Discrete Spin Research Articles

Magnetization States and Coupled Spin-Wave Modes in Concentric Double Nanorings.

Concentric multiple nanorings have previously been fabricated and investigated mainly for their different static magnetization states. Here, we present a theoretical analysis for the magnetization dynamics in double nanorings arranged concentrically, where there is coupling across a nonmagnetic spacer due to the long-range dipole-dipole interactions. We employ a microscopic, or Hamiltonian-based, formalism to study the discrete spin waves that exist in the magnetic states where the individual rings may be in either a vortex or an onion state. Numerical results are shown for the frequencies and the spatial amplitudes (with relative phase included) of the spin-wave modes. Cases are considered in which the magnetic materials of the rings are the same (taken to be permalloy) or two different materials such as permalloy and cobalt. The dependence of these properties on the mean radial position of the spacer were studied, showing, in most cases, the existence of two distinct transition fields. The special cases, where the radial spacer width becomes very small (less than 1 nm) were analyzed to study direct interfaces between dissimilar materials and/or effects of interfacial exchange interactions such as Ruderman-Kittel-Kasuya-Yoshida coupling. These spin-wave properties may be of importance for magnetic switching devices and sensors.

Student understanding of eigenvalue equations in quantum mechanics: Symbolic blending and sensemaking analysis

As part of an effort to examine students’ mathematical sensemaking (MSM) in a spins-first quantum mechanics course during the transition from discrete (spin) to continuous (position) systems, students were asked to construct an eigenvalue equation for a one-dimensional position operator. A subset of responses took the general form of an eigenvalue equation written in Dirac notation. Symbolic blending, a combination of symbolic forms and conceptual blending, as well as a categorical framework for MSM, were used in the analysis. The data suggest two different symbolic forms for an eigenvalue equation that share a symbol template but have distinct conceptual schemata: A transformation that reproduces the original and to operate is to act. These symbolic forms, when blended with two sets of contextual knowledge, form the basis of three different interpretations of eigenvalue equations modeled here as conceptual blends. The analysis in this study serves as a novel example of, and preliminary evidence for, student engagement in sensemaking activities in the transition from discrete to continuous systems in a spins-first quantum mechanics course. Published by the American Physical Society 2024

Collision of perturbed soliton in discrete ferromagnetic spin chain with nearest neighbor and next nearest neighbor Dzyaloshinskii–Moriya interaction

Collision of perturbed soliton in discrete ferromagnetic spin chain with nearest neighbor and next nearest neighbor Dzyaloshinskii–Moriya interaction

Nonlinear localized modes in a higher-order anisotropic ferromagnetic nanowire with octupole–dipole interaction

Increasing demand for advanced technologies that depends on magnetic phenomena, understanding and controlling the behavior of discrete breather in ferromagnetic nanowires are crucial for enhancing the efficiency and performance of such devices. The presence of octupole–dipole interactions signifies a unique aspect that could potentially influence the stability and localization of breather excitations. Hence, we adopted a multifaceted approach to investigate the Heisenberg anisotropic ferromagnetic nanowire discrete model with the following interactions: bilinear, octupole–dipole, anisotropy and its higher-order terms. The dynamics is governed by a discrete nonlinear Schrödinger equation (DNLS) arrived with the aid of Holstein–Primakoff transformation. This transformation was facilitated by utilizing the Glauber coherent representation of the boson operators. Subsequently, the dynamical equation is incorporated to the Modulational Instability (MI) analysis which is a systematical gateway to explore the breather excitation in the region of instability influenced by the octupole–dipole interaction coupling parameter. Then, we pictorially demonstrated that the octupole–dipole interaction plays a pivotal role in promoting the localization of discrete breather on the surface of the spin lattice sites in the discrete ferromagnetic nanowire. The energy density distribution also implies that the increase in octupole–dipole interaction results in the highly dense breather localization. The result shows that the increment in the octupole–dipole interaction parameter increases the amplitude of the localized breathers. These discrete breathers could hold immense promise for applications in magnetic storage and Spintronic devices, where maintaining stable localized modes is crucial for the device functionality. Our novelty lies in being pioneers in the exploration of a fully discrete model that encompasses higher-order interactions, such as the octupole–dipole interaction. We already have confirmed the existence of instability region on the discrete spin lattice by incorporating the octupole–dipole interaction [T. Pavithra, L. Kavitha, Prabhu and A. Mani, Modulational instability analysis in an isotropic ferromagnetic nanowire with higher order octopole-dipole interaction, in Nonlinear Dynamics and Applications: Proceedings of the ICNDA 2022 (Springer, 2022), p. 1209], we attempting to explore the generation of discrete breathers in a discrete anisotropic ferromagnetic nanowire. This effectively bridges the gap between theoretical understanding and practical implications, paving the way for innovative advancements in magnetic technology.

Unusual Electronic Structures of an Electron Transfer Series of [Cr(μ-η1 : η1 -N2 )Cr]0/1+/2.

In dinitrogen (N2 ) fixation chemistry, bimetallic end-on bridging N2 complexes M(μ-η1 : η1 -N2 )M can split N2 into terminal nitrides and hence attract great attention. To date, only 4d and 5d transition complexes, but none of 3d counterparts, could realize such a transformation. Likewise, complexes {[Cp*Cr(dmpe)]2 (μ-N2 )}0/1+/2+ (1-3) are incapable to cleave N2 , in contrast to their Mo congeners. Remarkably, cross this series the N-N bond length of the N2 ligand and the N-N stretching frequency exhibit unprecedented nonmonotonic variations, and complexes 1 and 2 in both solid and solution states display rare thermally activated ligand-mediated two-center spin transitions, distinct from discrete dinuclear spin crossovers. In-depth analyses using wave function based ab initio calculations reveal that the Cr-N2 -Cr bonding in complexes 1-3 is distinguished by strong multireference character and cannot be described by solely one electron configuration or Lewis structure, and that all intriguing spectroscopic observations originate in their sophisticate multireference electronic structures. More critical is that such multireference bonding of complexes 1-3 is at least a key factor that contributes to their kinetic inertness toward N2 splitting. The mechanistic understanding is then used to rationalize the disparate reactivity of related 3d M(μ-η1 : η1 -N2 )M complexes compared to their 4d and 5d analogs.

Unusual Electronic Structures of an Electron Transfer Series of [Cr(μ‐η1 : η1‐N2)Cr]0/1+/2+

AbstractIn dinitrogen (N2) fixation chemistry, bimetallic end‐on bridging N2 complexes M(μ‐η1 : η1‐N2)M can split N2 into terminal nitrides and hence attract great attention. To date, only 4d and 5d transition complexes, but none of 3d counterparts, could realize such a transformation. Likewise, complexes {[Cp*Cr(dmpe)]2(μ‐N2)}0/1+/2+ (1–3) are incapable to cleave N2, in contrast to their Mo congeners. Remarkably, cross this series the N−N bond length of the N2 ligand and the N−N stretching frequency exhibit unprecedented nonmonotonic variations, and complexes 1 and 2 in both solid and solution states display rare thermally activated ligand‐mediated two‐center spin transitions, distinct from discrete dinuclear spin crossovers. In‐depth analyses using wave function based ab initio calculations reveal that the Cr‐N2‐Cr bonding in complexes 1–3 is distinguished by strong multireference character and cannot be described by solely one electron configuration or Lewis structure, and that all intriguing spectroscopic observations originate in their sophisticate multireference electronic structures. More critical is that such multireference bonding of complexes 1–3 is at least a key factor that contributes to their kinetic inertness toward N2 splitting. The mechanistic understanding is then used to rationalize the disparate reactivity of related 3d M(μ‐η1 : η1‐N2)M complexes compared to their 4d and 5d analogs.

Spin-state versatility in FeII4L6 supramolecular cages with a pyridyl-hydrazone ligand scaffold modulated by solvents and counter anions.

Discrete spin crossover (SCO) tetranuclear cages are a unique class of materials that have potential use in next-generation molecular recognition and sensing. In this work, two new edge-bridged SCO FeII4L6 (L = 2,7-bis(((E)-pyridin-2-ylmethylene)amino)benzo[lmn] [3,8]phenanthroline-1,3,6,8(2H,7H)-tetraone) supramolecular cages with different counter anions: ClO4- (2) and CF3SO3- (3) were constructed via subcomponent self-assembly to investigate both solvent and anion influences on their magnetic properties and compare them to cage 1 with a BF4- anion. Pyridyl-hydrazone bidentate ligand scaffolds were employed to replace the 'classical' imidazole/thiazolyl-imine coordination units to induce SCO behaviour in these cages. 2 and 3 were structurally characterized by single-crystal X-ray diffraction analysis and electrospray ionization time-of-flight mass spectrometry. Magnetic susceptibilities of 1-3 and 1-3·desolvated indicate that the solvents' presence is in favor of the low-spin (LS) state. While different counter anions in 1-3·desolvated affect the spin-state configurations of the four FeII metal centers. According to the 57Fe Mössbauer spectral analysis, the spin-state distributions in 1-3 at 80 K are [2 high-spin (HS)-2LS], [1HS-3LS] and [2HS-2LS], respectively and density functional theory calculations were employed to investigate the reasons. These findings provide insights to regulate the spin-state versatility of SCO FeII cage systems in the solid state.

Application of the path optimization method to a discrete spin system

Application of the path optimization method to a discrete spin system

Effects of Dzyaloshinskii–Moriya interactions on dipole-exchange spin waves in finite-length ferromagnetic chains

A spin-wave theory that includes the antisymmetric Dzyaloshinskii–Moriya exchange interactions and long-range dipole–dipole interactions, in addition to the Heisenberg bilinear exchange and the applied magnetic field, is presented for finite-length ferromagnetic spin chains. It is found that three different physical situations arise, depending on the direction chosen in this geometry for the axial vector of the Dzyaloshinskii–Moriya interactions. In some cases this leads to a tilting of the equilibrium orientations near the ends of the chain due to interfacial effects and with consequential effects on the spectrum of discrete dipole-exchange spin waves. When variations are introduced for the dominant bilinear exchange interactions at the ends of the spin chain, it is shown that localized spin waves with spatial decay characteristics may occur.

Spin Crossover Induced by Changing the Identity of the Secondary Metal Ion from PdII to NiII in a Face-Centered FeII 8 MII 6 Cubic Cage.

Discrete spin crossover (SCO) heteronuclear cages are a rare class of materials which have potential use in next-generation molecular transport and catalysis. Previous investigations of cubic cage [Fe8 Pd6 L8 ]28+ constructed using semi-rigid metalloligands, found that FeII centers of the cage did not undergo spin transition. In this work, substitution of the secondary metal center at the face of the cage resulted in SCO behavior, evidenced by magnetic susceptibility, Mössbauer spectroscopy and single crystal X-ray diffraction. Structural comparisons of these two cages shed light on the possible interplay of inter- and intramolecular interactions associated with SCO in the NiII analogue, 1 ([Fe8 Ni6 L8 (CH3 CN)12 ]28+ ). The distorted octahedral coordination environment, as well as the occupation of the CH3 CN in the NiII axial positions of 1, prevented close packing of cages observed in the PdII analogue. This led to offset, distant packing arrangements whereby important areas within the cage underwent dramatic structural changes with the exhibition of SCO.

Continuous symmetry breaking in a two-dimensional Rydberg array.

Spontaneous symmetry breaking underlies much of our classification of phases of matter and their associated transitions1-3. The nature of the underlying symmetry being broken determines many of the qualitative properties of the phase; this is illustrated by the case of discrete versus continuous symmetry breaking. Indeed, in contrast to the discrete case, the breaking of a continuous symmetry leads to the emergence of gapless Goldstone modes controlling, for instance, the thermodynamic stability of the ordered phase4,5. Here, we realize a two-dimensional dipolar XY model that shows a continuous spin-rotational symmetry using a programmable Rydberg quantum simulator. We demonstrate the adiabatic preparation of correlated low-temperature states of both the XY ferromagnet and the XY antiferromagnet. In the ferromagnetic case, we characterize the presence of a long-range XY order, a feature prohibited in the absence of long-range dipolar interaction. Our exploration of the many-body physics of XY interactions complements recent works using the Rydberg-blockade mechanism to realize Ising-type interactions showing discrete spin rotation symmetry6-9.

Non-monotonic behavior of the Binder parameter in discrete spin systems

Abstract We study a non-monotonic behavior of the Binder parameter, which appears in discrete spin systems. We show that the Binder parameters of the Potts model are non-monotonic for q = 3 and 4, while they are monotonic for the Ising case (q = 2). Using the Fortuin–Kasteleyn graph representation, we find that the improved estimator of the Binder parameter consists of two terms with values only in the high- and low-temperature regions. The non-monotonic behavior is found to originate from the low-temperature term. With the appropriately defined order parameter, we can reduce the influence of the low-temperature term and, as a result, the non-monotonic behavior can also be reduced. We propose new definitions for the order parameter, which reduces or eliminates the non-monotonic behavior of the Binder parameter in a system for which the improved estimator of the Binder parameter is unknown.

Infinite Volume Gibbs States and Metastates of the Random Field Mean-Field Spherical Model

For the discrete random field Curie–Weiss models, the infinite volume Gibbs states and metastates have been investigated and determined for specific instances of random external fields. In general, there are not many examples in the literature of non-trivial limiting metastates for discrete or continuous spin systems. We analyze the infinite volume Gibbs states of the mean-field spherical model, a model of continuous spins, in a general random external field with independent identically distributed components with finite moments of some order larger than four and non-vanishing variances of the second moments. Depending on the parameters of the model, we show that there exist three distinct phases: ordered ferromagnetic, ordered paramagnetic, and spin glass. In the ordered ferromagnetic and ordered paramagnetic phases, we show that there exists a unique infinite volume Gibbs state almost surely. In the spin glass phase, we show the existence of chaotic size dependence, provide a construction of the Aizenman–Wehr metastate, and consider both the convergence in distribution and almost sure convergence of the Newman–Stein metastates. The limiting metastates are non-trivial and their structure is universal due to the presence of Gaussian fluctuations and the spherical constraint.

Classical-quantum correspondence of special and extraordinary-log criticality: Villain's bridge

There has been much recent progress on exotic surface critical behavior, yet the classical-quantum correspondence of special and extraordinary-log criticality remains largely unclear. Employing worm Monte Carlo simulations, we explore the surface criticality at an emergent superfluid-Mott insulator critical point in the Villain representation, which is believed to connect classical and quantum O(2) critical systems. We observe a special transition with the thermal and magnetic renormalization exponents $y_t=0.58(1)$ and $y_h=1.690(1)$ respectively, which are close to recent estimates from models with discrete spin variables. The existence of extraordinary-log universality is evidenced by the critical exponent $\hat{q}=0.58(2)$ from two-point correlation and the renormalization-group parameter $\alpha=0.28(1)$ from superfluid stiffness, which obey the scaling relation of extraordinary-log critical theory and recover the logarithmic finite-size scaling of critical superfluid stiffness in open-edge quantum Bose-Hubbard model. Our results bridge recent observations of surface critical behavior in the classical statistical mechanical models [Parisen Toldin, Phys. Rev. Lett. 126, 135701 (2021); Hu $et$ $al.$, $ibid.$ 127, 120603 (2021); Parisen Toldin $et$ $al.$, $ibid.$ 128, 215701 (2022)] and the open-edge quantum Bose-Hubbard model [Sun $et$ $al.$, Phys. Rev. B 106, 224502 (2022)].

Atomic-scale spin-wave polarizer based on a sharp antiferromagnetic domain wall

We theoretically study the scattering of spin waves from a sharp domain wall in an antiferromagnetic spin chain. While the continuum model for an antiferromagnetic material yields the well-known result that spin waves can pass through a wide domain wall with no reflection, here we show that, based on the discrete spin Hamiltonian, spin waves are generally reflected by a domain wall with a reflection coefficient that increases as the domain-wall width decreases. Remarkably, we find that, in the interesting case of an atomically sharp domain wall, the reflection of spin waves exhibits strong dependence on the state of circular polarization of the spin waves, leading to mainly reflection for one polarization while permitting partial transmission for the other, thus realizing an atomic-scale spin-wave polarizer. The polarization of the transmitted spin wave depends on the orientation of the spin in the sharp domain wall, which can be controlled by an external field or spin torque. Our utilization of a sharp antiferromagnetic domain wall as an atomic-scale spin-wave polarizer leads us to envision that ultra-small magnetic solitons such as domain walls and skyrmions may enable realizations of atomic-scale spin-wave scatterers with useful functionalities.

Spin and Contextuality in Extended de Broglie-Bohm-Bell Quantum Mechanics

This paper introduces an extension of the de Broglie-Bohm-Bell formulation of quantum mechanics, which includes intrinsic particle degrees of freedom, such as spin, as elements of reality. To evade constraints from the Kochen-Specker theorem the discrete spin values refer to a specific basis -- i.e., a single spin vector orientation for each particle; these spin orientations are, however, not predetermined, but dynamic and guided by the (reduced, spin-only) wave function of the system, which is conditional on the realized location values of the particles. In this way, the unavoidable contextuality of spin is provided by the wave function and its realized particle configuration, whereas spin is still expressed as a local property of the individual particles. This formulation, which furthermore features a rigorous discrete-time stochastic dynamics, allows for numerical simulations of particle systems with entangled spin, such as Bohm's version of the EPR experiment.

Quantum scattering theory of spin transfer torque, spin pumping, and fluctuations

Spin transfer torque and spin pumping are central reciprocal phenomena in spintronics. The author demonstrates a way to understand these effects within a quantum out-of-equilibrium path-integral model. At a finite temperature, frequency, or spin accumulation, the magnet also experiences fluctuating torques. In the quantum regime, transport coefficients related to electron shot noise caused by the discrete spin angular momentum of electrons govern the fluctuations at low temperatures. The results open a path for exploring low-temperature magnetization dynamics and spin caloritronics.

Ultrananoporous supercapacitor with ionic liquid comprised of two-site cation: an Ising model study (II)

A four-state one-dimension discrete spin model with the nearest neighbor and partial next nearest neighbor lattice interactions is proposed for describing electrical double layer formed by ionic liquid in cylindrical pore that can accommodate only one row of particles. The model, in which cation is modeled as a dimer formed by two hard spheres (HSs): one is positively charged with diameter , while the other is neutral with diameter , and anion is modeled by charged HS with diameter , is designed to investigate effects of pore diameter , ion transfer free energy, ion size and electrical valence on behaviors of specific differential capacitance and specific energy storage and its saturation value . Relevant Kramers–Wannier transfer matrix is , which gives system partition function by numerically solving maximum real root of the relevant characteristic equation. Main findings are briefly described below. (i) The ion valence has little effect on the value, but does reduce the threshold voltage strength , beyond which the energy storage reaches . However, the ion valence (whether co- or counter-ion) raises both the and values as the relevant ion size decreases enough. (ii) Decreasing of the value weakly reduces the value, but raises the peak height and the value obviously; correlation between the value and value becomes stronger with the ions getting more pore hostile. (iii) With the counter-ion or co-ion charged site size decreasing, both the value and value rise. However, the effect of the co-ion charged site size is weakened as the co-ion gets more pore hostile, and the cation neutral site size influences on the value less than the cation charged site size does. (iv) Pore friendly co-ion or pore hostile counter-ion always helps in raising the value; the two have significant synergistic effect with the co-ion pore friendliness playing more important role than the counter-ion pore hostility.

Realistic simulations of spin squeezing and cooperative coupling effects in large ensembles of interacting two-level systems

We describe an efficient numerical method for simulating the dynamics of interacting spin ensembles in the presence of dephasing and decay. The method builds on the discrete truncated Wigner approximation for isolated systems, which combines the mean-field dynamics of a spin ensemble with a Monte Carlo sampling of discrete initial spin values to account for quantum correlations. Here we show how this approach can be generalized for dissipative spin systems by replacing the deterministic mean-field evolution by a stochastic process, which describes the decay of coherences and populations while preserving the length of each spin. We demonstrate the application of this technique for simulating nonclassical spin-squeezing effects or the dynamics and steady states of cavity QED models with hundred thousand interacting two-level systems and without relying on any symmetries. This opens up the possibility to perform accurate real-scale simulations of a diverse range of experiments in quantum optics or with solid-state spin ensembles under realistic laboratory conditions.

Non-Clausius heat transfer in the classic mean-field systems

For systems with long-range interactions, it is common to observe the negative heat capacities as well as the temperature jumps in the microcanonical ensemble. If we connect two long-range interacting subsystems of different particle numbers by a weak short-range coupling in microcanonical ensemble, the heat could flow from the cold body to the hot one spontaneously in a certain parameter region. This adverse heat flow is recognized as non-Clausius heat transfer which has been reported by using the discrete spin models recently (Hou, 2019). However, the discrete models cannot depict the dynamical process of the heat flow, making the result not perfect enough. In this paper, both classic dynamical model and molecular dynamical simulation are used to identify the non-Clausius heat transfer. Furthermore, it is also proved that obtaining temperature by equipartition theorem in simulation leads to the identical results with the Maxwell relation.