United States

Cobalt ferrite nanoparticles (NP) are competitive systems in technological and biomedical applications due to a suitable combination of excellent chemical and magnetic characteristics, such as a high chemical stability, surface active sites, and ease of synthesis and functionalization, together with a high anisotropy constant, a high coercivity, and a moderate saturation magnetization. However, in order to control the functional response of Co-ferrite NP, one of the biggest challenges is to quantitatively disentangle the dependence of the overall magnetic response on the composition, structure, or surface chemistry.&lt;br/&gt;In this work, we address the key role of the structural defects on the magnetic properties of Co-ferrite NP investigated by element- and site-specific X-ray magnetic circular dichroism (XMCD) combined with high-resolution transmission electron microscopy of individual NP [1]. We studied a series of samples of monodisperse 8 nm NP, prepared by chemical routes [2,3], with similar stoichiometry and cation distribution but with a tunable number of structural defects. Element- specific XAS and XMCD spectra and hysteresis loops reveal that the collinear alignment of Co&lt;sup&gt;2+&lt;/sup&gt; (O&lt;sub&gt;h&lt;/sub&gt;) cations is much more affected by the structural disorder than that of the Fe&lt;sup&gt;3+&lt;/sup&gt; cations. This is because structural defects give rise to effective local anisotropy axes, causing a prevalent Co&lt;sup&gt;2+&lt;/sup&gt; spin canting through the spin−orbit coupling due to the relatively large value of the partially unquenched moment of these cations. As the structural disorder is further increased, the rest of the cations in the two sublattices are progressively dragged off the ferromagnetic alignment, being Fe&lt;sup&gt;3+&lt;/sup&gt;(Td) cations the least sensitive to defects due to the smaller number of next-nearest neighbors in the T&lt;sub&gt;d&lt;/sub&gt;-sublattice. Our work highlights the importance of combining advanced synthesis with the use of complementary local probes with element, valence, site, and structural sensitivity to enhance the performance of nanoscale magnetic materials.

![](https://assets.underline.io/uploads/markdown_image/1/image/a5aa5eb0e8a24261183ee2e55ee59892.jpg)

HRTEM images for Co-ferriteNP with increasing crystalline quality. Bottom panel: XMCD hysteresis loops measured at 2 K for Co2+ cations in Oh sites for highly-defective (left) and highly-crystalline (right) NP.

2022 Joint MMM-INTERMAG

Disentangling Atom- and Site- Selective Spin Canting in Co-ferrite Nanoparticles with Tunable Structural Disorder

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.

Cobalt ferrite nanoparticles (NP) are competitive systems in technological and biomedical applications due to a suitable combination of excellent chemical and magnetic characteristics, such as a high chemical stability, surface active sites, and ease of synthesis and functionalization, together with a high anisotropy constant, a high coercivity, and a moderate saturation magnetization. However, in order to control the functional response of Co-ferrite NP, one of the biggest challenges is to quantitatively disentangle the dependence of the overall magnetic response on the composition, structure, or surface chemistry. In this work, we address the key role of the structural defects on the magnetic properties of Co-ferrite NP investigated by element- and site-specific X-ray magnetic circular dichroism (XMCD) combined with high-resolution transmission electron microscopy of individual NP [1]. We studied a series of samples of monodisperse 8 nm NP, prepared by chemical routes [2,3], with similar stoichiometry and cation distribution but with a tunable number of structural defects. Element- specific XAS and XMCD spectra and hysteresis loops reveal that the collinear alignment of Co2+ (Oh) cations is much more affected by the structural disorder than that of the Fe3+ cations. This is because structural defects give rise to effective local anisotropy axes, causing a prevalent Co2+ spin canting through the spin−orbit coupling due to the relatively large value of the partially unquenched moment of these cations. As the structural disorder is further increased, the rest of the cations in the two sublattices are progressively dragged off the ferromagnetic alignment, being Fe3+(Td) cations the least sensitive to defects due to the smaller number of next-nearest neighbors in the Td-sublattice. Our work highlights the importance of combining advanced synthesis with the use of complementary local probes with element, valence, site, and structural sensitivity to enhance the performance of nanoscale magnetic materials.

![](https://assets.underline.io/uploads/markdown_image/1/image/a5aa5eb0e8a24261183ee2e55ee59892.jpg)

HRTEM images for Co-ferriteNP with increasing crystalline quality. Bottom panel: XMCD hysteresis loops measured at 2 K for Co2+ cations in Oh sites for highly-defective (left) and highly-crystalline (right) NP.

technical paper

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

Investigation of magnetic domain nucleation in exchange-biased nanostructures

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.



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

Thin ferromagnetic films with perpendicular anisotropy exhibit nano-sized magnetic domains forming various patterns. When an external magnetic field is applied and cycled, the domains pattern is usually lost. However, if the ferromagnetic layer is coupled with an underlying antiferromagnetic layer, it may show magnetic domain memory (MDM). [1-3] MDM is the ability of the magnetic domains to retain their exact same domain topology upon field cycling. We are studying the effect that illumination by coherent resonant x-rays may have on MDM in a [Co / Pd] / IrMn multilayers. Our x-ray resonant magnetic scattering (XRMS) data suggests that under high dose of x-ray illumination, the material may lose its existing MDM. To investigate this possible effect we have used magneto-transport measurements [4,5] to track the exchange bias while the sample is illuminated by x-rays, using synchrotron radiation (see Fig.1a). Magneto-transport is here used to measure the magnetization loop from which we can extract a bias field. A loss of exchange bias would indicate that the x-rays illumination dose may alter the strength of the exchange couplings and ultimately the amount of MDM. Knowing if a loss of exchange bias has occurred requires collecting magneto-transport data (Fig.1b) as well as XRMS data (Fig.1c) and correlating the observed changes under various dose of x-ray illumination.These measurements include Hall effect signal and as well as magnetoresistance signal, collected both on inner contacts and on outer contacts. For the outer contacts, the spacing between wire bonds is ~1cm, whereas for the inner contacts, the spacing between wire bonds is ~100 . These measurements help us understand the shape of the magneto-transport data collected under x-ray illumination and determine if x-ray illumination has an effect on exchange couplings, and ultimately MDM.

![](https://assets.underline.io/uploads/markdown_image/1/image/766a2108304b1d8f9a1fe3c41b68e2d2.jpg)

a) Instrument used for our x-ray resonant magnetic scattering (XRMS) experiment at the APS, showing the vacuum scattering chamber and the octupolar magnet to apply a field in any direction. b) Magneto-transport measurement taken while [Co/Pd] / IrMn multilayers was illuminated with x-rays. c) XRMS speckle pattern from the [Co/Pd] / IrMn film, measured at the Co L3 edge.

The effect of x-ray illumination on magnetic domain memory in [Co/Pd] / IrMn multilayers

Advances in synthesis and characterization of magnetic nanoparticles (NPs) have yielded great gains in the understanding of their complex magnetic behaviour, with implications for numerous applications. Recent work using Ni NPs as a model soft ferromagnetic (FM) system achieved quantitative understanding of the superparamagnetic blocking temperature-particle diameter relationship1. This hinged, however, on the assumption of an FM NP volume lower than the chemical volume due to a non-FM surface dead shell, indirectly deduced from magnetometry. Here, we completely determine both the chemical and magnetic internal structure of such Ni NPs, via unpolarized, half-polarized, and fully-polarized small-angle neutron scattering (SANS) measurements and analyses, coupled with X-ray diffraction and magnetometry. The postulated magnetic dead shell is not only detected but conclusively identified as a Ni phosphide, derived from the trioctylphosphine commonly used in hot-injection syntheses. The shell thickness (t*) can be controlled by synthesis temperature (Ts), falling to as little as 0.5 nm at 170 °C (Fig. 1). Polarized SANS further reveals bulk-like ferromagnetism in the Ni core, the magnetic scattering length density (SLD) being in ideal agreement with magnetometry (Fig. 2), quantitatively supporting prior modeling of superparamagnetism. These findings advance the understanding of synthesis-structure-property relationships in metallic magnetic NPs, point to a route to ligand-free stabilization, and highlight the power of polarized SANS measurement and analysis capabilities for magnetic NP science and technology. Work supported by the UMN DOE Center for Quantum Materials.

![](https://assets.underline.io/uploads/markdown_image/1/image/d1fcb57216327d31778b53fae71eebc0.jpg)

Fig. 2. Ni core magnetic SLD vs. T (circles) from half-polarized SANS for the NPs at Ts = 170 °C, superimposed on magnetometry field-cooled (FC) (solid line) and zero field-cooled (ZFC) (dashed line) data measured at 50 Oe.


![](https://assets.underline.io/uploads/markdown_image/1/image/9a9b611d4e7684db8891288e9cd064ae.jpg)

Fig. 2. Ni core magnetic SLD vs. T (circles) from half-polarized SANS for the NPs at Ts = 170 °C, superimposed on magnetometry field-cooled (FC) (solid line) and zero field-cooled (ZFC) (dashed line) data measured at 50 Oe.

Disentangling Atom- and Site- Selective Spin Canting in Co-ferrite Nanoparticles with Tunable Structural Disorder

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Disentangling Atom- and Site- Selective Spin Canting in Co-ferrite Nanoparticles with Tunable Structural Disorder

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Apparent permeability of ordered magnetically soft nanowire and microwire arrays

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Magnetic properties of Ce85Al15 doped NdFeB sintered magnet by grain boundary diffusion of Tb70Cu30 powders

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