Nature of electric and magnetic dipoles gleaned from the Poynting theorem and the Lorentz force law of classical electrodynamics

Starting with the most general form of Maxwell's macroscopic equations in which the free charge and free current densities, ρ_free and J_free, as well as the densities of polarization and magnetization, P and M, are arbitrary functions of space and time, we compare and contrast two versions of the Poynting vector, namely, S = μ_o^− 1E × B and S = E × H. Here E is the electric field, H is the magnetic field, B is the magnetic induction, and μ_o is the permeability of free space. We argue that the identification of one or the other of these Poynting vectors with the rate of flow of electromagnetic energy is intimately tied to the nature of magnetic dipoles and the way in which these dipoles exchange energy with the electromagnetic field. In addition, the manifest nature of both electric and magnetic dipoles in their interactions with the electromagnetic field has consequences for the Lorentz law of force. If the conventional identification of magnetic dipoles with Amperian current loops is extended beyond Maxwell's macroscopic equations to the domain where energy, force, torque, momentum, and angular momentum are active participants, it will be shown that “hidden energy” and “hidden momentum” become inescapable consequences of such identification with Amperian current loops. Hidden energy and hidden momentum can be avoided, however, if we adopt S = E × H as the true Poynting vector, and also accept a generalized version of the Lorentz force law. We conclude that the identification of magnetic dipoles with Amperian current loops, while certainly acceptable within the confines of Maxwell's macroscopic equations, is inadequate and leads to complications when considering energy, force, torque, momentum, and angular momentum in electromagnetic systems that involve the interaction of fields and matter.     

Cubic helimagnets in magnetic field and at pressure

Cubic helimagnets with B20 structure display several unusual properties such as anisotropy of the spin-wave spectrum al small momenta q, rotation of the helix vector k in magnetic field and quantum phase transition at pressure. We demonstrate that first two phenomena are a result of umklapp processes mixing excitations with momenta q, q+k and q−k. At very low magnetic field perpendicular to k the helical structure remains stable due to spin-wave gap Δ. Its square is sum of two parts. The first one is a result of the magnon interaction and the second negative part stems from magneto-elastic interaction. It is suggested that competition between these parts leads to the quantum phase transition observed in MnSi and FeGe. For MnSi from rough estimations at ambient pressure was shown that both parts are comparable with the experimentally observed gap. The magneto-elastic interaction is also responsible for 2k modulation of the lattice and contributes to the magnetic anisotropy. Experimental observation by X-ray and neutron scattering of this lattice modulation allows to determine the strength of the magneto-elastic interaction responsible for above phenomena and the lattice helicity.     

Performance of a slow positron beam using a hybrid lens design

The University of Hong Kong positron beam employs conventional magnetic field transport to the target, but has a special hybrid lens design around the positron moderator that allows the beam to be focused to millimeter spot sizes at the target. The good focusing capabilities of the beam are made possible by extracting work-function positrons from the moderator in a magnetic field free region using a conventional Soa lens thus minimizing beam canonical angular momentum. An Einzel lens is used to focus the positrons into the magnetic funnel at the end of transportation magnetic field while at the same time bringing up the beam energy to the intermediate value of 7.5 keV. The beam is E × B filtered at this intermediate energy. The final beam energy is obtained by floating the Soa-Einzel system, E × B filter and flight tube, and accelerating the positrons just before the target. External beam steering saddle coils fine tune the position, and the magnetic field around the target chamber is adjusted so as to keep one of the beam foci always on the target. The system is fully computer controlled. Variable energy-Doppler broadened annihilation radiation (VEDBAR) data for a GaN sample are shown which demonstrate the performance of the positron beam system.     

Shift of the superconducting critical parameters due to correlated disorder

In a nonuniform superconductor with randomly distributed local critical temperature both the macroscopic critical temperature and the upper critical magnetic field strongly depend on the characteristic correlation length ρ₀ of correlated disorder. The shift of the macroscopic critical parameters from those for non-correlated disorder, which does not exist for white noise, is obtained for small ρ₀ in the framework of the Ginzburg-Landau theory.     

Eu(III) and Tb(III) luminescent lanthanide systems derived from DTPA-bisamide and DTTA-based ligands incorporating bipyridine antenna

Four new polycarboxylate ligands H₃Lⁿ have been synthesized by the attachment of two or one 2,2′-bipyridine subunits onto a diethylenetriamine pentacarboxylic acid (DTPA-bisamide derivatives: H₃L¹, H₃L²) or a diethylenetriamine tricarboxylic acid (DTTA derivatives: H₃L³, H₃L⁴) core. The neutral Eu^III and Tb^III complexes of these chelates have been prepared and studied from their UV-vis and luminescence data. The main photophysical characteristics of these complexes, i.e. the absorption and luminescence spectra, the metal-centred lifetimes and the overall luminescence yields (Φ) were measured in buffered aqueous solutions. In addition the role played by non-radiative paths (vibrational energy transfer involving coordinated water molecules, involvement of ligand-to-metal charge-transfer excited states, or metal→ligand back-transfer) was investigated. In all complexes, we found that the bidentate bipyridine chromophore is not coordinated to the lanthanide ion, allowing one (LnL¹, LnL²) or two (LnL³, LnL⁴) water molecules to penetrate the first coordination sphere of the metal. Although the bipyridine chromophore behaves as remote (from the binding site) light-harvesting unit for the lanthanide ion in these systems, a sizeable sensitization of the Eu- and Tb-centred luminescence can be effective (LnL², LnL³, Φ=16-19% in aerated D₂O solutions). Our photophysical investigations show that overall non-radiative deactivation is not dependant of thermally activated non-radiative channels but the efficiency of the ligand→Ln intramolecular energy transfer has to be taken into account to explain the obtained results.     

Organic radical molecular solids based on [(TCNQ)n] (n=1 or 2): Syntheses, crystal structures, magnetic properties and DFT analyses

Four molecular solids consisting of the 7,7,8,8-tetracyanoquinodimethane (TCNQ) radical and benzylpyridinium or benzylquinolinium derivatives with molar ratios of 1:1 (1-3) and 2:1 (4) have been prepared and characterized. In the crystals of 1 and 3, TCNQ⁻ monoanions and the corresponding cations form segregated stacks, which are regular in 1 but irregular in 3. Instead of segregated stacks, TCNQ⁻ monoanions in 2 form isolated π-dimers. In the crystals of 4, two crystallographic independent TCNQ species possess almost equal fractional negative charge (ca. −0.5). Two types of TCNQ species form a tetrad, these tetrads make a TCNQ stack with the pattern …BAAB…BAAB… along the crystallographic a-b direction. The magnetisms for 1-4 can be simply explained by the formation of singlet spin state. A broken symmetry approach in a density functional theory framework at the ub3lyp/6-31 g level was used to calculate the magnetic exchange constants in 1-4. The results qualitatively demonstrate the observed magnetic properties.     

Magnetic and electronic properties of Cr- and Mn-doped SnO2: ab initio calculations

The ab initio calculations, based on the Korringa–Kohn–Rostoker (KKR) approximation method combined with the coherent potential approximation (CPA), indicated as KKR–CPA, have been used to study the stability of ferromagnetic and ferrimagnetic states, for systems that are SnO₂ doped and co-doped with two transition metals, that is, chromium and manganese. Our results indicate that the ferromagnetic state is more stable than the spin-glass state for the (Sn_1−xCr_xO₂; x = 0.07, 0.09, 0.12 and 0.15)-doped system, while the spin-glass state is more stable than the ferromagnetic state for the (Sn_1−xMn_xO₂; x = 0.02 and 0.05)-doped system. However, the ferromagnetic and/or the ferrimagnetic states are stable for the (Sn_0.98−xMn_0.02Cr_xO₂; x = 0.05, 0.09 and 0.13)-doped system depending on the Cr concentration. Moreover, we estimated the Curie temperature (T_c) for the Cr-doped tin dioxide (SnO₂), and we explained the origin of magnetic behaviour through the total density of states for different doped and co-doped SnO₂ systems.     

Effect of C and SiC additions into in situ or mechanically alloyed MgB2 deformed in Ti sheath

Effect of 3.4 wt.% C and 5 wt.% SiC doping into the standard in situ (IN) process and mechanically alloyed (MA) MgB₂ was studied. Powders of IN and MA process were carried out in air and in argon filled glove box, respectively. Wire samples were prepared by two-axial rolling deformation of IN and MA powders inside the Ti tube. Titanium as sheath material allows to use higher sintering temperatures, we used 700 °C and 800 °C for 30 min in Argon. Critical current densities (J_c) were measured at variable temperatures 4.2 K, 10 K, 15 K and 20 K in the external magnetic fields ranging to 15 T. Critical temperatures, upper critical fields and irreversibility fields of IN and MA with SiC and C additions are compared and discussed. The highest transport properties were observed for wires with MA SiC doped MgB₂ in the whole scale of temperatures 4.2–20 K. Upper critical field was rapidly enhanced in the case of carbon doped MA samples at 4.2 K. MA samples have shown decreased J_c values for higher temperatures (15 K, 20 K), in some case even worse than for the not doped reference IN sample. Carbon substitution and grain connectivity of analyzed samples are compared and discussed. Presented results show that for 20 K applications some new ways (additions) have to be found for increasing the J_c substantially.     

Synthesis,structures and near-infrared luminescence properties of Ho and Yb coordination complexes

Four Ln³⁺ coordination complexes with the formulas [Ln(p-toluylate)₂(Ac)(H₂O)]_n (Ln=Ho 1, Yb 2) and {[Ln₂(OOCCH₂CH₂COO)₃(H₂O)₄]·6H₂O}_n (Ln=Ho 3, Yb 4) were synthesized hydrothermally. Their structures were determined by single-crystal X-ray diffraction. Complexes 1 and 2 are isomorphic and form infinite 2D network structures comprising p-toluylate and acetate (Ac^–) moieties. Complexes 3 and 4 are also isomorphic and possess infinite 2D structures in which succinate acts as bridging ligands that are connected to a 3D hydrogen bonding network by O–H…O hydrogen bonds. Solid-state IR and UV-Vis-NIR spectra, excitation and emission spectra were determined for the four complexes at room temperature. Complexes 1 and 2 exhibit characteristic NIR emission bands of Ln³⁺ ions but these are shifted and split relative to the theoretical positions. This is also evident for their UV-Vis-NIR spectra. The influence of ligands on enhancing the NIR luminescence of Ln³⁺ ions in complexes is discussed.     

Energy, momentum, and force in classical electrodynamics: Application to negative-index media

The classical theory of electromagnetism is based on Maxwell's macroscopic equations, an energy postulate, a momentum postulate, and a generalized form of the Lorentz law of force. These seven postulates constitute the foundation of a complete and consistent theory, thus eliminating the need for physical models of polarization P and magnetization M — these being the distinguishing features of Maxwell's macroscopic equations. In the proposed formulation, P(r, t) and M(r, t) are arbitrary functions of space and time, their physical properties being embedded in the seven postulates of the theory. The postulates are self-consistent, comply with special relativity, and satisfy the laws of conservation of energy, linear momentum, and angular momentum. The Abraham momentum density p_EM(r,t) = E(r,t) × H(r,t) / c² emerges as the universal electromagnetic momentum that does not depend on whether the field is propagating or evanescent, and whether or not the host media are homogeneous, transparent, isotropic, linear, dispersive, magnetic, hysteretic, negative-index, etc. Any variation with time of the total electromagnetic momentum of a closed system results in a force exerted on the material media within the system in accordance with the generalized Lorentz law.     

Nonlinear optical absorption and fluorescence of phosphine-substituted bithiophenes in the violet-blue spectral region

The nonlinear optical absorptions of two 5,5′-bis(diphenylphosphino)-2,2′-bithiophene derivatives, Ph₂(X)P(C₄H₂S)₂P(X)Ph₂ (X = O, 1; S, 2), have been investigated by direct transmission measurement with both picosecond and nanosecond laser pulses from 420 nm to 480 nm. Saturated dichloromethane solutions of 1 and 2 exhibit strong nonlinear optical absorptions in this violet-blue spectral region with that of 2 being stronger at all wavelengths. In the picosecond regime, at 420 nm, the transmittance rapidly falls to 50% when the incident fluence is 0.22 J/cm² for 1 and 0.11 J/cm² for 2. Two-photon absorption appears to be the primary mechanism for this nonlinear absorption. The two-photon absorption coefficients β for 1 (2.1 cm/GW) and 2 (4.4 cm/GM) were obtained by fitting the measurement of transmittance as the function of incident beam intensity at 420 nm. These β values are comparable with some of the best results obtained for organic materials in the green, red and infrared spectral region. Both compounds also show fluorescence with an emission peak at 390 nm for 1 and 400 nm for 2. The fluorescence of 1 is considerably stronger than is that of 2. The combination of the wide band gap and strong fluorescence emission of 1 makes it a promising candidate as a host material for blue organic light emitting diodes.     

Intermolecular photoinduced electron-transfer processes between C60 and aniline derivatives in benzonitrile

The quenching behavior of the triplets of C₆₀ by various aniline derivatives (1a-d and 2a-e) was investigated by means of laser flash photolysis in benzonitrile at 293 K. Electron transfer process was proposed to be the main mechanism because of the direct detection of radical ions of aniline derivatives and C₆₀ in time-resolved transient absorption spectra. The quenching rate constants (k_q) of by different substrates determined at 740 nm approach or reach the diffusion-controlled limit. DFT method was employed to calculate the unknown oxidation potentials of substrates in solution. With these E_ox values, free energy changes (ΔG) were obtained through Rehm-Weller equation. Dependence of observed quenching rate constants on the free energy changes further indicates the photoinduced reactions between ³C₆₀^* and substrates proceed through an electron transfer mechanism. Obtained k_q values for the aniline derivatives are impacted obviously by ground-state configurations and the kinds substituents quantified by Hammett σ constant. Good correlation between log k_q and σ values conforms to the empirical Hammett equation. A more negative ρ value (−3.356) was gained for anilines (2a-e) than that of N,N-dimethylanilines (1a-d) (−1.382), which suggests a more susceptible reactivity for the former substrates. Charge density distribution of reaction center “N” originated from quantum calculation supports this suggestion. In addition, a relationship between quenching rate constants and solvent viscosity was gained from C₆₀/dimethyl-p-toluidine system in altered mixtures of acetonitrile and toluene.     

Luminescence and crystal-field fitting of two optical isomeric complexes of europium

FT-IR and Raman vibrational spectra and electronic emission spectra have been recorded for enantiomers of europium complexes with DBM: dibenzoylmethanate 1,2, and TTFA: 2-thenoyltrifluoroacetonate 3,4, employing the chiral ligands L_SS(+)- and L_RR(-)-4,5-pinene bipyridine. Contrary to the previously published X-ray data, where geometrical differences were stated to occur for particular enantiomers, the vibrational (and the emission) spectra of the individual optical isomers of a complex are not distinguishable. Using excitation into the Eu³⁺⁵D₂ multiplet term, the emission intensity is weak from ⁵D₁, whereas a complex structure is observed for the ⁵D₀→⁷F_J transitions. Features in the vibronic sidebands exhibit similar derived vibrational energies to those observed in the Raman spectra. Fittings of 25 4f⁶ crystal-field energy levels of 2 and 4 have been attempted with some approximations concerning the local Eu³⁺ environments. The ⁵D₀ emission lifetimes are monoexponential and are 0.5 (1,2) and 0.9 ms (3,4) at room temperature.     

TOWARDS DEEP AND SIMPLE UNDERSTANDING OF THE TRANSCENDENTAL EIGENPROBLEM OF STRUCTURAL VIBRATIONS

When using exact methods for undamped free vibration problems the generalized linear eigenvalue problem (K−ω²M) D=0 of approximate methods, e.g., finite elements, is replaced by the transcendental eigenvalue problem K (ω) D=0. Here ω is the circular frequency; D is the displacement amplitude vector; M and K are the mass and static stiffness matrices; and K (ω) is the dynamic stiffness matrix, with coefficients which include trigonometric and hyperbolic functions involving ω and mass because elements (for example, bars or beams) are analyzed exactly by solving their governing differential equations. The natural frequencies of this transcendental eigenvalue problem are generally found by the Wittrick-Williams algorithm which gives the number of natural frequencies below ω_t, a trial value of ω, as ∑J_m+s{K (ω_t)} wheres {} denotes the readily computed sign count property of K (ω) and the summation is over the clamped-clamped natural frequencies of all elements of the structure. Understanding the alternative solution forms of the transcendental eigenvalue problem is important both to accelerate convergence to natural frequencies, e.g., by plotting ∣K (ω)∣, and to improve the mode calculations, which lack the complete reliability of natural frequencies obtained by using the Wittrick-Williams algorithm. The three solution forms are: ∣K (ω)∣=0; D=0 with ∣K (ω)∣→∞; and ∣K (ω)∣≠0 with D≠0. The literature covers the first two forms thoroughly but the third form has been almost totally ignored. Therefore, it is now examined thoroughly, principally by analytical studies of simple bar structures and also by confirmatory numerical results for a rigidly jointed plane frame. Although structures are unlikely to have exactly the properties giving this form, it needs to be understood, particularly because ill-conditioning can occur for structures approximating those for which it occurs.     

Three-dimensional magnetic properties of soft magnetic composite materials

A three-dimensional (3-D) magnetic property measurement system, which can control the three components of the magnetic flux density B vector and measure the magnetic field strength H vector in a cubic sample of soft magnetic material, has been developed and calibrated. This paper studies the relationship between the B and H loci in 3-D space, and the power losses features of a soft magnetic composite when the B loci are controlled to be circles with increasing magnitudes and ellipses evolving from a straight line to circle in three orthogonal planes. It is found that the B and H loci lie in the same magnetization plane, but the H loci and power losses strongly depend on the orientation, position, and process of magnetization. On the other hand, the H vector evolves into a unique locus, and the power loss approaches a unique value, respectively, when the B vector evolves into the round locus with the same magnitude from either a series of circles or ellipses.     

Preparation and magnetic properties of Mn12 clusters with 4-cyanobenzenecarboxylate ligand, [Mn12O12(O2CC6H4-p-CN)16(H2O)4] and its tetraphenylphosphonium salts

The new Mn₁₂ magnetic clusters with 4-cyanobenzenecarboxylate ligand, [Mn₁₂O₁₂(O₂CC₆H₄-p-CN)₁₆(H₂O)₄] (1) and its singly (2) and doubly (3) reduced analogs as their tetraphenylphosphonium salts, have been synthesized and characterized by elemental analyses, Raman, ESI-MS spectra and magnetic measurements with a SQUID magnetometer. Unlike the known Mn₁₂ oxocarboxylate clusters, which are very soluble in CH₃CN or CH₂Cl₂, the complex 1 is not dissolved in organic solvents providing an indication for strong intermolecular interactions which lead to strong dipole–dipole interactions between clusters and affect the magnetic behavior. The one-electron and two-electron reduced clusters (2, 3) contain the bulk counterion and dissolve in CH₃CN. They show magnetic properties characteristic for anion Mn₁₂ single-molecule magnets.     

Synthesis, characterization and optical limiting effect of nickel complexes of multi-sulfur 1,2-dithiolene

Three nickel complexes with a new multi-sulfur 1,2-dithiolene ligand, (n-Bu₄N)[Ni(cddt)₂] 1, (Ph₄P)[Ni(cddt)₂] 2 and [Ni(cddt)₂] 3 (cddt=4a, 6, 7, 7a-5H-cyclopenta[b]-1,4-dithiin-2,3-dithiolate), have been synthesized and characterized by electrochemical measurements, IR, EPR and UV-Vis-NIR spectroscopies. The crystal structure of complex 2 is determined. Their optical nonlinearities are measured by the Z-scan technique with an 8 ns pulsed laser at 532 nm and all exhibit NLO absorptive abilities. Complexes 1 and 2 both exhibit effective self-defocusing performance (n₂=−5.81×10⁻¹⁰ esu for 1 and −4.51×10⁻¹⁰ esu for 2). The optical limiting (OL) effects were observed with nanosecond and picosecond laser pulses. The OL capability of complex 3 is superior to C₆₀ at the same experimental condition in ns measurements.     

Viscous mhd solutions with no transfer of energy through the spectrum

Exact space periodic solutions to the viscous magnetohydrodynamics equations with arbitrary vector periods p₁, p₂, p₃ are derived. A complete classification of the p_j-periodic MHD solutions with pairwise noninteracting Fourier modes is obtained. The solutions have no transfer of energy through the spectrum and are smooth for all values of the time variable t ≥ 0.     

Photoluminescent properties of heteroleptic cyclometalated platinum(II) complexes bearing 1,3-bis(3,4-dibutoxyphenyl)propane-1,3-dionate as an ancillary ligand

A new series of heteroleptic cyclometalated platinum(II) complexes Pt-1a-f was synthesized, employing 2-arylpyridine (or 1-arylisoquinoline) (HC^∧N-1) and 1,3-bis(3,4-dibutoxyphenyl)propane-1,3-dione (HO^∧O-1) for cyclometalation and as ancillary ligands, respectively, and photoluminescent properties were investigated. Focusing on red-shifted phosphorescence, C^∧N ligands containing π-extended aromatics and electron-rich heterocycles were examined. All obtained complexes exhibited photoluminescence at ambient temperature, and the emission maxima ranged from green (λ_PL=518 nm) to far red (λ_PL=708 nm). The large Stokes shifts of more than 100 nm and sub-microsecond or microsecond emission lifetimes revealed that these complexes are phosphorescent emissive. The quantum yield of Pt-1 ranged from 0.02 to 0.59 at ambient temperature and decreased as the emission maximum was red-shifted. In comparison with the reference platinum(II) complexes, Pt-2 bearing an aliphatic ancillary ligand, such as 2,2,6,6-tetramethylheptane-3,5-dionate (O^∧O-2), the ligand O^∧O-1 did not significantly affect the photoluminescence emission maxima, indicating that the energy gap between the singlet ground state and the triplet level was predominantly dependent on the C^∧N ligand.     

Whence the Minkowski momentum?

Electromagnetic waves carry the Abraham momentum, whose density is given by p_EM = S(r,t) / c². Here S(r,t) = E(r,t) × H(r,t) is the Poynting vector at point r in space and instant t in time, E and H are the local electromagnetic fields, and c is the speed of light in vacuum. The above statement is true irrespective of whether the waves reside in vacuum or within a ponderable medium, which medium may or may not be homogeneous, isotropic, transparent, linear, magnetic, etc. When a light pulse enters an absorbing medium, the force experienced by the medium is only partly due to the absorbed Abraham momentum. This absorbed momentum, of course, is manifested as Lorentz force (while the pulse is being extinguished within the absorber), but not all the Lorentz force experienced by the medium is attributable to the absorbed Abraham momentum. We consider an absorptive/reflective medium having the complex refractive index n₂ + iκ₂, submerged in a transparent dielectric of refractive index n₁, through which light must travel to reach the absorber/reflector. Depending on the impedance-mismatch between the two media, which mismatch is dependent on n₁, n₂, κ₂, either more or less light will be coupled into the absorber/reflector. The dependence of this impedance-mismatch on n₁ is entirely responsible for the appearance of the Minkowski momentum in certain radiation pressure experiments that involve submerged objects.