Transverse Susceptibility Research Articles

Damping and Magnetic Anisotropy of Epitaxial Fe1.7Ge Ultrathin Films Grown on Ge(111) Substrates

6, 10 and 20[Formula: see text]nm thick hexagonal Fe[Formula: see text]Ge thin films have been grown on face-centered-cubic Ge(111) substrates by molecular beam epitaxy. X-ray diffraction investigations revealed an excellent epitaxy of the Fe[Formula: see text]Ge films, with crystallographic [Formula: see text] and [Formula: see text] axes lying in the sample plane. Ferromagnetic resonance, magneto-optical Kerr effect and transverse bias initial inverse susceptibility and torque (TBIIST) measurements reveal that the in-plane anisotropy results from the superposition of a uniaxial and a sixfold symmetry terms. The sixfold anisotropy field, which is in agreement with the crystal structure of the samples, increases with the film thickness suggesting an enhancement of the sample quality, while the small uniaxial anisotropy field does not show regular thickness dependence. Frequency and angular dependences of the FMR linewidth show two-magnon scattering and inhomogeneities contributions which depend on the film thickness. A Gilbert damping parameter as low as 0.0064 is found.

Frustrated Heisenberg Antiferromagnets on Cubic Lattices: Magnetic Structures, Exchange Gaps, and Non-Conventional Critical Behaviour

We have studied the Heisenberg antiferromagnets characterized by the magnetic structures with the periods being two times larger than the lattice period. We have considered all the types of the Bravais lattices (simple cubic, bcc and fcc) and divided all these antiferromagnets into 7 classes i.e. 3 plus 4 classes denoted with symbols A and B correspondingly. The order parameter characterizing the degeneracies of the magnetic structures is an ordinary Neel vector for A classes and so-called 4-complex for B classes. We have taken into account the fluctuation corrections for these states within the spin-wave and large-N expansions ($N$ is the number of spin components). Below the Neel temperature $T_{\rm{N}}$ quantum and thermal fluctuations lift the degeneracy making simple one-wave vector collinear structure preferable for all the classes. A satellite of this effect is opening of the exchange gaps at certain wave vectors in the spin wave spectrum (there is an analogous effect for the nonuniform static transverse susceptibility). However, as the temperature approaches $T_{\rm{N}}$, the exchange gaps are closing. We have calculated the critical indices $\eta$ and $\nu$ to order of $1/N$ and found that they differ for A and B classes.

Magnetic behaviors of a transverse spin-1/2 Ising cubic nanowire with core/shell structure

The surface shell exchange coupling effect on the magnetic properties (surface shell, core, total longitudinal and total transverse magnetizations, susceptibility, phase diagram and hysteresis loops) of a transverse spin-12 Ising cubic nanowire is investigated, in the present work, by employing the effective-field theory based on the probability distribution technique with correlations, for both ferro- and antiferromagnetic cases. We have found that this parameter has a strong effect on the magnetic properties in both cases. In the ferromagnetic case, the total longitudinal magnetization curves display Q- and S-type behaviors and the hysteresis loop has just one loop, whereas in the antiferromagnetic case, the N-type behavior, in which one compensation temperature appears below the critical temperature, exists in the total longitudinal magnetization curve versus reduced temperature, and triple hysteresis loops are found. The effect of applied field is also investigated on the total longitudinal magnetization for the both cases, and we have found that a large applied field value can overcome the antiferromagnetic coupling leading to a ferromagnetic-like behavior.

The spin-half XXZ antiferromagnet on the square lattice revisited: A high-order coupled cluster treatment

We use the coupled cluster method (CCM) to study the ground-state properties and lowest-lying triplet excited state of the spin-half XXZ antiferromagnet on the square lattice. The CCM is applied to it to high orders of approximation by using an efficient computer code that has been written by us and which has been implemented to run on massively parallelized computer platforms. We are able therefore to present precise data for the basic quantities of this model over a wide range of values for the anisotropy parameter Δ in the range −1≤Δ<∞ of interest, including both the easy-plane (−1<Δ<1) and easy-axis (Δ>1) regimes, where Δ→∞ represents the Ising limit. We present results for the ground-state energy, the sublattice magnetization, the zero-field transverse magnetic susceptibility, the spin stiffness, and the triplet spin gap. Our results provide a useful yardstick against which other approximate methods and/or experimental studies of relevant antiferromagnetic square-lattice compounds may now compare their own results. We also focus particular attention on the behaviour of these parameters for the easy-axis system in the vicinity of the isotropic Heisenberg point (Δ=1), where the model undergoes a phase transition from a gapped state (for Δ>1) to a gapless state (for Δ≤1), and compare our results there with those from spin-wave theory (SWT). Interestingly, the nature of the criticality at Δ=1 for the present model with spins of spin quantum number s=12 that is revealed by our CCM results seems to differ qualitatively from that predicted by SWT, which becomes exact only for its near-classical large-s counterpart.

Effect of magnetic nanoparticle shape on flux amplification in inductive coil magnetic resonance detection

We model and analyze the effect of particle shape on the signal amplification in inductive coil magnetic resonance detection using the reversible transverse magnetic susceptibility of oriented magnetic nanostructures. Utilizing the single magnetic domain Stoner-Wohlfarth model of uniform magnetization rotation, we reveal that different ellipsoidal particle shapes can have a pronounced effect on the magnetic flux enhancement in detection configurations typical of magnetic resonance settings. We compare and contrast the prolate ellipsoids, oblate ellipsoids, and exchange-biased spheres and show that the oblate ellipsoids and exchange-biased spheres have a significantly higher flux amplification effect than the prolate ellipsoids considered previously. In addition, oblate ellipsoids have a much broader polarizing magnetic field range over which their transverse flux amplification is significant. We show the dependence of transverse flux amplification on magnetic resonance bias field and discuss the resulting signal-to-noise ratio of inductive magnetic resonance detection due to the magnetic nanoparticle-filled core of the magnetic resonance detection coil.

Nonequilibrium itinerant-electron magnetism: A time-dependent mean-field theory

We study the dynamical magnetic susceptibility of a strongly correlated electronic system in the presence of a time-dependent hopping field, deriving a generalized Bethe-Salpeter equation which is valid also out of equilibrium. Focusing on the single-orbital Hubbard model within the time-dependent Hartree-Fock approximation, we solve the equation in the non-equilibrium adiabatic regime, obtaining a closed expression for the transverse magnetic susceptibility. From this, we provide a rigorous definition of non-equilibrium (time-dependent) magnon frequencies and exchange parameters, expressed in terms of non-equilibrium single-electron Green functions and self-energies. In the particular case of equilibrium, we recover previously known results.

Acoustic magnons in the long-wavelength limit: Investigating the Goldstone violation in many-body perturbation theory

Collective spin excitations in magnetic materials arise from the correlated motion of electron-hole pairs with opposite spins. The pair propagation is described by the transverse magnetic susceptibility, which we calculate within many-body perturbation theory from first principles employing the full-potential linearized augmented-plane-wave formalism. Ferromagnetic materials exhibit a spontaneously broken global rotation symmetry in spin space leading to the appearance of acoustic magnons (zero gap) in the long-wavelength limit. However, due to approximations used in the numerical scheme, the acoustic magnon dispersion exhibits a small but finite gap at $\mathrm{\ensuremath{\Gamma}}$. We analyze this violation of the Goldstone mode and present an approach that implements the magnetic susceptibility using a renormalized Green function instead of the Kohn-Sham one. This much more expensive approach shows substantial improvement of the Goldstone-mode condition. In addition, we discuss a possible correction scheme, which involves an adjustment of the Kohn-Sham exchange splitting, which is motivated by the spin-wave solution of the one-band Hubbard model. The new exchange splittings turn out to be closer to experiment. We present corrected magnon spectra for the elementary ferromagnets Fe, Co, and Ni.

Neuromelanin Imaging and Dopaminergic Loss in Parkinson's Disease.

Parkinson's disease (PD) is a progressive neurodegenerative disorder in which the major pathologic substrate is a loss of dopaminergic neurons from the substantia nigra. Our main objective was to determine the correspondence between changes in the substantia nigra, evident in neuromelanin and iron sensitive magnetic resonance imaging (MRI), and dopaminergic striatal innervation loss in patients with PD. Eighteen patients and 18 healthy control subjects were included in the study. Using neuromelanin-MRI, we measured the volume of the substantia nigra and the contrast-to-noise-ratio between substantia nigra and a background region. The apparent transverse relaxation rate and magnetic susceptibility of the substantia nigra were calculated from dual-echo MRI. Striatal dopaminergic innervation was measured as density of dopamine transporter (DAT) by means of single-photon emission computed tomography and [123I] N-ω-fluoropropyl-2b-carbomethoxy-3b-(4-iodophenyl) tropane. Patients showed a reduced volume of the substantia nigra and contrast-to-noise-ratio and both positively correlated with the corresponding striatal DAT density. The apparent transverse relaxation rate and magnetic susceptibility values of the substantia nigra did not differ between patients and healthy controls. The best predictor of DAT reduction was the volume of the substantia nigra. Clinical and imaging correlations were also investigated for the locus coeruleus. Our results suggest that neuromelanin-MRI can be used for quantifying substantia nigra pathology in PD where it closely correlates with dopaminergic striatal innervation loss. Longitudinal studies should further explore the role of Neuromelanin-MRI as an imaging biomarker of PD, especially for subjects at risk of developing the disease.

Classical impurities and boundary Majorana zero modes in quantum chains

We study the response of classical impurities in quantum Ising chains. The Z2 degeneracy they entail renders the existence of two decoupled Majorana modes at zero energy, an exact property of a finite system at arbitrary values of its bulk parameters. We trace the evolution of these modes across the transition from the disordered phase to the ordered one and analyze the concomitant qualitative changes of local magnetic properties of an isolated impurity. In the disordered phase, the two ground states differ only close to the impurity, and they are related by the action of an explicitly constructed quasi-local operator. In this phase the local transverse spin susceptibility follows a Curie law. The critical response of a boundary impurity is logarithmically divergent and maps to the two-channel Kondo problem, while it saturates for critical bulk impurities, as well as in the ordered phase. The results for the Ising chain translate to the related problem of a resonant level coupled to a 1d p-wave superconductor or a Peierls chain, whereby the magnetic order is mapped to topological order. We find that the topological phase always exhibits a continuous impurity response to local fields as a result of the level repulsion of local levels from the boundary Majorana zero mode. In contrast, the disordered phase generically features a discontinuous magnetization or charging response. This difference constitutes a general thermodynamic fingerprint of topological order in phases with a bulk gap.

Ground-state phases of the spin-1J1−J2Heisenberg antiferromagnet on the honeycomb lattice

We study the zero-temperature quantum phase diagram of a spin-1 Heisenberg antiferromagnet on the honeycomb lattice with both nearest-neighbor exchange coupling $J_{1}>0$ and frustrating next-nearest-neighbor coupling $J_{2} \equiv \kappa J_{1} > 0$, using the coupled cluster method implemented to high orders of approximation, and based on model states with different forms of classical magnetic order. For each we calculate directly in the bulk thermodynamic limit both ground-state low-energy parameters (including the energy per spin, magnetic order parameter, spin stiffness coefficient, and zero-field uniform transverse magnetic susceptibility) and their generalized susceptibilities to various forms of valence-bond crystalline (VBC) order, as well as the energy gap to the lowest-lying spin-triplet excitation. In the range $0 < \kappa < 1$ we find evidence for four distinct phases. Two of these are quasiclassical phases with antiferromagnetic long-range order, one with 2-sublattice N\'{e}el order for $\kappa < \kappa_{c_{1}} = 0.250(5)$, and another with 4-sublattice N\'{e}el-II order for $\kappa > \kappa_{c_{2}} = 0.340(5)$. Two different paramagnetic phases are found to exist in the intermediate region. Over the range $\kappa_{c_{1}} < \kappa < \kappa^{i}_{c} = 0.305(5)$ we find a gapless phase with no discernible magnetic order, which is a strong candidate for being a quantum spin liquid, while over the range $\kappa^{i}_{c} < \kappa < \kappa_{c_{2}}$ we find a gapped phase, which is most likely a lattice nematic with staggered dimer VBC order that breaks the lattice rotational symmetry.

Quantitative Susceptibility Mapping Indicates a Disturbed Brain Iron Homeostasis in Neuromyelitis Optica - A Pilot Study.

Dysregulation of brain iron homeostasis is a hallmark of many neurodegenerative diseases and can be associated with oxidative stress. The objective of this study was to investigate brain iron in patients with Neuromyelitis Optica (NMO) using quantitative susceptibility mapping (QSM), a quantitative iron-sensitive MRI technique. 12 clinically confirmed NMO patients (6 female and 6 male; age 35.4y±14.2y) and 12 age- and sex-matched healthy controls (7 female and 5 male; age 33.9±11.3y) underwent MRI of the brain at 3 Tesla. Quantitative maps of the effective transverse relaxation rate (R2*) and magnetic susceptibility were calculated and a blinded ROI-based group comparison analysis was performed. Normality of the data and differences between patients and controls were tested by Kolmogorov-Smirnov and t-test, respectively. Correlation with age was studied using Spearman’s rank correlation and an ANCOVA-like analysis. Magnetic susceptibility values were decreased in the red nucleus (p<0.01; d>0.95; between -15 and -22 ppb depending on reference region) with a trend toward increasing differences with age. R2* revealed significantly decreased relaxation in the optic radiations of five of the 12 patients (p<0.0001; -3.136±0.567 s-1). Decreased relaxation in the optic radiation is indicative for demyelination, which is in line with previous findings. Decreased magnetic susceptibility in the red nucleus is indicative for a lower brain iron concentration, a chemical redistribution of iron into less magnetic forms, or both. Further investigations are necessary to elucidate the pathological cause or consequence of this finding.

Molecular density functional theory of water including density–polarization coupling

We present a three-dimensional molecular density functional theory of water derived from first-principles that relies on the particle’s density and multipolar polarization density and includes the density–polarization coupling. This brings two main benefits: (i) scalar density and vectorial multipolar polarization density fields are much more tractable and give more physical insight than the full position and orientation densities, and (ii) it includes the full density–polarization coupling of water, that is known to be non-vanishing but has never been taken into account. Furthermore, the theory requires only the partial charge distribution of a water molecule and three measurable bulk properties, namely the structure factor and the Fourier components of the longitudinal and transverse dielectric susceptibilities.

Charge and Paramagnetic Spin Susceptibilities of Doped Gapped Graphene-Like Structures

We address spin polarization dependence of dynamical charge and spin susceptibilities of doped gapped graphene-like structures in the context of tight binding model Hamiltonian. The frequency behavior of both longitudinal and transverse spin susceptibilities has been calculated via calculating correlation function of spin density operators. Our results show the increase of electronic concentration corresponding to chemical potential leads to enhance the intensity of charge spectral function. We also show that longitudinal spin susceptibility reduces at fixed frequency with gap parameter associated with on-site energy difference between two types of sublattice atoms. Furthermore, the resonance peak in longitudinal spin susceptibility goes to higher frequencies with gap parameter. The effect of magnetization on the longitudinal spin susceptibility indicates two different behaviors depending on frequency region. Finally, the effects of magnetization and gap parameter on the frequency behavior of transverse spin susceptibility have been studied in details.

Electric field induced orientational order of gold nanorods in dilute organic suspensions

The electric field controlled alignment of gold nanorods offers a paradigm for anisotropic molecules with the potential for a wide variety of phases and structures. We experimentally study the optical absorption from gold nanorod suspensions aligned using external electric fields. We show that the absorption from these suspensions depends linearly on the orientational order parameter. We provide evidence that the critical electric field needed to orient the gold nanorods is proportional to the nanorod volume and depolarization anisotropy. Utilizing this critical field dependence, we demonstrate for suspensions with two different nanorod sizes that the alignment of each population can be controlled. We also develop a technique to determine the imaginary parts of the longitudinal and transverse electric susceptibilities of the nanorods. The ability to selectively address specific parts of the nanorod populations in a mixture using external fields may have significant potential for future display and optical filter applications.

The absence of intraband scattering in a consistent theory of Gilbert damping in pure metallic ferromagnets

Damping of magnetization dynamics in a ferromagnetic metal, arising from spin–orbit coupling, is usually characterised by the Gilbert parameter α. Recent calculations of this quantity, using a formula due to Kambersky, find that it is infinite for a perfect crystal owing to an intraband scattering term which is of third order in the spin–orbit parameter ξ. This surprising result conflicts with recent work by Costa and Muniz who study damping numerically by direct calculation of the dynamical transverse susceptibility in the presence of spin–orbit coupling. We resolve this inconsistency by following the approach of Costa and Muniz for a slightly simplified model where it is possible to calculate α analytically. We show that to second order in ξ one retrieves the Kambersky result for α, but to higher order one does not obtain any divergent intraband terms. The present work goes beyond that of Costa and Muniz by pointing out the necessity of including the effect of long-range Coulomb interaction in calculating damping for large ξ. A direct derivation of the Kambersky formula is given which shows clearly the restriction of its validity to second order in ξ so that no intraband scattering terms appear. This restriction has an important effect on the damping over a substantial range of impurity content and temperature. The experimental situation is discussed.

Velocity of excitations in ordered, disordered, and critical antiferromagnets

We test three different approaches, based on quantum Monte Carlo simulations, for computing the velocity $c$ of triplet excitations in antiferromagnets. We consider the standard $S=1/2$ one- and two-dimensional Heisenberg models, as well as a bilayer Heisenberg model at its critical point. Computing correlation functions in imaginary time and using their long-time behavior, we extract the lowest excitation energy versus momentum using improved fitting procedures and a generalized moment method. The velocity is then obtained from the dispersion relation. We also exploit winding numbers to define a cubic space-time geometry, where the velocity is obtained as the ratio of the spatial and temporal lengths of the system when all winding number fluctuations are equal. The two methods give consistent results for both ordered and critical systems, but the winding-number estimator is more precise. For the Heisenberg chain, we accurately reproduce the exactly known velocity. For the two-dimensional Heisenberg model, our results are consistent with other recent calculations, but with an improved statistical precision; $c=1.65847(4)$. We also use the hydrodynamic relation $c^2=\rho_s/\chi_\perp(q\to 0)$ between $c$, the spin stiffness $\rho_s$, and the transversal susceptibility $\chi_\perp$, using the smallest non-zero momentum $q=2\pi/L$. This method also is well controlled in two dimensions, but the cubic criterion for winding numbers delivers better numerical precision. In one dimension the hydrodynamic relation is affected by logarithmic corrections which make accurate extrapolations difficult. As an application of the winding-number method, for the quantum-critical bilayer model our high-precision determination of the velocity enables us to quantitatively test, at an unprecedented level, field-theoretic predictions for low-temperature scaling forms where $c$ enters.

Static and dynamic magnetic properties of Co2FeAl-based stripe arrays

25nm to 50nm Co2FeAl (CFA) thick wire arrays with varying widths and spacing have been patterned from continuous CFA films deposited on MgO(001) using e-beam lithography and Ar ion milling. Magneto-optical Kerr effect, transverse bias initial inverse susceptibility and torque measurements reveal that the in-plane magnetic anisotropy of the wires is dominantly monitored by a uniaxial term, in contrast with the continuous films where it is governed by the superposition of a fourfold term and of a smaller uniaxial term. The microstrip ferromagnetic resonance spectra performed using a magnetic field H, applied in the plane of the studied sample along various directions, or perpendicularly to this plane, gave us access to various quantized modes originating from the patterning. In addition, Brillouin light scattering also exhibits quantized modes. A large part of the experimental observations can be quantitatively interpreted as resulting from the demagnetizing terms induced by the geometrical patterning. However, the presented model, simply built on the effect of the demagnetizing field, is not able to give account of all the quantized modes present in the resonance spectra. When H is parallel to the wires, a more complete description is used: it considers the wave-vector quantization induced by the patterning. For the magnetic modes concerned by both approaches, the correspondence between the 2 models is easily established. When H is not parallel to the wires quantitative descriptions of the behavior of the field dependence of the observed modes still can often be performed. Finally, in all the studied patterned samples, the uniform magnetic mode, termed “film mode”, relative to the parent continuous film is observed by ferromagnetic resonance: such a behavior, which has been reported previously, remains to be completely interpreted.

Effect of γ→α Phase Transformation on Refining Austenite Grains of Microalloyed Steel in Continuous Casting by Simulation

Abstract The formation of coarse prior austenite grain is a key factor to promote transverse crack, and the transverse crack susceptibility can be reduced by refining the austenite grain size. In the present study, the high-temperature confocal laser scanning microscope (CLSM) was used to simulate and study the effect of two γ→α phase transformation conditions on the refinement of the prior austenite grains. Under the condition of the uniform distribution of the second phase precipitation, the effect of the distribution of the proeutectoid ferrite at different cooling rates and refinement of prior austenite grain were investigated. The results indicate that, at a cooling rate of 5.0°C s–1, the austenite grain size undergoing TH1 thermal cycle was 31% smaller than the austenite grain undergoing TH0 thermal cycle. Under TH0 cooling system, the proeutectoid ferrite was uniformly distributed in the austenite matrix; under TH1 cooling, the proeutectoid ferrite precipitated and mainly concentrated along the austenite grain boundaries to form developed-film-like ferrite, which is favorable to break the prior austenite grain boundaries. After the first phase transformation, the film-like ferrite improved the nucleation conditions of new austenite grains, thus more new austenite grains splitted the prior austenite grains, ultimately refining the prior austenite grains.

Breakdown of the adiabatic approach for magnetization damping in metallic ferromagnets

We present a microscopic theory for magnetization relaxation in metallic ferromagnets of nanoscopic dimensions that is based on the calculation of the dynamic spin response matrix in the presence of spin-orbit coupling. Our approach takes into account the collective character of spin excitations in ferromagnetic metals. We show that calculations of the Gilbert damping based on a mean-field, adiabatic approximation fail to describe the relaxation of collective excitations in the ballistic regime. Namely, we show that collective spin excitations such as the ferromagnetic resonance mode have finite damping rates even for perfectly crystalline systems, whereas existing microscopic approaches, based on adiabatic and mean-field approximations, predict infinite damping rates. Moreover, we demonstrate that within a finite frequency approach the relaxation properties are not completely determined by the transverse susceptibility alone, and that the damping rate has a non-negligible frequency dependence in experimentally relevant situations. Our results indicate that the widely used adiabatic approach for spin dynamics breaks down for metallic nanostructures in the presence of strong spin-orbit coupling.

CoFe/MnIr 박막 재료에서 저자장 마이크로파 흡수 특성 분석

본 연구에서는 교환 결합력을 갖는 CoFe/MnIr 박막 재료에서 강자성 공명 장치를 이용하여 자기장 방향에 따른 저자장 마이크로파 흡수(Low field microwave absorption, LFMA) 및 강자성 공명 신호를 측정하였다. 낮은 자기장 영역에서 나타나는 LFMA 신호는 자구의 회전 밀접하게 관계됨을 자화 곡선으로부터 알 수 있었다. 이러한 LFMA 신호 특성을 분석하기 위하여 강자성 공명 신호로부터 측정한 교환 바이어스(<TEX>$H_{ex}$</TEX> = 58.5 Oe) 및 일축 이방성 자기장(<TEX>$H_k$</TEX> = 30Oe)을 S-W model에 적용하여 자화과정의 횡방향 자화량(transverse magnetization, <TEX>$M_{\tau}$</TEX>) 및 투자율(transverse susceptibility, <TEX>${\mu}_{\tau}$</TEX>)을 계산하였다. 자화 곤란축에서 측정된 LFMA 신호는 <TEX>$M_{\tau}$</TEX> 비례하는 경향을 보였지만, 자화 곤란축과 수직 방향으로 접근하면 <TEX>$M_{\tau}$</TEX> 및 <TEX>${\mu}_{\tau}$</TEX> 모두에 의존하는 특성을 보였다. We measured the low field microwave absorption (LFMA) and ferromagnetic resonance (FMR) signals at various magnetic field angle in exchange biased CoFe/MnIr thin film. The LFMA signals were dominantly related to the magnetization rotation process. In order to analyze the LFMA signal, we calculated transverse magnetization (<TEX>$M_{\tau}$</TEX>) and permeability (<TEX>${\mu}_{\tau}$</TEX>) for CoFe/MnIr thin film by using S-W model, which magnetic parameters of exchange bias (<TEX>$H_{ex}$</TEX> = 58.5 Oe) and uniaxial anisotropy field (<TEX>$H_k$</TEX> = 30Oe) was obtained from FMR signals. The LFMA signal at hard axis showed similar behavior compared with that of <TEX>$M_{\tau}$</TEX>. As the magnetic field angle approach to the perpendicular to hard axis, the LFMA signals were depending on both of <TEX>$M_{\tau}$</TEX> and <TEX>${\mu}_{\tau}$</TEX>.