Nonequilibrium Magnetization Research Articles

Magnetization diffusion in duct flow: The magnetic entrance length and the interplay between hydrodynamic and magnetic timescales

In this work, computational fluid dynamics simulations of a ferrofluid plane Poiseuille flow in the presence of a constant applied magnetic field are performed. The orientation of the field is perpendicular to the direction of the flow. An original numerical methodology for calculating magnetic and hydrodynamic fields is proposed, including an important discussion about an identified magnetization entrance region. Three different magnetization models are considered to calculate the magnetization field. These models are implemented and validated according to analytic and asymptotic theories, including the one developed in this manuscript. Discrepancies between the models are discussed and interpreted physically. An intricate balance between different physical mechanisms is shown to be responsible for a diffusive-like behavior of the magnetization field. This balance is governed by a competition between the flow’s vorticity and the mechanisms of magnetic relaxation. The physical parameters responsible for this non-equilibrium magnetization dynamics are identified and interpreted using the problem’s timescales. It seems that the combination of three different timescales governs the dynamics of non-equilibrium magnetization: the Brownian diffuse timescale, a hydrodynamic (convective) timescale, and a controllable magnetic timescale associated with the intensity of the applied magnetic field. The results indicate toward the possibility of controlling the development of the flow’s magnetization field through the applied magnetic field, particle size distribution, fluid concentration, and flow rate. In addition, several results are presented regarding the fully developed flow, including magnetization profiles and angles between the applied field H and the magnetization field M.

Chiral Pumping of Spin Waves.

We report a theory for the coherent and incoherent chiral pumping of spin waves into thin magnetic films through the dipolar coupling with a local magnetic transducer, such as a nanowire. The ferromagnetic resonance of the nanowire is broadened by the injection of unidirectional spin waves that generates a nonequilibrium magnetization in only half of the film. A temperature gradient between the local magnet and film leads to a unidirectional flow of incoherent magnons, i.e., a chiral spin Seebeck effect.

Self-induced Berry flux and spontaneous non-equilibrium magnetism

When a physical system is governed by statistical or dynamical equations possessing certain symmetries, its stationary states can be classified into phases according to which of those symmetries are preserved, and which are broken1,2. Near equilibrium, the properties of the system’s collective excitations reflect the symmetries of the underlying phase and thereby provide means for detecting these phases3,4. Here, we show that, in driven systems, the collective modes may take on a separate life, exhibiting their own spontaneous symmetry-breaking phenomena independent of the underlying equilibrium phase. We illustrate this principle by demonstrating a mechanism through which a non-magnetic interacting metal subjected to a linearly polarized driving field can spontaneously magnetize. The strong internal a.c. fields of the metal driven close to its plasmonic resonance5,6 enable Berryogenesis: the spontaneous generation of a self-induced Bloch band Berry flux. The self-induced Berry flux supports and is sustained by a chiral circulating plasmonic motion that breaks the mirror symmetry of the system. This non-equilibrium phase transition may be of either continuous or discontinuous type. Berryogenesis can occur in a wide variety of multiband metals with high-quality plasmons, as available in present-day graphene devices7–9. The authors predict that Berry flux can be spontaneously generated in a metal by plasmonic oscillations in response to illumination by light. They show that this topological ‘Berryogenesis’ can work in graphene.

Magnetic Anisotropy Energy Barrier Distribution and Surface Magnetism in CoPt Nanoparticle

The magnetization of the protein shell (PepA) encapsulated CoPt nanoparticle (average diameter = 2.1 nm) specimen was investigated by implementing non-equilibrium magnetization calculation scheme and Curie-Weiss type formula. In doing that, the magnetization measurement sequence of SQUID (Superconducting Quantum Interference Device) magnetometer was modified to comply with the numerical analysis scheme. Applying the analysis methodology to the CoPt nanoparticles, we extract the values of zero-temperature coercive field and Bloch coefficient, which are in good agreement with the previously reported values. Remarkably, the distribution of the zero-field zero-temperature anisotropy energy barrier follows an exponential type function, which is uncorrelated with the known size distribution of the particles. The lacking correlation between them was reported in ferritin, suggesting that it is a generic feature of certain magnetic nanoparticle systems having a range of disorders and imperfections. In addition, we analyze non-saturating behavior of a field dependent magnetization curve in terms of Curie-Weiss type formula, allowing a separation of the surface magnetic moments from the core moments.

All-optical nonequilibrium pathway to stabilising magnetic Weyl semimetals in pyrochlore iridates

Nonequilibrium many-body dynamics is becoming a central topic in condensed matter physics. Floquet topological states were suggested to emerge in photodressed bands under periodic laser driving. Here we propose a viable nonequilibrium route without requiring coherent Floquet states to reach the elusive magnetic Weyl semimetallic phase in pyrochlore iridates by ultrafast modification of the effective electron-electron interaction with short laser pulses. Combining ab initio calculations for a time-dependent self-consistent light-reduced Hubbard U and nonequilibrium magnetism simulations for quantum quenches, we find dynamically modified magnetic order giving rise to transiently emerging Weyl cones that can be probed by time- and angle-resolved photoemission spectroscopy. Our work offers a unique and realistic pathway for nonequilibrium materials engineering beyond Floquet physics to create and sustain Weyl semimetals. This may lead to ultrafast, tens-of-femtoseconds switching protocols for light-engineered Berry curvature in combination with ultrafast magnetism.

Spin noise and damping in individual metallic ferromagnetic nanoparticles

We introduce a highly sensitive and relatively simple technique to observe magnetization motion in single Ni nanoparticles, based on charge sensing by electron tunneling at millikelvin temperature. Sequential electron tunneling via the nanoparticle drives nonequilibrium magnetization dynamics, which induces an effective charge noise that we measure in real time. In the free spin diffusion regime, where the electrons and magnetization are in detailed balance, we observe that magnetic damping time exhibits a peak with the magnetic field, with a record long damping time of $\simeq 10$~ms.

Novel models of magnetic dynamics for characterization of nanoparticles biodegradation in a body from Mössbauer and magnetization measurements

We discuss ways of an improvement of the analytic technique for characterization of magnetic nanoparticles and their chemical transformation to ferritin-like forms after their injection in a living organism by means of measuring and analyzing the Mössbauer spectra and magnetization curves. This is based first on the theoretical achievements in developing models of magnetic dynamics of antiferromagnetic nanoparticles for describing thermodynamic properties of ferritin and related proteins. Generalization of the approach for ferrimagnetic nanoparticles allows one to take directly into account the magnetic nature of nanoparticles in analyzing the corresponding experimental data. Another way is to extend this technique with measuring and analyzing non-equilibrium magnetization curves (hysteresis loops) which allows one to more reliably evaluate time changes in the residual nanoparticles and iron-containing proteins characteristics during biodegradation.

Superspin glass state in a diluted nanoparticle system stabilized by interparticle interactions mediated by an antiferromagnetic matrix

In nanoparticle systems consisting of two magnetic materials (bi-magnetic nanoparticles or nanoparticles embedded in a magnetic matrix), there is a constantly growing interest in the investigation of the interplay between interparticle interactions and the nanoparticle-matrix interface exchange coupling, because of its enormous impact on a number of technological applications. The understanding of the mechanisms of such interplay is a great challenge, as it would allow controlling equilibrium and non-equilibrium magnetization dynamics of exchange coupled nanoparticles systems and finely tuning their anisotropy. Here, we provide evidence that this interplay leads to a collective superspin glass (SSG) behavior in a system of diluted ferromagnetic (FM) nanoparticles embedded in an antiferromagnetic (AFM) matrix (5% volume fraction of Co particles in Mn film matrix). We have developed a novel mesoscopic model to study the influence of interparticle interaction on the exchange bias (EB) and the dynamical behavior of assemblies of FM nanoparticles embedded in a granular AFM matrix. Our mesoscopic model is based on reducing the amount of simulated spins to the minimum number necessary to describe the magnetic structure of the system and introducing the adequate exchange parameters between the different spins. The model replicates remarkably well the observed static and dynamical SSG properties as well as the EB behavior. In addition, the proposed model well explains the role of the significant Co/Mn alloying and of the granularity of the matrix in mediating interparticle interactions through exchange and dipole–dipole coupling between the uncompensated moments of its grains and the exchange interaction at the Co/Mn interface.

Spin-orbit-coupling induced torque in ballistic domain walls: Equivalence of charge-pumping and nonequilibrium magnetization formalisms

To study the effect of spin-orbit coupling (SOC) on spin-transfer torque in magnetic materials, we have implemented two theoretical formalisms that can accommodate SOC. Using the "charge-pumping" formalism, we find two contributions to the out-of-plane spin-transfer torque parameter $\beta$ in ballistic Ni domain walls (DWs). For short DWs, the nonadiabatic reflection of conduction electrons caused by the rapid spatial variation of the exchange potential results in an out-of-plane torque that increases rapidly with decreasing DW length. For long DWs, the Fermi level conduction channel anisotropy that gives rise to an intrinsic DW resistance in the presence of SOC leads to a linear dependence of $\beta$ on the DW length. To understand this counterintuitive divergence of $\beta$ in the long DW limit, we use the "nonequilibrium magnetization" formalism to examine the spatially resolved spin-transfer torque. The SOC-induced out-of-plane torque in ballistic DWs is found to be quantitatively consistent with the values obtained using the charge-pumping calculations indicating the equivalence of the two theoretical methods.

Quantum process tomography with informational incomplete data of two J-coupled heterogeneous spins relaxation in a time window much greater than T1

We reconstruct the time dependent quantum map corresponding to the relaxation process of a two-spin system in liquid-state NMR at room temperature. By means of quantum tomography techniques that handle informational incomplete data, we show how to properly post-process and normalize the measurements data for the simulation of quantum information processing, overcoming the unknown number of molecules prepared in a non-equilibrium magnetization state (Nj) by an initial sequence of radiofrequency pulses. From the reconstructed quantum map, we infer both longitudinal (T1) and transversal (T2) relaxation times, and introduce the J-coupling relaxation times (), which are relevant for quantum information processing simulations. We show that the map associated to the relaxation process cannot be assumed approximated unital and trace-preserving for times greater than

Effective Hamiltonians for Rapidly Driven Many-Body Lattice Systems: Induced Exchange Interactions and Density-Dependent Hoppings.

We consider 1D lattices described by Hubbard or Bose-Hubbard models, in the presence of periodic high-frequency perturbations, such as uniform ac force or modulation of hopping coefficients. Effective Hamiltonians for interacting particles are derived using an averaging method resembling classical canonical perturbation theory. As is known, a high-frequency force may renormalize hopping coefficients, causing interesting phenomena such as coherent destruction of tunneling and creation of artificial gauge fields. We find explicitly additional corrections to the effective Hamiltonians due to interactions, corresponding to nontrivial processes such as single-particle density-dependent tunneling, correlated pair hoppings, nearest neighbor interactions, etc. Some of these processes arise also in multiband lattice models, and are capable of giving rise to a rich variety of quantum phases. The apparent contradiction with other methods, e.g., Floquet-Magnus expansion, is explained. The results may be useful for designing effective Hamiltonian models in experiments with ultracold atoms, as well as in the field of ultrafast nonequilibrium magnetism. An example of manipulating exchange interaction in a Mott-Hubbard insulator is considered, where our corrections play an essential role.

Quasiclassical Theory of Spin Imbalance in a Normal Metal-Superconductor Heterostructure with a Spin-Active Interface

Non-equilibrium phenomena in superconductors have attracted much attention since the first experiments on charge imbalance in the early 1970's. Nowadays a new promising line of research lies at an intersection between superconductivity and spintronics. Here we develop a quasiclassical theory of a single junction between a normal metal and a superconductor with a spin-active interface at finite bias voltages. Due to spin-mixing and spin-filtering effects of the interface a non-equilibrium magnetization (or spin imbalance) is induced at the superconducting side of the junction, which relaxes to zero in the bulk. A peculiar feature of the system is the presence of interface-induced Andreev bound states, which influence the magnitude and the decay length of spin imbalance. Recent experiments on spin and charge density separation in superconducting wires required external magnetic field for observing a spin signal via non-local measurements. Here, we propose an alternative way to observe spin imbalance without applying magnetic field.

Time-resolved imaging of domain pattern destruction and recovery via nonequilibrium magnetization states

The authors have built an X-ray microscope capable of taking snapshots of the domain formation process with a high spatial resolution down to a few ten nanometers. By exposing the sample to intense magnetic field pulses, they destroy the stable domain pattern and probe the rapid time-evolution of the sample magnetization stroboscopically with soft X-ray flashes created by the storage ring PETRA III at DESY in Hamburg. These flashes enable resolving very fast changes in the domain configuration occurring at a few hundred picoseconds and thus a video of the domain destruction and relaxation dynamics can be recorded in slow motion. Visualizing the process of domain formation and reorganization in real time helps developing future magnetic storage devices where digital information is contained in the alignment of nanometer sized domains.

Exponential blocking-temperature distribution in ferritin extracted from magnetization measurements

We developed a direct method to extract the zero-field zero-temperature anisotropy energy barrier distribution of magnetic particles in the form of a blocking-temperature distribution. The key idea is to modify measurement procedures slightly to make nonequilibrium magnetization calculations (including the time evolution of magnetization) easier. We applied this method to the biomagnetic molecule ferritin and successfully reproduced field-cool magnetization by using the extracted distribution. We find that the resulting distribution is more like an exponential type and that the distribution cannot be correlated simply to the widely known log-normal particle-size distribution. The method also allows us to determine the values of the zero-temperature coercivity and Bloch coefficient, which are in good agreement with those determined from other techniques.

Hysteretic phenomena in a 2DEG in the quantum Hall effect regime, studied in a transport experiment

We investigated experimentally non-equilibrium state of a two-dimensional electron gas (2DEG) in the quantum Hall effect (QHE) regime, studying the hysteresis of magnetoresistance of a 2DEG with a constriction. The large amplitude of the hysteresis enabled us to make the consistent phenomenological description of the hysteresis. We studied the dependence on the magnetic field sweep prehistory (minor loop measurements), recovered the anhysteretic curve, and studied the time dependence of the magnetoresistance. We showed that the hysteresis of magnetoresistance of a 2DEG in the QHE regime has significant phenomenological similarities with the hysteresis of magnetization of ferromagnetic materials, showing multistability, jumps of relaxation, and having the anhysteretic curve. Nevertheless, we revealed the crucial difference, manifested itself in an unusual inverted (anti-coercive) behavior of the magnetoresistance hysteresis. The time relaxation of the hysteresis has fast and slow regimes, similar to that of non-equilibrium magnetization of a 2DEG in QHE regime pointing to their common origin. We studied the dependence of the hysteresis loop area on the lithographic width of the constriction and found the threshold value of width $\sim$1.35 $\mu$m beyond which the hysteresis is not observed. This points to the edge nature of the non-equilibrium currents (NECs) and allows us to determine the width of the NECs area ($\sim$0.5 $\mu$m). We suggest the qualitative picture of the observed hysteresis, based on non-equilibrium redistribution of the electrons among the Landau level states and assuming huge imbalance between the population of bulk and edge electronic states.

Spin Current and Its Electrical Detection in Semiconductors

The idea of utilizing the electron spin in semiconductor devices leads to the growth of the field semiconductor spintronics. This may result in the development of novel electronic devices with advantages over conventional electronics. However, the basic requirements necessary in developing semiconductor spintronic devices are the efficient generation/injection of spins (or spin current) in/into a semiconductor such that they can be transported reliably, i.e., without spin relaxation, over reasonable distances and, finally, detection of them. Since in spintronic devices, the information is carried by the electron spin, an electrical means of detecting spin current in semiconductors is desirable for fully exploring the possibility of utilizing spin degree of freedom and for possible device applications. Here, I describe an experiment which detects the spin current electrically in semiconductors by investigating the effect of a longitudinal electric field on the spin-polarized electrons generated by a circularly polarized light. The experiment observes the effect as a pure anomalous Hall voltage resulting from non-equilibrium magnetization induced by the spin-carrier electrons accumulating at the transverse edges of the sample as a result of asymmetries in scattering for spin-up and spin-down electrons in the presence of spin-orbit interaction. The results are presented by discussing the dominant spin relaxation mechanisms in semiconductors, and in relation with the recent understanding in this area.

Magnetic behaviors of frustrated Ising spin-chain system: Wang–Landau simulation for three-dimensional lattice

The magnetic behaviors of triangular spin-chain system Ca3Co2O6 have been investigated using the Wang–Landau method based on the Ising model for three-dimensional lattice. Our simulation shows that the equilibrium state of the model produces the two-step magnetization curve at low temperature even when the intra-chain interaction is considered. As a consequence, this work indicates that the four-step magnetization curve observed in experiments must arise from the non-equilibrium magnetization, which is consistent with earlier report.

Critical magnetization and hysteresis of nanogranular films with perpendicular anisotropy

The magnetic-field dependences of the stability boundaries of the nonequilibrium magnetic states that exist in a nanogranular film with perpendicular anisotropy in tilted magnetic fields are theoretically described, and the corresponding critical magnetization is calculated. The field dependences of the critical magnetization of the film are analyzed at various ratios of the anisotropy field of particles to the maximum possible demagnetizing field of the film. In a tilted magnetic field, the magnetization reversal curves, which include hysteresis loops, are shown to consist of segments of the following three types: equilibrium stable magnetization, nonequilibrium stable magnetization, and critical type of magnetization.

Effective spin diffusion in spin-polarized equilibrium and quasiequilibrium Fermi liquids

We calculate the effective spin diffusion coefficient of weak ferromagnet and quasiequilibrium paramagnetic systems using Landau Fermi liquid theory. We find that the behavior of the diffusion coefficient of the quasiequilibrium system is determined primarily by the internal magnetic field, which, in turn, depends upon the nonequilibrium magnetization and the antisymmetric Landau parameters. We also show that this is qualitatively similar to the diffusion coefficient of the weak ferromagnetic system. We discuss its implication for the spin-polarized state created in cold atom systems.

Dynamic magnetization process in the frustrated Shastry-Sutherland system TmB4

The dynamic magnetization behaviors of the classical Ising model on the Shastry-Sutherland lattice with additional long-range interactions are investigated by means of the Glauber dynamics, in order to understand the fascinating magnetization plateaus and the hysteresis loop observed in TmB4. With this algorithm, the experimental 1/n (n = 7, 9, 11) magnetization plateaus as well as the main 1/2 one can be reproduced at low temperatures. Furthermore, the hysteresis loop can also be well explained by the present theory. It is indicated that the formation of domain walls due to the non-equilibrium magnetization process may be responsible for the emergence of the fractional plateaus.