Magnetocrystalline Easy Axis Research Articles

Micro-magnetoelastic modeling of Terfenol-D for spintronics

This article focuses on computational studies evaluating the influence of crystallinity, residual stresses, and out-of-plane (OOP) deterministic switching on Terfenol-D nano/microstructures. The computational models use both coupled and uncoupled Landau–Liftshitz–Gilbert equations with elastodynamics to study strain-induced magnetization reorientation. A Voronoi tessellation approach models the crystal distribution in the microstructures subjected to residual stresses with good agreement to experimental data including large changes in coercivity values, i.e., from 100 to 3000 Oe. Parametric studies show how the coercivity is manipulated with residual stresses, including a magnetoelastically induced perpendicular-magnetic-anisotropy (PMA), important for memory applications. Additional parametric studies focus on epitaxially deposited micro-disks, revealing that residual stresses can create magnetoelastically dominant easy axes along the ⟨110⟩ directions, which are energetically favorable relative to the intrinsic ⟨111⟩ magnetocrystalline easy axes. Modification of the global easy axis is used to design a strain-mediated multiferroic composite consisting of a 20 nm epitaxially deposited Terfenol-D memory bit with PMA grown on a PZT substrate. The multiferroic disk achieves OOP deterministic clocking with an applied voltage.

Magnetic states and dynamics of bistable square Fe nanoislands

The low energy magnetic configurations in square 300 nm Fe islands, having their magneto-crystalline easy axes aligned along the diagonals of the squares, are studied by micromagnetic simulations with the help of the mumax3 package. For thicknesses above 2.4 nm vortex configurations become the lowest energy states. However for the thickness range 1.5–2.5 nm “leaf”, vortex and “C” state configurations have comparable energies and can be all stabilized as the energy barriers that separate them are substantial (209 kBT to 401 kBT) and much larger than their energy differences. Therefore in ordered arrays of such elements different states could be simultaneously present depending on the local interactions and previous history. In view of their use as tunable magnonic metamaterials the high frequency response of each configuration is micromagnetically simulated. The resonance frequencies in single elements as well as for arrays, and the localized spin wave modes that correspond to each resonance, are extracted for each of the low energy micromagnetic states.

Magnetization reversal in cobalt nanowires with combined magneto-crystalline and shape anisotropies

Abstract In the present study, we present new experimental and calculated results of Co nanowires synthesized by the solvothermal method. The coercivity of 8.7 kOe and the energy product of 31.4 MGOe were obtained for wires of average diameters of 20 nm and average lengths of 200 nm. The experimental and numerical results of nanowires were discussed. Micromagnetic simulations were conducted to study the dependence of the magnetic properties on the nanowire aspect ratios, diameters, and various magneto-crystalline easy axis deviation angles from the long axis of Co nanowires. The calculation with a magneto-crystalline easy axis deviations from long axis show a better accordance with experimental results. The state graphs for reversal modes versus the magneto-crystalline easy axis deviation angles in Co nanowires were presented.

Spin waves and stability of zigzag order in the Hubbard model with spin-dependent hopping terms: Application to the honeycomb lattice compounds Na2IrO3 and α-RuCl3

Spin waves in the zigzag ordered state on a honeycomb lattice are investigated within a Hubbard model with spin-dependent hopping terms. Roles of the emergent Kitaev, Heisenberg, Dzyaloshinskii-Moriya, and symmetric-off-diagonal spin interactions are investigated on the stability of the zigzag order. While the DM interactions are found to destabilize the zigzag order, the secondary spin-dependent hopping terms (associated with structural distortions) are shown to strongly stabilize the zigzag order and account for magnetocrystalline anisotropy, easy axis, and spin wave gap. The calculated spin wave dispersion and energy scale are in good agreement with inelastic neutron scattering measurements on $\rm \alpha - RuCl_3$ and $\rm Na_2 Ir O_3$.

Remanence enhancement for stray field-based applications in arrays of crystalline nanomagnets

With the aim of achieving stable, substantial remanences adequate for exploitation in stray field-based applications, we report on the hysteresis behavior occurring in arrays of single-crystal Fe motifs, e-beam lithographed into prisms with triangular bases and different orientations of their magnetocrystalline axes with respect to the morphological symmetry axes. From both experimental and simulational analyses we recognize the fact that the magnetization reversal processes of our samples were mediated by motif-sized vortices. Their nucleation and annihilation fields and sites within the motifs, and their field-induced displacements, are discussed in terms of the magnetocrystalline and configurational anisotropies and inter-motif dipolar interactions. From our data, we conclude that reduced remanences as large as 0.85 (sufficient for the application requirements), protected by nucleation fields of several tens of Oe, can be produced in arrays where magnetocrystalline easy axes reinforce and partly compensate the easiest and hardest configurational ones, respectively. The angular dependence of the reduced remanence associated with interplay of these anisotropies corresponds to a symmetry reduction from the triaxial one linked to the triangular morphology down to an effective uniaxial one. We also identify, for the particular case of inter-nanoprism distances that are short in comparison with the dimensions of the motif base, a contribution to the remanence enhancement originating from the dipolar interactions.

Direct imaging of antiferromagnetic domains in Mn2Au manipulated by high magnetic fields

In the field of antiferromagnetic (AFM) spintronics, information about the N\'eel vector, AFM domain sizes, and spin-flop fields is a prerequisite for device applications but is not available easily. We have investigated AFM domains and spin-flop induced changes of domain patterns in Mn2Au(001) epitaxial thin films by X-ray magnetic linear dichroism photoemission electron microscopy (XMLD-PEEM) using magnetic fields up to 70 T. As-prepared Mn$_2$Au films exhibit AFM domains with an average size $\sim$ 1 $\mu$m. Application of a 30T field, exceeding the spin-flop field, along a magnetocrystalline easy axis, dramatically increases the AFM domain size with N\'eel vectors perpendicular to the applied field direction. The width of N\'eel type domain walls (DW) is below the spatial resolution of the PEEM and therefore can only be estimated from an analysis of the DW profile to be smaller than 80 nm. Furthermore, using the values for the DW width and the spin-flop field, we evaluate an in-plane anisotropy constant ranging between 1 and 17 $\mu$eV/f.u.

One-dimensional in-plane edge domain walls in ultrathin ferromagnetic films

We study existence and properties of 1D edge domain walls in ultrathin ferromagnetic films with uniaxial in-plane magnetic anisotropy. In these materials, the magnetization vector is constrained to lie entirely in the film plane, with the preferred directions dictated by the magnetocrystalline easy axis. We consider magnetization profiles in the vicinity of a straight film edge oriented at an arbitrary angle with respect to the easy axis. To minimize the micromagnetic energy, these profiles form transition layers in which the magnetization vector rotates away from the direction of the easy axis to align with the film edge. We prove existence of edge domain walls as minimizers of the appropriate 1D micromagnetic energy functional and show that they are classical solutions of the associated Euler–Lagrange equation with a Dirichlet boundary condition at the edge. We also perform a numerical study of these 1D domain walls and uncover further properties of these domain wall profiles.

Effective anisotropies in magnetic nanowires using the torque method

The effective anisotropy of Co-based nanowires such as CoFe, monocrystalline hcp Co and polycrystalline Co with a mixture of fcc and hcp grains has been evaluated through micromagnetic modeling based on the magnetization torque simulations. We retrieve the experimental profile of the torque curves and show that the non-harmonic forms observed at low fields correspond to the presence of open vortices at the nanowire ends. Our results show that strong hcp anisotropy of Co cannot overcome the uniaxial character of the effective anisotropy which always remains parallel to the nanowire axis, even in the case of magnetocrystalline easy axis perpendicular to the nanowire. We evaluate effective anisotropy values for monocrystalline Co nanowires with different easy axis orientations and polycrystalline Co nanowires with different mixtures of hcp and fcc grains.

Measuring magnetisation reversal in micron-sized Nd2Fe14B single crystals by microbeam x-ray magnetic circular dichroism

Magnetisation reversal of micron-sized Nd2Fe14B single crystals with magnetisation as weak as 10−9 emu (1 µm size) was studied. Single-crystal specimens (cylinders with diameter and height of 1 to 6 µm) were prepared by focused-ion beam so that both the magnetic easy and hard axes were included in the basal plane. Their magnetic hysteresis loops were measured when they were rotated with respect to the cylindrical axis by using microbeam hard-x-ray magnetic circular dichroism (XMCD) under transmission geometry. It was found that coercivity is inversely proportional to the cosine of the angle between the magnetocrystalline easy axis and magnetic-field direction and that the magnetisation reversal is dominated by domain-wall pinning in two different modes. One is related to penetration of the reversed domain nucleated in a subsurface soft layer into the bulk hard phase, of which the hysteresis loops exhibit a single-stage abrupt jump in magnetization. The other mode is pinning of the walls within the bulk grain, of which the hysteresis loops exhibit a plateau. The multi-domain structure associated with the pinning was confirmed by XMCD mapping. The proposed method fills the gap between conventional bulk magnetic measurement and submicron-scale electrical-transport measurement for nanofabricated thin films and/or fine particles. It is expected to provide new insights into elemental magnetisation processes in micron-scale regions.

Tunable magnetocrystalline easy axis in cobalt nanowire arrays by zinc additive

Abstract A new approach to tuning the crystalline characteristics and magnetic properties of cobalt nanowire (NW) arrays embedded in AAO templates is reported using zinc additive. This is realized by adding low concentrations of Zn when pulse-electrodepositing cobalt NWs while also increasing the solution pH from 3 to 5. Using hysteresis loop measurements with a magnetic field applied parallel to the NW axis, coercivity and squareness of pure cobalt NWs increased from 890 Oe and 0.45 to 2150 Oe and 0.93 in Co 97 Zn 3 NWs, respectively, using a Zn concentration of 0.01 M at pH = 4. XRD patterns obtained from the cobalt-rich CoZn NWs revealed that the crystalline texture of cobalt changes from [1 0 0] direction to [1 0 1] and [0 0 2] at pH = 3 and 4, respectively. For the latter, the magnetocrystalline easy axis of cobalt rotates from nearly perpendicular to parallel to the NW axis, induced by the incorporation of zinc into the hcp structure of cobalt.

Magnetic Properties of Cobalt Nanowires and Nanotubes

Development of novel magnetic materials has played an important role in modern day science and technology. Nanomagnetism research not only sparks interests in fundamental physics, but also renders promising technological applications. Ferromagnetic Co nanowires, synthesized via low voltage electrodeposition method. High resolution transmission electron microscopy and x-ray diffraction results show that the nanowires are uniform in size, and consist predominantly hcp structure with the magnetocrystalline easy axis (c-axis) perpendicular to the wire axis. SQUID measurement illustrates the dominance of shape anisotropy, manifested by the weak temperature dependence of the enhanced coercive field along the wire axis. Furthermore, the magnetic domain structures of individual, segmented or multiple nanowires are studied via magnetic force microscopy. It shows a strong dipole at the ends of the wire, together with a spatial magnetization modulation along the wire with a period around 700 nm. Based on theoretical modeling, such intrinsic modulation originates from the competition between the magnetocrystalline polarization along the easy axis and the shape anisotropy along the wire axis. Low temperature magnetoresistance measurement shows irreversible magnetization switching in addition to the anisotropic behavior due to magnetization orientation dependent electron scattering.On the other hand, Cobalt nanotube arrays embedded in hexagonally ordered anodic aluminum oxide templates are fabricated by direct electrodeposition with low current density under several mA/cm2. The wall thickness is about 15 nm and outer diameters are in accordance with pore diameter around 80 nm. Nearly 100% filling rate is achieved which benefits from the through pores which enable the efficient penetration of electrolyte. Transmission electron microscopy and selected-area electron diffraction are performed to show that the nanotubes are predominantly hcp single crystals with c-axis (easy axis) perpendicular to the tube axis. SQUID and MFM results indicate that the magnetization follows a circumferential direction around the tube, which is manifested in the weak magnetic signal in the MFM imaging as well as a sheared hysteresis dependence for field applied along the tube axis. This phenomenon has been confirmed by theoretical modeling taking into account the magnetocrystalline, shape demagnetization and magnetic exchange energies.

Hydrogen-plasma-induced magnetocrystalline anisotropy ordering in self-assembled magnetic nanoparticle monolayers

Self-assembled two-dimensional arrays of either 14 nm hcp-Co or 6 nm ε-Co particle components were treated by hydrogen plasma for various exposure times. A change of hysteretic sample behavior depending on the treatment duration is reported, which can be divided in two time scales: oxygen reduction increases the particle magnetization during the first 20 min, which is followed by an alteration of the magnetic response shape. The latter depends on the respective particle species. Based on the Landau–Lifshitz equations for a discrete set of magnetic moments, we propose a model that relates the change of the hysteresis loops to a dipole-driven ordering of the magnetocrystalline easy axes within the particle plane due to the high spatial aspect ratio of the system.

A superconducting/magnetic hybrid rectifier based on Fe single-crystal nanocentres: role of magnetic and geometric asymmetries

Vortex lattice motion driven by alternating forces on asymmetric pinning potentials generates a net flow of vortices. This rectifier (ratchet) effect is studied in hybrid samples fabricated with arrays of Fe single-crystal nanotriangles embedded in Nb films. In these samples two different asymmetric potentials generate the ratchet effect: (i) potentials with geometric asymmetry and (ii) potentials with magnetic asymmetry. The asymmetry of the geometric potential cannot be manipulated, but the asymmetry of the magnetic potential can be tailored. In geometric ratchet interstitial vortices play a crucial role and they permit tuning the output voltage polarity. In magnetic ratchet the output voltage amplitude can be controlled by tailoring the magnetic stray field configurations due to different magnetic remanent states of the Fe single-crystal nanostructures. These configurations are modified by changing the direction of the saturating applied field and also by using different orientations of the Fe magnetocrystalline easy axes within the triangles. When both mechanisms coexist, the geometric potential governs the rectifier effect behaviour.

Piezoelectric control of the magnetic anisotropy via interface strain coupling in a composite multiferroic structure

We investigate theoretically the magnetic dynamics in a ferroelectric/ferromagnetic heterostructure mediated by a strain-induced magnetoelectric interaction. The epitaxial strain involves a strong piezoelectricity and interfacial magnetoelastic coupling, the interplay of both gives rise to an electrically tunable uniaxial magnetic anisotropy. We predict an electric-field–induced magnetic switching in the plane perpendicular to the magneto-crystalline easy axis while the total magnetization remains stable. We trace this effect back to the ferroelectric control of the magnetic anisotropy. We also inspect the magnetic remanence and the electric coercivity and demonstrate a pronounced dynamic magnetic response to an electric field in a thin ferromagnetic layer.

Influence of crystal orientation on magnetic properties of hcp Co nanowire arrays

In this paper we develop a convenient way to control the direction of uniaxial magnetocrystalline easy axis in ac electrodeposited hcp Co nanowire arrays. The c-axis of hcp cobalt can be oriented parallel or perpendicular to the long axis of the wire by adjusting the temperature of the electrolyte. Magnetic characterizations suggest that the direction of the hcp c-axis plays an important role in the magnetization reversal process. A three-dimensional object oriented micromagnetic framework code was used to confirm the conclusion. It can be seen that the crystal orientation influences the magnetization and demagnetization process observably when the magnetocrystalline anisotropy energy is comparable to the shape anisotropy energy.

Shape Anisotropy and Magnetization Modulation in Hexagonal Cobalt Nanowires

AbstractFerromagnetic cobalt nanowires with high‐crystalline quality are synthesized using a low‐voltage electrodeposition method. High‐resolution transmission electron microscopy (HRTEM) and X‐ray diffraction (XRD) results show that the nanowires are uniform in size, and consist of predominantly hexagonal close‐packed (hcp) structure with the magnetocrystalline easy axis (c‐axis) perpendicular to the wire axis. Superconducting quantum interference device (SQUID) measurements illustrate the dominance of shape anisotropy, manifested by the weak temperature dependence of the enhanced coercive field along the wire axis. Furthermore, the magnetic structures of individual, segmented, or intersected nanowires are studied using magnetic force microscopy. This reveals a strong dipole at the two ends of the wire, together with a spatial magnetization modulation along the wire. Based on theoretical modeling, such intrinsic modulation is attributed to magnetization frustration due to the competition between the magnetocrystalline polarization along the easy axis and the shape anisotropy along the wire axis.

Probing of micromagnetic configuration in manganite channels by transport measurements

We explore the possibility of tracking magnetization orientation in artificial structures patterned in ${\mathrm{La}}_{0.7}{\mathrm{Sr}}_{0.3}\mathrm{Mn}{\mathrm{O}}_{3}$ epitaxial films by magnetotransport measurements, exploiting the anisotropic magnetoresistance effect. We perform resistance measurements as a function of temperature, magnetic field, and angle between the applied in-plane magnetic field and the channel or crystalline axes in micrometric channels of different widths. We analyze quantitatively our results and extract information about magnetization easy axes, crystalline anisotropy, domain wall resistance, anisotropic magnetoresistance, energy of magnetic domain pinning, and magnetic reversal mechanisms. For channel widths larger than a few micrometers, the magnetization direction at low field $(\ensuremath{\leqslant}200\phantom{\rule{0.3em}{0ex}}\mathrm{Oe})$ is determined by magnetocrystalline easy axes, whereas for channel widths of $\ensuremath{\sim}1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ or smaller, the shape anisotropy forces the magnetization to align along the channel axis. This gives a precise indication on how artificial patterning can be used to force the magnetization direction in manganite based spintronic devices. Values of magnetocrystalline constant up to $8000\phantom{\rule{0.3em}{0ex}}\mathrm{J}∕{\mathrm{m}}^{3}$ and anisotropic magnetoresistance values between 0.1% and 0.6% are found. Our data also indicate that, in the low field $(\ensuremath{\leqslant}200\phantom{\rule{0.3em}{0ex}}\mathrm{Oe})$ hysteretic regime, magnetization reversal occurs by thermal activated hopping of domain walls, with a characteristic hopping distance of $4--5\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$.

Nanoscale magnetic properties of iron minerals in bacteria

We have used a combination of advanced transmission electron microscopy techniques to study the physical and chemical properties of intracellular ferrimagnetic magnetite (Fe3O4) and greigite (Fe3S4) nanocrystals insidemagnetotactic bacteria that were collected from lakes and streams. The relative orientations and themorphologies of magnetic nanocrystals in magnetosome chains were identified using electron diffraction, highresolution electron microscopy and high-angle annular dark field electron tomography. Whereas magnetite chains were found to be analogous to beads on a string, in which biological control set the [111] magnetocrystalline easy axes of the crystals parallel to each chain axis, greigite crystals had more random orientations. Within each bacterial strain, magnetite magnetosomes were observed to have distinct and well-controlled morphologies. In contrast, greigite crystals appeared to have more irregular shapes. We used off-axis electron holography to record magnetic induction maps from the magnetosome chains. The magnetic signal was dominated by inter-particle interactions and by the shapes of the individual crystals. Magnetite nanocrystals were found to be uniformly magnetized, parallel to the magnetosome chain axes. In contrast, the disordered three-dimensional arrangement of multiple chains of greigite crystals resulted in the magnetic field following a meandering path between adjacent crystals. Over a three-year period, with the sample stored in air, each greigite crystal developed an amorphous iron oxide shell and its magnetic moment decreased. Our results are useful for obtaining an insight into biomineralization processes, and for studying the fundamental effects that influence the magnetic properties of closely-spaced nanoscale magnets. m12.o02

Biomineralization and self-assembled nanostructures – structure determination and material properties

We have used a combination of advanced transmission electron microscopy techniques to study the physical and chemical properties of intracellular ferrimagnetic magnetite (Fe3O4) and greigite (Fe3S4) nanocrystals insidemagnetotactic bacteria that were collected from lakes and streams. The relative orientations and themorphologies of magnetic nanocrystals in magnetosome chains were identified using electron diffraction, highresolution electron microscopy and high-angle annular dark field electron tomography. Whereas magnetite chains were found to be analogous to beads on a string, in which biological control set the [111] magnetocrystalline easy axes of the crystals parallel to each chain axis, greigite crystals had more random orientations. Within each bacterial strain, magnetite magnetosomes were observed to have distinct and well-controlled morphologies. In contrast, greigite crystals appeared to have more irregular shapes. We used off-axis electron holography to record magnetic induction maps from the magnetosome chains. The magnetic signal was dominated by inter-particle interactions and by the shapes of the individual crystals. Magnetite nanocrystals were found to be uniformly magnetized, parallel to the magnetosome chain axes. In contrast, the disordered three-dimensional arrangement of multiple chains of greigite crystals resulted in the magnetic field following a meandering path between adjacent crystals. Over a three-year period, with the sample stored in air, each greigite crystal developed an amorphous iron oxide shell and its magnetic moment decreased. Our results are useful for obtaining an insight into biomineralization processes, and for studying the fundamental effects that influence the magnetic properties of closely-spaced nanoscale magnets. m12.o02

Experimental and computational analysis of the angular dependence of the hysteresis processes in an antidots array

We have experimentally characterized the magnetization processes of a square array of micron sized circular antidots lithographed on a Fe(001)/GaAs film with its diagonals along the Fe magnetocrystalline easy axes (100). Both the anisotropy and the angular dependence of the magnetization reversal were measured by means of magnetooptic techniques. The coercivity of the loops along the easy and in-plane hard axes of the array increases approximately 2.5 times with respect to that measured in the continuous film region, and the first order anisotropy constant remains equal to that of bulk Fe. The magnetization reversal takes place in two steps for all the loops measured out of the easy and hard axes. We have simulated the magnetization reversal using two different micromagnetic models. In the first one, assuming that the reversal takes place fully inside the array, we have observed that the reversal nucleates at the magnetic inhomogeneities occurring at the antidot boundaries and resulting from magnetostatic energy minimization. In our second model we artificially introduced a domain wall outside the antidot region that governs the magnetization reversal showing a qualitative agreement with the angular dependence of coercivity.