Local Method Of Moments Research Articles

Machine learning study of highly spin-polarized Heusler alloys at finite temperature

A huge magnetoresistance (MR) ratio exceeding 2000% at cryogenic temperature that was reported for half-metallic Heusler alloy based magnetic tunnel junctions showed large degradation at room temperature, which impedes practical application of Heusler alloy based MR devices. This motivates us to explore alternative Heusler alloys that show high spin polarization at finite temperatures. Here, we propose half-metallic Heusler alloys based on finite-temperature first-principles calculation via the disordered local moment method together with machine learning. We found several prospective materials at room temperature such as ${\mathrm{Co}}_{2}{\mathrm{MnGa}}_{0.2}{\mathrm{As}}_{0.8}$ and ${\mathrm{Co}}_{2}{\mathrm{FeAl}}_{0.4}{\mathrm{Sn}}_{0.6}$. We also investigated two combinatorial series, ${\mathrm{Co}}_{2}{\mathrm{MnGa}}_{y}{\mathrm{As}}_{1\text{\ensuremath{-}}y}$ and ${\mathrm{Co}}_{2}{\mathrm{FeAl}}_{y}{\mathrm{Sn}}_{1\text{\ensuremath{-}}y}$, to understand the effect of alloy mixing on temperature dependence and found that Fermi level tuning significantly improved the spin polarization and its temperature dependence, especially in ${\mathrm{Co}}_{2}{\mathrm{FeAl}}_{y}{\mathrm{Sn}}_{1\text{\ensuremath{-}}y}$.

Direct probing of temperature-independent bulk half-metallicity in Co2MnSi by spin-resolved hard x-ray photoemission

We have performed the bulk-sensitive spin-resolved hard x-ray photoelectron spectroscopy (HAXPES) to directly clarify the spin-dependent valence band electronic states and spin polarization of $L{2}_{1}$-ordered ${\mathrm{Co}}_{2}\mathrm{MnSi}$ as a predicted half-metal. The spin-resolved valence band HAXPES spectra clearly exhibited the difference in the majority and minority spin states in the bulk region of a 30-nm-thick ${\mathrm{Co}}_{2}\mathrm{MnSi}(001)$ thin film buried under a MgO(2 nm) layer at both temperatures of 21 and 300 K. As expected from the half-metallicity in ${\mathrm{Co}}_{2}\mathrm{MnSi}$, we found that the majority (minority) spin spectrum shows a metallic Fermi edge (a band gap), leading the high spin polarization of \ensuremath{\sim}90% at around the Fermi level at a temperature of 21 K. The spin-resolved HAXPES experiments revealed that the half-metallicity of ${\mathrm{Co}}_{2}\mathrm{MnSi}$ in the bulk region is independent on the temperature up to 300 K. The experiments also revealed the slight changes in the majority spin spectral shapes and the shift of the valence band maximum of the minority spin states with temperature. By comparing the experimental results with the first-principles calculations at a finite temperature obtained by the disordered local moment method, it is suggested that the slight changes in the majority and minority spin HAXPES spectra of ${\mathrm{Co}}_{2}\mathrm{MnSi}$ with temperature is mainly caused by the temperature-dependent Co $3d$ electronic states. It is also suggested that the conduction band minimum of the minority spin states is located sufficiently above the Fermi level at temperature up to 300 K.

Effects of intrinsic defects and alloying with Fe on the half-metallicity of Co2MnSi

The electronic structure and half-metallic gap of Co$_{2}$MnSi in the presence of crystallographic defects, partial Fe substitution for Mn, and thermal spin fluctuations are studied using the coherent potential approximation and the disordered local moment method. In the presence of 5\% Co or Mn vacancies the Fermi level shifts down to the minority-spin valence-band maximum. In contrast to NiMnSb, both types of Mn antisite defects in Co$_{2}$MnSi are strongly exchange-coupled to the host magnetization, and thermal spin fluctuations do not strongly affect the half-metallic gap. Partial substitution of Mn by Fe results in considerable changes in the Bloch spectral function near the Fermi level, which strongly deviate from the rigid-band picture. In particular, a light band with the Fe character crosses the Fermi level at about 50\% concentration. At room temperature, Fe substitution of up to 30\% slightly increases the spin polarization at the Fermi level.

Origin of spin reorientation transitions in antiferromagnetic MnPt-based alloys

Antiferromagnetic MnPt exhibits a spin reorientation transition (SRT) as a function of temperature, and off-stoichiometric Mn-Pt alloys also display SRTs as a function of concentration. The magnetocrystalline anisotropy in these alloys is studied using first-principles calculations based on the coherent potential approximation and the disordered local moment method. The anisotropy is fairly small and sensitive to the variations in composition and temperature due to the cancellation of large contributions from different parts of the Brillouin zone. Concentration and temperature-driven SRTs are found in reasonable agreement with experimental data. Contributions from specific band-structure features are identified and used to explain the origin of the SRTs.

Estimating the Spot Covariation of Asset Prices—Statistical Theory and Empirical Evidence

ABSTRACTWe propose a new estimator for the spot covariance matrix of a multi-dimensional continuous semimartingale log asset price process, which is subject to noise and nonsynchronous observations. The estimator is constructed based on a local average of block-wise parametric spectral covariance estimates. The latter originate from a local method of moments (LMM), which recently has been introduced by Bibinger et al.. We prove consistency and a point-wise stable central limit theorem for the proposed spot covariance estimator in a very general setup with stochastic volatility, leverage effects, and general noise distributions. Moreover, we extend the LMM estimator to be robust against autocorrelated noise and propose a method to adaptively infer the autocorrelations from the data. Based on simulations we provide empirical guidance on the effective implementation of the estimator and apply it to high-frequency data of a cross-section of Nasdaq blue chip stocks. Employing the estimator to estimate spot covariances, correlations, and volatilities in normal but also unusual periods yields novel insights into intraday covariance and correlation dynamics. We show that intraday (co-)variations (i) follow underlying periodicity patterns, (ii) reveal substantial intraday variability associated with (co-)variation risk, and (iii) can increase strongly and nearly instantaneously if new information arrives. Supplementary materials for this article are available online.

Functional stable limit theorems for quasi-efficient spectral covolatility estimators

We consider noisy non-synchronous discrete observations of a continuous semimartingale with random volatility. Functional stable central limit theorems are established under high-frequency asymptotics in three setups: one-dimensional for the spectral estimator of integrated volatility, from two-dimensional asynchronous observations for a bivariate spectral covolatility estimator and multivariate for a local method of moments. The results demonstrate that local adaptivity and smoothing noise dilution in the Fourier domain facilitate substantial efficiency gains compared to previous approaches. In particular, the derived asymptotic variances coincide with the benchmarks of semiparametric Cramér–Rao lower bounds and the considered estimators are thus asymptotically efficient in idealized sub-experiments. Feasible central limit theorems allowing for confidence bounds are provided.

Estimating the Spot Covariation of Asset Prices Statistical Theory and Empirical Evidence

We propose a new estimator for the spot covariance matrix of a multi-dimensional continuous semi-martingale log asset price process which is subject to noise and non-synchronous observations. The estimator is constructed based on a local average of block-wise para- metric spectral covariance estimates. The latter originate from a local method of moments (LMM) which recently has been introduced by Bibinger et al. (2014). We prove consistency and a point-wise stable central limit theorem for the proposed spot covariance estimator in a very general setup with stochastic volatilities, leverage and for general noise distributions. Moreover, we extend the LMM estimator to be robust against autocorrelated noise and propose a method to adaptively infer the autocorrelations from the data. Based on simulations we provide empirical guidance on the optimal implementation of the estimator and apply it to high-frequency data of a cross-section of NASDAQ blue chip stocks. Employing the estimator to estimate spot covariances, correlations and volatilities in normal but also unusual periods yields novel insights into intraday covariance and correlation dynamics. We show that intraday (co-)variations (i) follow underlying periodicity patterns, (ii) reveal substantial intraday variability associated with (co-)variation risk, (iii) are strongly serially correlated, and (iv) can increase strongly and nearly instantaneously if new information arrives.

Estimating the quadratic covariation matrix from noisy observations: Local method of moments and efficiency

An efficient estimator is constructed for the quadratic covariation or integrated co-volatility matrix of a multivariate continuous martingale based on noisy and nonsynchronous observations under high-frequency asymptotics. Our approach relies on an asymptotically equivalent continuous-time observation model where a local generalised method of moments in the spectral domain turns out to be optimal. Asymptotic semi-parametric efficiency is established in the Cramér–Rao sense. Main findings are that nonsynchronicity of observation times has no impact on the asymptotics and that major efficiency gains are possible under correlation. Simulations illustrate the finite-sample behaviour.

Estimating the Spot Covariation of Asset Prices Statistical Theory and Empirical Evidence

We propose a new estimator for the spot covariance matrix of a multi-dimensional continuous semi-martingale log asset price process which is subject to noise and non-synchronous observations. The estimator is constructed based on a local average of block-wise parametric spectral covariance estimates. The latter originate from a local method of moments (LMM) which recently has been introduced. We prove consistency and a point-wise stable central limit theorem for the proposed spot covariance estimator in a very general setup with stochastic volatility, leverage effects and general noise distributions. Moreover, we extend the LMM estimator to be robust against autocorrelated noise and propose a method to adaptively infer the autocorrelations from the data. Based on simulations we provide empirical guidance on the effective implementation of the estimator and apply it to high-frequency data of a cross-section of Nasdaq blue chip stocks. Employing the estimator to estimate spot covariances, correlations and volatilities in normal but also unusual periods yields novel insights into intraday covariance and correlation dynamics. We show that intraday (co-)variations (i) follow underlying periodicity patterns, (ii) reveal substantial intraday variability associated with (co-)variation risk, and (iii) can increase strongly and nearly instantaneously if new information arrives.

Estimating the Quadratic Covariation Matrix from Noisy Observations: Local Method of Moments and Efficiency

An efficient estimator is constructed for the quadratic covariation or integrated covolatility matrix of a multivariate continuous martingale based on noisy and non-synchronous observations under high-frequency asymptotics. Our approach relies on an asymptotically equivalent continuous-time observation model where a local generalised method of moments in the spectral domain turns out to be optimal. Asymptotic semiparametric efficiency is established in the Cramer-Rao sense. Main findings are that non-synchronicity of observation times has no impact on the asymptotics and that major efficiency gains are possible under correlation. Simulations illustrate the finite-sample behaviour.

Effect of pressure on itinerant magnetism and spin disorder in cubic FeGe

The results of ab initio calculations of the pressure dependence of Fe magnetism in cubic FeGe are presented. We find that when the pressure–volume scale is set by means of generalized gradient approximation total energies and magnetism is described by means of the local density approximation, the critical pressure at which the magnetic phase transition occurs is estimated at ≈18 GPa, which is in good agreement with experiments. Using the disordered local moment method we find a localized to itinerant model cross-over of Fe magnetism in cubic FeGe, as a function of volume. Moreover, our calculations also suggest subtle signatures of longitudinal spin fluctuations in cubic FeGe, and that the stiffness parameter softens with increasing pressure. We associate the retention of metallicity in FeGe under pressure with the spin-disorder scattering. The effect of spin–orbit coupling on the electronic structure is also discussed.

A higher-order Nystro/spl uml/m scheme for electromagnetic scattering by arbitrarily shaped surfaces

A higher-order Nystro/spl uml/m scheme is developed for electromagnetic scattering by arbitrary conducting scatterers. In our implementation, we employ a superparametric geometry mapping for arbitrary curvilinear surfaces to minimize the geometry error. The local correction for singular integral kernels is manipulated efficiently with the Lagrange interpolation of the unknown functions followed by singularity extraction and Duffy's transformation. Since this local correction approach removes the local method of moments (MoM) procedure, the scheme is easier to implement and more efficient in controlling errors compared with other higher-order Nystro/spl uml/m schemes. Two numerical examples for scattering by sharp-corner scatterers are conducted to demonstrate the robustness of this method.

Ab initio treatment of noncollinear magnets with the full-potential linearized augmented plane wave method

The massively parallelized full-potential linearized augmented plane-wave bulk and film program FLEUR for first-principles calculations in the context of density functional theory was adapted to allow calculations of materials with complex magnetic structures---i.e., with noncollinear spin arrangements and incommensurate spin spirals. The method developed makes no shape approximation to the charge density and works with the continuous vector magnetization density in the interstitial and vacuum region and a collinear magnetization density in the spheres. We give an account of the implementation. Important technical aspects, such as the formulation of a constrained local moment method in a full-potential method that works with a vector magnetization density to deal with specific preselected nonstationary-state spin configurations, the inclusion of the generalized gradient approximation in a noncollinear framework, and the spin-relaxation method are discussed. The significance and validity of different approximations are investigated. We present examples to the various strategies to explore the magnetic ground state, metastable states, and magnetic phase diagrams by relaxation of spin arrangements or by performing calculations for constraint spin configurations to invest the functional dependence of the total energy and magnetic moment with respect to external parameters.

Itinerant Magnets on a Triangular Cu(111) Lattice

We investigate complex spin structures of frustrated two-dimensional Cr, Mn, and Fe monolayer magnets on a triangular lattice provided by the Cu(111) substrate. First we establish a zero-temperature phase diagram of possible spin structures on the basis of the classical Heisenberg model up to the third-nearest neighbor exchange interaction. Second we carried out first-principles total energy calculations on the basis of the vector-spin density formulation of the density functional theory using the full potential linearized augmented plane wave (FLAPW) method in film geometry for a set of complex non-collinear spin structures. We found, the ground state of Fe is ferromagnetic, Cr exhibits a coplanar, two-dimensional non-collinear 120 Néel state and Mn a three-dimensional non-collinear ground state, the 3Q-state. Incommensurate spin-spiral states are expected for a FeMn alloy on Cu(111). We employ the constrained local moment method to estimate the exchange parameters of the model Hamiltonians. We show that for Mn higher-order spin interactions are the origin of the 3Q-state for Mn. The combination of ab initio calculations and model Hamiltonians provides a powerful tool to investigate the magnetic structures of complex magnetic systems.