Analyzer-free, intensity-based, wide-field magneto-optical microscopy

In conventional Kerr and Faraday microscopy, the sample is illuminated with plane-polarized light, and a magnetic domain contrast is generated by an analyzer making use of the Kerr or Faraday rotation. Here, we demonstrate possibilities of analyzer-free magneto-optical microscopy based on magnetization-dependent intensity modulations of the light. (i) The transverse Kerr effect can be applied for in-plane magnetized material, as demonstrated for an FeSi sheet. (ii) Illuminating that sample with circularly polarized light leads to a domain contrast with a different symmetry from the conventional Kerr contrast. (iii) Circular polarization can also be used for perpendicularly magnetized material, as demonstrated for garnet and ultrathin CoFeB films. (iv) Plane-polarized light at a specific angle can be employed for both in-plane and perpendicular media. (v) Perpendicular light incidence leads to a domain contrast on in-plane materials that is quadratic in the magnetization and to a domain boundary contrast. (vi) Domain contrast can even be obtained without a polarizer. In cases (ii) and (iii), the contrast is generated by magnetic circular dichroism (i.e., differential absorption of left- and right-circularly polarized light induced by magnetization components along the direction of light propagation), while magnetic linear dichroism (differential absorption of linearly polarized light induced by magnetization components transverse to propagation) is responsible for the contrast in case (v). The domain-boundary contrast is due to the magneto-optical gradient effect. A domain-boundary contrast can also arise by interference of phase-shifted magneto-optical amplitudes. An explanation of these contrast phenomena is provided in terms of Maxwell-Fresnel theory. © 2021 Author(s)

Рекуррентные алгоритмы вычисления корня произвольной степени в кольце вычетов

У даній роботі отримано критерій степеневості елемента скінченого поля та наведено прості алгоритми обчислення кубічного кореня та рекурентні алгоритми обчислення коренів більш високого степеню з елементу поля, який є відповідним степеневим лишком. Алгоритми розпізнавання степеневості та добування кореня за складеним модулем (наприклад, за модулем n=pq) повністю визначаються відповідними алгоритмами за простим модулем, за умови, що відомий розклад числа п на прості множники. Цікаво також зазначити, що задача розкладу на прості множники та задача добування кореня є поліноміально еквівалентними відносно імовірнісного алгоритму. Дані алгоритми є, перш за все, цікавими з математичної точки зору, а їх поодинокий випадок – алгоритми добування кубічного кореня – можуть бути використані як допоміжні при обчислення базової точки кривої та при "вкладанні" відкритого тексту у точку кривої, у тому числі і якщо крива задана над кільцем лишків, а не над полем.In this paper, the criterion of power element of finite field is obtained and simple algorithms for calculating the cubic root and recursive algorithms for calculating the roots of higher powers are constructed. Power recognition algorithm and rooting for composite module (particularly for modulo n=pq) are completely determined by the corresponding algorithms for a simple modules, provided that factorization is known. It is also interesting to note that for n=pq the factorization problem and rooting problem are polynomial equivalent relatively probabilistic algorithm. These algorithms are primarily interesting from a mathematical point of view, and their particular case – the cubic root extraction algorithm – can be used as aids in calculating the base point of the elliptic curve and for "imbedding" of plaintext into curve point, also if curve is defined over the residue rings instead of the field.В данной работе получен критерий степенности элемента конечного поля и приведены простые алгоритмы вычисления кубичного коня и рекуррентные алгоритмы вычисления корней более высоких степеней из элемента поля, который является соответствующим степенным вычетом. Алгоритмы распознавания степенности и вычисления корня по составному модулю (например, по модулю n=pq) полностью определяются соответствующими алгоритмами для простого модуля, при условии, что известно разложение модуля на простые множители. Интересно также заметить, что задача разложения на простые множители и задача вычисления корня являются полиномиально эквивалентными относительно вероятностного алгоритма. Данные алгоритмы являются, прежде всего, интересными с математической точки зрения, а их частный случай – алгоритмы вычисления кубического корня – могут быть использованы как вспомогательные при вычислении базовой точки кривой и при "вложении" открытого текста в точку кривой, в том числе и если кривая задана над кольцом вычетов, а не над полем

Photovoltage spectroscopy of dipolar spin waves in Dy micromagnets

We report on a sensitive spectroscopic technique for probing the spin excitations of individual submicron magnets. This technique uses a high mobility two dimensional electron gas (2DEG) confined in a GaAs/AlGaAs heterojunction to pick up the oscillating dipolar magnetic field emanating from the individual spin wave modes of micromagnets fabricated at its surface. We review a range of dynamic phenomena that demonstrate the formation of magnetostatic waves in finger gate arrays, dipolar edge spin waves in bar magnets, vortex hysteresis in magnetic dots and the photovoltage dependence on microwave polarization.</jats:p

Field-free spin-orbit torque switching enabled by interlayer Dzyaloshinskii-Moriya interaction

Perpendicularly magnetized structures that are switchable using a spin current under field-free conditions can potentially be applied in spin-orbit torque magnetic random-access memory(SOT-MRAM).Several structures have been developed;however,new structures with a simple stack structure and MRAM compatibility are urgently needed.Herein,a typical structure in a perpendicular spin-transfer torque MRAM,the Pt/Co multilayer and its synthetic antiferromagnetic counterpart with perpendicular magnetic anisotropy, was observed to possess an intrinsic interlayer chiral interaction between neighboring magnetic layers,namely the interlayer Dzyaloshinskii-Moriya interaction (DMI) effect. Furthermore, using a current parallel to the eigenvector of the interlayer DMI, we switched the perpendicular magnetization of both structures without a magnetic field, owing to the additional symmetry-breaking introduced by the interlayer DMI. This SOT switching scheme realized in the Pt/Co multilayer and its synthetic antiferromagnet structure may open a new avenue toward practical perpendicular SOT-MRAM and other SOT devices

Fabrication of high-resolution nanostructures of complex geometry by the single-spot nanolithography method

The paper presents a method for the high-resolution production of polymer nanopatterns with controllable geometrical parameters by means of a single-spot electron-beam lithography technique. The essence of the method entails the overexposure of a positive-tone resist, spin-coated onto a substrate where nanoscale spots are exposed to an electron beam with a dose greater than 0.1 pC per dot. A single-spot enables the fabrication of a nanoring, while a chain of spots placed at distance of 5–30 nm from each other allows the production of a polymer pattern of complex geometry of sub-10 nm resolution. We demonstrate that in addition to the naturally oxidized silicon substrates, gold-coated substrates can also successfully be used for the single-spot nanopattering technique. An explanation of the results related to the resist overexposure was demonstrated using Monte Carlo simulations. Our nanofabrication method significantly accelerates (up to 10 times) the fabrication rate as compared to conventional lithography on positive-tone resist. This technique can be potentially employed in the electronics industry for the production of nanoprinted lithography molds, etching masks, nanoelectronics, nanophotonics, NEMS and MEMS devices

Analyzer-free, intensity-based, wide-field magneto-optical microscopy

In conventional Kerr and Faraday microscopy, the sample is illuminated with plane-polarized light, and a magnetic domain contrast is generated by an analyzer making use of the Kerr or Faraday rotation. Here, we demonstrate possibilities of analyzer-free magneto-optical microscopy based on magnetization-dependent intensity modulations of the light. (i) The transverse Kerr effect can be applied for in-plane magnetized material, as demonstrated for an FeSi sheet. (ii) Illuminating that sample with circularly polarized light leads to a domain contrast with a different symmetry from the conventional Kerr contrast. (iii) Circular polarization can also be used for perpendicularly magnetized material, as demonstrated for garnet and ultrathin CoFeB films. (iv) Plane-polarized light at a specific angle can be employed for both in-plane and perpendicular media. (v) Perpendicular light incidence leads to a domain contrast on in-plane materials that is quadratic in the magnetization and to a domain boundary contrast. (vi) Domain contrast can even be obtained without a polarizer. In cases (ii) and (iii), the contrast is generated by magnetic circular dichroism (i.e., differential absorption of left- and right-circularly polarized light induced by magnetization components along the direction of light propagation), while magnetic linear dichroism (differential absorption of linearly polarized light induced by magnetization components transverse to propagation) is responsible for the contrast in case (v). The domain-boundary contrast is due to the magneto-optical gradient effect. A domain-boundary contrast can also arise by interference of phase-shifted magneto-optical amplitudes. An explanation of these contrast phenomena is provided in terms of Maxwell-Fresnel theory

Manipulation of magnetic vortex parameters in disk-on-disk nanostructures with various geometry

Magnetic nanostructures in the form of a sandwich consisting of two permalloy (Py) disks with diameters of 600 and 200 nm separated by a nonmagnetic interlayer are studied. Magnetization reversal of the disk-on-disk nanostructures depends on the distance between centers of the small and big disks and on orientation of an external magnetic field applied during measurements. It is found that manipulation of the magnetic vortex chirality and the trajectory of the vortex core in the big disk is only possible in asymmetric nanostructures. Experimentally studied peculiarities of a motion path of the vortex core and vortex parameters by the magneto-optical Kerr effect (MOKE) magnetometer are supported by the magnetic force microscopy imaging and micromagnetic simulations