to study these system in experiments with a high energy resolution turning not only the experimental but the theoretical interest to this way. In the present work we introduce an ab initio approach employing multiple scattering theory and Green's function embedding for the calculation of the spectral properties of magnetic impurities embedded onto the surface of a superconducting host. We consider different Fe clusters separated by a single Au overlayer on Nb(110) which is highly motivated by experiments. We perform systematic calculations for dimers and chains along different crystallographic directions, with different distances of the Fe atoms and in different magnetic configurations. Based on the local density of states (LDOS) we study the conditions under which Majorana zero modes might appear.

![](https://assets.underline.io/uploads/markdown_image/1/image/95e695f41378765994be56999251c555.jpg)

Fig.1 The spatial distribution of a YSR state for an Fe dimer on Au/Nb(110)

Theoretical study of Yu-Shiba-Rusinov states and Shiba bands for Fe dimers and chains on Au/Nb(110)

Artificial spin ices (ASI) are magnetic metamaterials comprising geometrically-tiled interacting nanomagnets. Typically each nanoisland is magnetized along its long axis giving an Ising ‘macrospin’. There has been significant recent interest in these systems for functional magnonics due to their large reconfigurable dipolar field landscape. Here we present recent advances using a width modification scheme where artificial spin ice is modified by widening a subset of bars relative to the rest of the array. There are two principal benefits to the width modification. Firstly, Increasing width decreases the coercive field of the macrospins, so certain geometric tilings of the wide bars allow preparation of any ordered macrospin vertex state via simple global-field protocols1. Secondly at a certain width the macrospin spin state will be energetically equivalent with the vortex state so the wide bars can be tuned to be metastable in the macrospin and vortex states, yielding Artificial Spin-Vortex Ice (ASVI)2. The precise control of both nanoisland magnetism and vertex configuration by the width modification enables us to demonstrate the efficacy of zero-field ferromagnetic resonance measurements of the spin-wave spectrum as a fingerprint of the local dipolar field environment and vertex populations in magnetic nanostructures3. Artificial Spin-Vortex Ice allows a cross over experimentally from the classic 2-state Ising ASI to a 4-state Potts model system where the macrospins can convert into closed vortices. Unlike in a ‘clock model’ Potts system, the dipolar interactions are almost completely eliminated in the vortex state.4 The enhanced bi-texture microstate space gives rise to emergent physical memory phenomena, with ratchet-like vortex training and history-dependent nonlinear training dynamics. We observe vortex-domain formation alongside MFM tip vortex-writing. Tip-written vortices dramatically alter local reversal and memory dynamics. The precise control and the dramatic differences in local dipolar environment are very promising for reconfigurable magnonics. In the width modified macrospin ASI, we obtain shifts in ferromagnetic resonance frequency of the order of hundreds of MHz and access states with mode hybridization. ASVI yield much stronger contrast in dipolar environment such that the gap between the macrospin and the vortex peak is around 3.8 GHz.

Reconfigurable magnetism in a bi-stable nanomagnetic array: Artificial Spin-Vortex Ice.

Artificial spin ice (ASI) [1] systems are two-dimensional arrays of single-domain nanomagnetic islands that are designed to study collective behavior of interacting magnetic systems. These nanoislands usually have a stadium shape so that the magnetization orients along the longer axis, i.e., the moments are Ising-like. Most research on ASI systems focuses on different arrangements of nanoisland arrays [2], but, recently, some studies have focused on modifying the shapes of nanoislands [3,4]. Here, we introduce a new design of nanoislands, the Y-shape island, which has three equal-length arms joining at the center, with 120° separation. This island has six possible moment configurations in which the magnetization on each arm points either toward the center or away from it. We fabricated such nanoislands from permalloy, arranged in a hexagonal lattice geometry (Fig 1). Since permalloy has little magnetocrystalline anisotropy, the magnetization of the nanoislands can be well-controlled by utilizing shape anisotropy. We annealed such samples above the Curie temperature and examined the moment configurations using magnetic force microscopy after the samples cooled back to room temperature. We find strong correlations among the complex moment arrangements of these islands, suggesting the possibility of new types of moment ordering and new phenomenological ways of describing these novel magnetic objects associated with their unusual symmetry. Work at Yale University was funded by the US Department of Energy, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under Grant No. DE-SC0020162. Work at the University of Minnesota was supported by NSF through Grants No. DMR-1807124 and DMR-2103711.

![](https://assets.underline.io/uploads/markdown_image/1/image/2edd3e78dd111803b2e2fb7c7778f707.jpg)

Figure 1. (a) A scanning electron microscopy image of Y-shape nanoislands in hexagonal geometry. (b) A magnetic force microscopy image taken after annealing at 550 degree C. The white and black dots correspond to the poles of the island moments. (c) The corresponding moment schematic.

Artificial Spin Ice with Y-shaped Nanomagnets

The fundamental building blocks of artificial spin ice (ASI) systems are magnetic nanoislands designed for Ising-like single domain configurations magnetized along the nanoisland length due to shape anisotropy. The dipolar interaction between these macrospins serve as the basis for investigating geometric frustration in ASIs with a variety of array geometries ranging from square-like arrangements to quasicrystals. Using X-ray photoemission electron microscopy (X-PEEM) to perform magnetic domain imaging, we studied thermally demagnetized La0.7Sr0.3MnO3-based brickwork ASIs and showed that non-Ising domains, which we call complex spin textures (CSTs), can be stabilized through appropriate selection of nanoisland width, W, and ASI lattice parameter, a. While W-dependent formation of CSTs can be explained due to the dominance of shape anisotropy, the a-dependence was unexpected for nanoislands possessing identical W, suggesting that inter-island effects play an important role. MuMax3 micromagnetic simulations indicated that an intermediate range of 100 nm ≤ W &lt; 150 nm and 600 nm ≤ a ≤ 700 nm exists where the formation of Ising states are preferred over CSTs as shown in Fig. 1. For larger values of W and a that reside above the black border in the energy diagram of Fig. 1, CST formation becomes energetically favorable over an arrangement of Ising states in higher energy vertex configurations. Energy analysis suggests that while magnetostatic energy dominates the energetics, the small contribution from exchange energy determines whether nanoislands can exist in Ising or CST states. The nanoisland magnetic state changes the magnetostatics arising from both intra-island shape anisotropy and inter-island dipolar interaction. These results suggest the potential to create tunable nanoisland domain states, providing a new direction in the development of ASI systems with exotic phase transitions as well as novel nanomagnetic logic architectures.

![](https://assets.underline.io/uploads/markdown_image/1/image/12c68623b9c39a06d7d5874092f9e981.jpg)

Energetics of complex spin textures in LSMO artificial spin ice structures

Role of Chiral Switching Barriers on Relaxation Kinetics in Artificial Square Ice

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