Antisymmetric Research Articles

Dynamical characteristics of the surface plasmon-polariton wave supported by a thin metal film

We study the energy and momentum of the surface plasmon-polariton (SPP) excited in a symmetric three-layer ‘insulator–metal–insulator’ structure, which is known to support the symmetric (S) mode (which, under certain conditions, possesses the negative group velocity) as well as the antisymmetric (AS) mode with always positive energy flow. The electric and magnetic field vectors are calculated via both the phenomenological and the microscopic approach; the latter involves the hydrodynamic model accounting for the quantum statistical effects for the electron gas in metal. Explicit representation for the energy and momentum constituents in the dielectric and in the metal film are obtained, and the wavenumber dependences of the energy and momentum contributions for the whole SPP are analyzed numerically. The various energy and momentum constituents are classified with respect to their origin (‘field’ or ‘material’), and the physical nature (orbital (canonical) and spin (Belinfante) momentum contributions). The pictures characteristic for the S and AS modes are systematically compared. The results can be useful for the studies and applications of the SPP-induced thin-film effects, in particular, for the charge and spin dynamics in thin-film plasmonic systems.

Study of electronic band structure in a 75-nm-wide n-GaAs/AlGaAs quantum well by surface acoustic waves

From measured magnetic field dependences of attenuation and velocity of surface acoustic waves (SAW), we calculated the real part of electron the conductivity in a 75-nm-wide n-GaAs/AlGaAs quantum well in magnetic fields of up to 18 T at frequencies of 30–300 MHz in the temperature range 20–500 mK. We observed slow magneto-oscillations of the conductivity depended on SAW intensity and occurred due to elastic intersubband scattering between the symmetric (S) and antisymmetric (AS) subbands formed by Coulomb repulsion between the electrons. Our theoretical description of the magneto-oscillations allowed estimating the quantum and the intersubband scattering times. The experimentally obtained subband splitting value 0.42 meV was close to the theoretically found 0.57 meV. Additionally, in tilted magnetic fields of 0.5–1.5, T we observed crossings of the Landau levels between the S and AS subbands. According to the developed theory, the crossings at the in-plane field below 1.5 T occur due to different dependences of cyclotron energies in the subbands on the in-plane field. Namely, the cyclotron energy in the S (AS) subband decreases (increases) with the rising of the in-plane field. Work supported by “BASIS,” NSF DMR-1644779 and DMR-1420541, GBMF4420, and State of Florida.]

Experimental investigation of vortex shedding past a circular cylinder in the high subcritical regime

Vortex shedding in the near wake of a circular cylinder is investigated using surface pressure measurements and two component Particle Image Velocimetry (2C PIV) for 1.49 × 105 ≤ Re ≤ 5 × 105. Space-time distribution of surface pressure shows that regular vortex shedding is interspersed with bursts of weakened activity. Its occurrence increases with an increase in Re. As a result, the rms of the lift coefficient decreases significantly in the subcritical regime with an increase in Re. Proper Orthogonal Decomposition (POD) of the surface pressure data and the 2C PIV data at the midspan of the cylinder shows that most of the energy is contained within the antisymmetric (AS) and symmetric (S) modes. The AS mode is responsible for the regular von Karman vortex shedding, while the S mode is related to intermittent expansion and contraction of the vortex formation region. The energy of the AS mode decreases at a faster rate as compared to that of the S mode with an increase in Re. The S mode is the most dominant mode beyond Re ∼ 3.2 × 105. In the critical regime, the POD modes are modified due to the presence of the intermittent Laminar Separation Bubble (LSB). 2C PIV at the midspan of the cylinder reveals that the weakening of the AS mode is accompanied by an increase in the formation length, Lf. (Lf/d) increases from 1.4 in the low subcritical to 2.0 in the high subcritical regime, where d is the diameter of the cylinder. The weakening of the AS mode and increase in Lf/d collectively lead to a significant decrease in fluctuating lift with an increase in Re. 2C PIV of a spanwise section shows that weakening of vortex shedding is nearly uniform along the span of the cylinder.

Electronic band structure in n-type GaAs/AlGaAs wide quantum wells in tilted magnetic field

Oscillations of the real component of AC conductivity in a magnetic field were measured in the n-AlGaAs/GaAs structure with a wide (75 nm) quantum well by contactless acoustic methods at mK. In a wide quantum well, the electronic band structure is associated with the two-subband electron spectrum, namely the symmetric (S) and antisymmetric (AS) subbands formed due to electrostatic repulsion of electrons. A change of the oscillations amplitude in tilted magnetic field observed in the experiments occurs due to crossings of Landau levels of different subbands (S and AS) at the Fermi level. The theory developed in this work shows that these crossings are caused by the difference in the cyclotron energies in the S and AS subbands induced by the in-plane magnetic field.

Magnetic modulation of surface plasmon modes in magnetoplasmonic metal-insulator-metal cavities

The magnetic modulation of the surface plasmon-polariton (SPP) wavevector is experimentally and theoretically studied for the plasmonic modes excited in metal-insulator-metal (MIM) magnetoplasmonic cavities. For this purpose, Ag/SiO₂/Ag multilayers with different SiO₂ layer thickness in which a thin Co layer is positioned near the top Ag/SiO₂ interface, near the bottom SiO₂/Ag one, or near both of them, are studied. The magnetoplasmonic MIM cavities present symmetric (SM) and antisymmetric (AM) plasmonic modes, of different wavevector and electromagnetic field profiles inside the MIM cavity. We show that the magnetic SPP wavevector modulation strongly depends on which mode is considered, the cavity thickness, and the number and specific location of Co layers within the structure. With only one ferromagnetic layer, a net modulation is obtained, of higher magnitude as we reduce the SiO₂ layer thickness. The introduction of a second Co layer in the structure reduces the modulation due to the non-reciprocal character of SPP modes under an applied magnetic field. Moreover, we demonstrate that the non-reciprocal nature of the SPP modulation can be experimentally visualized in the magnetic hysteresis loops under plasmon excitation conditions by using two Co layers with different magnetization switching fields.

Phase diagrams of SU(N) gauge theories with fermions in various representations

We minimize the one-loop effective potential for SU(N) gauge theories including fermions with finite mass in the fundamental (F), adjoint (Adj), symmetric (S), and antisymmetric (AS) representations. We calculate the phase diagram on S1 ? 3 as a function of the length of the compact dimension, ?, and the fermion mass, m, for various N and Nf. We consider the effect of periodic boundary conditions [PBC(+)] on fermions as well as antiperiodic boundary conditions [ABC(-)]. With standard ABC(-) on fermions only the deconfined phase is found at one-loop for all representations considered. However, the use of PBC(+) produces a rich phase structure. These phases are distinguished by the eigenvalues of the Polyakov loop P. In the case of fundamental representation fermions [QCD(F,+)], a phase in which Re?Tr P is minimized (and negative) is favoured for all values of m?. For N odd charge conjugation () symmetry is spontaneously broken in this phase due to (1/N) effects. Minimization of the effective potential for QCD(AS/S,+) results in a phase where |Im?Tr P| is maximized, resulting in -breaking for all N and all values of m?, however, the partition function is the same up to (1/N) corrections as when ABC are applied. Therefore, regarding orientifold planar equivalence, we argue that in the one-loop approximation -breaking in QCD(AS/S,+) resulting from the application of PBC on fermions does not invalidate the large N equivalence with QCD(Adj,-). Similarly, with respect to orbifold planar equivalence, breaking of Z2 interchange symmetry resulting from application of PBC to bifundamental (BF) representation fermions does not invalidate equivalence with QCD(Adj,-) in the one-loop perturbative limit because the partition functions of QCD(BF,-) and QCD(BF,+) are the same. Of particular interest as well is the case of adjoint fermions where for 1$>Nf > 1 Majorana flavour confinement is obtained for sufficiently small m?, and deconfinement for sufficiently large m?. For N ? 3 these two phases are separated by one or more additional phases, some of which can be characterized as partially-confining phases.

Field induced crossover in antiferromagnetic spin-frustrated clusters: Influence of static and dynamic structural deformations

We propose a theoretical study of the magnetic behavior of spin frustrated trinuclear clusters in the region of the field induced crossover of the levels which are crucial for the description of the static magnetization and dynamic behavior in a sweeping field. The emphasis is made on a competitive role of the antisymmetric (AS) exchange and static structural distortions of the metal center network as well as on the consequences of the dynamic pseudo Jahn–Teller (JT) instability that is closely related to spin frustration. The structural conformations are shown to be controlled by the magnetic field in the anticrossing region (magnetoelastic coupling). We employ the three-spin model for the cluster anion present in K 6 [ V 15 IV As 6 O 42 ( H 2 O ) ] · 8 H 2 O (V 15 cluster) and analyze the role of different components of AS exchange in the shape of the magnetic susceptibility vs field. Both types of deformations (static and dynamic) are shown to be competitive to the AS exchange and tend to reduce the magnetic anisotropy caused by the AS exchange.

Crossover of the magnetic sublevels in spin frustrated clusters: The role of static and dynamic deformations

We model the magnetic behavior of spin frustrated trinuclear clusters in the region of field induced crossover of the levels. The emphasis is made on a competitive role of the antisymmetric (AS) exchange and static structural distortions as well as on the consequences of the dynamic pseudo-Jahn–Teller (JT) instability. We employ the three-spin model for the cluster anion present in K 6 [ V 15 IV As 6 O 42 ( H 2 O ) ] · 8 H 2 O (V 15 cluster) and analyze the role of different components of AS in the half step magnetization. Both types of deformations (static and dynamic) are shown to be competitive with the AS exchange and tend to reduce the magnetic anisotropy caused by AS.

Nanoscopic Molecular Cluster V15: High-Field Epr and Magnetization at Ultra-Low Temperatures

In this paper we give a short overview of our efforts in the understanding of the magnetic properties of the fascinating nanoscopic cluster K6[VIV15As6O42(H2O)]·8H2O (hereafter V15) exhibiting layers of magnetization. We analyze EPR and adiabatic magnetization of the V15 cluster with a triangular VIV3 array causing spin frustration. A model for V15 includes isotropic and antisymmetric (AS) exchange interactions in the general form compatible with the trigonal symmetry. Orientation of the AS vector (but not only its absolute value) is shown to play an important physical role in spin-frustrated systems. We were able to reach perfect fit to the experimental data on the stepwise dependence of magnetization vs. field at ultra-low temperatures. Furthermore, it was possible for the first time to estimate precisely two components of the AS vector coupling constant, namely, in-plane component and the perpendicular part. We show that only intramultiplet transitions in EPR are allowed when the vector of AS exchange is normal to the plane of vanadium triangle, meanwhile the in-plane part of AS exchange gives rise to a series of weak intermultiplet transitions. Experimental data on high-frequency EPR of V15 at low temperatures are discussed. The spin-vibronic effects in trimeric spin frustrated clusters are also studied and an important role of the interplay between the AS exchange and Jahn-Teller interaction is revealed. The results clarify the concept of spin-frustration in view of its magnetic and spectroscopic manifestations in metal clusters.

Rotational parity and separation of water molecules into spin isomers

A theoretical explanation is proposed for the effect of variations in concentration of water molecule spin isomers in the gas phase during the interaction of molecules with a solid adsorbent surface. The explanation is based on antisymmetric (AS) correlation between proton spin moments and molecule rotation. A new AS correlation occurs during the interaction of the molecule with a dc electric field near the surface. Due to the new (external) AS correlation, ortho-and parawater molecules are formed; separation into spin modifications occurs over degenerate states of each rotational level of the molecule. Water molecule separation into spin modifications at the previous (internal) AS correlation occurs over rotational levels of molecules. The ratio of ortho-and parawater concentrations in the gas phase at the external AS correlation is compared with experimental data on chromatographic separation of water spin isomers. Quantitative agreement is observed between the calculated ratio and the ratio measured for water molecules at the final separation stage.

Antisymmetric exchange and pseudo Jahn–Teller instability in spin-frustrated metal clusters

In this article, we analyze the interplay between the antisymmetric (AS) exchange interaction and Jahn–Teller (JT) vibronic coupling in spin-frustrated systems with triangular units. AS exchange in these systems creates a strong first order magnetic anisotropy related to the orbitally degenerate frustrated ground state that is analyzed for the unique structure of the cluster anion present in K 6 [ V 15 IV As 6 O 42 ( H 2 O ) ] · 8 H 2 O (V 15 cluster) exhibiting layers of different magnetization. Spin-frustration inherently related to the orbital degeneracy creates a structural instability that is shown to be competitive to the AS exchange. The vibronic pseudo JT coupling arising from the modulation of the exchange interaction by the double degenerate molecular vibrations is shown to reduce AS exchange giving rise to a restoration of magnetization quenched by AS exchange. This leads to an essential reduction of the magnetic anisotropy in spin-frustrated triangular clusters so that in the limit of strong JT coupling the isotropic exchange model becomes adequate.

Static Magnetization of V15 Cluster at Ultra-Low Temperatures: Precise Estimation of Antisymmetric Exchange

In this article, the low-temperature static (adiabatic) magnetization data of the nanoscopic V15 cluster present in K6[VIV15As6O42(H2O)] x 8H2O is analyzed. The cluster anion, which attracted much attention in the past, contains a triangular VIV3 array causing frustration as a function of applied field and temperature. In the analysis, a three-spin (S = 1/2) model of V15 was employed that includes isotropic antiferromagnetic exchange interaction and antisymmetric (AS) exchange in the most general form compatible with the trigonal symmetry of the system. It was shown that, along with the absolute value of AS exchange, the orientation of the AS vector plays a significant physical role in spin-frustrated systems. In this context, the role of the different components of the AS in the low-temperature magnetic behavior of V15 was analyzed, and we were able to reach a perfect fit to the experimental data on the staircaselike dependence of magnetization versus field in the whole temperature range including extremely low temperature. Furthermore, it was possible for the first time to precisely estimate the two components of the AS vector coupling constant in a triangular unit, namely, the effective in-plane component, Dperpendicular, and the perpendicular part, Dn.

Low temperature EPR spectra of the mesoscopic cluster V15: The role of antisymmetric exchange

The low temperature EPR spectra of the unique nanometer-scale molecular magnet V(15) are analyzed within the three-spin model preserving trigonal symmetry. The Hamiltonian includes isotropic and antisymmetric (AS) exchange interactions introduced by Dzyaloshinsky (Zh. Eksp. Teor. Fiz. 32, 1547 (1957) [Sov. Phys. JETP 5, 1259 (1957)]) and [Moria Phys. Rev. 120, 91 (1960)]. With the aid of pseudoangular momentum representation the exact selection rules for the EPR transitions are deduced. AS exchange in the frustrated triangular system gives rise to a first order zero-field splitting of two low lying spin doublets and to a second order splitting of the excited quadruplet. This leads to a peculiar series of strong intramultiplet transitions and weak intermultiplet transitions. We show that the intramultiplet transitions are allowed only when the vector of the AS exchange is normal to the plane of vanadium triangle, but the series of weak intermultiplet transitions are a consequence of the in-plane part of the AS exchange. We have revealed a special temperature dependence of the EPR pattern with a peculiar shape of the full spectrum. Experimental data on high-frequency EPR of V15 at ultralow temperature are discussed.

High-field magnetization of V 15 cluster at ultra-low temperatures: Importance of antisymmetric exchange and its precise estimation

The low temperature adiabatic magnetization of the nanoscopic V 15 cluster exhibiting a triangular spin-frustrated V 3 IV array is analyzed within the model that includes isotropic exchange interactions and antisymmetric (AS) exchange. Along with the absolute value of AS exchange the orientation of the AS vector is shown to play an important physical role in the spin-frustrated systems. We were able to reach a perfect fit to the experimental data on the stepwise magnetization vs. field in the whole temperature range and for the first time to estimate precisely two components of the AS vector, namely, in-plane and the perpendicular parts.

Spin–orbit coupling in the double exchange model 2. Comparison of the antisymmetric double exchange with the Dzialoshinsky–Moriya antisymmetric exchange, spin canting and ZFS

The Dzialoshinsky–Moriya (D–M) antisymmetric exchange interaction is considered and compared with antisymmetric (AS) double exchange in the mixed-valence [Fe(II)Fe(III)] clusters. It is shown that the antisymmetric double exchange interaction ( H 1 X = i K X [ ( S ^ aX - S ^ bX ) T ^ ab + T ^ ab ( S ^ bX - S ^ aX ) ] ) is stronger than the D–M exchange interaction ( H DM X = G X [ S → a × S → b ] X ) in the valence-delocalized [Fe 2.5+ Fe 2.5+] cluster with strong double exchange, K X / G X = −5 B/2 J, K X ≫ G X . The mixing of the ground valence-delocalized state Φ - 0 ( S = 9 / 2 , M ) with the first excited Φ - 0 ( 7 / 2 , M ′ ) state ( S′ = S − 1) of the same parity depends on both the AS double exchange and D–M exchange. In the valence-delocalized cluster, the admixture of the excited double exchange states to the ground valence-delocalized state Φ - 0 ( S = 9 / 2 ) by the AS double exchange and D–M exchange results in non-zero expectation values of the local spins 〈 s aY 〉 = −〈 s bY 〉 in Y-direction, that leads to the canting of the spins in the plane (YZ) perpendicular to the direction of the vectors K X of the antisymmetric double exchange and G X of the D–M exchange. In the valence-delocalized S gr = (9/2) deloc state, the deviations of spins from the parallel alignment, anisotropy of hyperfine (internal) fields on the Fe nuclei, anisotropy of the hyperfine constants depend on the parameters K X , G X , B and J. The spin canting induced by the AS double exchange and D–M exchange in the valence-delocalized [Fe 2.5+Fe 2.5+] cluster ( S gr = (9/2) deloc) is larger than the spin canting induced by the D–M exchange in the ferromagnetic localized [Fe(II)Fe(III)] loc cluster ( S gr = (9/2) loc). The mixing of the double exchange levels results in the antisymmetric double exchange and D–M exchange contributions to the ZFS parameters of the ground valence-delocalized state S gr = (9/2) deloc.

Antisymmetric double exchange in mixed-valence clusters

Abstract Taking into account the spin–orbit interaction in the double exchange (DE) model results in an antisymmetric (AS) DE interaction and anisotropic DE coupling. In the mixed-valence (MV) dimers, the effective AS DE Hamiltonian H ASDE =2i K → ab T ab ( S → b − S → a ) describes the vector type spin-transfer interaction ( K → ab =− K → ba , T ab is the isotropic transfer operator). The AS DE coupling mixes the DE terms and contributes to the cluster ZFS parameters. In the MV trimers, AS DE results in the linear AS DE splittings of the 2S+1 E DE terms, strong magnetic anisotropy and anisotropy of the EPR spectra.

Axial baryon number nonconserving antisymmetric tensor four-quark effective interaction

We discuss the phenomenological consequences of the ${U}_{A}(1)$ symmetry-breaking two-flavor four-fermion antisymmetric (AS) Lorentz tensor interaction Lagrangians. We use the recently developed methods that respect the ``duality'' symmetry of this interaction. Starting from the Fierz transform of the two-flavor 't Hooft interaction (a four-fermion Lagrangian with AS tensor interaction terms augmented by a Nambu--Jona-Lasinio- type Lorentz scalar interaction responsible for dynamical symmetry breaking and quark mass generation), we find the following. (1) Four antisymmetric tensor and four antisymmetric pseudotensor bosons exist which satisfy a mass relation previously derived for scalar and pseudoscalar mesons from the 't Hooft interaction. (2) Antisymmetric tensor bosons mix with vector bosons via one-fermion-loop effective couplings so that both kinds of bosons have their masses shifted and the fermions (quarks) acquire anomalous magnetic moment form factors that explicitly violate chiral symmetry. (3) The mixing of massive antisymmetric tensor fields with vector fields leads to two sets of spin-one states. The second set of spin-one mesons is heavy and has not been observed. Moreover at least one member of this second set is tachyonic, under standard assumptions about the source and strength of the antisymmetric tensor interaction. The tachyonic state also shows up as a pole in the spacelike region of the EM form factors. (4) The axial-vector fields' mixing with antisymmetric tensor bosons is proportional to the (small) isospin-breaking up-down quark mass difference, so the mixing-induced mass shift of axial vector mesons is negligible. (5) The antisymmetric tensor version of the Veneziano-Witten ${U}_{A}(1)$ symmetry-breaking interaction does not lead to tachyons, or any antisymmetric tensor field propagation to leading order in ${N}_{C}.$

EPR spectra of the double triangular polyoxovanadates with exchange and electron transfer effects: Symmetry breaking and effective motional averaging

The interplay of isotropic exchange, antisymmetric (AS) exchange, and electron delocalization has been theoretically investigated for a system comprising two triangles, one with three localized d1 spins, which gives rise to spin frustration effects, and the other with one d1 center delocalized on the three sites. In the localized limit the AS exchange is partially reduced by the low symmetry components of an isotropic exchange (inter-triangle interaction) and splits the spin triplets only in the second order, contrary to what is found for a single triangular system where splitting of the spin doublet levels occurs in the first order. Zero-field splitting parameters depend on both AS exchange parameters and low symmetry components of the isotropic exchange. The EPR spectrum consists of intratriplet (Heisenberg type) and intertriplet (non-Heisenberg type) lines. AS exchange also induces singlet-triplet transitions. The EPR spectra of powder samples are generated for a domain of key parameters. Two different situations occur depending on the symmetry of the electronic states when the electron delocalization is taken into account. The orbital doublets of the localized system indicate a complete averaging of the exchange interactions, which results in effective enhancement of AS exchange. Unlike triplets, the orbital singlets are unaffected by a transfer process, developing only second-order AS exchange. Coexistence of localized and delocalized states is expected to be an intrinsic feature of exchange systems with partial delocalization. The relevance of these effects to the magnetic properties of exchange clusters is briefly discussed.