Magnetic Correlation Functions Research Articles

On the Relevance of Magnetic Correlation Functions in Energetic Particle Transport Theory

On the Relevance of Magnetic Correlation Functions in Energetic Particle Transport Theory

Amplification of the anomalous scaling in the Kazantsev-Kraichnan model with finite-time correlations and spatial parity violation.

By using the field theoretic renormalization group technique together with the operator product expansion, simultaneous influence of the spatial parity violation and finite-time correlations of an electrically conductive turbulent environment on the inertial-range scaling behavior of correlation functions of a passively advected weak magnetic field is investigated within the corresponding generalized Kazantsev-Kraichnan model in the second order of the perturbation theory (in the two-loop approximation). The explicit dependence of the anomalous dimensions of the leading composite operators on the fixed point value of the parameter that controls the presence of finite-time correlations of the turbulent field as well as on the parameter that drives the amount of the spatial parity violation (helicity) in the system is found even in the case with the presence of the large-scale anisotropy. In accordance with the Kolmogorov's local isotropy restoration hypothesis, it is shown that, regardless of the amount of the spatial parity violation, the scaling properties of the model are always driven by the anomalous dimensions of the composite operators near the isotropic shell. The asymptotic (inertial-range) scaling form of all single-time two-point correlation functions of arbitrary order of the passively advected magnetic field is found. The explicit dependence of the corresponding scaling exponents on the helicity parameter as well as on the parameter that controls the finite-time velocity correlations is determined. It is shown that, regardless of the amount of the finite-time correlations of the given Gaussian turbulent environment, the presence of the spatial parity violation always leads to more negative values of the scaling exponents, i.e., to the more pronounced anomalous scaling of the magnetic correlation functions. At the same time, it is shown that the stronger the violation of spatial parity, the larger the anomalous behavior of magnetic correlations.

Small-scale dynamo with finite correlation times.

Fluctuation dynamos occur in most turbulent plasmas in astrophysics and are the prime candidates for amplifying and maintaining cosmic magnetic fields. A few analytical models exist to describe their behavior, but they are based on simplifying assumptions. For instance, the well-known Kazantsev model assumes an incompressible flow that is δ-correlated in time. However, these assumptions can break down in the interstellar medium as it is highly compressible and the velocity field has a finite correlation time. Using the renewing flow method developed by Bhat and Subramanian (2014), we aim to extend Kazantsev's results to a more general class of turbulent flows. The cumulative effect of both compressibility and finite correlation time over the Kazantsev spectrum is studied analytically. We derive an equationfor the longitudinal two-point magnetic correlation function in real space to first order in the correlation time τ and for an arbitrary degree of compressibility (DOC). This generalized Kazantsev equationencapsulates the original Kazantsev equation. In the limit of small Strouhal numbers St∝τ we use the Wentzel-Kramers-Brillouin approximation to derive the growth rate and scaling of the magnetic power spectrum. We find the result that the Kazantsev spectrum is preserved, i.e., M_{k}(k)∼k^{3/2}. The growth rate is also negligibly affected by the finite correlation time; however, it is reduced by the finite magnetic diffusivity and the DOC together.

Entanglement gap in 1D long-range quantum spherical models

We investigate the finite-size scaling of the entanglement gap in the one-dimensional long-range quantum spherical model (QSM). We focus on the weak long-range QSM, for which the thermodynamic limit is well-defined. This model exhibits a continuous phase transition, separating a paramagnetic from a ferromagnet phase. The universality class of the transition depends on the long-range exponent α. We show that in the thermodynamic limit the entanglement gap is finite in the paramagnetic phase, and it vanishes in the ferromagnetic phase. In the ferromagnetic phase the entanglement gap is understood in terms of standard magnetic correlation functions. The half-system entanglement gap decays as , where the constant C α depends on the low-energy properties of the model and L is the system size. This reflects that the lower part of the dispersion is affected by the long range physics. Finally, multiplicative logarithmic corrections are absent in the scaling of the entanglement gap, in contrast with the higher-dimensional case.

Magnetic nanoprecipitates and interfacial spin disorder in zero-field-annealed Ni50Mn45In5 Heusler alloys as seen by magnetic small-angle neutron scattering.

Shell ferromagnetism is a new functional property of certain off-stoichiometric Ni-Mn-In Heusler alloys, with a potential application in non-volatile magnetic memories and recording media. One key challenge in this field remains the determination of the structural and magnetic properties of the nanoprecipitates that are the result of an annealing-induced segregation process. Thanks to its unique mesoscopic length scale sensitivity, magnetic small-angle neutron scattering appears to be a powerful technique to disclose the microstructure of such annealing-induced nanoprecipitates. In this study, the microstructure of a zero-field-annealed off-stoichiometric Ni50Mn45In5 Heusler alloy is investigated by unpolarized magnetic small-angle neutron scattering. The neutron data analysis reveals a significant spin-misalignment scattering, which is mainly related to the formation of annealing-induced ferromagnetic nanoprecipitates in an antiferromagnetic matrix. These particles represent a source of perturbation which, due to dipolar stray fields, gives rise to canted spin moments in the surroundings of the particle-matrix interface. The presence of anticorrelations in the computed magnetic correlation function reflects the spatial perturbation of the magnetization vector around the nanoprecipitates. The magnetic field dependence of the zero crossing and the minima of the magnetic correlation function are qualitatively explained using the law of approach to ferromagnetic saturation for inhomogeneous spin states. More specifically, at remanence, the nanoprecipitates act magnetically as one superdefect with a correlation length that lies outside the experimental q range, whereas near saturation the magnetization distribution follows each individual nanoprecipitate. Analysis of the neutron data yields an estimated size of 30 nm for the spin-canted region and a value of about 75 nm for the magnetic core of the individual nanoprecipitates.

Photon correlation spectroscopy with heterodyne mixing based on soft x-ray magnetic circular dichroism

Many magnetic equilibrium states and phase transitions are characterized by fluctuations. Such magnetic fluctuation can in principle be detected with scattering-based x-ray photon correlation spectroscopy (XPCS). However, in the established approach of XPCS, the magnetic scattering signal is quadratic in the magnetic scattering cross section, which results not only in often prohibitively small signals but also in a fundamental inability to detect negative correlations (anticorrelations). Here, we propose to exploit the possibility of heterodyne mixing of the magnetic signal with static charge scattering to reconstruct the first-order (linear) magnetic correlation function. We show that the first-order magnetic scattering signal reconstructed from heterodyne scattering now directly represents the underlying magnetization texture. Moreover, we suggest a practical implementation based on an absorption mask rigidly connected to the sample, which not only produces a static charge scattering signal but also eliminates the problem of drift-induced artificial decay of the correlation functions. Our method thereby significantly broadens the range of scientific questions accessible by magnetic x-ray photon correlation spectroscopy.

Explaining the temperature effects on the magnetization dynamics of non-interacting antiferromagnetic nanoparticles across wide ranges of frequencies and damping

Owing to their ultrafast spin dynamics, antiferromagnetic nanoparticles based materials are very promising for electronic memory devices that require a specific control of interaction between the spin current and local magnetization of the sublattice. Hence, the elucidation of the dynamics of the magnetization of antiferromagnetic nanoparticles is an essential. In this work, we report an exploration of the dynamics of the magnetization of antiferromagnetic nanoparticles using Fokker–Planck equation susceptive to describe the behavior of the distribution function of the magnetization of non-interacting nanoparticles. The dynamic equation is treated within the framework of matrix continued fractions approach using numerical method for which the magnetization correlation function as well as the complex susceptibility are assessed for different values of temperature across wide ranges of frequencies and damping. The analysis performed within these circumstances reveal that the application of strong magnetic field at any arbitrary angle to the easy axis of the nanoparticle trains a substantial modification of the magnetization dynamics of the corresponding nanoparticle. Moreover, using the simple asymptotic formulae, the obtained results relative to the estimation of the greatest relaxation time reveal a decent agreement with the relaxation time calculated from the infinite hierarchy of linear differential-recurrence equations for the statistical moments. We show that the great sensitivity of the magnetization dynamics to the thermal agitation provides unique information regarding the coupling between the precession of the magnetization and its thermally activated reversal over the saddle point, resulting from influence of the dc field orientation and strength as well as the damping.

Von Karman Correlation Similarity of the Turbulent Interplanetary Magnetic Field

Abstract A major development underlying much of hydrodynamic turbulence theory is the similarity decay hypothesis due to von Karman and Howarth here extended empirically to magnetic field fluctuations in the solar wind. In similarity decay the second-order correlation experiences a continuous transformation based on a universal functional form and a rescaling of energy and characteristic length. Solar wind turbulence follows many principles adapted from classical fluid turbulence, but previously this similarity property has not been examined explicitly. Here we analyze an ensemble of magnetic correlation functions computed from Advanced Composition Explorer data at 1 au, and demonstrate explicitly that the two-point correlation functions undergo a collapse to a similarity form of the type anticipated from von Karman’s hypothesis. This provides for the first time a firm empirical basis for employing the similarity decay hypothesis to the magnetic field, one of the primitive variables of magnetohydrodynamics, and one frequently more accessible from spacecraft instruments. This approach is of substantial utility in space turbulence data analysis, and for adopting von Karman-type heating rates in global and subgrid-scale dynamical modeling.

Probing magnetic correlations with spin-echo modulated small angle neutron scattering (SEMSANS)

The first measurements of magnetic correlation functions are presented using time-of-flight Spin-echo modulated small angle neutron scattering (SEMSANS) on the Larmor instrument at the ISIS pulsed neutron source. The accessible length scale is beyond that of the conventional SANS. A simplified model is presented to calculate the expected correlation functions for various magnetisation fields applied to the sample. As an example, we present the experimental data of a soft iron sample at various configurations of magnetisation field.

Evidence for enhancement of anisotropy persistence in kinematic magnetohydrodynamic turbulent systems with finite-time correlations.

Using the field-theoretic renormalization group approach and the operator product expansion technique in the second order of the corresponding perturbative expansion, the influence of finite-time correlations of the turbulent velocity field on the scaling properties of the magnetic field correlation functions as well as on the anisotropy persistence deep inside the inertial range are investigated in the framework of the generalized Kazantsev-Kraichnan model of kinematic magnetohydrodynamic turbulence. Explicit two-loop expressions for the scaling exponents of the single-time two-point correlation functions of the magnetic field are derived and it is shown that the presence of the finite-time velocity correlations has a nontrivial impact on their inertial-range behavior and can lead, in general, to significantly more pronounced anomalous scaling of the magnetic field correlation functions in comparison to the rapid-change limit of the model, especially for the most interesting three-dimensional case. Moreover, by analyzing the asymptotic behavior of appropriate dimensionless ratios of the magnetic field correlation functions, it is also shown that the presence of finite-time correlations of the turbulent velocity field has a strong impact on the large-scale anisotropy persistence deep inside the inertial interval. Namely, it leads to a significant enhancement of the anisotropy persistence, again, especially in three spatial dimensions.

Unconventional low-temperature features in the one-dimensional frustrated q-state Potts model.

Here we consider a one-dimensional q-state Potts model with an external magnetic field and an anisotropic interaction that selects neighboring sites that are in the spin state 1. The present model exhibits unusual behavior in the low-temperature region, where we observe an anomalous vigorous change in the entropy for a given temperature. There is a steep behavior at a given temperature in entropy as a function of temperature, quite similar to first-order discontinuity, but there is no jump in the entropy. Similarly, second derivative quantities like specific heat and magnetic susceptibility also exhibit strong acute peaks similar to second-order phase transition divergence, but once again there is no singularity at this point. Correlation length also confirms this anomalous behavior at the same given temperature, showing a strong and sharp peak which easily one may confuse with a divergence. The temperature where this anomalous feature occurs we call the pseudocritical temperature. We have analyzed physical quantities, like correlation length, entropy, magnetization, specific heat, magnetic susceptibility, and distant pair correlation functions. Furthermore, we analyze the pseudocritical exponents that satisfy a class of universality previously identified in the literature for other one-dimensional models; these pseudocritical exponents are for correlation length ν=1, specific heat α=3, and magnetic susceptibility μ=3.

Low-temperature enhancement of ferromagnetic Kitaev correlations in α−RuCl3

Kitaev-type interactions between neighbouring magnetic moments emerge in the honeycomb material ${\alpha}$-RuCl3. It is debated however whether these Kitaev interactions are ferromagnetic or antiferromagnetic. With electron energy loss spectroscopy (EELS) we study the lowest excitation across the Mott-Hubbard gap, which involves a d4 triplet in the final state and therefore is sensitive to nearest-neighbor spin-spin correlations. At low temperature the spectral weight of these triplets is strongly enhanced, in accordance with optical data. We show that the magnetic correlation function that determines this EELS spectral weight is directly related to a Kitaev-type spin-spin correlator and that the temperature dependence agrees very well with the results of a microscopic magnetic Hamiltonian for ${\alpha}$-RuCl3 with ferromagnetic Kitaev coupling.

Unraveling Nanostructured Spin Textures in Bulk Magnets

One of the key challenges in magnetism remains the determination of the nanoscopic magnetization profile within the volume of thick samples, such as permanent ferromagnets. Thanks to the large penetration depth of neutrons, magnetic small‐angle neutron scattering (SANS) is a powerful technique to characterize bulk samples. The major challenge regarding magnetic SANS is accessing the real‐space magnetization vector field from the reciprocal scattering data. In this study, a fast iterative algorithm is introduced that allows one to extract the underlying 2D magnetic correlation functions from the scattering patterns. This approach is used here to analyze the magnetic microstructure of Nanoperm, a nanocrystalline alloy which is widely used in power electronics due to its extraordinary soft magnetic properties. It can be shown that the computed correlation functions clearly reflect the projection of the 3D magnetization vector field onto the detector plane, which demonstrates that the used methodology can be applied to probe directly spin textures within bulk samples with nanometer resolution.

Persistence of power-law correlations in nonequilibrium steady states of gapped quantum spin chains

The existence of quasi-long range order is demonstrated in nonequilibrium steady states in isotropic $XY$ spin chains including of two types of additional terms that each generate a gap in the energy spectrum. The system is driven out of equilibrium by initializing a domain-wall magnetization profile through application of an external magnetic field and switching off the magnetic field at the same time the energy gap is activated. An energy gap is produced by either applying a staggered magnetic field in the $z$ direction or introducing a modulation to the $XY$ coupling. The magnetization, spin current, and spin-spin correlation functions are computed analytically in the thermodynamic limit at long times after the quench. For both types of systems, we find the persistence of power-law correlations despite the ground-state correlation functions exhibiting exponential decay.

Influence of Finite-Time Velocity Correlations on Scaling Properties of the Magnetic Field in the Kazantsev-Kraichnan Model: Two-Loop Renormalization Group Analysis

Using the field theory renormalization group method and the operator product expansion technique in the two-loop approximation, we investigate the influence of the finite-time correlations of a turbulent velocity field on the anomalous scaling behavior of the single-time two-point correlation functions of the passive magnetic field in the framework of the generalized kinematic Kazantsev-Kraichnan model with the presence of large-scale anisotropy in the three-dimensional case. We briefly discuss the scaling regimes of the model and find two-loop expressions for the anomalous dimensions of the leading composite operators in the operator product expansion as explicit functions of the parameter determining the finite-time correlations of the velocity field in the studied model. We show that the anomalous dimensions of the composite operators near the isotropic shell play a central role in the scaling properties of the model and this allows uniquely determining the two-loop expressions for the scaling exponents of all single-time two-point correlation functions of the magnetic field that drive their scaling properties deep inside the inertial interval. We show that the presence of the finite-time correlations of the velocity field leads to a significantly more pronounced anomalous scaling of the magnetic correlation functions compared with the standard Kazantsev-Kraichnan rapid-change model with the δ-time correlated Gaussian velocity field.

Thermodynamic geometry of Ising ferromagnet in an external magnetic field: A self-consistent field theory calculation

We present a complete geometrical description for the ferromagnetic Ising model in the pair approximation as introduced by Balcerzak (2003) using self-consistent field theory. A metric is defined in a two-dimensional phase space of magnetization (M) and nearest-neighbour correlation function (C). Based on the metric elements an expression for the thermodynamic Ricci scalar (R) is derived in terms of the lattice coordination number q. We study R as the temperature (T), magnetic field (h) and exchange energy coupling (J) are varied and show that there are T and h dependent critical properties for q=6. By direct comparison, we demonstrate that the special case q=2 provides a consistent behaviour with the already known exact formula in Janyszek and Mrugała work (1989) for the one-dimensional Ising model.

Heisenberg spin- 12 XXZ chain in the presence of electric and magnetic fields

We study the interplay of electric and magnetic order in the one dimensional Heisenberg spin-1/2 XXZ chain with large Ising anisotropy in the presence of the Dzyaloshinskii-Moriya (D-M) interaction and with longitudinal and transverse magnetic fields, interpreting the D-M interaction as a coupling between the local electric polarization and an external electric field. We obtain the ground state phase diagram using the density matrix renormalization group method and compute various ground state quantities like the magnetization, staggered magnetization, electric polarization and spin correlation functions, etc. In the presence of both longitudinal and transverse magnetic fields, there are three different phases corresponding to a gapped N\'{e}el phase with antiferromagnetic (AF) order, gapped saturated phase and a critical incommensurate gapless phase. The external electric field modifies the phase boundaries but does not lead to any new phases. Both external magnetic fields and electric fields can be used to tune between the phases. We also show that the transverse magnetic field induces a vector chiral order in the N\'{e}el phase (even in the absence of an electric field) which can be interpreted as an electric polarization in a direction parallel to the AF order.

Temperature Induced Spin Polarization in Magnetically Stripped Ferromagnetic Film: The Coexisting Phases and the Two Regime Behavior

The paper deals with the study of coexisting majority and minority components in thin ferromagnetic film which is magnetically stripped by applying external magnetic field in selected regions. There occurs continuous transition from ferromagnetic barriers to a coexisting phase separated region through the formation of a depletion layer. Formation of magnetic barriers, channels and step like structure have been explored. Temperature induced two regime behavior is observed – first one dominated by the ferroic nature of the film and the second one by the paramagnetic nature of film. Two sizes of lattice in 3 dimensions of 100 × 100 × 100 and 200 × 100 × 100 are used for Monte Carlo simulation using Ising model with Metropolis algorithm. The spin polarization, average magnetization and spin correlation functions are plotted to reveal the underlying physics. The micrographs of the magnetic barrier and phase separated regions are also shown.

Magnetic helicity generation in the frame of Kazantsev model

Using a magnetic dynamo model, suggested by Kazantsev (J. Exp. Theor. Phys. 1968, vol. 26, p. 1031), we study the small-scale helicity generation in a turbulent electrically conducting fluid. We obtain the asymptotic dependencies of dynamo growth rate and magnetic correlation functions on magnetic Reynolds numbers. Special attention is devoted to the comparison of a longitudinal correlation function and a function of magnetic helicity for various conditions of asymmetric turbulent flows. We compare the analytical solutions on small scales with numerical results, calculated by an iterative algorithm on non-uniform grids. We show that the exponential growth of current helicity is simultaneous with the magnetic energy for Reynolds numbers larger than some critical value and estimate this value for various types of asymmetry.

Electromagnon dispersion probed by inelastic X-ray scattering in LiCrO2.

Inelastic X-ray scattering with meV energy resolution (IXS) is an ideal tool to measure collective excitations in solids and liquids. In non-resonant scattering condition, the cross-section is strongly dominated by lattice vibrations (phonons). However, it is possible to probe additional degrees of freedom such as magnetic fluctuations that are strongly coupled to the phonons. The IXS spectrum of the coupled system contains not only the phonon dispersion but also the so far undetected magnetic correlation function. Here we report the observation of strong magnon–phonon coupling in LiCrO2 that enables the measurement of magnetic correlations throughout the Brillouin zone via IXS. We find electromagnon excitations and electric dipole active two-magnon excitations in the magnetically ordered phase and heavily damped electromagnons in the paramagnetic phase of LiCrO2. We predict that several (frustrated) magnets with dominant direct exchange and non-collinear magnetism show surprisingly large IXS cross-section for magnons and multi-magnon processes.