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&lt;br/&gt;Spin glasses, generally defined as disordered systems with randomized competing interactions that result in an extensively degenerate ground state&lt;sup&gt;1, 2&lt;/sup&gt;, are a widely investigated complex system. Theoretical models describing spin glasses are broadly used in other complex systems, such as those describing brain function&lt;sup&gt;3&lt;/sup&gt;, error-correcting codes&lt;sup&gt;4&lt;/sup&gt;, or stock-market dynamics&lt;sup&gt;5&lt;/sup&gt;. This wide interest in spin glasses provides strong motivation to generate an artificial spin glass within the framework of artificial spin ice systems&lt;sup&gt;6&lt;/sup&gt;. Here, we present the first experimental realization of an artificial spin glass, consisting of dipolar coupled single-domain Ising-type nanomagnets arranged onto an interaction network that replicates the aspects of a Hopfield neural network&lt;sup&gt;7&lt;/sup&gt;. Using cryogenic x-ray photoemission electron microscopy (XPEEM), we performed temperature dependent imaging of thermally driven moment fluctuations within these networks and observed characteristic features of a two-dimensional Ising spin glass. Specifically, the temperature dependence of the spin glass correlation function follows a power law trend predicted from theoretical models on two-dimensional spin glasses. Furthermore, we observe clear signatures of the hard to observe rugged spin glass free energy&lt;sup&gt;1&lt;/sup&gt; in the form of sub-aging, out of equilibrium autocorrelations&lt;sup&gt;1&lt;/sup&gt; and a transition from convergent to divergent dynamics&lt;sup&gt;1, 8&lt;/sup&gt;.

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2022 Joint MMM-INTERMAG

Direct observation of a Dynamical Glass Transition in a Nanomagnetic Artificial Hopfield Network

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Spin glasses, generally defined as disordered systems with randomized competing interactions that result in an extensively degenerate ground state1, 2, are a widely investigated complex system. Theoretical models describing spin glasses are broadly used in other complex systems, such as those describing brain function3, error-correcting codes4, or stock-market dynamics5. This wide interest in spin glasses provides strong motivation to generate an artificial spin glass within the framework of artificial spin ice systems6. Here, we present the first experimental realization of an artificial spin glass, consisting of dipolar coupled single-domain Ising-type nanomagnets arranged onto an interaction network that replicates the aspects of a Hopfield neural network7. Using cryogenic x-ray photoemission electron microscopy (XPEEM), we performed temperature dependent imaging of thermally driven moment fluctuations within these networks and observed characteristic features of a two-dimensional Ising spin glass. Specifically, the temperature dependence of the spin glass correlation function follows a power law trend predicted from theoretical models on two-dimensional spin glasses. Furthermore, we observe clear signatures of the hard to observe rugged spin glass free energy1 in the form of sub-aging, out of equilibrium autocorrelations1 and a transition from convergent to divergent dynamics1, 8.

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technical paper

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

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.

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Waveform and timing diagram for PR electroplating to develop nanomaterials from a single bath.

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(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.

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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.

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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.

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Energetics of complex spin textures in LSMO artificial spin ice structures

Energetics of complex spin textures in LSMO artificial spin ice structures

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.

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

Bi-component magnonic crystals have shown promising applications in magnonics and spintronics [1,2]. Arrays of two-dimensional exchange and magnetostatically coupled bi-component nanotriangles (BNTs) comprising of alternating permalloy (Py) and cobalt (Co) in hexagonal arrangement were fabricated by self-aligned stepwise nanosphere lithography [3]. The separation (S) between constituent NTs was varied to investigate the effects of exchange and magnetostatic interaction. Static magnetic properties of BNTs were investigated by OOMMF simulations and compared to homogeneous Py NTs [4]. Fig 1(a) shows simulated M-H loops for BNTs during hard axis magnetization with different S values. The loops exhibit distinct two-step switching corresponding to magnetization reversal of Py and Co NTs at different fields. Py NTs are observed to switch at a lower field shown in Fig 1(d) for S=0 nm. For homogeneous Py NTs in Fig 1(b), multiple kinks were also observed for S=0 & -60 nm (overlapping NTs) but these represent the domain changes in individual NTs. For S= -60nm, antiparallel alignment was displayed in each NT pair during reversal. For S=60nm, the NTs react independently due to the lack of strong exchange coupling. Hence switching is random and independent of location. For S=0, the NTs within the inner ring switched at a lower field, as shown in Fig 1(e). Fig 2 shows MFM images of BNTs with S=0 during hard axis field reversal. The magnetic domains of BNTs at remanence after saturation is in good agreement with simulation in Fig 1(c). In contrast to Fig 1(d), Co NTs were observed to reverse at a lower field. This is attributed to the smaller fabricated Co size compared to Py NTs. We will discuss the effect of material difference and separation between constituent NTs in detail via OOMMF simulation and field reversal study.

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Fig. 1 Simulated M-H loops for S= -60, 0, +60 nm for (a) Co/Py NTs; (b) Py/Py NTs. Simulated spin states for (c-d) BNTs; (e) Py/Py NTs at different fields. Colored arrows indicate spin orientations.


![](https://assets.underline.io/uploads/markdown_image/1/image/8285bc51588ea41eb64cd46369774d8f.jpg)

Fig. 2 (a) AFM; (b-d) MFM of BNTs with S=0 nm at remanence after applying field of 3500, -400 and -600 Oe. White arrow indicates the applied field direction. Colored circles indicate a change in magnetic domain.

Static Magnetic Properties of Bi-component Nanotriangles in Hexagonal Arrangement Fabricated by Stepwise Nanosphere Lithography

We have studied the use of self-assembled block copolymers to pattern multilayers of Co and Pd on silicon wafers. Stacks ranging from 4 to 12 bilayers of Co(0.3 nm)/Pd(0.8 nm) were sputtered onto Ta/Pd seed layers and capped with 3 nm of Ta, and were found to have perpendicular magnetic anisotropy as-deposited. The block copolymer, PS-PFS, was dissolved in toluene and spun onto the wafers. After heat treatment to phase-separate the polymers, the PS was removed by oxygen plasma ashing. The remaining polymer, PFS, formed self-assembled spheres that were used as masks to ion-mill the Co/Pd multilayers into nanopillars [1]. To study the effect of etch time and etch angle on the coercivity distribution, we synthesized samples in a “design of experiments” grid in these two variables. Scanning electron micrographs showed nanopillars ranging from 10 to 30 nm in diameter, depending primarily on etch time (Fig. 1). M-H loops measured on both patterned and unpatterned wafers showed an increase of up to 113% in coercivity upon patterning. First Order Reversal Curves (FORC) were measured, and the resulting FORC distributions showed different features for the nanopatterned vs. unpatterned films. Fig. 2 shows the FORC curves and the resulting FORC distribution for an unpatterned multilayer [Co/Pd] plotted by (1) FORC+ (MagVis.org), which shows the exact measured FORC density without averaging and (2) the more often used averaged color map, in which information is lost. Both displays show a large positive peak with coercivity (Hc) about 500 Oe, with a “dipole tail” characteristic of switching by domain nucleation and wall motion [2]. In the FORC+ plot, the tail consists of a string of negative (blue, on the left) and positive (orange, on the right) pixels – the variation of density along the tail is smaller in the averaged curve, but this comes at the expense of greatly overestimating the separation between the positive and negative tails.

![](https://assets.underline.io/uploads/markdown_image/1/image/fd0faa405db6b295f8638cd9fef73451.jpg)

Fig. 1. SEM image of a patterned [Co(0.3 nm)/Pd(0.8 nm)]12 film: 20 nm diameter pillars.

![](https://assets.underline.io/uploads/markdown_image/1/image/5959a0e19128eea71ab4aa949fd706fa.jpg).

Fig. 2. Top: FORC curves M(H). Bottom right: FORC+ distribution. Orange is positive, blue negative Left: Smoothed FORC distribution, on the same scale but displaced to left, with color legend.

FORC Analysis of Nanopatterned vs. Unpatterned Films: Coercivity and Switching Mechanisms

Non-collinear antiferromagnetic orders are of strong interest in the fields of spintronics, topological magnetism and multiferroicity [1]. However, the magnetic imaging of these materials is particularly challenging due to their zero net magnetization. Dy epitaxial films exhibit an antiferromagnetic helical phase and strong X-ray magnetic scattering at the Dy L3 edge [2] These characteristics make it a perfect candidate to fully vectorial reconstruction of a non-collinear magnetic order, enabled by the new combination of Resonant X-ray Magnetic Scattering (RXMS) [3] and Coherent Diffraction Imaging (CDI) [4]. In order to implement this technique, micro-objects are required as model samples. The micropatterning of Dy nanofilms (top-down approach) is however particularly challenging due to the high reactiveness of Dy. In this work, we present the results of this microfabrication process, from the growth of Dy epitaxial nanofilms to the patterning and full characterization of the µ-disks. The high crystalline quality of the Dy(0001) films, grown on A-plane sapphire/(110) Nb templates, is kept after the optical lithography followed by Ion Beam Etching. X-ray diffraction (Fig.1) indicates a moderate decrease in coherence length (10%) and an increase in mosaicity (17%) in 2 mm disks compared with continuous films. However, an FCC phase is formed, likely due to hydrogenation during the patterning process [5] SQUID measurements and RXMS (BM28-ESRF) confirm the occurrence of the helical phase in the Dy µ-disks, with similar Néel and Curie temperatures as in continuous films, but with a slight increase in critical fields. The temperature dependence of (002-t) magnetic satellites reveals that helical turn angles in the patterned samples do not differ significantly from those observed in epitaxial films [6](Fig. 2). The effect of the buffer layer (Nb or Nb/Y) is also studied and correlated to the role of epitaxial strains.

![](https://assets.underline.io/uploads/markdown_image/1/image/8129cbfe6c8f62f2fcbd865b2993bdcd.jpg)

(0 0 L) scans at the Dy L3 edge at 130 K measured for Nb/Dy (green), Nb/Y/Dy (orange) and their respective µ-disks. Grey region indicates the magnetic satellites. Insert: SEM tilted view of Dy µ-disks.

![](https://assets.underline.io/uploads/markdown_image/1/image/45d553476adcd2f5d6198955784f0389.jpg)

Turn angle of the Dy helical phase as a function of temperature (same samples as in Fig.1).

Direct observation of a Dynamical Glass Transition in a Nanomagnetic Artificial Hopfield Network

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

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Direct observation of a Dynamical Glass Transition in a Nanomagnetic Artificial Hopfield Network

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

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Translating time in humans and other species from brain transcriptional and structural variation.

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