Frequency-dependent Susceptibilities Research Articles

Computer simulations and mode-coupling theory of glass-forming confined hard-sphere fluids.

We present mode-coupling theory (MCT) results for densely packed hard-sphere fluids confined between two parallel walls and compare them quantitatively to computer simulations. The numerical solution of MCT is calculated using the full system of matrix-valued integro-differential equations. We investigate several dynamical properties of supercooled liquids including scattering functions, frequency-dependent susceptibilities, and mean-square displacements. Close to the glass transition, we find quantitative agreement between the coherent scattering function predicted from theory and that evaluated from simulations, which enables us to make quantitative statements on caging and relaxation dynamics of the confined hard-sphere fluid.

Homogenized transition conditions for plasmonic metasurfaces

The present study aims to model the optical response of plasmonic metasurfaces made of a periodic arrangement of metallic particles with arbitrary shape and subwavelength dimensions. By combining homogenization with quasistatic plasmonic eigenmode expansion, the metasurface is replaced by a zero-thickness interface associated with frequency-dependent effective susceptibilities. The resulting discontinuities of the fields are responsible for strong interaction with the incoming light at the resonances when the complex permittivity of the metal passes close to the real permittivity of an eigenmode. Our modeling provides a physical picture of resonances in plasmonic metasurfaces, and it allows for a huge decrease in the numerical cost of their computations. In addition, comparisons with direct numerics in two dimensions evidence its predictive force at any incidence, particle shape, and arrangement.

Wavelength dependence of polarization-resolved second harmonic generation from ferroelectric SnS few layers

Two-dimensional group-IV monochalcogenides such as GeS, GeSe, SnS, and SnSe were theoretically predicted as multiferroic materials with two or more ferroic properties. However, most of their bulk crystals are stacked layer by layer with an antiferroelectric manner, which lose the macroscopic in-plane ferroelectricity. In this work, we studied SnS in which the layers are stacked in a ferroelectric manner both experimentally and theoretically. We utilized polarization-resolved second harmonic generation (SHG) microscopy to investigate numerous flakes of ferroelectric SnS few layers on mica substrates. We found the SHG polar patterns dramatically varied in the range of 800 nm and 1000 nm due to the frequency-dependent SHG susceptibilities. First-principles calculations have been performed to study the frequency-dependent and layer-dependent SHG susceptibilities in the ferroelectric SnS with AA and AC stacking orders. The variation trend of calculated SHG polar patterns as a function of frequency agrees well with that of the experimental results. Since polarization-resolved SHG is a noncontact and nondestructive technique to determine the crystal orientation, understanding of its properties is important, especially for monitoring the transition of different ferroic phases.

Modeling non-linear dielectric susceptibilities of supercooled molecular liquids.

Advances in high-precision dielectric spectroscopy have enabled access to non-linear susceptibilities of polar molecular liquids. The observed non-monotonic behavior has been claimed to provide strong support for theories of dynamic arrest based on the thermodynamic amorphous order. Here, we approach this question from the perspective of dynamic facilitation, an alternative view focusing on emergent kinetic constraints underlying the dynamic arrest of a liquid approaching its glass transition. We derive explicit expressions for the frequency-dependent higher-order dielectric susceptibilities exhibiting a non-monotonic shape, the height of which increases as temperature is lowered. We demonstrate excellent agreement with the experimental data for glycerol, challenging the idea that non-linear response functions reveal correlated relaxation in supercooled liquids.

Damped Oscillators within the General Theory of Casimir and van der Waals Forces

It is demonstrated that the general theory of Casimir and van der Waals forces describes the interaction-induced equilibrium thermodynamic potentials of the damped harmonic oscillator bilinearly coupled to the environment. An extended model for a damped oscillator is suggested along the lines of the general theory of Casimir and van der Waals forces, and the corresponding thermodynamic quantities obtained. While the original model involves a heat bath consisting of a large number of free oscillators having infinitesimal damping functions, the extended model allows any generally admissible frequency and temperature dependent dissipative susceptibilities of the heat bath constituents, influenced by the additional dissipative environmental channels that are not directly linked to the system oscillator. Consequently, the results obtained are applicable to the frequency and temperature dependent damping function of the system oscillator.

Expeditious computation of nonlinear optical properties of arbitrary order with native electronic interactions in the time domain

We adapted a recently proposed framework to characterize the optical response of interacting electrons in solids in order to expedite its computation without compromise in accuracy at the microscopic level. Our formulation is based on reliable parametrizations of Hamiltonians and Coulomb interactions, which allows economy and flexibility in obtaining response functions. It is suited to computing the optical response to fields of arbitrary temporal shape and strength, to arbitrary order in the field, and natively accounts for excitonic effects. We demonstrate the approach by computing the frequency-dependent susceptibilities of $\mathrm{Mo}{\mathrm{S}}_{2}$ and hexagonal BN monolayers up to the third harmonic. Grounded on a generic nonequilibrium many-body perturbation theory, this framework allows extensions to handle generic interaction models or to describe electronic processes taking place at ultrafast time scales.

Static and optical anapole magnetizabilities and polarizabilities.

The anapolar response of a molecule exposed to a nonhomogeneous magnetic field B with spatially uniform curl C = ∇ × B is rationalized via second-rank tensors, a nonsymmetric aαβ, and a symmetric bαβ, referred to as static anapole magnetizabilities, which can be evaluated by quantum-mechanical Rayleigh-Schrödinger perturbation theory or allowing for the definitions of electronic current densities JB(r) and JC(r) induced in the electron cloud. The isotropic part of bαβ is even under the fundamental symmetry operations of charge conjugation C, parity P, and time reversal T and does not vanish for all matter and antimatter. The isotropic part of aαβ is even under C and T, but odd under P, and is exhibited only by chiral compounds. In the presence of optical fields, represented for simplicity by a monochromatic plane wave of frequency ω, dynamic anapole magnetizabilities and various anapole polarizabilities are taken into account. Assuming, within the electric quadrupole approximation for the impinging wave, that the electric field at the origin of the coordinate system is E(0), with uniform gradient ∇E, and magnetic field is B, the anapolar response is interpreted by second-rank aαβ(ω), aαβ '(ω), fαβ(ω), fαβ '(ω) and third-rank gα,βγ(ω), gα,βγ '(ω) frequency-dependent tensors. The same basic definitions are arrived at introducing frequency-dependent electronic current densities JB(r, ω) and JC(r, ω). As the frequency-dependent anapole susceptibilities depend on the origin of the coordinate system, relationships connecting them for two different origins are reported.

Assessing Magnetic Susceptibility Profiles of Topsoils under Different Occupations

Magnetic susceptibility measurements at low and high frequencies (χlf, χhf) were carried out on topsoil samples from reforested, cultivated, and pasture lands from a catchment located at the north of Morocco. The aims of this study were to investigate the impact of land use or human activity on χlf of soil overlying the same substrate, to discriminate allochthonous material or pollution from autochthonous or inherited ones, and to assess the origin and contribution of superparamagnetic (SP) grains to the global magnetic susceptibility χlf. Measurements of χlf indicated significant enhancement, with values ranging from 12.4 to 252.82 × 10-8 m3 kg−1 with a mean value of 107.087 × 10-8 m3 kg−1 for the reforested lands. In the cultivated lands, χlf were from 8.4 to 88.65 × 10-8 m3 kg1 with a mean value of 42.69 × 10-8 m3 kg−1, while in the pasture lands, χlf was comprised between 14.34 × 10-8 m3 kg−1 and 133.35 × 10-8 m3 kg−1 with a mean value of 57.33 × 10-8 m3 kg−1. The magnetic enhancement indicates high concentration of ferrimagnetic minerals in the top soil. The magnetic susceptibility enhancement decreases as the human activity increases, while the underlying bedrock is almost the same: reforested land > pastures land > cultivated land. The analysis of the variations of χlf and frequency dependent susceptibilities (χfd and %χfd), along the profiles of soil, indicate a pedogenic origin of the topsoil magnetic susceptibility enhancement.

Ab initio calculations of the linear and nonlinear susceptibilities of N2 , O2 , and air in midinfrared laser pulses

We present first-principles calculations of the linear and nonlinear susceptibilities of N$_2$, O$_2$, and air in the mid-infrared wavelength regime, from $1-4$ $\mu$m. We extract the frequency-dependent susceptibilities from the full time-dependent dipole moment that is calculated using time-dependent density functional theory. We find good agreement with curves derived from experimental results for the linear susceptibility, and with measurements for the nonlinear susceptibility up to 2.4 $\mu$m. We also find that the susceptibilities are insensitive to the laser intensity even in the strong field regime up to $5\times 10^{13}$ W/cm$^2$. Our results will allow accurate calculations of the long-distance propagation of intense MIR laser pulses in air.

Anisotropies of in-phase, out-of-phase, and frequency-dependent susceptibilities in three loess/palaeosol profiles in the Czech Republic; methodological implications

The relationship between the anisotropy of frequency-dependent magnetic susceptibility (fdAMS) and the anisotropy of out-of-phase magnetic susceptibility (opAMS) was investigated theoretically and also empirically at three loess/palaoesol profiles in Prague and in Southern Moravia. The data treatment was made in terms of mean susceptibility, degree of AMS, and orientations of principal susceptibilities. It has shown that the fdAMS and opAMS can serve as indicators of the preferred orientations of ultrafine magnetic particles that are on transition between superparamagnetic and stable single domain states in rocks, soils and environmental materials. In loess/palaeosol sequences, the fdAMS and opAMS correlate reasonably, because they are due to magnetic particles of similar grain sizes. The fdAMS and opAMS can be both coaxial with standard AMS (i.e. anisotropy of in-phase susceptibility - ipAMS) or non-coaxial indicating slightly different orientations of viscous magnetic particles.

A family of multi-spin rare-earth complexes based on a triazole nitronyl nitroxide radical: synthesis, structure and magnetic properties.

The combination of LnIII ions (GdIII, TbIII or DyIII) and a triazole nitronyl nitroxide radical (4-Me-3-NITtrz) as spin carriers results in two mononuclear and one binuclear compounds, namely, [Ln(hfac)3(4-Me-3-NITtrz)(H2O)] (Ln = Gd(1), Tb(2); hfac = hexafluoroacetylacetone; 4-Me-3-NITtrz = 2-[3-(4-methyl-l,2,4-triazolyl)]-4,4,5,5-tetramethylimidazoline-1-oxyl-3-oxide) and [Dy(hfac)2(4-Me-3-NITtrz)2][Dy(hfac)4]·CHCl3. Compounds 1 and 2 are isostructural and crystallize in the P1̄ space group, whereas compound 3 crystallizes in the P21/n space group. In 1 and 2, the central LnIII ions are nine-coordinated (LnNO8) in a distorted spherical capped square antiprism geometry (C4v) finished by three bischelate hfac anions and one bidentate triazole radical and one aqua molecule. While 3 is a mixed-coordinated binuclear compound with Dy1 in a triangular dodecahedron (D2d) coordination sphere and Dy2 in a biaugmented trigonal prism (C2v) coordination sphere. Magnetic studies show that compound 2 exhibits field-induced single-molecule magnet (SMM) behavior.

Tuning of Exchange Coupling and Switchable Magnetization Dynamics by Displacing the Bridging Ligands Observed in Two Dimeric Manganese(III) Compounds

Two Mn(III)-based dimers, [Mn2(bpad)2(CH3O)4]n (1) and [Mn2(bpad)2(pa)2]n·2H2O (2) (Hbpad = N3-benzoylpyridine-2-carboxamidrazone, H2pa = phthalic acid), have been assembled from a tridentate Schiff-base chelator and various anionic coligands. Noteworthily, compound 1 could be identified as a reaction precursor to transform to 2 in the presence of phthalic acid, resulting in a rarely structural conversion process in which the bridges between intradimer Mn(III) ions alter from methanol oxygen atom with μ2-O mode in 1 (Mn Mn distance of 3.046 Å) to syn-anti carboxylate in 2 (Mn Mn distance of 4.043 Å), while the Mn(III) centers retain hexa-coordinated geometries with independently distorted octahedrons in two compounds. The dc magnetic determinations reveal that ferromagnetic coupling between two metal centers with J = 1.31 cm−1 exists in 1, whereas 2 displays weak antiferromagnetic interactions with the coupling constant J of −0.56 cm−1. Frequency-dependent ac susceptibilities in the absence of dc field for 1 suggest slow relaxation of the magnetization with an energy barrier of 13.9 K, signifying that 1 features single-molecule magnet (SMM) behavior. This work presents a rational strategy to fine-tune the magnetic interactions and further magnetization dynamics of the Mn(III)-containing dinuclear units through small structural variations driven by the ingenious chemistry.

Syntheses, structures and magnetic properties of the lanthanide complexes of the pyrimidyl-substituted nitronyl nitroxide radical.

Four 2p-4f LnIII-radical complexes, [(NIT-2-Pm)Ln(hfac)3]·0.5C7H16 (NIT-2-Pm = 2-pyrimidyl-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazol-1-oxy-3-oxide, hfac = hexafluoroacetylacetonato, Ln = Tb (1), Dy (2), Ho (3) and Er (4)), and four 4f-2p-4f LnIII-radical-LnIII complexes, [(μ-NIT-2-Pm)Ln2(hfac)6(H2O)2]·0.5C7H16 (Ln = Tb (5), Dy (6), Ho (7) and Er (8)) have been synthesized and characterized structurally and magnetically. These compounds can be selectively obtained by controlling the reaction ratio of Ln(hfac)3·2H2O to the radical ligand NIT-2-Pm. The crystal structures show that in the former four complexes 1-4, the NIT-2-Pm radical acts as a terminal bidentate ligand chelating to one LnIII ion, while in 5-8, the NIT-2-Pm acts as a bridging ligand linking two LnIII ions to form a binuclear three-spin system. Magnetic studies revealed that complexes 1-4 and 6 show frequency-dependent ac magnetic susceptibilities, suggesting a possible single-molecule magnet behavior. To the best of our knowledge, complexes 3 and 4 are the first Ho-NIT and Er-NIT compounds showing slow magnetic relaxation. Compounds 5-8 represent a rare family of compounds showing the NIT bridged 4f-2p-4f three-spin motif, while complex 6 is a rare NIT bridged multinuclear lanthanide compound possessing SMM-like behaviour. Ab initio calculations were performed on all these complexes. The fitting of the magnetic susceptibilities of these compounds suggests weak antiferromagnetic coupling between the LnIII and NIT radical in 1-8 and weak ferromagnetic LnIII-LnIII interactions in 5-8.

Mineral magnetic characteristics of the late Quaternary coastal red sands of Bheemuni, East Coast (India)

The voluminous red sand deposits of Bheemuni in the east coast of India provide record of coastal land-sea interaction during the late Quaternary climatic and eustatic oscillations. Limited information on the origin and depositional environments of these red sands and their chronology is available. We studied two inland to coast cross profiles from Bheemuni red sand deposits using mineral magnetism, color characteristics and Citrate-bicarbonate-dithionite (CBD) extractable pedogenic iron oxides over 23 horizons along with optically stimulated luminescence (OSL) chronology at 6 horizons. The oldest exposed bed had an optical age of ~48.9±1.7ka. Differential ages between the two parallel sections (SOS=~48.9±1.7 to 12.1±0.3ka and IMD=~29.3±3.5ka) suggest laterally shifting fluvial sedimentation.Both the profiles show significant amount of antiferromagnetic oxide (hematite) along with ferrimagnetic (magnetite/maghemite) mineral composition. The granulometric (/domain-) sensitive parameters (χFD, χARM, SIRM/χLF and χARM/χLF) indicate variable concentration of superparamagnetic (SP) and single domain (SD) particles between the two profiles. The higher frequency dependent and pedogenic magnetic susceptibilities (χFD and χpedo) in the younger (IMD) profile suggest enhanced pedogenesis under a warm-wet climate post ~29.3ka and also during Holocene. A combination of hard isothermal remanent magnetization (HIRM) and redness rating (RR) index indicates distinct but variable concentration of a) crystalline and b) poorly crystalline (pigmentary) hematites in both the profiles. We consider that the former (#a) is derived from hinterland red soils and possibly due to post-depositional diagenesis, and the latter (#b) precipitated from the dissolved iron under fluvial regime imparting the unique red coloration to Bheemuni sands. Partial to complete alteration of ferromagnesian minerals due to pedogenesis in hinterlands under warm-wet climate was therefore the principal source of reddening of the Bheemuni sands.

Cu–Ln compounds based on nitronyl nitroxide radicals: synthesis, structure, and magnetic and fluorescence properties

Three series of nitronyl nitroxide radical 3d–4f compounds, namely, [Ln(hfac)3Cu(hfac)2NIT-5Br-3Py]n (LnIII = La (1), Pr (2)), [Ln(hfac)3Cu(hfac)2NIT-5Br-3Py] (LnIII = Gd (3), Tb (4), Dy (5)) and [Ln(hfac)3Cu(hfac)2(NIT-5Br-3Py)2]n (LnIII = Gd (6), Tb (7), Dy (8); NIT-5Br-3Py = 2-(5-bromo-3-pyridyl)-4,4,5,5-tetramethyl-imidazoline-1-oxyl-3-oxide; hfac = hexafluoroacetylacetonate) have been successfully obtained. Single crystal X-ray crystallographic analysis reveals that complexes 1 and 2 consist of 1D chains built up by Ln(hfac)3 units bridged by the radical ligands through their NO moieties and the additional Cu ions are coordinated to the nitrogen atoms of the radicals. Complexes 3–5 are rare hetero-binuclear Cu–Ln compounds bridged by the nitronyl nitroxide radicals while complexes 6–8 possess one-dimensional chain structures with a repeating [Cu–Rad–Ln–Rad] sequence. DC magnetic studies show ferromagnetic interaction between the LnIII ion and the coordinated NO group in compounds 3–8. Tb–Cu derivatives (complexes 4 and 7) display frequency dependent ac magnetic susceptibilities, indicating slow magnetic relaxation behavior. The room-temperature photoluminescence spectra of complexes 4 and 7 exhibit strong characteristic emissions in the visible region.

Magnetic Susceptibility of Soils from Eastern Botswana: A Reconnaissance Survey and Potential Applications

<p class="zhengwen">Soil magnetic properties measurements are relatively fast and inexpensive but have been proved to be sufficient for preliminary investigations in diverse socio-developmental issues. This paper presents results of a reconnaissance study of soil colour and magnetic susceptibility (c) in eastern Botswana, where ~80% of the population resides. The work is a first step to creating a database of rock and soil magnetic properties and to document spatial variations in magnetic properties in the country. These measurements are important as constraints for interpretation of available aeromagnetic data and can also be exploited for environmental soil research (pollution) and land-use planning (agriculture). The soils sampled include derivatives of varying types and provenance such as Archean gneissic granitoids, metamorphosed rocks (granulites), volcano-sedimentary assemblages, Karoo basalts, and alluvial sediments. A soil colour chart was used since soil colours and magnetic properties are diagnostic of its parent rock sources and weathering profiles. Soil magnetic susceptibilities were measured at both low frequency (0.46 MHz, clf) and high frequency (4.6 MHz, chf), thus allowing calculation of frequency-dependent susceptibility (cfd, cfd%) for detecting ultra-fine ferromagnetic minerals.</p>It was found that soils with Hues ranging from 7.5YR to 10YR have appreciable amount of magnetic materials and soils with Hues of 2.5YR are generally nonmagnetic. The results of soil magnetic susceptibility profiles show spatial variation closely related to the variation in basement rocks, which provides excellent evidence that the magnetic susceptibility variation reflects basement rocks or bedrock composition (soil parent material). In relation to the Botswana physiographic units, soils from the hardveld (Precambrian) show the highest susceptibilities, followed by those from the sandveld, with the lowest values being from the alluvial. The frequency dependent magnetic susceptibilities indicate the presence of ultra-fine super-paramagnetic minerals such as magnetite/maghemite. It is suggested that a systematic and continuous programme of rock and soil magnetic measurements would benefit various socio-economic and development priority sectors of Botswana. This also applies to many developing countries in Africa where soil physics and measurement of soil susceptibility in particular, is generally still at an embryonic stage.

The superparamagnetic response of transient AEM data

SUMMARY Several lines of VTEM data flown at different system elevations across a known sulphide body and surface cover with elevated superparamagnetic (SPM) properties were analysed with MAXWELL, layered-earth inversions, LEROIAIR and LEROI. The SPM material was modelled with frequency-dependent magnetic susceptibilities at shallow depth. Due to their slow late-time decay, SPM responses can be confused with responses of deep conductors and vice versa. Depending on the parameter weighting used, 1D inversions model all late-time responses as deep conductive material or as surficial SPM material. However, the joint 1D inversion of data acquired at different system elevations manages to recover a deep conductor from the sulphide anomaly and elevated SPM values at the location of the SPM response. For the modelled parameters, the VTEM data sets from two elevations (at 70 and 80 m) require a vertical separation of about 10 m to allow for the discrimination between the SPM and sulphide responses. For lower system elevations, less sensor separation is necessary due to the strong gradient of the SPM response. We suggest that two vertically separated receivers could be used to measure the AEM gradient and depending on the flying height of the transmitter, the vertical offset of the receivers should be between 2 and 40 m.

Modelling the superparamagnetic response of AEM data

Several lines of VTEM data flown at different system elevations across a known sulphide body and surface cover with elevated superparamagnetic (SPM) properties were analysed with MAXWELL, layered-earth inversions (LEI), LEROIAIR and LEROI. The SPM material was modelled with frequency-dependent magnetic susceptibilities at shallow depth.Due to their slow late-time decay, SPM responses can be confused with responses of deep conductors and vice versa. Depending on the parameter weighting used, 1D inversions model all late-time responses as deep conductive material or as surficial SPM material. However, the joint 1D inversion of data acquired at different system elevations manages to recover a deep conductor from the sulphide anomaly and elevated SPM values at the location of the SPM response. For the modelled parameters, the VTEM datasets from two elevations (at 70 and 80 m) require a vertical separation of ~10 m to allow for the discrimination between the SPM and sulphide responses. For lower system elevations, less sensor separation is necessary due to the strong gradient of the SPM response.Following the determination of SPM parameters from VTEM survey data, these values were used to hypothesise the SPM response for a range of system geometries, showing that larger transmitter loops and larger offsets between transmitter and receiver loops reduce SPM effects. We suggest that two vertically separated receivers could be used to measure the airborne electromagnetic (AEM) gradient and depending on the flying height of the transmitter, the vertical offset of the receivers should be between 2 and 40 m. If gradient data are not collected, then EM responses measured during the transmitter on-time and x-component data, if available, might offer some model discrimination.Whereas synthetic data of the examined helicopter TEM systems VTEM, AEROTEM and HELITEM indicate a fairly high sensitivity to SPM effects, fixed-wing MEGATEM data are much less affected, due to the higher transmitter elevation and large transmitter loop – receiver separation. SPM effects on data of frequency-domain systems such as the RESOLVE system are also small.

Slow magnetic relaxation and field-induced metamagnetism in nitronyl nitroxide-Dy(III) magnetic chains.

The combination of lanthanide ions and nitronyl nitroxide radicals resulted in four new Ln-radical one-dimensional compounds, namely, [Ln(hfac)3{NIT-Ph(OMe)2}]n(Ln(III) = Sm (1), Eu (2), Gd (3), Dy (4); hfac = hexafluoroacetylacetonate; NIT-Ph(OMe)2 = 2-(2',4'-dimethoxyphenyl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazolyl-1-oxyl-3-oxide). The four complexes were found to be isomorphous and exhibit nitronyl nitroxide radicals-bridged lanthanides linear chains. DC magnetic susceptibilities show that the directly bonded nitronyl nitroxide interacts ferromagnetically with Gd and Dy ions. The Dy complex exhibits three-step metamagnetism and frequency-dependent ac magnetic susceptibilities, indicating single-chain magnet behavior. This work shows that the magnetic behaviors of one-dimensional Ln-nitronyl nitroxide chains can be fine tuned by the substituents of the radicals.

A family of rare earth complexes with chelating furan biradicals: syntheses, structures and magnetic properties

Six LnIII–furan-biradical tri-spin complexes have been synthesized, they exhibit interesting magnetic properties. DyIIIcomplex shows frequency-dependent ac magnetic susceptibilities, which suggests the presence of slow magnetic relaxation.