The resistivity, ρ, of ceramic La1−xCaxMn1−yFeyO3 with x = 0.3 and y = 0.0–0.09 is found to obey, between a temperature Tv ≈ 310–330 K and the ferromagnetic-to-paramagnetic transition temperature, TC = 259–119 K (decreasing with y), the Shklovskii–Efros-type variable-range hopping conductivity law, ρ(T) = ρ0 (T) exp [(T0 /T)1/2 ]. This behaviour is governed by generation of a soft Coulomb gap Δ ≈ 0.42 eV in the density of localized states and a rigid gap δ(T) ≈ δ(Tv)(T/Tv)1/2 with δ(Tv) ≈ 0.16, 0.13 and 0.12 eV at y = 0.03, 0.07 and 0.09, respectively. Deviations from the square root dependence of δ(T), decreasing when y is increased, are observed as T → TC. The prefactor of the resistivity follows the law ρ0 (T) ∼ Tm, where m changes from 9/2 at y = 0 to 5/2 in the investigated samples with y = 0.03, 0.07 and 0.09, which is connected to introduction of an additional fluctuating short-range potential by doping with Fe.

Document VersionPublisher's PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication:• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. The developed theory of the orientational mobility of individual segments of a perfectly branched dendrimer is used to calculate the relaxation spectrum of a dendrimer. Frequency dependences of NMR relaxation 1 / T 1 and of the nuclear Overhauser effect have been theoretically calculated from the Brownian dynamics simulation data. The dendrimer segmental orientational mobility is governed by three main relaxation processes: ͑i͒ the rotation of the dendrimer as a whole, ͑ii͒ the rotation of the dendrimer's branch originated from a given segment, and ͑iii͒ the local reorientation of the segment. The internal orientational mobility of an individual dendrimer segment depends only on the topological distance between this segment and the terminal shell of the dendrimer. Characteristic relaxation times of all processes and their contributions to the segmental mobility have been calculated. The influence of the number of generations and the number of the generation shell on the relaxation times has been studied. The correlation between the characteristic times and the calculated relaxation spectrum of the dendrimer has been established.

NMR relaxation experiments are widely used to investigate the local orientation mobility in dendrimers. In particular, the NMR method allows one to measure the spin-lattice relaxation rate, 1/T1, which is connected with the orientational autocorrelation function (ACF) of NMR active groups. We calculate the temperature (Θ) and frequency (ω) dependences of the spin-lattice NMR relaxation rates for segments and NMR active CH2 groups in poly-L-lysine (PLL) dendrimers in water, on the basis of full-atomic molecular dynamics simulations. It is shown that the position of the maximum of 1/T1(ω) depends on the location of the segments inside the dendrimer. This dependence of the maximum is explained by the restricted flexibility of the dendrimer. Such behavior has been predicted recently by the analytical theory based on the semiflexible viscoelastic model. The simulated temperature dependences of 1/T1 for terminal and inner groups in PLL dendrimers of n = 2 and n = 4 generations dissolved in water are in good agreement with the NMR experimental data, which have been obtained for these systems previously by us. It is shown that in the case of PLL dendrimers, the traditional procedure of the interpretation of NMR experimental data - when smaller values of 1/T1 correspond to higher orientation mobility - is applicable to the whole accessible frequency interval only for the terminal groups. For the inner groups, this procedure is valid only at low frequencies.

Vortex structures in the ferromagnet/type-II superconductor bilayer are investigated when the ferromagnet has domain structure and perpendicular magnetic anisotropy. It is found that two equilibrium vortex structures can be realized: straight vortices with alternating directions corresponding to the direction of the magnetization in the ferromagnetic domains and vortex semiloops connecting the ferromagnetic domains with opposite direction of the magnetization. These states are separated by an energy barrier. The values of the critical magnetization for the formation of these vortex structures are determined.

We propose a new theory of the topological Hall effect (THE) in systems with non-collinear magnetization textures such as magnetic skyrmions. We solve the problem of electron scattering on a magnetic skyrmion exactly, for an arbitrary strength of exchange interaction and the skyrmion size. We report the existence of different regimes of THE and resolve the apparent contradiction between the adiabatic Berry phase theoretical approach and the perturbation theory for THE. We traced how the topological charge Hall effect transforms into the spin Hall effect upon varying the exchange interaction strength or the skyrmion size. This transformation has a nontrivial character: it is accompanied by an oscillating behavior of both charge and spin Hall currents. This hallmark of THE allows one to identify the chirality driven contribution to Hall response in the experiments.

We present a theory of electron scattering on a magnetic Skyrmion for the case when the exchange interaction is moderate so that the adiabatic approximation and the Berry phase approach are not applicable. The theory explains the appearance of a topological Hall current in the systems with magnetic Skyrmions, the special importance of which is its applicability to dilute magnetic semiconductors with a weak exchange interaction.

An electric current controlled spin-wave logic gate based on a width-modulated dynamic magnonic crystal is realized. The device utilizes a spin-wave waveguide fabricated from a single-crystal Yttrium Iron Garnet film and two conducting wires attached to the film surface. Application of electric currents to the wires provides a means for dynamic control of the effective geometry of the waveguide and results in a suppression of the magnonic band gap. The performance of the magnonic crystal as an AND logic gate is demonstrated.