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.     

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.     

A theoretical and numerical consideration of the longitudinal and transverse relaxations in the rotating frame

We previously derived a simple equation for solving time-dependent Bloch equations by a matrix operation. The purpose of this study was to present a theoretical and numerical consideration of the longitudinal (R_1ρ = 1/T_1ρ) and transverse relaxation rates in the rotating frame (R_2ρ = 1/T_2ρ), based on this method. First, we derived an equation describing the time evolution of the magnetization vector (M(t)) by expanding the matrix exponential into the eigenvalues and the corresponding eigenvectors using diagonalization. Second, we obtained the longitudinal magnetization vector in the rotating frame (M_1ρ(t)) by taking the inner product of M(t) and the eigenvector with the smallest eigenvalue in modulus, and then we obtained the transverse magnetization vector in the rotating frame (M_2ρ(t)) by subtracting M_1ρ(t) from M(t). For comparison, we also computed the spin-locked magnetization vector. We derived the exact solutions for R_1ρ and R_2ρ from the eigenvalues, and compared them with those obtained numerically from M_1ρ(t) and M_2ρ(t), respectively. There was excellent agreement between them. From the exact solutions for R_1ρ and R_2ρ, R_2ρ was found to be given by R_2ρ = (2R₂ + R₁)/2 − R_1ρ/2, where R₁ and R₂ denote the conventional longitudinal and transverse relaxation rates, respectively. We also derived M_1ρ(t) and M_2ρ(t) for bulk water protons, in which the effect of chemical exchange was taken into account using a 2-pool chemical exchange model, and we compared the R_1ρ and R_2ρ values obtained from the eigenvalues and those obtained numerically from M_1ρ(t) and M_2ρ(t). There was also excellent agreement between them. In conclusion, this study will be useful for better understanding of the longitudinal and transverse relaxations in the rotating frame and for analyzing the contrast mechanisms in T_1ρ- and T_2ρ-weighted MRI.     

States of cobalt fluoride in a strong magnetic field

The behavior of the magnetic subsystem of cobalt fluoride is investigated in a strong magnetic field oriented in an arbitrary direction in space. In the case where the magnetic field is out of the planes passing through the easiest magnetization axis A and the axis [100] ‖ X or through the easiest magnetization axis A and the axis [010] ‖ Y, it follows from the derived system of equations that the antiferromagnetic vector l does not change direction to be align with the basal plane, provided the magnetic field has a nonzero component along the A axis. It is demonstrated that the antiferromagnetic vector l becomes parallel to the basal plane only when the magnetic field is perpendicular to the A axis. The case of the magnetic field directed parallel to the [110] axis is examined thoroughly. The critical value of the magnetic field is determined at which the antiferromagnetic vector l becomes parallel to the basal plane and perpendicular to the external magnetic field H for H _⊥ → ∞.     

Photophysical characteristics of 4,4′-bis(N-carbazolyl)tolan derivatives and their application in organic light emitting diodes

4,4′-bis(N-carbazolyl)tolan (BCT) and 4,4′-bis[N-(3,6-di-t-butyl)carbazolyl]tolan (BCT-t-Bu) were synthesized as π-expanded analogs of 4,4′-bis(N-carbazolyl)biphenyl. Their photophysical characteristics both in solution and films were thoroughly investigated. Interestingly, the phosphorescence spectrum of BCT was significantly medium-dependent, and the emission maximum was red-shifted by 131 nm from 489 nm in solution at 77 K to 620 nm in a deposited film at 5 K, suggesting the presence of strong intermolecular interactions in the film. BCT and BCT-t-Bu were found to be useful as host materials for fluorescence-based organic light emitting diodes (OLEDs). However, their low triplet energy levels in films negated their potential to act as hosts in phosphorescence-based OLEDs.     

Magnetic anisotropy and electronic structure of iron films on W(1 1 0) by spin-polarized two-electron spectroscopy

Low-energy spin-polarized two-electron spectroscopy was applied to study the spin-dependent electronic structure of 3 ML and 50 ML epitaxial iron films grown on single crystal W(1 1 0). Such films are known to show an in-plane rotation of the easy magnetization axis between thicknesses [M. Donath, Journal of Physics: Condensed Matter 11 (48) (1999) 9421; D. Sander, Journal of Physics: Condensed Matter (20) (2004) R603, O. Fruchart, J.P. Nozieres, D. Givord, Journal of Magnetism and Magnetic Materials 207 (1999) 158, H.J. Elmers, U. Gradmann, Applied Physics A: Materials Science & Processing 51 (3) (1990) 255]. Momentum distributions of correlated electron pairs I(k₁, k₂) excited from the films by 25 eV primary electrons were measured for two opposite polarizations of the incident beam. Energy and momentum conservation laws in the electron scattering events allow the extraction of information on the spin-dependent Bloch spectral density function of the valence electrons in iron films. The observed difference in the electronic structure of these two films is most likely due to the different crystal structures of the films.     

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.     

Nonlinear dynamics of domain walls with a vortex internal structure in magnetouniaxial films with planar anisotropy

The nonlinear and generally unsteady dynamics of domain walls with a vortex internal structure in a constant magnetic field H is investigated on the basis of the numerical solution of the Landau-Lifshitz equation for a 2D distribution of magnetization M in magnetic films with planar anisotropy taking into account exactly the main interaction, including the dipole-dipole interaction. It is shown that in addition to field H _c (bifurcation field) above which the motion of a wall becomes unsteady and its internal structure experiences global dynamic changes, there exists a field H₀ separating two steady motions of the wall with different structures. The data clarifying the physical origin of the nonlinear dynamic rearrangement of the wall structure are presented. New rearrangement mechanisms associated with the generation and attenuation of vortices as well as their tunneling through the central surface of the wall are established. The existence of subperiod oscillations of the wall velocity in a static field in addition to the oscillations associated with the precession of M around the easy magnetization axis is predicted. The period T of dynamic variations of the wall structure is studied, and an empirical formula is proposed for describing the singular behavior of the T(H) dependence near H=H _Hc with the critical index depending on the film parameters. The bifurcation process is studied, and a nonlinear dependence of the critical field H _c on the film thickness and the saturation magnetization is established. The possibility of direct experimental investigation of the dynamic rearrangement of the internal structure of the wall is indicated.     

Self-consistent treatment of spin and magnetization dynamic effect in spin transfer switching

The effect of itinerant spin moment (m) dynamic in spin transfer switching has been ignored in most previous theoretical studies of the magnetization (M) dynamics. Thus in this paper, we proposed a more refined micromagnetic model of spin transfer switching that takes into account in a self-consistent manner of the coupled m and M dynamics. The numerical results obtained from this model further shed insight on the switching profiles of m and M, both of which show particular sensitivity to parameters such as the anisotropy field, the spin torque field, and the initial deviation between m and M.     

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.     

An explicit derivation of a relation between magnetization M and saturation magnetization Ms

An explicit relationship between a magnetization vector M and its saturation magnetization M_s is derived using the definition of M along with assumptions of the continuum exchange theory. The obtained expression is found to be an extension of the commonly used fixed-length constraint and represents the continuous analog of it for the elementary moment per unit volume. The derivation of this relation is carried out in detail and important potential implications relating to equations for M are also highlighted.     

A new quasi-one-dimensional molecular solid based on Ni(mnt)2 anion: Crystal structure and spin-gap transition

A new molecular solid, [1-(4′-bromo-2′-fluorobenzyl)-4-dimetylaminopyridinium]-bis(maleonitriledithiolato)nickel(III), (BrFBzPyN(CH₃)₂(Ni(mnt)₂)(1), has been prepared and characterized by elemental analyses, IR, ESI-MS spectra, single crystal X-ray diffraction and magnetic measurements. Compound 1 crystallizes in the orthorhombic space group Pnma, a=20.579(4) Å, b=7.078(1) Å, c=17.942(4) Å, α=β=γ=90°, V=2613.3(9) Å³, Z=4. The Ni(III) ions of 1 form a quasi-one-dimensional Zigzag magnetic chain within a Ni(mnt)₂⁻ column through Ni?S, S?S, Ni?Ni, or π?π interactions with an Ni?Ni distance of 4.227 Å. Magnetic susceptibility measurements in the temperature range 2-300 K show that 1 exhibits a spin-gap transition around 200 K, and antiferromagnetic interaction in the high-temperature phase (HT) and spin gap in the low-temperature phase (LT). The transition for 1 is second-order phase transition as determined by DSC analyses.     

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.     

Photoconductivity of thin organic films

Thin organic films were deposited on silicon oxide surfaces with golden interdigitated electrodes (interelectrode gap was 2 μm), and the film resistivities were measured in dark and under white light illumination. The compounds selected for the measurements include molecules widely used in solar cell applications, such as polythiophene (PHT), fullerene (C₆₀), pyrelene tetracarboxylic diimide (PTCDI) and copper phthalocyanine (CuPc), as well as molecules potentially interesting for photovoltaic applications, e.g. porphyrin-fullerene dyads. The films were deposited using thermal evaporation (e.g. for C₆₀ and CuPc films), spin coating for PHT, and Langmuir-Schaeffer for the layer-by-layer deposition of porphyrin-fullerene dyads. The most conducting materials in the series are films of PHT and CuPc with resistivities 1.2 × 10³ Ω m and 3 × 10⁴ Ω m, respectively. Under light illumination resistivity of all films decreases, with the strongest light effect observed for PTCDI, for which resistivity decreases by 100 times, from 3.2 × 10⁸ Ω m in dark to 3.1 × 10⁶ Ω m under the light.     

The magnetic structure of the compound Ho5Sb3

We have investigated the magnetic behavior of Ho₅Sb₃ compound (Mn₅Si₃-type, hexagonal; a=0.8865(1) nm, c=0.6232(1) nm, as derived from X-ray Guinier powder pattern) by using the techniques of magnetization, electrical resistivity, heat capacity and neutron diffraction. We find that Ho₅Sb₃ exhibits a ferrimagnetic type (Ferrimagnet I) ordering below 60 K with propagation vectors K₀=[0, 0, 1] and K₁=[±K_x, 0, 0]. Below 40 K, the thermal variation of magnetic reflections and the appearance of an additional magnetic component with propagation vector K₂=[0, 1/2, 0] show the onset of an antiferromagnetic type of ordering in the magnetic structure; which evolves into yet another ferrimagnetic structure (Ferrimagnet II) as the temperature is lowered down to 2 K. The magnetic moments of the Ho atoms at the (4d) and (6g) sites with magnitudes of nearly 7.4 and 6.3 μ_B at 2 K, respectively, are inclined approximately at 70° to the c-axis.     

Reversible photomagnetism in a cobalt layered compound coupled with photochromic diarylethene

Photomagnetism is one of the most attractive topics in recent research on molecular solids. In order to produce a photo-controllable magnet, we have synthesized a novel organic-inorganic hybrid system coupled with a photochromic diarylethene anion, 2,2′-dimethyl-3,3′-(perfluorocyclopentene-1,2-diyl)bis(benzo[b]thiophene-6-sulfonate) (1a) and cobalt LDHs (layered double hydroxides). Based on the elemental analysis, the title compound, which was synthesized by the anion exchange reaction between Co₂(OH)₃(CH₃COO)·H₂O (2) and 1a, has the chemical composition, Co₄(OH)₇(1a)_0.5·3H₂O (3). Powder X-ray diffraction analysis revealed the interlayer distance of c=27.8 Å. The magnetic susceptibility measurements elucidated the ferromagnetic intra- and inter-layer interactions and the Curie temperature of T_c=9 K. By UV irradiation of 313 nm, 3 shows the photo-isomerization of diarylethene anion from the open form to the closed one in solid state, which leads to the decreases in the coercive field and the remnant magnetization. Furthermore, the photo-excited state is returned to the initial state (open form) almost reversibly by visible irradiation of 550 nm.     

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.     

Second-order optical nonlinearities from χ gratings induced by holographic all-optical poling

The paper presents the second-order optical nonlinearities from χ⁽²⁾ gratings induced by holographic all-optical poling for azobenzene polymer. Second harmonic (SH) signal along the directions with two different vectors was measured. One is strong SH signal diffracted in the same direction as 2ω writing beam with wave vector k_2ω and the other is weak SH signal diffracted in the direction of wave vector of 4k_ω - k_2ω + Δk where k_ω is wave vector of ω beam and Δk is the wave vector mismatch whose vector is parallel to k_ω. The latter signal was used as a tool to monitor the formation of holographic χ⁽²⁾ gratings in real-time because it has off-axis wave vector different from both k_ω and k_2ω. The increase of 2ω intensity on poling process led to the large increase of second-order optical nonlinearity. The real-time monitoring showed that it also gave the large relaxation of second-order optical nonlinearity on poling process. The increase of 2ω (532 nm) energy enhanced the increase of local heating, which led to easier alignment of azobenzene chromophore and also larger relaxation of aligned chromophore.     

Relative power loss of misalignment based on electro-optical printed circuit board

In this paper, the power loss values between 45° total internal reflecting waveguide mirror (TIRWM) and the polymer optical waveguide layer are obtained by vector finite element method. There are some misalignments during an actual fabrication of electro-optical printed circuit board (EOPCB). And, b, a, c correspond to the error value of alignment in the x-axis, y-axis and z-axis direction, respectively. Another, four effective refractive indices of the 45° TIRWM and polymer optical waveguide layer are calculated, separately. And, n_eff1 = 1.425211 is uniquely chosen. Next, these relative power errors Δ are calculated, when a, b, c separately change. Moreover, these error values are plotted into some curved surface figures. By these figures, it is easy to find the relationship between a, b, c and Δ. Furthermore, it is beneficial for us to avoid the region of larger power loss during an actual fabrication of EOPCB.     

Phase diagram of antiferromagnetic cobalt fluoride

The H-T phase diagram of antiferromagnetic cobalt fluoride in an external magnetic field H perpendicular to the easy magnetization axis A is completed and used to construct a phase diagram in the variables H _z and H _y . In this diagram, the lines corresponding to second-order phase transitions (between an angular phase and a phase with antiferromagnetic vector I ⊥ A) begin and end in fields of a spin-flip transition (i.e., in an exchange field). A peculiarity of these lines of phase transitions is that each of them has two tricritical points at which this line of second-order phase transitions transforms into a line of first-order phase transitions. A critical angle between the direction of the external magnetic field and the basal plane within which the first-order phase transition takes place is determined.