Dipolar interactions and origin of spin ice in ising pyrochlore magnets

Recent experiments suggest that the Ising pyrochlore magnets Ho2Ti2O7 and Dy2Ti2O7 display qualitative properties of the nearest-neighbor "spin ice" model. We discuss the dipolar energy scale present in both these materials and discuss how spin-ice behavior can occur despite the presence of long-range dipolar interactions. We present results of numerical simulations and a mean field analysis of Ising pyrochlore systems. Based on our quantitative theory, we suggest that the spin-ice behavior in these systems is due to long-range dipolar interactions, and that the nearest-neighbor exchange in Dy2Ti2O7 is antiferromagnetic.     

Boundary Stabilization and Disturbance Rejection for Time Fractional Order Diffusion–Wave Equations

This paper considers boundary control of time fractional order diffusion–wave equation. Both boundary stabilization and disturbance rejection are considered. This paper, for the first time, has confirmed, via hybrid symbolic and numerical simulation studies, that the existing two schemes for boundary stabilization and disturbance rejection for (integer order) wave/beam equations are still valid for time fractional order diffusion–wave equations. The problem definition, the hybrid symbolic and numerical simulation techniques, outlines of the methods for boundary stabilization and disturbance rejection are presented together with extensive simulation results. Different dynamic behaviors are revealed for different fractional orders which may stimulate new future research opportunities.     

Three-coordinate NiII: tracing the origin of an unusual, facile Si-C(sp3) bond cleavage in [(tBu2PCH2SiMe2)2N]Ni+

All attempts to synthesize (PNP)Ni(OTf) form instead ((t)Bu(2)PCH(2)SiMe(2)NSiMe(2)OTf)Ni(CH(2)P(t)Bu(2)). Abstraction of F(-) from (PNP)NiF by even a catalytic amount of BF(3) causes rearrangement of the (transient) (PNP)Ni(+) to analogous ring-opened [((t)Bu(2)PCH(2)SiMe(2)NSiMe(2)F)]Ni(CH(2)P(t)Bu(2)). Abstraction of Cl(-) from (PNP)NiCl with NaB(C(6)H(3)(CF(3))(2))(4) in CH(2)Cl(2) or C(6)H(5)F gives (PNP)NiB(C(6)H(3)(CF(3))(2))(4), the key intermediate in these reactions is (PNP)Ni(+), [(PNP)Ni](+), in which one Si-C bond (together with N and two P) donates to Ni. This makes this Si-C bond subject to nucleophilic attack by F(-), triflate, and alkoxide/ether (from THF). This σ(Si-C) complex binds CO in the time of mixing and also binds chloride, both at nickel. Evidence is offered of a "self-healing" process, where the broken Si-C bond can be reformed in an equilibrium process. (PNP)Ni(+) reacts rapidly with H(2) to give (PN(H)P)NiH(+), which can be deprotonated to form (PNP)NiH. A variety of nucleophilic attacks (and THF polymerization) on the coordinated Si-C bond are envisioned to occur perpendicular to the Si-C bond, based on the character of the LUMO of (PNP)Ni(+).     

Influence of the metal orbital occupancy and principal quantum number on organoazide (RN3) conversion to transition-metal imide complexes

The reaction of phenyl azide with (PNP)Ni, where PNP = ( (t)Bu 2PCH 2SiMe 2) 2N (-), promptly evolves N 2 and forms a P=N bond in the product (PNP=NPh)Ni (I). A similar reaction with (PNP)FeCl proceeds to form a P=N bond but without N 2 evolution, to furnish (PNP=N-N=NPh)FeCl. An analogous reaction with (PNP)RuCl occurs with a more dramatic redox change at the metal (and N 2 evolution), to give the salt composed of (PNP)Ru(NPh) (+) and (PNP)RuCl 3 (-), together with equimolar (PNP)Ru(NPh). The contrast among these results is used to deduce what conditions favor N 2 loss and oxidative incorporation of the NPh fragment from PhN 3 into a metal complex.     

Influence of the d-Electron Count on CO binding by three-coordinate [(tBu2PCH2SiMe2)2N]Fe, -Co, and -Ni

Reduction of (PNP)MCl [PNP = ((t)Bu(2)PCH(2)SiMe(2))(2)N] with Mg gives three-coordinate, T-shaped (PNP)M for M = Fe(S = 3/2) and Ni. Their reactivity was tested toward CO; Ni binds one CO, but only reversibly (i.e., CO is completely lost in vacuum), and has a CO stretching frequency showing effective back-donation by NiI. The structure of (PNP)Ni(CO) is intermediate between planar and tetrahedral, in contrast to the planar d8 analogue, (PNP)Co(CO). This structural reorganization on carbonylation changes the singly occupied molecular orbital from having negligible phosphorus character [no P hyperfine structure in the electron paramagnetic resonance (EPR) spectrum of (PNP)Ni] to having enough P character to have a triplet structure in the EPR spectrum of the CO. The presence of one fewer electron in (PNP)Fe (vs the Co analogue) leads to binding of two CO, and (PNP)Fe(CO)(2) is characterized as a spin doublet with square-pyramidal structure. Density functional theory calculations strengthen the understanding of the structural and spectroscopic changes along this dn series (n = 7-9).     

O/C bond cleavage of CO2 by NiI

Reaction of (PNP)Ni, where PNP is [((t)Bu2PCH2SiMe2)2N](-1), with CO2 occurs rapidly even at -60 degrees C to form exclusively the product of transposition of the amide N and one CO2 oxygen: [((t)Bu2PCH2SiMe2)2O]Ni(NCO). DFT(B3LYP) evaluation of several candidate intermediates for breaking two Si/N and one C/O bond and forming two Si/O and one N/C bond reveal species at and below the energy of the separated particles, and establish the location of the spin densities in each.     

Exact scalar field cosmologies in a higher derivative theory

We obtain exact cosmological solutions of a higher derivative theory described by the Lagrangian L=R+2αR ² in the presence of interacting scalar field. The interacting scalar field potential required for a known evolution of the FRW universe in the framework of the theory is obtained using a technique different from the usual approach to solve the Einstein field equations. We follow here a technique to determine potential similar to that used by Ellis and Madsen in Einstein gravity. Some new and interesting potentials are noted in the presence of R ² term in the Einstein action for the known behaviours of the universe. These potentials in general do not obey the slow rollover approximation.     

The effect of one valence electron: contrasting (PNP)Ni(CO) with (PNP)Ni(NO) to understand the half-bent NiNO unit

Reaction of a (PNP)Ni radical with NO finishes in the time of mixing to form a 1:1 adduct with a NO stretching frequency of 1654 cm (-1). NMR data of this diamagnetic product indicate C 2 v symmetry, which is contradicted by the X-ray structure, which shows it to be nonplanar at Ni, with a geometry intermediate between planar and tetrahedral; the planar geometry is thus the transition state for fluxionality giving time-averaged C 2 v symmetry. The X-ray structure, together with DFT calculations, reveals that the "half-bent" NiNO unit and the intermediate coordination geometry result from a Ni --> NO charge transfer, which has a nonintegral value, resulting in a continuum between NO (+) (hence Ni (0)) and NO (-) (hence Ni (II)). This is related to the nonaxially symmetric character of the Ni --> NO back-donation caused by the (PNP) environment on Ni. Steric effects of ( t )Bu and even chelate constraints are ruled out as the cause of the unusual electronic and structural features.     

Orbital Angular Momentum in Scalar Diquark Model and QED

We compare the orbital angular momentum of the ‘quark’ in the scalar diquark model as well as that of the electron in QED (to order α) obtained from the Jaffe–Manohar decomposition to that obtained from the Ji relation. We estimate the importance of the vector potential in the definition of orbital angular momentum.