Characteristic Magnetic Length Research Articles

Writing 3D Nanomagnets Using Focused Electron Beams.

Focused electron beam induced deposition (FEBID) is a direct-write nanofabrication technique able to pattern three-dimensional magnetic nanostructures at resolutions comparable to the characteristic magnetic length scales. FEBID is thus a powerful tool for 3D nanomagnetism which enables unique fundamental studies involving complex 3D geometries, as well as nano-prototyping and specialized applications compatible with low throughputs. In this focused review, we discuss recent developments of this technique for applications in 3D nanomagnetism, namely the substantial progress on FEBID computational methods, and new routes followed to tune the magnetic properties of ferromagnetic FEBID materials. We also review a selection of recent works involving FEBID 3D nanostructures in areas such as scanning probe microscopy sensing, magnetic frustration phenomena, curvilinear magnetism, magnonics and fluxonics, offering a wide perspective of the important role FEBID is likely to have in the coming years in the study of new phenomena involving 3D magnetic nanostructures.

Thermodynamics and Exchange Stiffness of Asymmetrically Sandwiched Ultrathin Ferromagnetic Films with Perpendicular Anisotropy

Ultrathin asymmetrically sandwiched ferromagnetic films can support magnetic skyrmions and skyrmion bubbles, which are eyed as functional units for tomorrow's spintronic logic and memory devices. The type of object and its size and mobility are set by intrinsic magnetic parameters, which are largely unknown. The authors demonstrate that the exchange stiffness of ultrathin films can be determined by analysis of the temperature dependence of magnetization. This simple yet robust approach is crucial not only for the experimental community but also for theorists, as it determines domain-wall thickness, the period of a Dzyaloshinskii spiral, and the characteristic magnetic length.

Mechanisms of magnetic and temperature hysteresis in ErFeO3 and TmFeO3 single crystals

Magnetic hysteresis is studied in the orthoferrites ErFeO3 and TmFeO3 using the single crystal samples of millimeter dimensions. It is shown that in both materials one observes a temperature transition manifesting itself through the temperature hysteresis of the magnetic moment and a peculiar temperature evolution of the field hysteresis loop shapes near this transition. Experiments rule out the hypothesis that the ordering of the orthoferrite’s rare-earth magnetic moments plays an important role in these phenomena. The hysteresis curves can be explained by a few-domain magnetic state of the samples that results from the weak ferromagnetism of the orthoferrites. The phenomenon is generic for weak ferromagnets with temperature dependent magnetization. A large characteristic magnetic length makes the behavior of the relatively big samples analogous to that observed in the nanosize samples of strong ferromagnets.

Inhomogeneous configurations of magnetization of ferromagnetic films with biaxial anisotropy

The system of the Landau-Lifshitz equations and magnetostatic equations for a ferromagnetic film with biaxial anisotropy and a Q-factor smaller than unity is reduced to a single scalar equation for the magnetostatic potential. Such a procedure is possible if the magnetization modulation scale in the sample considerably exceeds the characteristic magnetic length. The solutions to this equation describing inhomogeneous periodic magnetic configurations are obtained. The energy analysis of these configurations is carried out.

Resonant microwave absorption determination of characteristic magnetic length in magnetic-field-annealed Vitroperm

The first direct resonant microwave absorption determination of the thermal renormalization of exchange stiffness, average magnetic anisotropy constant, and characteristic magnetic length in “field-annealed” Vitroperm samples with an initial magnetic permeability of μi=20000 and 150 000 has been presented and discussed.

New class of quantum bound states: Diprotons in extreme magnetic fields

This paper considers the possibility that two charged particles with an attractive short-ranged potential between them which is not strong enough to form bound states in free space, may bind in uniform magnetic fields. It is shown that in the formal limit where Coulomb repulsion is negligible ($q\ensuremath{\rightarrow}0\phantom{\rule{0.3em}{0ex}}\text{and}\phantom{\rule{0.3em}{0ex}}{B}_{0}\ensuremath{\rightarrow}\ensuremath{\infty}\phantom{\rule{0.3em}{0ex}}\text{with}\phantom{\rule{0.3em}{0ex}}q{B}_{0}\phantom{\rule{0.3em}{0ex}}\text{fixed}$, where $q$ is the charge and ${B}_{0}$ the field strength) there always exists a bound state for a system of two identical charged particles in a constant magnetic field, provided that there is a short-range uniformly attractive potential between them. Moreover, it is shown that in this limit any potential with an attractive s-wave scattering length will possess bound states provided that the range of the potential is much smaller than the characteristic magnetic length, ${r}_{0}\ensuremath{\equiv}(\frac{q{B}_{0}}{4}){}^{\ensuremath{-}1/2}$. For this case, the binding is computed numerically. We estimate the size of the magnetic field needed to approximately reach a regime where the formal limit considered becomes a good approximation to the dynamics. These numerical estimates indicate that two protons in an extremely strong magnetic field such as might be found in a magnetar will bind to form a diproton.

Small angle neutron scattering investigations of spin disorder in nanocomposite soft magnets

The technique of SANS (small angle neutron scattering) furnishes unique information on the characteristic magnetic length scales and local magnetic anisotropies at the nanoscale in nanocomposite ferromagnets. Such information is not presently available using any other microscopic technique. The basic principles and results of the technique will be presented with regard to a unique and unexpected observation of a dipole field controlled spin disorder in a prototypical soft nanocomposite ferromagnet of the Nanoperm type.

Magnetism in future

As a backdrop to help focus on the shape of magnetism in future, seven ages in the history of magnetism from ancient times to the 20th century are discussed. Drivers and beneficiaries are identified in each age. Some current trends in the areas of hard magnets, soft magnets and magnetic recording are described and extrapolated. Key developments are the ability to structure materials and devices on characteristic magnetic length scales in the nanometer range, and the emergence of the new science of spin electronics. Some speculative suggestions about areas where breakthroughs could be expected in future are included.

Plasma–wall interaction in an oblique magnetic field: Model of the space-charge sheath for large potentials and small Debye lengths

An analytical model of the space-charge sheath around a planar wall is derived for the case of (i) uniform magnetic field B incident at any angle into the wall, (ii) large wall potentials (relative to the plasma temperature): φW≫1, and (iii) Debye length, λd, much smaller than thermal Larmor radius of the attracted species, λm. It is found that, irrespective of the angle of incidence: (i) The potential threshold for a magnetized sheath is φW=O(λd4/λm4); (ii) the characteristic magnetic length in the sheath is λm3/λd2, much larger than λm and proportional to |B|−3 and the plasma flow into the sheath; (iii) the electric field E increases towards the wall and produces a noncycloidal plasma drift that breaks down magnetic insulation. Plasma dynamics in a magnetized sheath consists of an E-aligned region, a drift region, and a B-aligned region. The drift region is relevant only for angles far from normal incidence and the density profile presents spatial oscillations there; for grazing incidence, the B-aligned region is not found. Different scaling laws of the sheath thickness versus wall potential and incidence angle are obtained; in particular, the thickness of a magnetized sheath at parallel incidence is the local Larmor radius at the wall. The applicability of the model to experiments in the ionosphere is commented.

Singularities in critical properties of superconductive superlattices as a function of magnetic field

The critical temperature singularities as a function of both magnetic field direction and value in periodic superconductive structure in metals have been predicted. The different types of lattices, modulation value (weak or strong), relation between characteristic magnetic length and lattice periods have been investigated on the basis of microscopic equations.

Impurity conduction and magnetoresistance in lightly dopedn-type GaAs

Measurements of the resistivity and magnetoresistance of epitaxially grownn-type GaAs (ND ~ 1–2 × 1015 cm−3) at 4.2 K and below are reported. The hopping resistivityρ3 depends onND according toρ3=ρ0 exp (1.88/N D 1/3 a) in agreement with predictions of percolation theory, wherea is the Bohr radius of the impurity ground state. The experimentally obtained preexponential factorρ0 is very close to a recent theoretical prediction, which was derived from the computation of the topology of an infinite cluster. In magnetic fields below 1.3T the resistivity is found to be proportional to exp\(\left( {\frac{{ta}}{{\lambda ^4 N_D }}} \right)\),t having a value of 0.06 in disagreement with a recent theoretical calculation oft=0.04. In the high magnetic field region above 3T the data are described byρ ∝ exp [q (λ2aBND)−1/2], whereλ is the characteristic magnetic length andaB is the magnetic field dependent Bohr radius. From the experiments a value ofq=0.68 is deduced, while the theory predictsq=0.98.

Analysis of a method for measuring the magnetocrystalline anisotropy of bubble materials

A method of measuring the uniaxial anisotropy of bubble materials is analyzed. The method consists of observing the in-plane field H∥* at which a stripe domain pattern disappears. Calculations, based on a model with uniaxial anisotropy, are presented which give a relation between H∥* and the uniaxial anisotropy field HK for different values of the characteristic magnetic length. It is shown that H∥* is always smaller than HK owing to the influence of the wall energy and the demagnetizing energy. The calculations are verified experimentally.