Search Results (7)

Electron paramagnetic resonance spectroscopy is a long-standing method for the exploration of electronic structures of transition ion complexes. The difficulty of its analysis varies considerably, not only with the nature of the spin system, but more so with the relative magnitudes of the magnetic interactions to which the spin is subject, where particularly challenging cases ensue when two interactions are of comparable magnitude. A case in point is the triplet system S = 1 of coordination complexes with two unpaired electrons when the electronic Zeeman interaction and the electronic zero-field interaction are similar in strength. This situation occurs in the X-band spectra of the thermally excited triplet state of dinuclear copper(II) complexes, exemplified by copper acetate monohydrate. In this study, applicability of the recently developed low-frequency broadband EPR spectrometer to S = 1 systems is investigated on the analysis of multi-frequency, 0.5–16 GHz, data from [Cu(CH₃COO)₂H₂O]₂. Global fitting affords the spin Hamiltonian parameters g_z = 2.365 ± 0.008; g_y = 2.055 ± 0.010; g_x = 2.077 ± 0.005; A_z = 64 gauss; D = 0.335 ± 0.002 cm⁻¹; E = 0.0105 ± 0.0003 cm⁻¹. The latter two define zero-field absorptions at ca. 630, 7730, and 10,360 MHz, which show up in the spectra as one half of a sharpened symmetrical line. Overall, the EPR line shape is Lorentzian, reflecting spin-lattice relaxation, which is a combination of an unusual, essentially temperature-independent, inverted Orbach process via the S = 0 ground state, and a Raman process proportional to T². Other broadening mechanisms are limited to at best minor contributions from a distribution in E values, and from dipolar interaction with neighboring copper pairs. Monitoring of a first-order double-quantum transition between 8 and 35 GHz shows a previously unnoticed very complex line shape behavior, which should be the subject of future research. Full article

¹H spin-lattice relaxation experiments have been performed for water–Bovine Serum Albumin (BSA) mixtures, including 20%wt and 40%wt of BSA. The experiments have been carried out in a frequency range encompassing three orders of magnitude, from 10 kHz to 10 MHz, versus temperature. The relaxation data have been thoroughly analyzed in terms of several relaxation models with the purpose of revealing the mechanisms of water motion. For this purpose, four relaxation models have been used: the data have been decomposed into relaxation contributions expressed in terms of Lorentzian spectral densities, then three-dimensional translation diffusion has been assumed, next two-dimensional surface diffusion has been considered, and eventually, a model of surface diffusion mediated by acts of adsorption to the surface has been employed. In this way, it has been demonstrated that the last concept is the most plausible. Parameters describing the dynamics in a quantitative manner have been determined and discussed. Full article

The static and dynamic magnetic properties and the specific heat of K₂Ni₂TeO₆ and Li₂Ni₂TeO₆ were examined and it was found that they undergo a long-range ordering at T_N = 22.8 and 24.4 K, respectively, but exhibit a strong short-range order. At high temperature, the magnetic susceptibilities of K₂Ni₂TeO₆ and Li₂Ni₂TeO₆ are described by a Curie–Weiss law, with Curie-Weiss temperatures Θ of approximately −13 and −20 K, respectively, leading to the effective magnetic moment of about 4.46 ± 0.01 μ_B per formula unit, as expected for Ni²⁺ (S = 1) ions. In the paramagnetic region, the ESR spectra of K₂Ni₂TeO₆ and Li₂Ni₂TeO₆ show a single Lorentzian-shaped line characterized by the isotropic effective g-factor, g = 2.19 ± 0.01. The energy-mapping analysis shows that the honeycomb layers of A₂Ni₂TeO₆ (A = K, Li) and Li₃Ni₂SbO₆ adopt a zigzag order, in which zigzag ferromagnetic chains are antiferromagnetically coupled, because the third nearest-neighbor spin exchanges are strongly antiferromagnetic while the first nearest-neighbor spin exchanges are strongly ferromagnetic, and that adjacent zigzag-ordered honeycomb layers prefer to be ferromagnetically coupled. The short-range order of the zigzag-ordered honeycomb lattices of K₂Ni₂TeO₆ and Li₂Ni₂TeO₆ is equivalent to that of an antiferromagnetic uniform chain, and is related to the short-range order of the ferromagnetic chains along the direction perpendicular to the chains. Full article

The magnetic response of a frustrated K₂Cr₃As₃ sample having triangular arrays of twisted tubes has been studied by means of dc magnetization measurements as a function of the magnetic field (H) at different temperatures ranging from 5 K up to 300 K. Looking at the magnetic hysteresis loops m(H), a diamagnetic behavior of the sample was inferred at temperatures higher than 60 K, whereas at lower temperatures the sample showed a hysteresis loop compatible with the presence of ferrimagnetism. Moreover, spike-like magnetization jumps, both positive and negative, were observed in a narrow range of the magnetic field around 800 Oe, regardless of the temperature considered and they were compared with the theoretical predictions on frustrated systems. The field position of the magnetization jumps was studied at different temperatures, and their distribution can be described by a Lorentzian curve. The analogies between the expected features and the experimental observations suggest that the jumps could be attributed to the magnetic frustration arising from the twisted triangular tubes present in the crystal lattice of this compound. Full article

We theoretically investigate a metal-to-insulator transition in artificial two-dimensional (2D) crystals (i.e., metasurfaces) of tightly coupled closed-ring resonators. Strong interaction between unit resonators in the metasurfaces yields the effective permittivity highly dependent on the lattice spacing of unit resonators. Through our rigorous theory, we provide a closed form of effective permittivity of the metasurface and reveal that the permittivity possesses a Lorentzian-type resonant behavior, implying that the transition of the effective permittivity can arise when the lattice spacing passes a critical value. Full article

The physics of heat and mass transfer from an object in its wake has significant importance in natural phenomena as well as across many engineering applications. Here, we report numerical results on the population density of the spatial distribution of fluid velocity, pressure, scalar concentration, and scalar fluxes of a wake flow past a sphere in the steady wake regime (Reynolds number 25 to 285). Our findings show that the spatial population distributions of the fluid and the transported scalar quantities in the wake follow a Cauchy-Lorentz or Lorentzian trend, indicating a variation in its sample number density inversely proportional to the squared of its magnitude. We observe this universal form of population distribution both in the symmetric wake regime and in the more complex three dimensional wake structure of the steady oblique regime with Reynolds number larger than 225. The population density distribution identifies the increase in dimensionless kinetic energy and scalar fluxes with the increase in Reynolds number, whereas the dimensionless scalar population density shows negligible variation with the Reynolds number. Descriptive statistics in the form of population density distribution of the spatial distribution of the fluid velocity and the transported scalar quantities is important for understanding the transport and local reaction processes in specific regions of the wake, which can be used e.g., for understanding the microphysics of cloud droplets and aerosol interactions, or in the technical flows where droplets interact physically or chemically with the environment. Full article

We consider certain $E_n$ -type root lattices embedded within the standard Lorentzian lattice ${\mathbb{Z}}^{n+1}(3\le n\le 8)$ and study their discrete geometry from the point of view of del Pezzo surface geometry. The lattice ${\mathbb{Z}}^{n+1}$ decomposes as a disjoint union of affine hyperplanes which satisfy a certain periodicity. We introduce the notions of line vectors, rational conic vectors, and rational cubics vectors and their relations to E-polytopes. We also discuss the relation between these special vectors and the combinatorics of the Gosset polytopes of type ${(n-4)}_{21}$ . Full article