Energies of knot diagrams

We introduce and begin the study of new knot energies defined on knot diagrams. Physically, they model the internal energy of thin metallic solid tori squeezed between two parallel planes. Thus the knots considered can perform the second and third Reidemeister moves, but not the first one. The energy functionals considered are the sum of two terms, the uniformization term (which tends to make the curvature of the knot uniform) and the resistance term (which, in particular, forbids crossing changes). We define an infinite family of uniformization functionals, depending on an arbitrary smooth function $f$ and study the simplest nontrivial case $f(x)=x^2$, obtaining neat normal forms (corresponding to minima of the functional) by making use of the Gauss representation of immersed curves, of the phase space of the pendulum, and of elliptic functions

Magnetic properties of (Fe1−x_{1-x}Cox_x)2_2B alloys and the effect of doping by 5dd elements

We have explored, computationally and experimentally, the magnetic properties of \fecob{} alloys. Calculations provide a good agreement with experiment in terms of the saturation magnetization and the magnetocrystalline anisotropy energy with some difficulty in describing Co$_2$B, for which it is found that both full potential effects and electron correlations treated within dynamical mean field theory are of importance for a correct description. The material exhibits a uniaxial magnetic anisotropy for a range of cobalt concentrations between $x=0.1$ and $x=0.5$. A simple model for the temperature dependence of magnetic anisotropy suggests that the complicated non-monotonous temperature behaviour is mainly due to variations in the band structure as the exchange splitting is reduced by temperature. Using density functional theory based calculations we have explored the effect of substitutional doping the transition metal sublattice by the whole range of 5$d$ transition metals and found that doping by Re or W elements should significantly enhance the magnetocrystalline anisotropy energy. Experimentally, W doping did not succeed in enhancing the magnetic anisotropy due to formation of other phases. On the other hand, doping by Ir and Re was successful and resulted in magnetic anisotropies that are in agreement with theoretical predictions. In particular, doping by 2.5~at.\% of Re on the Fe/Co site shows a magnetocrystalline anisotropy energy which is increased by 50\% compared to its parent (Fe$_{0.7}$Co$_{0.3}$)$_2$B compound, making this system interesting, for example, in the context of permanent magnet replacement materials or in other areas where a large magnetic anisotropy is of importance.Comment: 15 pages 17 figure

A multi-stage, first-order phase transition in LaFe11.8Si1.2: interplay between the structural, magnetic and electronic degrees of freedom

Alloys with a first-order magnetic transition are central to solid-state refrigeration technology, sensors and actuators, or spintronic devices. The discontinuous nature of the transition in these materials is a consequence of the coupling between the magnetic, electronic and structural subsystems, but in a real experiment, it is difficult to observe and analyze the simultaneous evolution of all the subsystems. As a result, it is very hard to determine the main mechanisms of the transition and purposefully develop these advanced magnetic materials. To resolve this issue, we changed the existing paradigm and conducted simultaneous measurements of the macroscopic properties - magnetization, temperature change of the sample, longitudinal and transversal magnetostrictions - to reveal the rich details of the magneto-structural, first-order transition occurring in the prototypical alloy LaFe11.8Si1.2. We complement these findings with experiments on the atomistic scale, i.e., x-ray absorption spectroscopy (XAS), x-ray magnetic circular dichroism (XMCD) and M\"ossbauer spectroscopy, and then combine them with first-principles calculations to reveal the full complexity and two-stage nature of the transition. This new approach can be successfully extended to a large class of advanced magnetic materials that exhibit analogous transformations.Comment: 24 page

Magnetocaloric and Magnetic Properties of Ni\u3csub\u3e2\u3c/sub\u3eMn\u3csub\u3e1-x\u3c/sub\u3eCu\u3csub\u3ex\u3c/sub\u3eGa Heusler Alloys: an Insight from the Direct Measurements and \u3ci\u3eab initio\u3c/i\u3e and Monte Carlo Calculations

We calculated magnetic exchange constants and magnetocaloric properties of Ni2Mn1-xCuxGa Heusler alloys by ab initio and Monte Carlo methods. The ab initio study of the influence of the Cu excess x on the strength of magnetic interactions revealed that Cu weakens Mn-Ni interaction and has a complex impact on the Mn-Mn interactions. Theoretically calculated magnetic phase diagram of Ni2Mn1-xCuxGa is in a good agreement with available experimental data. Calculated by the Monte Carlo method the isothermal magnetic entropy change Delta Smag in a Ni2Mn0.75Cu0.25Ga alloy is significantly smaller around the coupled magnetostructural phase transition temperature than the reported earlier experimental Delta Smag. This discrepancy is ascribed to an overestimation of the experimental Delta Smag at the magnetostructural phase transition. Theoretically determined adiabatic temperature change Delta Tad in Ni2Mn0.75Cu0.25Ga agrees well with Delta Tad measured experimentally by a direct method

Управление магнитными свойствами нанокомпозитов NiCo/C

The NiCo/C metal-carbon nanocomposites based on the NiCl2/CoCl2/Polyacrylonitrile (PAN) precursors were synthesized using IR heating. The results of studies of NiCo/C nanocomposites by X-ray phase analysis, transmission electron microscopy, and vibration magnetometry showed the dependence of the structure and properties of NiCo/C nanocomposites on the synthesis temperature, concentration, and metal ratio in the precursor. According to the results of the X-ray phase analysis, it was found that during the IR pyrolysis of the precursor, NiCo metal nanoparticles are stabilized in the carbon matrix, an increase in the synthesis temperature from 350 to 800 °C leads to an increase in the average size of nio nanoparticles from 10 to 80 nm, it is established that the formation of the alloy occurs due to the gradual dissolution of cobalt in nickel with the simultaneous transition of cobalt from the hcp modification to FCC. The structure of nanocomposites was shown by transmission electron microscopy of samples synthesized at 600 °C. It was found that with an increase in the metal concentration in the precursor from 10 to 40 wt.%, the average size of NiCo nanoparticles increases and the concentration of nanoparticles in the carbon matrix increases. The study of the magnetic properties of nanocomposites showed that with an increase in the content of metals in the precursor from 10 to 40 wt.%, an almost linear increase in the saturation magnetization from 5.94 to 25.7 A · m2/kg is observed. A change in the ratio of metals from Ni : Co = 4 : 1 to Ni : Co = 1 : 4 causes an increase in magnetization from 11.46 to 23.3 A · m2/kg.Разработка новых видов радиопоглощающих материалов актуальна в связи с интенсивным развитием устройств СВЧ-радиоэлектроники, увеличением их мощности и активным внедрением во все сферы жизнедеятельности. Радиопоглощающий материал на основе нанокомпозита NiCo/C может быть использован для уменьшения помех и обеспечения электромагнитной совместимости. Синтезированы металлоуглеродные нанокомпозиты NiCo/C на основе прекурсоров NiCl2/CoCl2/Полиакрилонитрил (ПАН) с использованием ИК-нагрева. Результаты исследований нанокомпозитов NiCo/C методами рентгенофазового анализа, просвечивающей электронной микроскопии и вибрационной магнитометрии показали зависимость структуры и свойств нанокомпозитов NiCo/C от температуры синтеза, концентрации и соотношения металлов в прекурсоре. По результатам рентгенофазового анализа установлено, что в процессе ИК-пиролиза прекурсора происходит формирование металлических наночастиц NiCo, стабилизированных в углеродной матрице. Увеличение температуры синтеза от 350 до 800 °С приводит к росту среднего размера наночастиц NiCo от 10 до 80 нм. Установлено, что формирование сплава происходит за счет постепенного растворения кобальта в никеле с одновременным переходом кобальта из ГПУ-модификации в ГЦК. Методом просвечивающей электронной микроскопии исследована структура образцов нанокомпозитов, синтезированных при 600 °С. Установлено, что с ростом концентрации металла в прекурсоре от 10 до 40 % (мас.) происходит рост среднего размера наночастиц NiCo в составе нанокомпозитов NiCo/C и увеличение концентрации наночастиц в углеродной матрице. Исследование магнитных свойств нанокомпозитов показало, что с увеличением содержания металлов в прекурсоре от 10 до 40 % (мас.) наблюдается практически линейный рост намагниченности насыщения от 5,94 до 25,7 А · м2/кг. Изменение соотношения металлов от Ni : Co = 4 : 1 до Ni : Co = 1 : 4 вызывает рост намагниченности от 11,46 до 23,3 А · м2/кг

Observation of the Decay Λ0b→Λ+cτ−¯ν

The first observation of the semileptonic b-baryon decay Λb0→Λc+τ-ν¯τ, with a significance of 6.1σ, is reported using a data sample corresponding to 3 fb-1 of integrated luminosity, collected by the LHCb experiment at center-of-mass energies of 7 and 8 TeV at the LHC. The τ- lepton is reconstructed in the hadronic decay to three charged pions. The ratio K=B(Λb0→Λc+τ-ν¯τ)/B(Λb0→Λc+π-π+π-) is measured to be 2.46±0.27±0.40, where the first uncertainty is statistical and the second systematic. The branching fraction B(Λb0→Λc+τ-ν¯τ)=(1.50±0.16±0.25±0.23)% is obtained, where the third uncertainty is from the external branching fraction of the normalization channel Λb0→Λc+π-π+π-. The ratio of semileptonic branching fractions R(Λc+)B(Λb0→Λc+τ-ν¯τ)/B(Λb0→Λc+μ-ν¯μ) is derived to be 0.242±0.026±0.040±0.059, where the external branching fraction uncertainty from the channel Λb0→Λc+μ-ν¯μ contributes to the last term. This result is in agreement with the standard model prediction