Three-dimensional macroporous silicon photonic crystal with large photonic band gap

Three-dimensional photonic crystals based on macroporous silicon are fabricated by photoelectrochemical etching and subsequent focused-ion-beam drilling. Reflection measurements show a high reflection in the range of the stopgap and indicate the spectral position of the complete photonic band gap. The onset of diffraction which might influence the measurement is discussed.

Three-dimensional photonic crystals based on macroporous silicon with modulated pore diameter

We report on the fabrication and optical characterization of a three-dimensional (3D) photonic crystal on the basis of macroporous silicon. The structure consists of a 2D array of air pores in silicon whose diameter is varied (modulated) periodically with depth. The bandstructure of the resulting 3D hexagonal photonic crystal is calculated and compared with transmission measurements. The described structure allows to adjust the dispersion relation along the pore axis almost independently from the dispersion relation in the plane perpendicular to the pore axis.

Lorentz TEM investigation of the switching behavior in artificial spin ice building blocks

Frustration – the inability to simultaneously satisfy all interactions – occurs in a wide range of systems including neural networks, water ice and magnetic systems. An example of the latter is the so called spin-ice in pyrochlore materials [1] which have attracted a lot of interest not least due to the emergence of magnetic monopole defects when the ‘ice rules’ governing the local ordering breaks down [2]. However it is not possible to directly measure the frustrated property – the direction of the magnetic moments – in such spin ice systems with current experimental techniques. This problem can be solved by instead studying artificial spin-ice systems where the molecular magnetic moments are replaced by nanoscale ferromagnetic islands [3-8]. Two different arrangements of the ferromagnetic islands have been shown to exhibit spin ice behaviour: a square lattice maintaining four moments at each vertex [3,8] and the Kagome lattice which has only three moments per vertex but equivalent interactions between them [4-7]. Magnetic monopole defects have been observed in both types of lattices [7-8]. One of the challenges when studying these artificial spin-ice systems is that it is difficult to arrive at the fully demagnetised ground-state [6-8].
Here we present a study of the switching behaviour of building blocks of the Kagome lattice influenced by the termination of the lattice. Ferromagnetic islands of nominal size 1000 nm by 100 nm were fabricated in five island blocks using electron-beam lithography and lift-off techniques of evaporated 18 nm Permalloy (Ni80Fe20) films. Each block consists of a central island with four arms terminated by a different number and placement of ‘injection pads’, see Figure 1. The islands are single domain and magnetised along their long axis. The structures were grown on a 50 nm thick electron transparent silicon nitride membrane to allow TEM observation, which was back-coated with a 5 nm film of Au to prevent charge build-up during the TEM experiments.
To study the switching behaviour the sample was subjected to a magnetic field strong enough to magnetise all the blocks in one direction, see Figure 1. Each block obeys the Kagome lattice ‘ice-rules’ of “2-in, 1-out” or “1-in, 2-out” in this fully magnetised state. Fresnel mode Lorentz TEM images of the sample were then recorded as a magnetic field of increasing magnitude was applied in the opposite direction. While the Fresnel mode is normally used to image magnetic domain structures [9] for these types of samples it is possible to deduce the direction of the magnetisation from the Lorentz contrast [5]. All images were recorded at the same over-focus judged to give good Lorentz contrast.
The magnetisation was found to switch at different magnitudes of the applied field for nominally identical blocks. However, trends could still be identified: all the blocks with any injection pads, regardless of placement and number, switched the direction of the magnetisation of their central island at significantly smaller magnitudes of the applied magnetic field than the blocks without injection pads. It can therefore be concluded that the addition of an injection pad lowers the energy barrier to switching the connected island, acting as a nucleation site for monopole defects. In these five island blocks the defects immediately propagate through to the other side, but in a larger lattice the monopoles could potentially become trapped at a vertex and observed [10].
References

[1] M J Harris et al, Phys Rev Lett 79 (1997) p.2554.
[2] C Castelnovo, R Moessner and S L Sondhi, Nature 451 (2008) p. 42.
[3] R F Wang et al, Nature 439 (2006) 303.
[4] M Tanaka et al, Phys Rev B 73 (2006) 052411.
[5] Y Qi, T Brintlinger and J Cumings, Phys Rev B 77 (2008) 094418.
[6] E Mengotti et al, Phys Rev B 78 (2008) 144402.
[7] S Ladak et al, Nature Phys 6 (2010) 359.
[8] C Phatak et al, Phys Rev B 83 (2011) 174431.
[9] J N Chapman, J Phys D 17 (1984) 623.
[10] The authors gratefully acknowledge funding from the EPSRC under grant number EP/D063329/1.

Complete nonlinear theory of longitudinal-to-transverse dust lattice mode coupling in a single-layer dusty plasma crystal

A comprehensive nonlinear model is put forward for coupled longitudinal to transverse displacements in a horizontal dust mono-layer, levitated under the combined influence of gravity and an electric and/or magnetic sheath field. A set of coupled nonlinear evolution equations are obtained in a discrete description, and a pair of coupled (Boussinesq-like) PDEs are obtained in the continuum approximation. Finally, the amplitude modulation of the coupled modes is discussed, pointing out the importance of the coupling. All these results are generic, i.e. valid for any assumed form of the inter-grain interaction potential U and the sheath potential Phi.

Effect of weak hydrogen bonding and included solvent on the crystal structure of the square-planar complex trans-Pt{PPh2(C16H15)}(2)Cl-2

Crystallisation of the square-planar complex trans-Pt{PPh2(C16H15)}(2)Cl-2 from dichloromethane-diethyl ether (1:1) affords two different solvates; trans-Pt{PPh2(C16H15)}(2)Cl-2. CH2Cl2 1 and trans-Pt{PPh2(C16H15)}(2)Cl-2. Et2O 2; the CH2Cl2 forms H-bonding interactions with the complex whereas the Et2O participates only in weak van der Waals interactions; these differences arise from the different hydrogen-bonding characteristics of each solvent.

Scaling of domain periodicity with thickness measured in BaTiO3 single crystal lamellae and comparison with other ferroics

The focused ion beam microscope has been used to cut parallel-sided {100}-oriented thin lamellae of single crystal barium titanate with controlled thicknesses, ranging from 530 nm to 70 nm. Scanning transmission electron microscopy has been used to examine domain configurations. In all cases, stripe domains were observed with {011}-type domain walls in perovskite unit-cell axes, suggesting 90 degrees domains with polarization in the plane of the lamellae. The domain widths were found to vary as the square root of the lamellar thickness, consistent with Kittel's law, and its later development by Mitsui and Furuichi and by Roytburd. An investigation into the manner in which domain period adapts to thickness gradient was undertaken on both wedge-shaped lamellae and lamellae with discrete terraces. It was found that when the thickness gradient was perpendicular to the domain walls, a continuous change in domain periodicity occurred, but if the thickness gradient was parallel to the domain walls, periodicity changes were accommodated through discrete domain bifurcation. Data were then compared with other work in literature, on both ferroelectric and ferromagnetic systems, from which conclusions on the widespread applicability of Kittel's law in ferroics were made.

Density-viscosity product of small-volume ionic liquid samples using quartz crystal impedance analysis

Quartz crystal impedance analysis has been developed as a technique to assess whether room-temperature ionic liquids are Newtonian fluids and as a small-volume method for determining the values of their viscosity-density product, rho eta. Changes in the impedance spectrum of a 5-MHz fundamental frequency quartz crystal induced by a water-miscible room-temperature ionic liquid, 1-butyl-3-methylimidazolium. trifluoromethylsulfonate ([C(4)mim][OTf]), were measured. From coupled frequency shift and bandwidth changes as the concentration was varied from 0 to 100% ionic liquid, it was determined that this liquid provided a Newtonian response. A second water-immiscible ionic liquid, 1-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide [C(4)mim][NTf2], with concentration varied using methanol, was tested and also found to provide a Newtonian response. In both cases, the values of the square root of the viscosity-density product deduced from the small-volume quartz crystal technique were consistent with those measured using a viscometer and density meter. The third harmonic of the crystal was found to provide the closest agreement between the two measurement methods; the pure ionic liquids had the largest difference of similar to 10%. In addition, 18 pure ionic liquids were tested, and for 11 of these, good-quality frequency shift and bandwidth data were obtained; these 12 all had a Newtonian response. The frequency shift of the third harmonic was found to vary linearly with square root of viscosity-density product of the pure ionic liquids up to a value of root(rho eta) approximate to 18 kg m(-2) s(-1/2), but with a slope 10% smaller than that predicted by the Kanazawa and Gordon equation. It is envisaged that the quartz crystal technique could be used in a high-throughput microfluidic system for characterizing ionic liquids.

Small volume laboratory on a chip measurements incorporating the quartz crystal microbalance to measure the viscosity-density product of room temperature ionic liquids

A microfluidic glass chip system incorporating a quartz crystal microbalance (QCM) to measure the square root of the viscosity-density product of room temperature ionic liquids (RTILs) is presented. The QCM covers a central recess on a glass chip, with a seal formed by tightly clamping from above outside the sensing region. The change in resonant frequency of the QCM allows for the determination of the square root viscosity-density product of RTILs to a limit of similar to 10 kg m(-2) s(-0.5). This method has reduced the sample size needed for characterization from 1.5 ml to only 30 mu l and allows the measurement to be made in an enclosed system.

Observation of stable phase jump lines in convection of a twisted nematic liquid crystal

We report observations of stable, localized, linelike structures in the spatially periodic pattern formed by nematic electroconvection, along which the phase of the pattern jumps by pi. With increasing electric voltage, these lines form a gridlike structure that goes over into a structure indistinguishable from the well-known grid pattern. We present theoretical arguments that suggest that the twisted cell geometry we are using is indirectly stabilizing the phase jump lines, and that the phase jump lines lattice is caused by an interaction of phase jump lines and a zig-zag instability of the surrounding pattern.

Study of the intergrain interaction potential and associated instability of dust-lattice plasma oscillations in the presence of ion flow

A comprehensive study of the Debye-Huckel repulsive and ion wakefield induced attractive potentials around a dust grain is presented, including ion flow. It is found that the modified interaction potential (especially the attractive wakefield force) can cause instability of linear dust oscillations propagating in a dusty plasma crystal composed of dust grains in a horizontal arrangement suspended in the sheath region near a conducting wall (electrode). The dependence of dust lattice modes on the ion flow is studied, revealing instability of dust lattice modes for certain values of the ion flow speed. (C) 2003 Elsevier B.V. All rights reserved.

Nonlinear modulation of transverse dust lattice waves in complex plasma crystals

The occurrence of the modulational instability in transverse dust lattice waves propagating in a one-dimensional dusty plasma crystal is investigated. The amplitude modulation mechanism, which is related to the intrinsic nonlinearity of the sheath electric field, is shown to destabilize the carrier wave under certain conditions, possibly leading to the formation of localized envelope excitations. Explicit expressions for the instability growth rate and threshold are presented and discussed. (C) 2004 American Institute of Physics.

Modulated wavepackets associated with longitudinal dust grain oscillations in a dusty plasma crystal

The nonlinear amplitude modulation of longitudinal dust lattice waves (LDLWs) propagating in a dusty plasma crystal is investigated in a continuum approximation. It is shown that long wavelength LDLWs are modulationally stable, while shorter wavelengths may be unstable. The possibility for the formation and propagation of different envelope localized excitations is discussed. It is shown that the total grain displacement bears a (weak) constant displacement (zeroth harmonic mode), due to the asymmetric form of the nonlinear interaction potential. The existence of asymmetric envelope localized modes is predicted. The types and characteristics of these coherent nonlinear structures are discussed. (C) 2004 American Institute of Physics.

Nonlinear theory of solitary waves associated with longitudinal particle motion in lattices - Application to longitudinal grain oscillations in a dust crystal

The nonlinear aspects of longitudinal motion of interacting point masses in a lattice are revisited, with emphasis on the paradigm of charged dust grains in a dusty plasma (DP) crystal. Different types of localized excitations, predicted by nonlinear wave theories, are reviewed and conditions for their occurrence (and characteristics) in DP crystals are discussed. Making use of a general formulation, allowing for an arbitrary (e.g. the Debye electrostatic or else) analytic potential form phi(r) and arbitrarily long site-to-site range of interactions, it is shown that dust-crystals support nonlinear kink-shaped localized excitations propagating at velocities above the characteristic DP lattice sound speed v(0). Both compressive and rarefactive kink-type excitations are predicted, depending on the physical parameter values, which represent pulse- (shock-)like coherent structures for the dust grain relative displacement. Furthermore, the existence of breather-type localized oscillations, envelope-modulated wavepackets and shocks is established. The relation to previous results on atomic chains as well as to experimental results on strongly-coupled dust layers in gas discharge plasmas is discussed.

Dust lattice wave dispersion relations in two-dimensional hexagonal crystals including the effect of dust charge polarization

A dusty plasma crystalline configuration with equal charge dust grains and mass is considered. Both charge and mass of each dust species are taken to be constant. Two differential equations for a two-dimensional hexagonal crystal on the basis of a Yukawa-type potential energy and a