Geometric approach to Fletcher's ideal penalty function

Original article can be found at: www.springerlink.com Copyright Springer. [Originally produced as UH Technical Report 280, 1993]In this note, we derive a geometric formulation of an ideal penalty function for equality constrained problems. This differentiable penalty function requires no parameter estimation or adjustment, has numerical conditioning similar to that of the target function from which it is constructed, and also has the desirable property that the strict second-order constrained minima of the target function are precisely those strict second-order unconstrained minima of the penalty function which satisfy the constraints. Such a penalty function can be used to establish termination properties for algorithms which avoid ill-conditioned steps. Numerical values for the penalty function and its derivatives can be calculated efficiently using automatic differentiation techniques.Peer reviewe

Doping Dependence of Spin Dynamics in Electron-Doped Ba(Fe1-xCox)2As2

The spin dynamics in single crystal, electron-doped Ba(Fe1-xCox)2As2 has been investigated by inelastic neutron scattering over the full range from undoped to the overdoped regime. We observe damped magnetic fluctuations in the normal state of the optimally doped compound (x=0.06) that share a remarkable similarity with those in the paramagnetic state of the parent compound (x=0). In the overdoped superconducting compound (x=0.14), magnetic excitations show a gap-like behavior, possibly related to a topological change in the hole Fermi surface (Lifshitz transition), while the imaginary part of the spin susceptibility prominently resembles that of the overdoped cuprates. For the heavily overdoped, non-superconducting compound (x=0.24) the magnetic scattering disappears, which could be attributed to the absence of a hole Fermi-surface pocket observed by photoemission.Comment: 6 pages, 5 figures, published versio

Stabilization of Polar Nano Regions in Pb-free ferroelectrics

Formation of polar nano regions through solid-solution additions are known to enhance significantly the functional properties of ferroelectric materials. Despite considerable progress in characterizing the microscopic behavior of polar nano regions, understanding their real-space atomic structure and dynamics of formation remains a considerable challenge. Here, using the method of dynamic pair distribution function, we provide direct insights into the role of solid-solution additions towards the stabilization of polar nano regions in the Pb-free ferroelectric of Ba(Zr,Ti)O3. It is shown that for an optimum level of substitution of Ti by larger Zr ions, the dynamics of atomic displacements for ferroelectric polarization are slowed sufficiently, which leads to increased local correlation among dipoles below THz frequencies. The dynamic pair distribution function technique demonstrates unique capability to obtain insights into locally correlated atomic dynamics in disordered materials, including new Pb-free ferroelectrics, which is necessary to understand and control their functional properties

Unusual giant magnetostriction in the ferrimagnet Gd2/3_{2/3}Ca1/3_{1/3}MnO3_3

We report an unusual giant linear magnetostrictive effect in the ferrimagnet Gd$_{2/3}$Ca$_{1/3}$MnO$_3$ ($T_{c} \approx$80 K). Remarkably, the magnetostriction, negative at high temperature ($T \approx T_{c}$), becomes positive below 15 K when the magnetization of the Gd sublattice overcomes the magnetization of the Mn sublattice. A rather simple model where the magnetic energy competes against the elastic energy gives a good account of the observed results and confirms that Gd plays a crucial role in this unusual observation. Unlike previous works in manganites where only striction associated with 3$d$ Mn orbitals is considered, our results show that the lanthanide 4$f$ orbitals related striction can be very important too and it cannot be disregarded.Comment: 6 pages, 3 figure

Charge order, dynamics, and magneto-structural transition in multiferroic LuFe2_2O4_4

We investigated the series of temperature and field-driven transitions in LuFe$_2$O$_4$ by optical and M\"{o}ssbauer spectroscopies, magnetization, and x-ray scattering in order to understand the interplay between charge, structure, and magnetism in this multiferroic material. We demonstrate that charge fluctuation has an onset well below the charge ordering transition, supporting the "order by fluctuation" mechanism for the development of charge order superstructure. Bragg splitting and large magneto optical contrast suggest a low temperature monoclinic distortion that can be driven by both temperature and magnetic field.Comment: 4 pages, 3 figures, PRL in prin

Antiferromagnetic Order in MnO Spherical Nanoparticles

We have performed unpolarized and polarized neutron diffraction experiments on monodisperse 8 nm and 13 nm antiferromagnetic MnO nanoparticles. For the 8 nm sample, the antiferromagnetic transition temperature $T_N$ (114 K) is suppressed compared to the bulk material (119 K) while for the 13 nm sample $T_N$ (120 K) is comparable to the bulk. The neutron diffraction data of the nanoparticles is well described using the bulk MnO magnetic structure but with a substantially reduced average magnetic moment of 4.2$\pm$0.3 $\mu_B$/Mn for the 8 nm sample and 3.9$\pm$0.2 $\mu_B$/Mn for the 13 nm sample. An analysis of the polarized neutron data on both samples shows that in an individual MnO nanoparticle about 80$$ of Mn ions order. These results can be explained by a structure in which the monodisperse nanoparticles studied here have a core that behaves similar to the bulk with a surface layer which does not contribute significantly to the magnetic order.Comment: 7 pages, 5 figure

Magnetic-Field-Induced Antiferromagnetism in Two-Dimensional Hubbard Model: Analysis of CeRhIn5_5

We propose the mechanism for the magnetic-field-induced antiferromagnetic (AFM) state in a two-dimensional Hubbard model in the vicinity of the AFM quantum critical point (QCP), using the fluctuation-exchange (FLEX) approximation by taking the Zeeman energy due to the magnetic field $B$ into account. In the vicinity of the QCP, we find that the AFM correlation perpendicular to $B$ is enhanced, whereas that parallel to $B$ is reduced. This fact means that the finite magnetic field increases $T_N$, with the AFM order perpendicular to $B$. The increment in $T_N$ can be understood in terms of the reduction of both quantum and thermal fluctuations due to the magnetic field, which is caused by the self-energy effect within the FLEX approximation. The present study naturally explains the increment in $T_N$ in CeRhIn_5 under the magnetic field found recently.Comment: 5 page

Magnetic properties of the S=1/2 quasi square lattice antiferromagnet CuF2(H2O)2(pyz) (pyz=pyrazine) investigated by neutron scattering

We have performed elastic and inelastic neutron experiments on single crystal samples of the coordination polymer compound CuF2(H2O)2(pyz) (pyz=pyrazine) to study the magnetic structure and excitations. The elastic neutron diffraction measurements indicate a collinear antiferromagnetic structure with moments oriented along the [0.7 0 1] real-space direction and an ordered moment of 0.60 +/- 0.03 muB/Cu. This value is significantly smaller than the single ion magnetic moment, reflecting the presence of strong quantum fluctuations. The spin wave dispersion from magnetic zone center to the zone boundary points (0.5 1.5 0) and (0.5 0 1.5) can be described by a two dimensional Heisenberg model with a nearest neighbor magnetic exchange constant J2d = 0.934 +/-0.0025 meV. The inter-layer interaction Jperp in this compound is less than 1.5% of J2d. The spin excitation energy at the (0.5 0.5 0.5) zone boundary point is reduced when compared to the (0.5 1 0.5) zone boundary point by ~10.3 +/- 1.4 %. This zone boundary dispersion is consistent with quantum Monte Carlo and series expansion calculations which include corrections for quantum fluctuations to linear spin wave theory.Comment: 7 pages, 6 figure

Crystalline Electric Field Excitations in the Heavy Fermion Superconductor CeCoIn_5

The crystalline electric field (CEF) energy level scheme of the heavy fermion superconductor CeCoIn_5 has been determined by means of inelastic neutron scattering (INS). Peaks observed in the INS spectra at 8 meV and 27 meV with incident neutron energies between E_i=30-60 meV and at a temperature T = 10 K correspond to transitions from the ground state to the two excited states, respectively. The wavevector and temperature dependence of these peaks are consistent with CEF excitations. Fits of the data to a CEF model yield the CEF parameters B^0_2=-0.80 meV, B^0_4=0.059 meV, and |B^4_4|= 0.137 meV corresponding to an energy level scheme: Gamma_7^(1) (0)[=0.487|+/-5/2> - 0.873|-/+3/2>], Gamma_7^(2) (8.6 meV, 100 K), and Gamma_6 (24.4 meV, 283 K).Comment: uses latex packages revtex4,amsmath,graphicx,natbib, 9th Annual MMM-Intermag Conference, (Accepted for publication in J. Appl. Phys.) 7 pages, 2 figure

Field-induced structural evolution in the spin-Peierls compound CuGeO3_3: high-field ESR study

The dimerized-incommensurate phase transition in the spin-Peierls compound CuGeO$_3$ is probed using multifrequency high-resolution electron spin resonance (ESR) technique, in magnetic fields up to 17 T. A field-induced development of the soliton-like incommensurate superstructure is clearly indicated as a pronounced increase of the ESR linewidth $\Delta B$ (magnon excitations), with a $\Delta B_{max}$ at $B_{c}\sim$ 13.8 T. The anomaly is explained in terms of the magnon-soliton scattering, and suggests that the soliton-like phase exists close to the boundary of the dimerized-incommensurate phase transition. In addition, magnetic excitation spectra in 0.8% Si-doped CuGeO$_3$ are studied. Suppression of the $\Delta B$ anomaly observed in the doped samples suggests a collapse of the long-range-ordered soliton states upon doping, that is consistent with high-field neutron scattering experiments.Comment: Accepted to Phys. Rev.