Nonequilibrium Magnetization Research Articles

Spontaneous anomalous Hall effect in magnetic and non-magnetic systems

Abstract We consider two cases of spontaneous anomalous Hall current. In a non-magnetic system with spin–orbit coupling (SOC), the applied bias results in the appearance of non-equilibrium magnetization and an anomalous Hall current. The latter demonstrates non-linear dependence on the applied bias. In a magnetic system with SOC, an anomalous current appears without applied bias. We perform the calculations in the framework of the free-electron model, whereas the common approach to this type of phenomenon is based on Berry connection. We demonstrate that anomalous currents acquire a measurable magnitude for reasonable model parameters.

Assessing nanobody interaction with SARS-CoV-2 Nsp9.

The interaction between SARS-CoV-2 non-structural protein Nsp9 and the nanobody 2NSP90 was investigated by NMR spectroscopy using the paramagnetic perturbation methodology PENELOP (Paramagnetic Equilibrium vs Nonequilibrium magnetization Enhancement or LOss Perturbation). The Nsp9 monomer is an essential component of the replication and transcription complex (RTC) that reproduces the viral gRNA for subsequent propagation. Therefore preventing Nsp9 recruitment in RTC would represent an efficient antiviral strategy that could be applied to different coronaviruses, given the Nsp9 relative invariance. The NMR results were consistent with a previous characterization suggesting a 4:4 Nsp9-to-nanobody stoichiometry with the occurrence of two epitope pairs on each of the Nsp9 units that establish the inter-dimer contacts of Nsp9 tetramer. The oligomerization state of Nsp9 was also analyzed by molecular dynamics simulations and both dimers and tetramers resulted plausible. A different distribution of the mapped epitopes on the tetramer surface with respect to the former 4:4 complex could also be possible, as well as different stoichiometries of the Nsp9-nanobody assemblies such as the 2:2 stoichiometry suggested by the recent crystal structure of the Nsp9 complex with 2NSP23 (PDB ID: 8dqu), a nanobody exhibiting essentially the same affinity as 2NSP90. The experimental NMR evidence, however, ruled out the occurrence in liquid state of the relevant Nsp9 conformational change observed in the same crystal structure.

Magneto-Permeability Effect in Ferrofluid Flow Through Porous Media Studied via Multiparticle Collision Dynamics

AbstractAs more and more promising applications of magnetic nanoparticles in complicated environments are explored, their flow properties in porous media are of increasing interest. We here propose a hybrid approach based on the multiparticle collision dynamics method extended to porous media via friction forces and coupled with Brownian dynamics simulations of the rotational motion of magnetic nanoparticles’ magnetic moment. We simulate flow in planar channels homogeneously filled with a porous medium and verify our implementation by reproducing the analytical velocity profile of the Darcy–Brinkman model in the non-magnetic case. In the presence of an externally applied magnetic field, the non-equilibrium magnetization and friction forces lead to field-dependent velocity profiles that result in effective, field-dependent permeabilities. We provide a theoretical expression for this magneto-permeability effect in analogy with the magneto-viscous effect. Finally, we study the flow through planar channels, where only the walls are covered with a porous medium. We find a smooth crossover from the Poiseuille profile in the center of the channel to Brinkman–Darcy flow in the porous layers. We propose a simple estimate of the thickness of the porous layer based on the flow rate and maximum flow velocity.

Magnons in a two-dimensional Weyl magnet

The discovery of topological states of matter has led to a revolution in condensed-matter science. While a non-trivial band topology in a material is often associated with intriguing transport properties, much less attention has been given to the impact on spin dynamics and non-equilibrium magnetization states. Here, we provide evidence that a chiral asymmetric magnon dispersion in the two-dimensional Weyl magnet Fe/W(110) is related to the presence of Weyl fermions close to the Fermi energy and surface Fermi arcs. We find that the large anomalous Hall conductivity and the Dzyaloshinskii–Moriya interaction are attributed to the non-trivial band topology in the composite momentum-magnetization space. Our results show the direct impact of Weyl fermions on both the charge and spin dynamics in a two-dimensional magnet. Unveiling these principles can promote innovative technologies in magnonics by utilizing topological materials, where magnons and non-trivial topological electronic states can be manipulated through magnetization.

Spin Diffusion and Oscillations of the Magnetization at High-Frequency Spin Injection

The frequency dependence of the nonequilibrium magnetization arising in an electron gas due to spin injection from a half-metallic ferromagnet into a nonmagnetic material is theoretically analyzed. It is shown that high-frequency spin injection gives rise to nonequilibrium magnetization waves, which decay at a length much smaller than the spin diffusion length. This reduces the efficiency of spin injection.

Spin torques and anomalous velocity in spin textures induced by fast electron injection from topological ferromagnets: The role of gauge fields

A new method for analyzing magnetization dynamics in spin textures under the influence of fast electron injection from topological ferromagnetic sources such as Dirac half metals has been proposed. These electrons, traveling at a velocity v with a non-negligible value of (where c is the speed of light), generate a non-equilibrium magnetization density in the spin-texture region, which is related to an electric dipole moment via relativistic interactions. When this resulting dipole moment interacts with gauge fields in the spin-texture region, an effective field is created that produces spin torques. These torques, like spin-orbit torques that occur when electrons are injected from a heavy metal into a ferromagnet, can display both damping-like and anti-damping-like properties. Finally, we demonstrate that such an interaction between the dipole moment and the gauge field introduces an anomalous velocity that can contribute to transverse electrical conductivity in the spin texture in a way comparable to the topological Hall effect.

Resonance Method for Measuring Parameters of the Spin Transport in a Spin-Valve Structure

The known methods for measuring the spin transport parameters in spin-valve structures are based on the Hanle effect, viz., electron spin precession in an external magnetic field and a decrease in the magnetoresistive signal. These methods make it possible to determine the spin relaxation time in the paramagnetic layer and the relative current polarization constant. We describe an alternative method of measuring in zero external magnetic field, which is based on the resonant increase in the magnetic susceptibility of the paramagnetic layer due to the paramagnetic resonance induced by the nonequilibrium magnetization due to the spin accumulation effect. The proposed method makes it possible to determine the absolute value of spin accumulation in a paramagnet, which can be used as a parameter for numerical solution of three-dimensional diffusion equations of spin transport.

Magnetic field induced deformation of the spin density wave microphases in Ca3Co2O6

The frustrated triangular Ising magnet Ca$_3$Co$_2$O$_6$ has long been known for an intriguing combination of extremely slow spin dynamics and peculiar magnetic orders, such as the evenly-spaced non-equilibrium metamagnetic magnetization steps and the long-wavelength spin density wave (SDW) order, the latter of which is essentially an emergent crystal of solitons. Recently, an elaborate field-cooling protocol to bypass the low-field SDW phase was proposed to overcome the extraordinarily long timescale of spin relaxation that impeded previous experimental studies in equilibrium, which may point to a deep connection between the low-temperature slow relaxation and the cooling process passing through the low-field SDW phase. As the first step to elucidate the conjectured connection, we investigate the magnetic field-induced deformation of the SDW state and incommensurate-commensurate transitions, thereby mapping out the equilibrium in-field phase diagram for a realistic three-dimensional lattice spin model by using Monte Carlo simulations. We also discuss Ginzburg-Landau theory that includes several Umklapp terms as well as an effective sine-Gordon model, which can qualitatively explain the observed magnetic field-induced deformation of the SDW microphases.

Spin diffusion in spin glasses requires two magnetic variables, M⃗ and m⃗

Experiment has established that spin-glasses can support a steady-state spin current $\vec{j}_{i}$. However, the accepted theory of spin glass dynamics permits oscillations but no steady-state spin current. Onsager's irreversible thermodynamics implies that the spin current is proportional to the gradient of a magnetization. We argue, however, that the magnon distribution function associated with the local equilibrium magnetization $\vec{M}$ cannot diffuse because it represents $10^{23}$ variables. We therefore invoke the non-equilibrium magnetization $\vec{m}$, which in spintronics is called the {\it spin accumulation}. Applying the theory of irreversible thermodynamics we indeed find that it predicts spin diffusion, and we consider other experimental consequences of the theory, including a wavelength-dependent coupling between the reactive and the diffusive degrees of freedom.

МАГНИТОДИНАМИКА РАЗБАВЛЕННОГО ФЕРРОКОЛЛОИДА В СДВИГОВОМ ПОТОКЕ

The work is devoted to a theoretical study of a dilute suspension of magnetic nanoparticles under the combined action of a simple shear flow and a constant magnetic field. The main attention is paid to the dynamics of the magnetization vector of the system. It is shown that at any nonzero temperature the magnetization takes a stationary orientation in a finite time. The direction of magnetization generally does not coincide with the direction of the field. Equilibrium and non-equilibrium magnetization components are calculated as functions of two dimensionless parameters – Mason number (i.e., ratio of hydrodynamic torque to magnetic) and Peclet number (i. e., ratio of hydrodynamic moment to thermal).

Simulating the flow of interacting ferrofluids with multiparticle collision dynamics.

Ferrofluid flow is fascinating since its fluid properties can conveniently be manipulated by external magnetic fields. Novel applications in micro- and nanofluidics as well as in biomedicine have renewed the interest in the flow of colloidal magnetic nanoparticles with a focus on small-scale behavior. Traditional flow simulations of ferrofluids, however, often use simplified constitutive models and do not include fluctuations that are relevant at small scales. Here we address these challenges by proposing a hybrid scheme that combines the multiparticle collision dynamics method for modeling hydrodynamics with Brownian dynamics simulations of a reliable kinetic model describing the microstructure, magnetization dynamics, and resulting stresses. Since both multiparticle collision dynamics and Brownian dynamics are mesoscopic methods that naturally include fluctuations, this hybrid scheme presents a promising alternative to more traditional approaches, also because of the flexibility to model different geometries and modifying the constitutive model. The scheme was tested in several ways. Poiseuille flow was simulated for various model parameters and effective viscosities were determined from the resulting flow profiles. The effective, field-dependent viscosities are found to be in very good agreement with theoretical predictions. We also study Stokes' second flow problem for ferrofluids. For weak amplitudes and low frequencies of the oscillating plate, we find that the velocity profiles are well described by the result for Newtonian fluids at the corresponding, field-dependent viscosity. Furthermore, the time-dependent profiles of the nonequilibrum magnetization component are well approximated by their steady-state values in stationary shear when evaluated with the instantaneous local shear rate. Finally, we also apply our scheme to simulate ferrofluid shear flow over a rough surface. We find characteristic differences in the nonequilibrium magnetization components when the external field is oriented in flow and in a gradient direction.

High-temperature magnetization reversal in the inertial regime

Motivated by the remarkable experimental observation of all-optical femtosecond-scale magnetization reversal at relatively high temperatures, a stochastic inertial Landau-Lifshitz-Gilbert-Bloch (iLLGB) equation is written to describe nonequilibrium magnetization dynamics in ferromagnets at elevated temperatures and at short enough timescales that an inertial effect manifests. The effect of thermal agitations is described by a Fokker-Planck equation derived from the iLLGB equation including the longitudinal relaxation effect, which is solved with perturbation theory valid at elevated temperatures. Considering a uniaxially symmetric ferromagnet with uniaxial anisotropy, a thermal diffusion-driven exponential mode and alternating field-driven nutation mode of stable magnetization reversal are identified. Our theory proposes a magnetization reversal mechanism based entirely on transfer of angular momentum to the local magnetization, but which takes into account thermal fluctuations and inertial effect at the same time. The theory explains several key observations in all-optical magnetization reversal experiments; the absence of the need for a static field, the subpicosecond switching timescale, the relative roles of thermal and field effects, and the relevance of circularly polarized light. Our results have direct implications for magnetic recording devices operating close to room temperatures and in the ultrafast regime.

Approaching Protein Aggregation and Structural Dynamics by Equilibrium and Nonequilibrium Paramagnetic Perturbation.

PENELOP (Paramagnetic Equilibrium vs Nonequilibrium magnetization Enhancement or LOss Perturbation) is the presented nuclear magnetic resonance (NMR) approach to identify at once the location of proteins' exposed surface, hindered accessibility, and exchange processes occurring on a μs-ms time scale. In addition to mapping the protein surface accessibility, the application of this method under specific conditions makes it possible to distinguish conformational mobility and chemical exchange processes, thereby providing an alternative to characterization by more demanding techniques (transverse relaxation dispersion, saturation transfer, and high-pressure NMR). Moreover, its high sensitivity enables studying samples at low, physiologically more relevant concentrations. Association, dynamics, and oligomerization are addressed by PENELOP for a component of SARS-CoV-2 replication transcription complex and an amyloidogenic protein.

Generalized phenomenological model for the magnetic field penetration and magnetization hysteresis loops of a type-II superconductor

A generalized phenomenological model for the critical state of type-II superconductors with magnetic field parallel to the superconducting plate is proposed. This model considers the global magnetization including both the equilibrium magnetization from surface screening current and the non-equilibrium magnetization from bulk pinning in a self-consistent way. Our model can be used to simulate the magnetization-hysteresis-loops (MHLs) and flux penetrating process of different type-II superconductors, from low- to high-kappa values. Here we take an optimally doped Ba0.6K0.4Fe2As2 single crystal as a testing example. The model can fit the data quite well and several important parameters can be extracted from the fitting. Thus, the model can be extended to a general case for studying the magnetization and flux penetration in other type-II superconductors.

Electroferrofluids with nonequilibrium voltage-controlled magnetism, diffuse interfaces, and patterns.

It has been recognized that driving matter to nonequilibrium states can lead to emergent behaviors and functionalities. Here, we show that uniform colloidal dispersions can be driven into dissipative nonuniform states with emerging behaviors. We experimentally demonstrate this with electrically driven weakly charged superparamagnetic iron oxide nanoparticles in a nonpolar solvent. The driving leads to formation of nonequilibrium concentration gradients that further translate to nonequilibrium magnetism, including voltage-controlled magnetization and susceptibility. The concentration gradients also serve as diffuse interfaces that respond to external magnetic fields, leading to novel dissipative patterns. We identify the closest nondissipative analogs, discuss the differences, and highlight the ability to directly quantify the dissipation and link it to the pattern formation. Beyond voltage-controlled magnetism, we foresee that the concept can be generalized to other functional colloids to create, e.g., optical, electrical, catalytic, and mechanical responses that are not possible in thermodynamic equilibrium.

Element‐Specific Magnetization Damping in Ferrimagnetic DyCo5 Alloys Revealed by Ultrafast X‐ray Measurements

In article number 2100047, Ilie Radu and co-workers provide experimental and theoretical evidence for an element-specific magnetic damping parameter by investigating the ultrafast magnetization response of ferrimagnetic DyCo alloys to femtosecond laser excitation. These novel insights are of utmost importance for understanding the physics of non-equilibrium magnetism as well as for modeling laser-driven magnetic recording phenomena and ultrafast spintronics.

Improved preclinical hyperpolarized 129 Xe ventilation imaging with constant flip angle 3D radial golden means acquisition and keyhole reconstruction.

Hyperpolarized (HP) 129 Xe MRI is increasingly used to noninvasively probe regional lung structure and function in the preclinical setting. As in human imaging, the primary barrier to quantitative imaging with HP gases is nonequilibrium magnetization, which is depleted by T1 relaxation and radio frequency excitation. Preclinical HP gas imaging commonly involves mechanically ventilating small animals and encoding k-space over tens or hundreds of breaths, with small subsets of k-space data collected within each breath. Breath-to-breath magnetization renewal enables the use of large flip angles, but the resulting magnetization decay generates large view-to-view differences in within-breath signal intensity, leading to artifacts and degraded image quality. This deleterious signal decay has motivated the use of variable flip angle (VFA) sampling schemes, in which the flip angle is progressively increased to maintain constant view-to-view signal intensity. However, VFA imaging complicates data acquisition and provides only a global correction that fails to compensate for regional differences in signal dynamics. When constant flip angle (CFA) imaging is used alongside 3D radial golden means acquisition, the center of k-space is sampled with every excitation, thereby encoding signal dynamics alongside imaging data. Here, keyhole reconstruction is used to generate multiple images to capture in-breath HP 129 Xe signal dynamics in mice and thus provide flip angle maps to quantitatively correct images without extra data collection. These CFA images display SNR that is not significantly different from VFA images, and further, high frequency k-space scaling can be used to mitigate decay-induced image artifacts. Results are supported by point spread function calculations and simulations of radial imaging with preclinical signal dynamics. Together, these results show that CFA 3D radial golden means ventilation imaging provides comparable image quality with VFA in small animals and allows for keyhole reconstruction, which can be used to generate flip angle maps and correct images for signal depletion.

Enhanced Spin Seebeck Thermopower in Pt/Holey MoS2/Y3Fe5O12 Hybrid Structure.

We first observed the spin-to-charge conversion due to both the inverse Rashba-Edelstein effect (IREE) and inverse spin-Hall effect in a holey multilayer molybdenum disulfide (MoS2) intermediate layer in a Pt/YIG structure via LSSE measurements under nonequilibrium magnetization. We found an enhancement of approximately 238%, 307%, and 290% in the longitudinal spin Seebeck effect (LSSE) voltage, spin-to-charge current, and thermoelectric (TE) power factor, respectively, compared with the monolayer MoS2 interlayer in a Pt/YIG structure. Such an enhancement in the LSSE performance of Pt/holey MoS2/YIG can be explained by the improvement of spin accumulation in the Pt layer by induced spin fluctuation as well as increased additional spin-to-charge conversion due to in-plane IREE. Our findings represent a significant achievement in the understanding of spin transport in atomically thin MoS2 interlayers and pave the way toward large-area TE energy-harvesting devices in two-dimensional transition metal dichalcogenide materials.

Non-equilibrium chiral domain wall dynamics excited by transverse magnetic field pulses

Non-equilibrium domain wall dynamics on a perpendicularly magnetized nanowire manipulated by the transverse magnetic field pulse are numerically investigated. We systematically observe the large displacements of the chiral domain wall and the domain wall tilting angles generated by Dzyaloshinskii–Moriya interaction during the competition between the precession torque and the magnetic damping process. The magnetic-property-dependent domain wall displacements exhibit that the lower magnetic damping constants and Dzyaloshinskii–Moriya energy densities generate the longer transition times and the significant larger domain wall displacements for the non-equilibrium magnetization dynamics. Compare with the spin-polarized-current-driven domain wall dynamics, the transverse magnetic field pulses guarantee faster domain wall movements without Walker breakdown and lower energy consumptions because it is free from the serious Joule heating issue. Finally, we demonstrate successive chiral domain wall displacements, which are necessary to develop multilevel resistive memristors for next-generation artificial intelligent devices based on magnetic domain wall motions.

Topology-Dependent Brownian Gyromotion of a Single Skyrmion.

Noninteracting particles exhibiting Brownian motion have been observed in many occasions of sciences, such as molecules suspended in liquids, optically trapped microbeads, and spin textures in magnetic materials. In particular, a detailed examination of Brownian motion of spin textures is important for designing thermally stable spintronic devices, which motivates the present study. In this Letter, through using temporally and spatially resolved polar magneto-optic Kerr effect microscopy, we have experimentally observed the thermal fluctuation-induced random walk of a single isolated Néel-type magnetic skyrmion in an interfacially asymmetric Ta/CoFeB/TaO_{x} multilayer. An intriguing topology-dependent Brownian gyromotion behavior of skyrmions has been identified. The onset of Brownian gyromotion of a single skyrmion induced by thermal effects, including a nonlinear temperature-dependent diffusion coefficient and topology-dependent gyromotion are further formulated based on the stochastic Thiele equation. The experimental and numerical demonstration of topology-dependent Brownian gyromotion of skyrmions can be useful for understanding the nonequilibrium magnetization dynamics and implementing spintronic devices.