arXiv subjects

Ziyan Luo

Publications and source records attributed to Ziyan Luo.

At least 37 records · Page 2Linked to original sources

arXiv2021

Eigenvalues and Singular Values of Dual Quaternion Matrices

The poses of $m$ robotics in $n$ time points may be represented by an $m \times n$ dual quaternion matrix. In this paper, we study the spectral theory of dual quaternion matrices. We introduce right and left eigenvalues for square dual quaternion matrices. If a right eigenvalue is a dual number, then it is also a left eigenvalue. In this case, this dual number is called an eigenvalue of that dual quaternion matrix. We show that the right eigenvalues of a dual quaternion Hermitian matrix are dual numbers. Thus, they are eigenvalues. An $n \times n$ dual quaternion Hermitian matrix is shown to have exactly $n$ eigenvalues. It is positive semidefinite, or positive definite, if and only if all of its eigenvalues are nonnegative, or positive and appreciable, dual numbers, respectively. We present a unitary decomposition of a dual quaternion Hermitian matrix, and the singular value decomposition for a general dual quaternion matrix. The singular values of a dual quaternion matrix are nonnegative dual numbers.

math.RA↗

arXiv2021

Computing One-bit Compressive Sensing via Double-Sparsity Constrained Optimization

One-bit compressive sensing gains its popularity in signal processing and communications due to its low storage costs and low hardware complexity. However, it has been a challenging task to recover the signal only by exploiting the one-bit (the sign) information. In this paper, we appropriately formulate the one-bit compressive sensing into a double-sparsity constrained optimization problem. The first-order optimality conditions for this nonconvex and discontinuous problem are established via the newly introduced $τ$-stationarity, based on which, a gradient projection subspace pursuit (\texttt{GPSP}) algorithm is developed. It is proven that \texttt{GPSP} can converge globally and terminate within finite steps. Numerical experiments have demonstrated its excellent performance in terms of a high order of accuracy with a fast computational speed.

math.OC↗

arXiv2021

Eigenvalues and Singular Value Decomposition of Dual Complex Matrices

We introduce right eigenvalues and subeigenvalues for square dual complex matrices. An $n \times n$ dual complex Hermitian matrix has exactly $n$ right eigenvalues and subeigenvalues, which are all real. The Hermitian matrix is positive semi-definite or definite if and only if all of its right eigenvalues and subeigenvalues are nonnegative or positive, respectively. A Hermitian matrix can be diagonalized if and only if it has no right subeigenvalues. Then we present the singular value decomposition for general dual complex matrices. The results are further extended to dual quaternion matrices.

math.RA↗

arXiv2021

A Note on Quaternion Skew-Symmetric Matrices

The product of a complex skew-symmetric matrix and its conjugate transpose is a positive semi-definite Hermitian matrix with nonnegative eigenvalues, with a property that each distinct positive eigenvalue has even multiplicity. This property plays a key role for Professor Loo-Keng Hua to establish the unitary equivalence theorem for complex skew-symmetric matrices. We show that this property is no longer true for quaternion skew-symmetric matrices. This poses a difficulty for finding the canonical form of a quaternion skew-symmetric matrix under unitary equivalence, which may be crucial for the spectral theory of dual quaternion matrices. We show that the inverse of a quaternion skew-symmetric matrix may not be skew-symmetric though the inverse of a nonsingular complex skew-symmetric matrix is always skew-symmetric. We also present the concept of basic quaternion skew-symmetric matrices.

math.RA↗

arXiv2021

Giant enhancement of anomalous Hall effect in Cr modulation-doped non-collinear antiferromagnetic Mn3Sn thin films

We report on Cr doping effect in Mn3Sn polycrystalline films with both uniform and modulation doping. It is found that Cr doping with low concentration does not cause notable changes to the structural and magnetic properties of Mn3Sn, but it significantly enhances the anomalous Hall conductivity, particularly for modulation-doped samples at low temperature. A Hall conductivity as high as 184.8 Ω-1 cm-1 is obtained for modulation-doped samples at 50 K, in a sharp contrast to vanishingly small values for undoped samples at the same temperature. We attribute the enhancement to the change of Fermi level induced by Cr doping

cond-mat.mtrl-sci↗

arXiv2021

Tubal Matrices

It was shown recently that the f-diagonal tensor in the T-SVD factorization must satisfy some special properties. Such f-diagonal tensors are called s-diagonal tensors. In this paper, we show that such a discussion can be extended to any real invertible linear transformation. We show that two Eckart-Young like theorems hold for a third order real tensor, under any doubly real-preserving unitary transformation. The normalized Discrete Fourier Transformation (DFT) matrix, an arbitrary orthogonal matrix, the product of the normalized DFT matrix and an arbitrary orthogonal matrix are examples of doubly real-preserving unitary transformations. We use tubal matrices as a tool for our study. We feel that the tubal matrix language makes this approach more natural.

math.NA↗

arXiv2021

A Lagrange-Newton Algorithm for Sparse Nonlinear Programming

The sparse nonlinear programming (SNP) problem has wide applications in signal and image processing, machine learning, pattern recognition, finance and management, etc. However, the computational challenge posed by SNP has not yet been well resolved due to the nonconvex and discontinuous $\ell_0$-norm involved. In this paper, we resolve this numerical challenge by developing a fast Newton-type algorithm. As a theoretical cornerstone, we establish a first-order optimality condition for SNP based on the concept of strong $β$-Lagrangian stationarity via the Lagrangian function, and reformulate it as a system of nonlinear equations called the Lagrangian equations. The nonsingularity of the corresponding Jacobian is discussed, based on which the Lagrange-Newton algorithm (LNA) is then proposed. Under mild conditions, we establish the locally quadratic convergence and the iterative complexity estimation of LNA. To further demonstrate the efficiency and superiority of our proposed algorithm, we apply LNA to solve two specific application problems arising from compressed sensing and sparse high-order portfolio selection, in which significant benefits accrue from the restricted Newton step in LNA.

math.OC↗

arXiv2020

Quaternion Matrix Optimization and The Underlying Calculus

Optimization models involving quaternion matrices are widely used in color image process and other engineering areas. These models optimize real functions of quaternion matrix variables. In particular, $\ell_0$-norms and rank functions of quaternion matrices are discrete. Yet calculus with derivatives, subdifferentials and generalized subdifferentials of such real functions is needed to handle such models. In this paper, we introduce first and second order derivatives and establish their calculation rules for such real functions. Our approach is consistent with the subgradient concept for norms of quaternion matrix variables, recently introduced in the literature. We develop the concepts of generalized subdifferentials of proper functions of quaternion matrices, and use them to analyze the optimality conditions of a sparse low rank color image denoising model. We introduce R-product for two quaternion matrix vectors, as a key tool for our calculus. We show that the real representation set of low-rank quaternion matrices is closed and semi-algebraic. We also establish first order and second order optimality conditions for constrained optimization problems of real functions in quaternion matrix variables.

math.OC↗

arXiv2020

Spin torque gate magnetic field sensor

Spin-orbit torque provides an efficient pathway to manipulate the magnetic state and magnetization dynamics of magnetic materials, which is crucial for energy-efficient operation of a variety of spintronic devices such as magnetic memory, logic, oscillator, and neuromorphic computing. Here, we describe and experimentally demonstrate a strategy for the realization of a spin torque gate magnetic field sensor with extremely simple structure by exploiting the longitudinal field dependence of the spin torque driven magnetization switching. Unlike most magnetoresistance sensors which require a delicate magnetic bias to achieve a linear response to the external field, the spin torque gate sensor can achieve the same without any magnetic bias, which greatly simplifies the sensor structure. Furthermore, by driving the sensor using an ac current, the dc offset is automatically suppressed, which eliminates the need for a bridge or compensation circuit. We verify the concept using the newly developed WTe2/Ti/CoFeB trilayer and demonstrate that the sensor can work linearly in the range of 3-10 Oe with negligible dc offset.

cond-mat.mes-hall↗

arXiv2020

Terahertz Emission From an Exchange-Coupled Synthetic Antiferromagnet

We report on terahertz emission from FeMnPt/Ru/FeMnPt and Pt/CoFeB/Ru/CoFeB/Pt synthetic antiferromagnet (SAF) structures upon irradiation by a femtosecond laser; the former is via the anomalous Hall effect, whereas the latter is through the inverse spin Hall effect. The antiparallel alignment of the two ferromagnetic layers leads to a terahertz emission peak amplitude that is almost double that for a corresponding single-layer or bilayer emitter with the same equivalent thickness. In addition, we demonstrate by both simulation and experiment that terahertz emission provides a powerful tool to probe the magnetization reversal processes of individual ferromagnetic layers in a SAF structure, as the terahertz signal is proportional to the vector difference of the magnetizations of the two ferromagnetic layers.

cond-mat.mtrl-sci↗

arXiv2019

Low-Rank Matrix Optimization Over Affine Set

The low-rank matrix optimization with affine set (rank-MOA) is to minimize a continuously differentiable function over a low-rank set intersecting with an affine set. Under some suitable assumptions, the intersection rule of the Fréchet normal cone to the feasible set of the rank-MOA is established. This allows us to propose the first-order optimality conditions for the rank-MOA in terms of the so-called F-stationary point and the $α$-stationary point. Furthermore, the second-order optimality analysis, including the necessary condition and the sufficient one, is proposed as well. All these results will enrich the theory of low-rank matrix optimization and give potential clues to designing efficient numerical algorithms for seeking low-rank solutions. Meanwhile, we illustrate our proposed optimality analysis for several specific applications of the rank-MOA including the Hankel matrix approximation problem in system identification and the low-rank representation on linear manifold in signal processing.

math.SP↗

arXiv2019

Terahertz emission from anomalous Hall effect in a single-layer ferromagnet

We report on terahertz emission from a single layer ferromagnet which involves the generation of backflow nonthermal charge current from the ferromagnet/dielectric interface by femtosecond laser excitation and subsequent conversion of the charge current to a transverse transient charge current via the anomalous Hall effect, thereby generating the THz radiation. The THz emission can be either enhanced or suppressed, or even the polarity can be reversed, by introducing a magnetization gradient in the thickness direction of the ferromagnet. Unlike spintronic THz emitters reported previously, it does not require additional non-magnetic layer or Rashba interface.

physics.app-ph↗

arXiv2019

In-situ study of oxygen exposure effect on spin-orbit torque in Pt/Co bilayers in ultrahigh vacuum

Oxygen incorporation has been reported to increase the current-induced spin-orbit torque in ferromagnetic heterostructures, but the underlying mechanism is still under active debate. Here, we report on an in-situ study of the oxygen exposure effect on spin-orbit torque in Pt/Co bilayers via controlled oxygen exposure, Co and Mg deposition, and electrical measurements in ultrahigh vacuum. We show that the oxygen exposure on Pt/Co indeed leads to an increase of spin-orbit torque, but the enhancement is not as large as those reported previously. Similar enhancement of spin-orbit torque is also observed after the deposition of an MgO capping layer. The results of ab initio calculations on the Rashba splitting of Pt/Co and Pt/Co/O suggest that the enhancement is due to enhanced Rashba-Edelstein effect by surface-adsorbed oxygen. Our findings shed some light on the varying roles of oxygen in modifying the spin torque efficiency reported previously.

cond-mat.mes-hall↗

arXiv2019

Disentangle magnon magnetoresistance from anisotropic and spin Hall magnetoresistance in NiFe/Pt bilayers

We conducted a systematic angular dependence study of nonlinear magnetoresistance in NiFe/Pt bilayers at variable temperature and field using the Wheatstone bridge method. We successfully disentangled magnon magnetoresistance from other types of magnetoresistances based on their different temperature and field dependences. Both the spin Hall/anisotropic and magnon magnetoresistances contain sine phi and sine 3 phi components with phi the angle between current and magnetization, but they exhibit different field and temperature dependence. The competition between different types of magnetoresistances leads to a sign reversal of sine 3 phi component at a specific magnetic field, which was not reported previously. The phenomenological model developed is able to account for the experimental results for both NiFe/Pt and NiFe/Ta samples with different layer thicknesses. Our results demonstrate the importance of disentangling different types of magnetoresistances when characterizing the charge-spin interconversion process in magnetic heterostructures.

cond-mat.mes-hall↗

arXiv2019

Spin-Orbit Torque in a Single Ferromagnetic Layer with Large Spin-Orbit Coupling

Spin-orbit torque in heavy metal/ferromagnet heterostructures with broken spatial inversion symmetry provides an efficient mechanism for manipulating magnetization using a charge current. Here, we report the presence of a spin torque in a single ferromagnetic layer in both asymmetric MgO/Fe0.8Mn0.2 and symmetric MgO/Fe0.8Mn0.2/MgO structures, which manifests itself in the form of an effective field transverse to the charge current. The current to effective field conversion efficiency, which is characterized using both the nonlinear magnetoresistance and second-order planar Hall effect methods, is comparable to the efficiency in typical heavy metal/ferromagnet bilayers. We argue that the torque is caused by spin rotation in the vicinity of the surface via impurity scattering in the presence of a strong spin-orbit coupling. Instead of cancelling off with each other, the torques from the top and bottom surfaces simply add up, leading to a fairly large net torque, which is readily observed experimentally.

cond-mat.mes-hall↗

arXiv2018

Magnetic angular position sensor enabled by spin-orbit torque

We propose a simple scheme for magnetic angular position sensor based on current-induced spin-orbit torque effect. A full range detection of 360o is realized with a pair of Hall crosses made of heavy metal/ferromagnet heterostructures. The current axes of the two Hall crosses are aligned orthogonal to each other such that when both devices are subject to a rotational in-plane magnetic field, the differential Hall voltage due to current pulses of opposite polarity exhibits a sine and cosine angular dependence on the field direction, respectively. The field rotational angle is then calculated from the sine and cosine output signals via the arctan2 function. A linear correspondence between the calculated and actual field angle is obtained in the field range of 500-2000 Oe, with an average angle error of 0.38-0.65o.

cond-mat.mtrl-sci↗

arXiv2018

Anomalous Hall magnetoresistance in a ferromagnet

The anomalous Hall effect, observed in conducting ferromagnets with broken time-reversal symmetry, offers the possibility to couple spin and orbital degrees of freedom of electrons in ferromagnets. In addition to charge, the anomalous Hall effect also leads to spin accumulation at the surfaces perpendicular to both the current and magnetization direction. Here we experimentally demonstrate that the spin accumulation, subsequent spin backflow, and spin-charge conversion can give rise to a different type of spin current related magnetoresistance, dubbed here as the anomalous Hall magnetoresistance, which has the same angular dependence as the recently discovered spin Hall magnetoresistance. The anomalous Hall magnetoresistance is observed in four types of samples: co-sputtered (Fe1-xMnx)0.6Pt0.4, Fe1-xMnx and Pt multilayer, Fe1-xMnx with x = 0.17 to 0.65 and Fe, and analyzed using the drift-diffusion model. Our results provide an alternative route to study charge-spin conversion in ferromagnets and to exploit it for potential spintronic applications.

cond-mat.mtrl-sci↗

arXiv2018

A Lagrangian Dual Based Approach to Sparse Linear Programming

A sparse linear programming (SLP) problem is a linear programming problem equipped with a sparsity (or cardinality) constraint, which is nonconvex and discontinuous theoretically and generally NP-hard computationally due to the combinatorial property involved. By rewriting the sparsity constraint into a disjunctive form, we present an explicit formula of its Lagrangian dual in terms of an unconstrained piecewise-linear convex programming problem which admits a strong duality. A semi-proximal alternating direction method of multipliers (sPADMM) is then proposed to solve this dual problem by taking advantage of the efficient computation of the proximal mapping of the vector Ky-Fan norm function. Based on the optimal solution of the dual problem, we design a dual-primal algorithm for pursuing a global solution of the original SLP problem. Numerical results illustrate that our proposed algorithm is promising especially for large-scale problems.

math.OC↗