Finite Exchange Research Articles

New classes of modules for which the finite exchange property implies the full exchange property

Let M be a right R-module. We call a summand A of M a special summand if there exists a summand B of M with A ≅ B and A ∩ B = 0 . An internal direct sum ⊕ i ∈ I A i of submodules Ai of M is called a special local summand if each Ai is a special summand and ⊕ i ∈ F A i is a summand of M for any finite subset F ⊆ I . In this paper we give two new classes of modules for which the finite exchange property implies the full exchange property, namely, modules whose special local summands are summands, and C4-modules for which the union of any chain of special summands is a summand. More precisely, we show that if either M is a module whose special local summands are summands or M is a C4-module such that the union of any chain of special summands of itself is a summand, then M has the finite exchange property if and only if it has the full exchange property if and only if it is a clean module. As immediate applications of the aforementioned results, we generalize and extend many of the fundamental results on the subject of exchange modules.

Volatility and jump with intraday periodicity and truncated power variation in Chinese yuan-US dollar exchange rates

ABSTRACT This study analyzes the discrete jump volatility of the Chinese yuan/U.S. dollar exchange rate returns using high-frequency five-minute returns from June 2012 to April 2021. Using periodicity filters of volatility, we conduct volatility jump tests for finite and infinite exchange rate jumps, and the truncated power variation does not exhibit upward or downward jumps. We use combined intraday jump statistics with local robust variance. All empirical results show that if we do not include periodicity filters of volatility, such as MAD and ShortH, the five-minute returns of the Chinese yuan/US dollar exchange rates have much lower intraday jump probabilities. Thus, the volatility and jumps of the Chinese yuan/US dollar ratio will be underestimated if we do not consider the periodicity filters of the volatility in the 2010s. We need to include periodicity filters of volatility and jumps to reduce forecast errors in future Chinese Yuan/US dollar exchange rates so that we obtain a better measure of current volatility and generate better hedging strategies for future volatility.

Nonsinusoidal current-phase relations in semiconductor–superconductor– ferromagnetic insulator devices

Coherent tunneling processes of multiple Cooper pairs across a Josephson junction give rise to high harmonics in the current phase relation. In this work, we propose and study Josephson junctions based on semiconductor--superconductor--ferromagnetic insulator heterostructures to engineer nonsinusoidal current-phase relations. The gate-tunability of the charge carriers' density in the semiconductor, together with the adjustable magnetization of the ferromagnetic insulator, provides control over the content of the supercurrent harmonics. At finite exchange field, hybrid junctions can undergo a $0 -- \ensuremath{\pi}$ phase transition, resulting in a supercurrent reversal. Close to the transition, single-pair tunneling is suppressed and the current-phase relation is dominated by the second-harmonic, indicating transport primarily by pairs of Cooper pairs. Finally, we demonstrate that noncollinear magnetization or spin-orbit coupling in the leads and the junction can lead to a gate-tunable Josephson diode effect with efficiencies of up to $\ensuremath{\sim}30%$.

Ultrafast magnetization reversal in ferromagnetic spin valves: An s−d model perspective

We present an extension to simple s-d models, aiming at simulating ultrafast magnetization dynamics and spin transport in metallic heterostructures. In particular, we consider an alternative spin dissipation channel due to a finite exchange splitting of the s band. From this theory, we show three different mechanisms governing the dynamics of spin accumulation. On top of the already widely discussed "-dM/dt" electron-magnon mechanism, we study the role of a dynamic change of exchange splitting (of conduction electrons) as well as the rotation of spins reflected at an interface with a ferromagnet. Finally, we use the presented theory to explain the recent observation of subpicosecond reversal of a ferromagnet in rare-earth free spin-valves. Our conclusion agrees with the one of reference [1] favoring magnetization reversal due to the rotation of the spin polarization of a reflected spin current.

Rotated odometers

AbstractWe describe the infinite interval exchange transformations, called the rotated odometers, which are obtained as compositions of finite interval exchange transformations and the von Neumann–Kakutani map. We show that with respect to Lebesgue measure on the unit interval, every such transformation is measurably isomorphic to the first return map of a rational parallel flow on a translation surface of finite area with infinite genus and a finite number of ends. We describe the dynamics of rotated odometers by means of Bratteli–Vershik systems, derive several of their topological and ergodic properties, and investigate in detail a range of specific examples of rotated odometers.

Magnetic Coupling in Cobalt-Doped Iron Oxide Core–Shell Nanoparticles: Exchange Pinning through Epitaxial Alignment

Tuning the core–shell morphology of bimagnetic nanoparticles and its associated exchange bias behavior is a promising way to overcome the superparamagnetic limit and stabilize the particle moment in extended time and temperature ranges. The intraparticle magnetization distribution and magnetic coupling between the two phases, however, is still unclear. We report a significant nonzero magnetization in the CoxFe(1–x)O core of native core–shell bimagnetic nanoparticles that is typically considered antiferro- or paramagnetic. Co0.14Fe0.86O@Co0.4Fe2.4O4 (6 nm@2 nm) and Co0.08Fe0.92O@Co0.58Fe2.28O4 (12 nm@2 nm) core–shell nanoparticles have been synthesized by thermal decomposition of a mixed cobalt–iron oleate with a similar Fe/Co distribution throughout the nanoparticle. We determine the exact phase composition and the magnetization distribution in the core and shell using a combination of X-ray and neutron small-angle scattering. Core and shell magnetization are traced separately with a varying magnetic field. Our results reveal that the magnetization of the core and the spinel-type shell phases are coupled at room temperature, i.e., rotating coherently with the magnetic field. This is a mandatory condition to observe a significant exchange bias effect at low temperatures. These findings highlight the enormous potential of finite size and exchange coupling in bimagnetic nanoparticles to control the magnetic properties via interface-induced magnetization.

Exciton condensation in strongly correlated quantum spin Hall insulators

Time-reversal symmetric topological insulators are generically robust with respect to weak local interaction unless symmetry-breaking transitions take place. Using dynamical mean-field theory, we solve an interacting model of quantum spin Hall insulators and show the existence at intermediate coupling of a symmetry-breaking transition to a nontopological insulator characterized by exciton condensation. This transition is of first order. For a larger interaction strength, the insulator evolves into a Mott one. The transition is continuous if magnetic order is prevented, and notably, for any finite Hund's exchange, it progresses through a Mott localization before the condensate coherence is lost. We show that the correlated excitonic state corresponds to a magneto-electric insulator, which allows for direct experimental probing. Finally, we discuss the fate of the helical edge modes across the excitonic transition.

Unconventional computing based on magnetic tunnel junction

The conventional computing method based on the von Neumann architecture is limited by a series of problems such as high energy consumption, finite data exchange bandwidth between processors and storage media, etc., and it is difficult to achieve higher computing efficiency. A more efficient unconventional computing architecture is urgently needed to overcome these problems. Neuromorphic computing and stochastic computing have been considered to be two competitive candidates for unconventional computing, due to their extraordinary potential for energy-efficient and high-performance computing. Although conventional electronic devices can mimic the topology of the human brain, these require high power consumption and large area. Spintronic devices represented by magnetic tunnel junctions (MTJs) exhibit remarkable high-energy efficiency, non-volatility, and similarity to biological nervous systems, making them one of the promising candidates for unconventional computing. In this work, we review the fundamentals of MTJs as well as the development of MTJ-based neurons, synapses, and probabilistic-bit. In the section on neuromorphic computing, we review a variety of neural networks composed of MTJ-based neurons and synapses, including multilayer perceptrons, convolutional neural networks, recurrent neural networks, and spiking neural networks, which are the closest to the biological neural system. In the section on stochastic computing, we review the applications of MTJ-based p-bits, including Boltzmann machines, Ising machines, and Bayesian networks. Furthermore, the challenges to developing these novel technologies are briefly discussed at the end of each section.

Spin parity effects in a monoaxial chiral ferromagnetic chain

While spin parity effects, physics crucially depending on whether the spin quantum number $S$ is half-odd integral or integral, have for decades been a source of new developments for the quantum physics of antiferromagnetic spin chains, the investigation into their possible ferromagnetic counterparts has remained largely unchartered, especially in the fully quantum (as opposed to the semiclassical) regime. Here we present such studies for monoaxial chiral ferromagnetic spin chains. We start by examining magnetization curves for finite-sized systems, where a magnetic field is applied perpendicular to the helical axis. For half-odd integer $S$, the curves feature discontinuous jumps identified as a series of level crossings, each accompanied by a shift of the crystal momentum $k$ by an amount of $\ensuremath{\pi}$. The corresponding curves for integer valued $S$ are continuous and exhibit crossover processes. For the latter case, $k=0$ throughout. These characteristics are observed numerically when the strength of the Dzyaloshinskii-Moriya interaction (DMI) $D$ is comparable to or larger than that of the ferromagnetic exchange interaction $J$. Solitons are known to be responsible for stepwise changes seen in magnetization curves in the classical limit. These findings therefore prompt us to revise the notion of a soliton, for arbitrary $S$, into a quantum mechanical entity. To unravel this phenomenon at the fully quantum level as is appropriate to spin chains with small $S$, we examine in detail special limiting Hamiltonians amenable to rigorous analysis, consisting of only the DMI and the Zeeman energy. Dubbed the $DH$ model (for $S=\frac{1}{2}$) and the projected $DH$ ($\mathrm{p}DH$) model (for general $S$), they have a set of $2S$ conserved quantities, each of which is the number of solitons of a specific integer-valued height (as measured in the ${S}_{z}$ basis), which ranges from 1 to $2S$. We discuss how to determine the exact crystal momentum of the lowest-energy state belonging to a sector with a given set of the $2S$ soliton numbers. Combined with energetic considerations, this information enables us to reproduce the spin parity effect in the magnetization curves. Finally, we show that the ground states of the special models have substantial numerical overlap with those for generic systems with a finite exchange interaction, suggesting the same physics to be valid there as well.

Phase diagrams and excitations of anisotropic S=1 quantum magnets on the triangular lattice

The $S=1$ bilinear-biquadratic Heisenberg exchange model on the triangular lattice with a single-ion anisotropy has previously been shown to host a number of exotic magnetic and nematic orders [Moreno-Cardoner $\textit{et al.}$, Phys. Rev. B $\textbf{90}$, 144409 (2014)], including an extensive region of "supersolid" order. In this work, we amend the model by an XXZ anisotropy in the exchange interactions. Tuning to the limit of an exactly solvable $S=1$ generalized Ising-/Blume-Capel-type model provides a controlled limit to access phases at finite transverse exchange. Notably, we find an additional macroscopically degenerate region in the phase diagram and study its fate under perturbation theory. We further map out phase diagrams as a function of the XXZ anisotropy parameter, ratio of bilinear and biquadratic interactions and single-ion anisotropy, and compute corrections to the total ordered moment in various phases using systematically constructed linear flavor-wave theory. We also present linear flavor-wave spectra of various states, finding that the lowest-energy band in three-sublattice generalized (i.e. with $S^z=\pm1,0$) Ising/Blume-Capel states, stabilized by strong exchange anisotropies, is remarkably flat, opening up the way to flat-band engineering of magnetic excitation via stabilizing non-trivial Ising-ordered ground states.

Direct complements almost unique

Direct complements in a right [Formula: see text]-module [Formula: see text] are said to be almost unique if, whenever [Formula: see text], then [Formula: see text] (also [Formula: see text], by symmetry). We will show that this new class of modules lies strictly between the dual-square-free and the summand-dual-square-free modules. While it is an open question whether right quasi-duo (equivalently, right dual-square-free) rings are left-right symmetric, we will prove that both notions “summand-dual-square-free” and “direct complements almost unique” are left-right symmetric. Furthermore, we will show that direct complements in a module [Formula: see text] are almost unique iff idempotents in [Formula: see text] are central modulo [Formula: see text], where [Formula: see text]. As an immediate consequence, if [Formula: see text] is an epi-projective module, then direct complements in [Formula: see text] are almost unique iff [Formula: see text] is strongly perspective (i.e. if [Formula: see text] and [Formula: see text] are isomorphic direct summands of [Formula: see text] and [Formula: see text], then [Formula: see text]. In particular, direct complements in a ring [Formula: see text] are almost unique iff [Formula: see text] is strongly perspective. Moreover, if [Formula: see text] is a module with the finite exchange whose direct complements are almost unique, then [Formula: see text] is clean, strongly perspective, and satisfy the full exchange.

Indirect exchange interaction in two-dimensional materials with quartic dispersion

We investigate the indirect magnetic exchange interaction between two magnetic moments in a two-dimensional semiconductor with quartic dispersion, featuring a singularity at the band edge. We obtain the Green's functions analytically to calculate the magnetic exchange interaction at zero temperature. We show that the singularity in the density of states (DOS) for quartic dispersion gives rise to an enhancement in the amplitude of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction as the Fermi energy is swept toward the band edge. Furthermore, a region of finite exchange interaction arises, with a range increasing as the Fermi energy approaches the band edge. The results lay the possibility of an electrical/chemical control over the exchange interactions.

A systematic methodology for targeting the thermodynamic limit of pressure-retarded osmosis with non-zero driving force

A thermodynamically oriented method is developed to identify the theoretical and practical limits of pressure-retarded osmosis (PRO) on converting salinity gradient power to mechanical energy under constant operating pressure with infinite and finite mass exchange area, respectively. It is proved that pinch analysis can be used to find the mass exchange limit of PRO, and according to which draw and feed streams can be plotted on a graph of net osmotic pressure - water exchange. Based on the graphical method, an expression of optimal pressure change is derived that achieves the maximum work extraction of a PRO process with single draw/feed stream. Moreover, problem table method is presented that serves as an analytical procedure to determine the maximum extractable work of the conceptualized multi-stream PRO process. Examples of both a PRO process with a draw stream (0.6 M NaCl seawater) and a feed stream feed (0.015 M NaCl river water) and a multi-stream PRO are included to illustrate the proposed methods. Results of the former example show that the counter-current design achieves 30.85% and 31.49% increase, respectively, in the maximum theoretical and practical work output, compared with the co-current design. The latter example shows that the problem table method produces a 20.47% increase in the work output, compared with the standalone design.

C4-modules with the exchange property

We prove that if M is a C4-module (D4-module) with the restricted ascending (descending) chain condition on direct summands, then M satisfies the finite exchange iff M is clean, iff M satisfies the full exchange. This result extends an earlier one by the authors on summand-square-free (summand-dual-square-free) modules. Moreover, as an immediate application, it follows that every exchange ring with the restricted DCC on direct summands is clean. The later result is a non-trivial and simultaneous extension of two fundamental results on exchange rings, the first of which is due to Nicholson and says that Abelian exchange rings are clean, and the second is due to Camillo and Yu and says that exchange rings with no infinite sets of orthogonal idempotents are clean.

Systematic application of the M3Y NN forces for describing the capture process in heavy-ion collisions involving deformed target nuclei

We present results of a systematic study of the capture process through the barrier penetration model. The nucleus-nucleus interaction potential is calculated using the double-folding model (DFM) with the M3Y Paris $\mathit{NN}$ forces. The nucleon densities entering the model are generated from the experimental three-parameter Fermi charge densities. The DFM has been extended to the case of deformed target nuclei. It is shown that the density-dependent M3Y $\mathit{NN}$ forces with the finite range exchange part can be mimicked successfully by the zero-range density-independent forces. The latter option significantly reduces the required computer time. For the nucleon densities and target nuclei deformations, we employ the values from the commonly used data bases. Thus, we do not vary any parameters to reach a better agreement with the data. The resulting cross sections are compared with data for 20 reactions with the product of the charge numbers ${Z}_{P}{Z}_{T}$ ranging from 216 up to 2576. We discuss the opinion met in the literature that the M3Y $\mathit{NN}$ forces provide a poorer description of the capture cross sections in heavy-ion collisions in comparison to the $\mathit{NN}$ forces coming from the relativistic mean-field approach. Our calculations show that the M3Y $\mathit{NN}$ forces give an agreement with the data which is not perfect yet is not worse than the one resulting from the relativistic mean-field approach $\mathit{NN}$ forces.

Perspectivity, exchange and summand-dual-square-free modules

Two direct-summands A and B of a right R-module M will be called strongly-perspective (s-perspective) if for any iff The module M will be called s-perspective if every two isomorphic direct-summands of M are s-perspective, and a ring R will be called s-perspective if R as a right R-module is s-perspective. In this paper, we study s-perspective rings and modules, and using ideas of Khurana and Nielsen, it follows that if M is s-perspective, then M has the finite exchange property iff M is clean, iff M has the full exchange property. In particular, if M is either summand-square-free or dual-summand-square-free with the finite exchange property, then M is clean, s-perspective and has the full exchange property.

Large relativistic effects in 119Sn NMR parameters: A case study of complex anions [Cp*M(SnCl3)nCl3−n]−, where M = Rh, Ir; n = 1, 2, 3

Relativistic effects and electron delocalization in transition metal complexes complicate the interpretation of their NMR parameters. It is very important to understand impact of such effects on structure–property relationships. Here we report a computational study of structure and NMR parameters of a series of bimetallic complex anions [Cp*M(SnCl3)nCl3−n]−, where M = Rh, Ir, n = 1, 2, 3. AIM and NBO analysis of chemical bonding was performed. Properties of SnM bonds determine large relativistic contributions for 119Sn NMR parameters. The difference in 119Sn NMR shifts between similar Ir and Rh complexes is defined mostly by large relativistic spin–orbit (SO) effects. We discuss Heavy-Atom-on-Vicinal-Heavy-Atom (HAVHA) effects. Finite nuclear model and exchange–correlation response kernel were tested in combination with various DFT functionals.

On Weak Projection Invariant Semisimple Modules

We introduce and investigate the notion of weak projection invariant semisimple modules. We deal with the structural properties of this new class of modules. In this trend we have indecomposable decompositions of the special class of the former class of modules via some module theoretical properties. As a consequence, we obtain when the finite exchange property implies full exchange property for the latter class of modules.

AB5*-modules with the exchange property

We prove that every -module has an indecomposable decomposition. As an immediate consequence, every -module M with the finite exchange is clean and has the full exchange. Moreover, in this case the module M admits an indecomposable decomposition with each Mi having local endomorphism ring, and the decomposition complements direct summands.

On Projection Invariant Semisimple Modules

In this paper, we introduce and investigate the notion of projection invariant semisimple modules. Some structural properties of aforementioned class of modules are studied. We obtain indecomposable decompositions of former class of modules under some module theoretical conditions. Moreover, we explore when the finite exchange property implies full exchange property for the class of projection invariant semisimple modules. Finally, we obtain that the endomorphism ring of a projection invariant semisimple modules is a π- Baer ring.