arXiv subjects

Piotr Graczyk

Publications and source records attributed to Piotr Graczyk.

At least 37 records · Page 2Linked to original sources

arXiv2020

Nonresonant amplification of coherent spin waves through voltage-induced interface magnetoelectric effect and spin-transfer torque

We present new mechanism for manipulation of the spin-wave amplitude through the use of the dynamic charge-mediated magnetoelectric effect in ultrathin multilayers composed of dielectric thin-film capacitors separated by a ferromagnetic bilayer. Propagating spin waves can be amplified and attenuated with rising and decreasing slopes of the oscillating voltage, respectively, locally applied to the sample. The way the spin accumulation is generated makes the interaction of the spin-transfer torque with the magnetization dynamics mode-selective and restricted to some range of spin-wave frequencies, which is in contrary to known types of the spin-transfer torque effects. The interfacial nature of spin-dependent screening allows to reduce the thickness of the fixed magnetization layer to a few nanometers, thus the proposed effect significantly contributes toward realization of the magnonic devices and also miniaturization of the spintronic devices.

cond-mat.mes-hall↗

arXiv2019

Potential kernels for radial Dunkl Laplacians

We derive two-sided bounds for the Newton and Poisson kernels of the $W$-invariant Dunkl Laplacian in geometric complex case when the multiplicity $k(α)=1$, i.e. for flat complex symmetric spaces. For the invariant Dunkl-Poisson kernel $P^W(x,y)$, the estimates are $$ P^W(x,y)\asymp \frac{P^{{\bf R}^d}(x,y)}{\prod_{α> 0 \ }|x-σ_αy|^{2k(α)}},$$ where the $α$'s are the positive roots of a root system acting in ${\bf R}^d$, the $σ_α$'s are the corresponding symmetries and $P^{{\bf R}^d}$ is the classical Poisson kernel in ${{\bf R}^d}$. Analogous bounds are proven for the Newton kernel when $d\ge 3$. The same estimates are derived in the rank one direct product case $\mathbb Z_2^N$ and conjectured for general $W$-invariant Dunkl processes. As an application, we get a two-sided bound for the Poisson and Newton kernels of the classical Dyson Brownian motion and of the Brownian motions in any Weyl chamber.

math.AP↗

arXiv2019

Experimental Evidence of Non-Negligible Imaginary Part of Spin Mixing Conductance and Its Impact on Magnetization Dynamics in Heavy-Metal|Ferromagnet Bilayers

The paper concerns experimental verification of the magnitude of imaginary part of spin mixing conductance in bilayers comprising heavy metals. We present results of broadband ferromagnetic resonance studies on heterostructures consisting of Finemet thin films covered by Pt and Ta wedge layers with the aim to observe spin pumping effects and to evaluate both the real and imaginary parts of the spin mixing conductance. The experimental results are analyzed in the framework of a recent microscopic theory which allows us to estimate the value of the interfacial spin-orbit interaction and confirm its important role. In particular, we show that the imaginary part of spin mixing conductance cannot be regarded as negligible and we discuss its influence on magnetization dynamics. For Finemet|Ta bilayers, the ratio $\mathrm{Re}[g_{eff}^{\uparrow\downarrow}]/\mathrm{Im}[g_{eff}^{\uparrow\downarrow}]=$ 0.38, that is, the field-like torque dominates over the damping-like torque in such system. Consequently, relatively small enhancement of precession damping with respect to significant total torque exerted on the magnetization in Finemet|Ta system offers an attractive perspective for an application in the next-generation magnetic random-access memory cells.

cond-mat.mes-hall↗

arXiv2019

Broadband magnetoelastic coupling in magphonic crystals for high-frequency nanoscale spin wave generation

Spin waves are promising candidates for information carriers in advanced technology. The interactions between spin waves and acoustic waves in magnetic nanostructures are of much interest because of their potential application for spin wave generation, amplification and transduction. We investigate numerically the dynamics of magnetoelastic excitations in a one-dimensional magphonic crystal consisting of alternating layers of permalloy and cobalt. We use the plane wave method and the finite element method for frequency- and time-domain simulations, respectively. The studied structure is optimized for hybridization of specific spin-wave and acoustic dispersion branches in the entire Brillouin zone in a broad frequency range. We show that this type of periodic structure can be used for efficient generation of high-frequency spin waves.

physics.app-ph↗

arXiv2019

Spin-polarized currents driven by spin-dependent surface screening

We have examined the spin polarization of the electron current in a ferromagnetic metal induced by the spin-dependent surface screening at the dielectric-ferromagnetic metal (D-FM) interface. In an applied ac voltage, the dynamic band splitting driven by the changes in the screening charge at the D-FM interface develops spin accumulation. The resultant spin accumulation gradient produces a time-dependent spin current. We have derived the rate of the spin accumulation on the rate of the screening charge density accumulation within the Stoner band model. The spin-charge dynamics in the system is then modeled by a set of diffusive equations with the contributions from spin-dependent surface screening ands spin-dependent conductivity. We show for MgO-Cu-Co-MgO system that the spin-dependent screening in thin Co film produces spin accumulation 7 times higher than that obtained by the spin-dependent conductivity in thick Co films. We propose an experimental approach to validate our numerical predictions and to distinguish between spin accumulation induced by the spin-dependent conductivity and by the spin-dependent surface screening.

cond-mat.mes-hall↗

arXiv2018

Magnonic band gap and mode hybridization in continuous Permalloy film induced by vertical coupling with an array of Permalloy ellipses

We investigate magnonic band structure in thin homogeneous permalloy film decorated with periodic array of elliptically shaped permalloy dots and separated by non-magnetic Pt spacer. We demonstrated experimentally formation of the magnonic band structure for Damon-Eshbach wave propagating in permalloy film with the band gap opened at the Brillouin zone border and band splitting at smaller wavenumbers, due to the Bragg interference and interaction of propagating wave of the continuous film with a standing resonant mode of the nano-ellipses, respectively. The shape anisotropy of the permalloy nanodots allows to control the spin wave dynamics through the switch between two states of the magnetization with respect to the underneath film magnetization, thus enabling magnonic band structure reprogrammability. With numerical analysis we show, that predominant role in formation of the magnonic band structure is played by a vertical dynamic coupling between propagating wave in the film and magnetization oscillations in the nanodots.

cond-mat.mes-hall↗

arXiv2018

Space and time inversions of stochastic processes and Kelvin transform

Let $X$ be a standard Markov process. We prove that a space inversion property of $X$ implies the existence of a Kelvin transform of $X$-harmonic, excessive and operator-harmonic functions and that the inversion property is inherited by Doob $h$-transforms. We determine new classes of processes having space inversion properties amongst transient processes {satisfying the} time inversion property. {For these processes, some explicit inversions, which are often not the spherical ones, and excessive functions are given explicitly.} We treat in details the examples of free scaled power Bessel processes, non-colliding Bessel particles, Wishart processes, Gaussian Ensemble and Dyson Brownian Motion.

math.PR↗

arXiv2018

Wishart laws and variance function on homogeneous cones

We present a systematic study of Riesz measures and their natural exponential families of Wishart laws on a homogeneous cone. We compute explicitly the inverse of the mean map and the variance function of a Wishart exponential family.

math.ST↗

arXiv2017

Co- and contra-directional vertical coupling between ferromagnetic layers with grating for short-wavelength spin wave generation

The possibility to generate short spin waves is of great interest in the field of magnonics nowadays. We present an effective and technically affordable way of conversion of long spin waves, which may be generated by conventional microwave antenna, to the short, sub-micrometer waves. It is achieved by grating-assisted resonant dynamic dipolar interaction between two ferromagnetic layers separated by some distance. We analyze criteria for the optimal conversion giving a semi-analytical approach for the coupling coefficient. We show by the numerical calculations the efficient energy transfer between layers which may be either of co-directional or contra-directional type. Such a system may operate either as a short spin wave generator or a frequency filter, moving foreward possible application of magnonics.

cond-mat.mes-hall↗

arXiv2017

On squared Bessel particle systems

We study the existence and uniqueness of SDEs describing squared Bessel particles systems in full generality. We define non-negative and non-colliding squared Bessel particle systems and we study their properties.

math.PR↗

arXiv2017

A Characterization of Wishart Processes and Wishart Distributions

A characterization of the existence of non-central Wishart distributions (with shape and non-centrality parameter) as well as the existence of solutions to Wishart stochastic differential equations (with initial data and drift parameter) in terms of their exact parameter domains is given. These two families are the natural extensions of the non-central chi-square distributions and the squared Bessel processes to the positive semidefinite matrices.

math.PR↗

arXiv2017

Coupled mode theory for the acoustic wave and spin wave interaction in the magphonic crystals: Propagating magnetoelastic waves

We have investigated co-directional and contra-directional couplings between spin wave and acoustic wave in one-dimensional periodic structure (magphonic crystal). The system consists of two ferromagnetic layers alternating in space. We have taken into consideration materials commonly used in magnonics: yttrium iron garnet, CoFeB, permalloy, and cobalt. The coupled mode theory (CMT) formalism have been successfully implemented to describe magnetoelastic interaction as a periodic perturbation in the magphonic crystal. The results of CMT calculations have been verified by more rigorous simulations by frequency-domain plane wave method and time-domain finite element method. The presented resonant coupling in the magphonic crystal is an active in-space mechanism which spatially transfers energy between propagating spin and acoustic modes, thus creating propagating magnetoelastic wave. We have shown, that CMT analysis of the magnetoelastic coupling is an useful tool to optimize and design a spin wave - acoustic wave transducer based on a magphonic crystals. The effect of spin wave damping has been included to the model to discuss the efficiency of such a device. Our model shows that it is possible to obtain forward conversion of the acoustic wave to the spin wave in case of co-directional coupling and backward conversion in case of contra-directional coupling.

cond-mat.other↗

arXiv2017

Wishart exponential families on cones related to An graphs

Let G = An be the graph corresponding to the graphical model of nearest neighbour interaction in a Gaussian character. We study Natural Exponential Families( NEF) ofWishart distributions on convex cones QG and PG, where PG is the cone of positive definite real symmetric matrices with obligatory zeros prescribed by G, and QG is the dual cone of PG. The Wishart NEF that we construct include Wishart distributions considered earlier by Lauritzen (1996) and Letac and Massam (2007) for models based on decomposable graphs. Our approach is however different and allows us to study the basic objects ofWishart NEF on the cones QG and PG.We determine Riesz measures generating Wishart exponential families on QG and PG, and we give the quadratic construction of these Riesz measures and exponential families. The mean, inverse-mean, covariance and variance functions, as well as moments of higher order are studied and their explicit formulas are given.

math.ST↗

arXiv2016

On the Green function and Poisson integrals of the Dunkl Laplacian

We prove the existence and study properties of the Green function of the unit ball for the Dunkl Laplacian $Δ_k$ in $\mathbb{R}^d$. As applications we derive the Poisson-Jensen formula for $Δ_k$-subharmonic functions and Hardy-Stein identities for the Poisson integrals of $Δ_k$. We also obtain sharp estimates of the Newton potential kernel, Green function and Poisson kernel in the rank one case in $\mathbb{R}^d$. These estimates contrast sharply with the well-known results in the potential theory of the classical Laplacian.

math.AP↗

arXiv2016

Wallach sets and squared Bessel particle systems

We determine the classical and the non-central Wallach sets $W_0$ and $W$ by classical probabilistic methods. We prove the Mayerhofer conjecture on $W$. We exploit the fact that $(x_0,β)\in W$ if and only if $x_0$ is the starting point and $2β$ is the drift of a squared Bessel matrix process $X_t$ on the cone $\bar{Sym^+(\mathbf{R},p)}$. Our methods are based on the study of SDEs for the symmetric polynomials of $X_t$ and for the eigenvalues of $X_t$, i.e. the squared Bessel particle systems.

math.PR↗

arXiv2016

Inversion, duality and Doob $h$-transforms for self-similar Markov processes

We show that any $\mathbb{R}^d\setminus\{0\}$-valued self-similar Markov process $X$, with index $α>0$ can be represented as a path transformation of some Markov additive process (MAP) $(θ,ξ)$ in $S_{d-1}\times\mathbb{R}$. This result extends the well known Lamperti transformation. Let us denote by $\widehat{X}$ the self-similar Markov process which is obtained from the MAP $(θ,-ξ)$ through this extended Lamperti transformation. Then we prove that $\widehat{X}$ is in weak duality with $X$, with respect to the measure $π(x/\|x\|)\|x\|^{α-d}dx$, if and only if $(θ,ξ)$ is reversible with respect to the measure $π(ds)dx$, where $π(ds)$ is some $σ$-finite measure on $S_{d-1}$ and $dx$ is the Lebesgue measure on $\mathbb{R}$. Besides, the dual process $\widehat{X}$ has the same law as the inversion $(X_{γ_t}/\|X_{γ_t}\|^2,t\ge0)$ of $X$, where $γ_t$ is the inverse of $t\mapsto\int_0^t\|X\|_s^{-2α}\,ds$. These results allow us to obtain excessive functions for some classes of self-similar Markov processes such as stable Lévy processes.

math.PR↗

arXiv2014

Strong solutions of non-colliding particle systems

We study systems of stochastic differential equations describing positions x_1,x_2,...,x_p of p ordered particles, with inter-particles repulsions of the form H_{ij}(x_i,x_j)/(x_i-x_j). We show the existence of strong and pathwise unique non-colliding solutions of the system with a colliding initial point x_1(0)\leq ...\leq x_p(0) in the whole generality, under natural assumptions on the coefficients of the equations.

math.PR↗

arXiv2014

Convolution of orbital measures on symmetric spaces of type $C_p$ and $D_p$

We study the absolute continuity of the convolution $δ_{e^X}^\natural \starδ_{e^Y}^\natural$ of two orbital measures on the symmetric spaces ${\bf SO}_0(p,p)/{\bf SO}(p)\times{\bf SO}(p)$, $\SU(p,p)/{\bf S}({\bf U}(p)\times{\bf U}(p))$ and $\Sp(p,p)/{\bf Sp }(p)\times\Sp(p)$. We prove sharp conditions on $X$, $Y\in\a$ for the existence of the density of the convolution measure. This measure intervenes in the product formula for the spherical functions.

math.PR↗