Representations of Hecke algebras on quotients of path algebras

Let $(W,S)$ be a Coxeter system. A $W$-graph encodes a representation of the Hecke algebra $\mathcal{H}$ of $W$. We construct universal representations of multi-parameter Hecke algebras on certain quotients of path algebras, and study their relationships with $W$-graph representations. We also study the quotients of path algebras on their own, motivated by one example where the quotient path algebra is isomorphic to an ideal of Lusztig asymptotic Hecke algebra. Finally, we describe a method to obtain a generating set for the ideals by which we quotient the path algebras

Magnetic field induced spin-wave energy focusing

Spin waves can transport both energy and angular momentum over long distances as they propagate. However, due to damping, their amplitude decreases exponentially as they move away from the source, leaving little capability for manipulating how much energy and angular momentum is to be delivered where. Here we show that a suitable local reduction of the effective field can lead to a large accumulation of spin wave energy far from the source. Moreover, both the location and the amount of energy to be delivered can be controlled accurately with geometry and externalm magnetic fields. Thus, we put forward a general, robust and flexible approach to convey both heat and spin in ferromagnets, which can be directly used in spintronic devices

Compensation temperature in spin-1/21/2 Ising trilayers: A Monte Carlo study

We study the magnetic and thermodynamic properties of a spin-$1/2$ Ising system containing three layers, each of which is composed exclusively of one out of two possible types of atoms, \textbf{A} or \textbf{B}. The \textbf{A-A} and \textbf{B-B} bonds are ferromagnetic while the \textbf{A-B} bonds are antiferromagnetic. The study is performed through Monte Carlo simulations using the Wolff algorithm and the data are analyzed with the aid of the multiple-histogram reweighting technique and finite-size scaling tools. We verify the occurrence of a compensation phenomenon and obtain the compensation and critical temperatures of the model as functions of the Hamiltonian parameters. The influence of each parameter on the overall behavior of the system is discussed in detail and we present our results in the form of phase diagrams dividing the parameter space in regions where the compensation phenomenon is present or absent. Our results may provide invaluable information for experimentalists seeking to build materials with desired characteristics.Comment: 8 pages of text; 20 figures. arXiv admin note: substantial text overlap with arXiv:1705.10192, arXiv:1710.1029

Pinned domain wall oscillator as tunable direct current spin wave emitter

Spin waves are perturbations in the relative orientation of magnetic moments in a continuous magnetic system, which have been proposed as a new kind of information carrier for spin-based low power applications. For this purpose, a major obstacle to overcome is the energy-efficient excitation of coherent short wavelength spin waves and alternatives to excitation via the Oersted field of an alternating current need to be explored. Here we show, by means of micromagnetic simulations, how, in a perpendicularly magnetized thin strip, a domain wall pinned at a geometrical constriction emits spin waves when forced to rotate by the application of a low direct current flowing along the strip. Spin waves propagate only in the direction of the electron's flow at the first odd harmonic of the domain wall rotation frequency for which propagation is allowed. Excitation is due to in-plane dipolar stray field of the rotating domain wall and that the resulting unidirectionality is a consequence of the domain wall displacement at the constriction. On the other hand, the application of an external field opposing domain wall depinning breaks the symmetry for spin wave propagation in the two domains, allowing emission in both directions but at different frequencies. The results presented define a new approach to produce tunable high frequency spin wave emitters of easy fabrication and low power consumption

Monte Carlo simulations of an Ising bilayer with non-equivalent planes

We study the thermodynamic and magnetic properties of an Ising bilayer ferrimagnet. The system is composed of two interacting non-equivalent planes in which the intralayer couplings are ferromagnetic while the interlayer interactions are antiferromagnetic. Moreover, one of the planes is randomly diluted. The study is carried out within a Monte Carlo approach employing the multiple histogram reweighting method and finite-size scaling tools. The occurrence of a compensation phenomenon is verified and the compensation temperature, as well as the critical temperature for the model, are obtained as functions of the Hamiltonian parameters. We present a detailed discussion of the regions of the parameter space where the compensation effect is present or absent. Our results are then compared to a mean-field-like approximation applied to the same model by Balcerzak and Sza{\l}owski (2014). Although the Monte Carlo and mean-field results agree qualitatively, our quantitative results are significantly different

Monte Carlo study of an anisotropic Ising multilayer with antiferromagnetic interlayer couplings

We present a Monte Carlo study of the magnetic properties of an Ising multilayer ferrimagnet. The system consists of two kinds of non-equivalent planes, one of which is site-diluted. All intralayer couplings are ferromagnetic. The different kinds of planes are stacked alternately and the interlayer couplings are antiferromagnetic. We perform the simulations using the Wolff algorithm and employ multiple histogram reweighting and finite-size scaling methods to analyze the data with special emphasis on the study of compensation phenomena. Compensation and critical temperatures of the system are obtained as functions of the Hamiltonian parameters and we present a detailed discussion about the contribution of each parameter to the presence or absence of the compensation effect. A comparison is presented between our results and those reported in the literature for the same model using the pair approximation. We also compare our results with those obtained through both the pair approximation and Monte Carlo simulations for the bilayer system.Comment: 13 figures. arXiv admin note: text overlap with arXiv:1607.0522

Computational study of microwave oscillations in absence of external field in nonstandard spin valves in the diffusive transport limit

An anomalous (inverse) spin accumulation in the nonmagnetic spacer may build up when the spin valve consists of magnetic films having different spin symmetries. This leads to wavy-like dependence of spin-transfer torque on the angle between magnetizations, as predicted by spin-dependent diffusive transport model, and also confirmed experimentally. Making use of these predictions, we have numerically studied the magnetization dynamics in presence of such a wavy-torque in Co(8 nm)/Cu(10 nm)/Py(8 nm) nanopillar, considering geometry with extended and etched Co layer. In both cases we specify conditions for the out-of-plane precession to appear in absence of external magnetic field and neglecting thermal fluctuations. We prove the assumption of wavy-like torque angular dependence to be fully consistent with experimental observations. We also show that some features reported experimentally, like nonlinear slope of frequency vs. current behavior, are beyond the applicability range of macrospin approximation and can be explained only by means of full micromagnetic analysis.Comment: 9 pages, 11 figure

Sobolev extremal polynomials with respect to mutually singular measures

We consider extremal polynomials with respect to a Sobolev-type $p$-norm, with $1<p<\infty$ and measures supported on compact subsets of the real line. For a wide class of such extremal polynomials with respect to mutually singular measures (i.e. supported on disjoint subsets of the real line), it is proved that their critical points are simple and contained in the interior of the convex hull of the support of the measures involved and the asymptotic critical point distribution is studied. We also find the $n$th root asymptotic behavior of the corresponding sequence of Sobolev extremal polynomials and their derivatives.Comment: 18 page

Perfect fluid brane-world model

By considering 5--dimensional cosmological models with a bulk filled with a perfect fluid and a cosmological constant, we have found regular instantonic solution which is free from any singularity at the origin of the extra--coordinate and describe 5--dimensional asymptotically anti de Sitter wormhole, when the bulk has a topology $R \times S^4$ and is filled with dust and a negative cosmological constant. Compactified brane-world instantons which are built up from such instantonic solution describe either a single brane or a string of branes. Their analytical continuation to the pseudo--Riemannian metric can give rise to either 4-dimensional inflating branes or solutions with the same dynamical behaviour for extra--dimension and branes, in addition to multitemporal solutions. Dust brane-world models with other spatial topologies are also considered.Comment: 14 pages, LateX2e, 4 figure

Lepton pair emission in the top quark decay t→bW+ℓ−ℓ+t \to bW^+\ell^-\ell^+

The heaviness of the top quark makes its 2-body decay mode $t \to bW^+$ to be dominant, at such level that hardly any other decay mode reaches a detectable branching ratio (BR) within the SM. Here we study the decay $t \to bW^+\ell^-\ell^+$ ($\ell=e, \mu, \tau$), which diverges for massless leptons, and it can reach a BR $\sim \mathcal{O}(10^{-5}\sim 10^{-6})$ for reasonable values of the low energy cut in the lepton-pair invariant mass. This rate surpasses almost any other rare decays such as $t \to cX$ ($X=\gamma,Z,g,H, W^+W^-$), and thus offers the possibility of being detectable. Furthermore, the estimate of this channel is relevant because it can mimic the signal arising from the lepton number violating decay $t\to bW^-\ell^+\ell^+$, when the $W$ boson decays into lepton channels.Comment: 9 pages, 4 figures, v2: comments and references added, matches with version accepted in Phys. Rev.