Table of contents

The technology to build and study nanowires with sizes ranging from individual atoms to tens of nanometres has been developing rapidly over the last few years. We survey the motivation behind these developments, and summarize the basics behind quantized conduction. Several of the different experimental techniques and materials systems used in the creation of nanowires are examined, and the range of theoretical methods developed both for examining open systems (especially their conduction properties) and for modelling large systems are considered. We present various noteworthy example results from the field, before concluding with a look at future directions.

One of the first theoretical proposals for understanding high-temperature superconductivity in the cuprates was Anderson's RVB theory using a Gutzwiller projected BCS wavefunction as an approximate ground state. Recent work by Paramekanti et al has shown that this variational approach gives a semi-quantitative understanding of the doping dependences of a variety of experimental observables in the superconducting state of the cuprates. In this paper we revisit these issues using the 'renormalized mean field theory' of Zhang et al based on the Gutzwiller approximation in which the kinetic and superexchange energies are renormalized by different doping-dependent factors g_t and g_S respectively. We point out a number of consequences of this early mean field theory for experimental measurements which were not available when it was first explored, and observe that it is able to explain the existence of the pseudogap, properties of nodal quasiparticles and approximate spin–charge separation, the latter leading to large renormalizations of the Drude weight and superfluid density. We use the Lee–Wen theory of the phase transition as caused by thermal excitation of nodal quasiparticles, and also obtain a number of further experimental confirmations. Finally, we remark that superexchange, and not phonons, is responsible for d-wave superconductivity in the cuprates.

Historically most materials in magnetic applications are based on inorganic materials. Recently, however, organic and molecular materials have begun to show increasing promise. Purely organic ferromagnets, based upon nitronyl nitroxide radicals, show long range magnetic order at very low temperatures in the region of 1 K, while sulfur based radicals show weak ferromagnetism at temperatures up to 36 K. It is also possible to prepare molecule based magnets in which transition metal ions are used to provide the magnetic moment, but organic groups mediate the interactions. This strategy has produced magnetic materials with a large variety of structures, including chains, layered systems and three-dimensional networks, some of which show ordering at room temperature and some of which have very high coercivity. Even if long range magnetic order is not achieved, the spin crossover effect may be observed, which has important applications. Further magnetic materials may be obtained by constructing charge transfer salts, which can produce metallic molecular magnets. Another development is single-molecule magnets, formed by preparing small magnetic clusters. These materials can show macroscopic quantum tunnelling of the magnetization and may have uses as memory devices or in quantum computation applications.

Using an inverse scattering method, we find the exact bright and dark soliton solutions of the nonlinear Gross–Pitaevskii equation with external potentials. We also investigate the nonlinear excitation of a Bose–Einstein condensate under external fields. We reveal an efficient means of controlling solitons in a Bose–Einstein condensate for use in future experiments.

The rapid solidification of Ti₃Al was studied with the constant-pressure and constant-temperature molecular dynamics (NPT-MD) technique to obtain an atomistic description of glass formation and crystallization in the alloy. The embedded atom method (EAM) potential for the Ti–Al binary system recently developed by Zope and Mishin (2003 Phys. Rev. B 68 024102) was applied in the simulations. The effects of different cooling rates on the glass formation and crystallization of liquid Ti₃Al were studied. In addition, the crystallization of the amorphous Ti₃Al as a function of increasing temperature was also studied. The calculated internal energy change and radial distribution function during cooling and heating processes provided a good picture of the structural transformations, and the results were consistent with the results obtained experimentally.

The Nd_1−xY_xCo_9.5V_2.5 compounds with x = 0–1 crystallize in the tetragonal ThMn₁₂ structure. The lattice parameters a,c and the cell volume V decrease with increasing Y content. The Curie temperature increases for , then decreases with increase of the Y content. The exchange field coefficient n_RCo was derived from the Curie temperature and follows the general trend of rare-earth–3d intermetallic interaction exchange. The high field saturation magnetization decreases with increase of the Y content. A domain wall pinning phenomenon was observed in all of the compounds and the substitution of Y for Nd makes this phenomenon less obvious. High field measurements of the magnetization show a field induced metamagnetic transition in each compound and the critical field H_crit^H decreases with increase of the Y content.

We present a detailed analysis of the interaction between intrinsic localized modes and plasmons in a doped polar semiconductor. The investigation has been performed for an anharmonic one-dimensional diatomic lattice with alternating interactions coupling successive neighbours. The system simulates a row of atoms in the direction of a III–V semiconductor. Specific calculations have been performed for GaN, because it has a large gap between the acoustic and optical phonon branches. The calculations of the intrinsic localized modes have been performed by using two-body potentials to describe the interactions. We have used the rotating wave approximation and we have found the intrinsic localized modes in the phonon gap. The interaction with the plasmon has been studied by adding to the equations of motion the alternating electric field which is related to the electron density of the plasmons. We obtain an expression for the electric dynamical polarization associated with the intrinsic localized modes and with the plasmons. We derive an expression for the dielectric function of the coupled system. The zeros of the dielectric function give the frequency of the combined modes. We have found two regimes in which combined modes are possible. One is related to small anharmonicity of the potential. The combined mode has a frequency above the top of the optical branch and can be explained in terms of the theory of the harmonic dielectric response of polar lattice vibrations. The second regime is related to high anharmonicity. The combined modes exist only for a finite slab. We show that on increasing the anharmonicity, i.e. the amplitude of the intrinsic localized mode, the width of the slab increases. The frequency of the combined mode is inside the phonon gap. We have also studied the dynamical stability of these modes.

The tracer diffusion of hydrogen is studied in amorphous Si₃N₄:H films which were produced by rf magnetron reactive sputtering. The diffusion experiments were carried out in the temperature range between 700 and 1000 °C with ion implanted deuterium isotopes. Secondary ion mass spectrometry was used for depth profile analysis. While a considerable part of the tracer is immobilized due to the interaction with the implantation damage, the other part migrates freely into the film, wherefrom diffusivities are extracted. These diffusivities coincide with those obtained from a control experiment with a gas exchange technique, demonstrating that the implantation damage has no significant influence on the determination of the correct diffusivities themselves.²H transport can be described by the concept of trap limited diffusion, where the tracer atoms are temporarily trapped by intrinsic film defects, presumably nitrogen dangling bonds. For the present case of a considerably high dissociation rate of trapped hydrogen, effective diffusivities are derived which obey an Arrhenius behaviour with a large activation energy of ΔE = 3.4 eV and a pre-exponential factor of D₀ = 5 × 10⁻⁴ m² s⁻¹. The effect on diffusion of pre-annealing the films prior to diffusion in nitrogen and possible structural rearrangements involved, as well as of charging the films with hydrogen up to 2.6 at.%, is analysed.

We investigate the phase diagram of the half-filled one-dimensional t–U–J model by the level-spectroscopy method. Due to the competition between the Coulomb repulsion U and the antiferromagnetic exchange J, the backward scattering may change sign from repulsive to attractive, leading to spin-gap instability. From the excitation spectra of finite-size clusters, the transition line U_c(J) can be accurately determined in the weak-coupling and intermediate-coupling regimes. With increasing J, U_c(J) deviates from that given by the weak-coupling theory based on the spin–charge separation hypothesis. Moreover, we find that the spin gap vanishes robustly when , irrespective of J.

The electronic structures of magnetic orderings of Zn_1−xTM_xO (TM = Cu, Mn) have been studied with the B3LYP hybrid density functional. The corrections for energy band dispersions with respect to the local density approximation (LDA) are similar to GW results, but lead to an improved energy gap. Cu and Mn are close to +2 valence in Zn_1−xTM_xO (TM = Cu, Mn), but Cu¹⁺ would be realized in n-type ZnO. Cu- and Mn-doped ZnO have ferromagnetic and antiferromagnetic ground states, respectively. Magnetic couplings between transition metal ions depend sensitively on the interatomic distance.

We report on first-principles calculations for multilayers of zinc-blende half-metallic ferromagnets CrAs and CrSb with III–V and II–VI semiconductors, in the [001] orientation. We examine the ideal and tetragonalized structures, as well as the case of an intermixed interface. We find that, as a rule, half-metallicity can be conserved throughout the heterostructures, provided that the character of the local coordination and bonding is not disturbed. We describe a mechanism operative at the interfaces with semiconductors that can also give a non-integer spin moment per interface transition atom, and derive a simple rule for evaluating it.

X-ray and neutron diffraction studies as well as magnetization and electrical resistivity measurements of Er_1−xY_xCo₃ compounds were performed. In the Er-rich compounds, , a temperature-induced metamagnetic transition takes place between weak and strong Co magnetic states. In the intermediate concentration region, , below 40 K a spin reorientation was observed. The magnetic structure below the spin-reorientation transition is non-collinear. The Er moments on the 'cubic' sites (6c) are tilted from the c-axis by an angle of about 55°, while those on the uniaxial 3a positions compose a smaller angle, of about 15°. The spin-reorientation transition is accompanied by a large orthorhombic distortion of the hexagonal PuNi₃-type crystal structure, which is accounted for by a large anisotropic magnetostriction of the Er sublattice. The distortion parameter varies linearly with x. Its extrapolated value for ErCo₃ is about 2 × 10⁻³. The concentration dependence of both types of magnetic instabilities is depicted in a magnetic phase diagram of the pseudobinary Er_1−xY_xCo₃ system for the low-temperature region.

We report the investigations of transport and thermoelectric measurements on the Heusler compounds Fe₂V Ga_1+x over the temperature range from 10 to 300 K. It is found that the electrical resistivity and Seebeck coefficient are very sensitive to the off-stoichiometry, while the thermal conductivity is relatively little affected with the composition change. With a removal of Ga content from the stoichiometric Fe₂V Ga, a sign change in the Seebeck coefficient accompanied by a broad minimum at around 130 K is observed. The latter feature can be interpreted as thermal excitation of carriers across band edges, in accord with band-structure calculations. Furthermore, an analysis of lattice thermal conductivity indicates that the off-stoichiometric effect on both electrical resistivity and Seebeck coefficient is not influenced by chemical disorder.

The impact of the dispersion of the transport coefficients on the structure of the energy distribution function for charge carriers far from equilibrium has been investigated in the effective medium approximation for a model density of states. The investigations show that two regimes can be observed in energy relaxation processes. Below a characteristic temperature the structure of the energy distribution function is determined by the dispersion of the transport coefficients. Thermal energy diffusion is irrelevant in this regime. Above the characteristic temperature the structure of the energy distribution function is determined by energy diffusion. The characteristic temperature depends on the degree of disorder and increases with increasing disorder. Explicit expressions for the energy distribution function in both regimes are derived for a constant and an exponential density of states.

We derive the quantum rate equations for an Aharonov–Bohm interferometer with two vertically coupled quantum dots embedded in each of two arms by means of the nonequilibrium Green function in the sequential tunnelling regime. Based on these equations, we investigate time-dependent resonant tunnelling under a small amplitude irradiation and find that the resonant photon-assisted tunnelling peaks in photocurrent demonstrate a combination behaviour of Fano and Lorentzian resonances due to the interference effect between the two pathways in this parallel configuration, which is controllable by threading the magnetic flux inside this device.

Electron transport through a quantum sphere with three one-dimensional wires attached to it is investigated. An explicit form for the transmission coefficient as a function of the electron energy is found from first principles. The asymmetric Fano resonances are detected in the transmission of the system. The collapse of the resonances is shown to appear under certain conditions. A two-terminal nanodevice with an additional gate lead is studied using the developed approach. Additional resonances and minima of transmission are indicated in the device.

The dynamics of ferroelectromagnetic (multiferroic) crystals RMn₂O₅ (R = Eu and Gd), showing magnetic and ferroelectric phase transitions with close transition temperatures (40 and 30 K for R = Eu and Gd, respectively), was studied in the frequency and temperature ranges 20–300 GHz and 5–50 K, respectively. It was found that magnetic resonance spectra of GdMn₂O₅ are characteristic for the homogeneous long-range magnetic order both of the antiferomagnetic Mn-subsystem and Gd magnetic subsystem, possessing a large ferromagnetic moment. In other RMn₂O₅ crystals (with nonmagnetic or weakly magnetic rare-earth ions) incommensurate or space-modulated magnetic structures in Mn-subsystem are present. The strong Gd–Mn and Gd–Mn–Gd exchange interactions are responsible for the homogeneous magnetic state. A strong effect of the magnetic state on the ferroelectric state was discovered in GdMn₂O₅ crystal. The temperature of the ferroelectric phase transition in GdMn₂O₅ is shifted to the lower temperature as compared with other RMn₂O₅ crystals. Mixed magnetoelectric excitations in GdMn₂O₅ were observed for the first time.

The local structure of the 2.5% ⁵⁷Fe-doped La_0.9MnO_x (x = 2.89, 2.92 and 2.93) manganites has been investigated by means of Mössbauer spectroscopy. In the paramagnetic phase, the Mössbauer spectra of all three samples consist of two quadrupole doublets which suggest two different iron positions distinguished by their local environment. It has been assumed that in the position with a large quadrupole splitting, QS1, the Fe³⁺ is surrounded by six Jahn–Teller Mn³⁺ ions. The second iron position with the smaller quadrupole splitting, QS2, corresponds to the manganese environment in which at least one manganese ion is in the Mn⁴⁺ state. In the magnetically ordered phase, these positions become indistinguishable. We conclude that even in the absence of Mn⁴⁺ ions the introduction of the non-Jahn–Teller Fe³⁺ ion in the Mn³⁺ environment leads to the local removal of static ordering of the Mn³⁺ d_3z²−r² orbitals that result in the ferromagnetic ordering of the Mn spins. The result indicates a key role of the dynamic orbital correlations in the formation of the ferromagnetic ordering in manganites.

The field dependence of the magnetization in antiferromagnetic Nd₆Fe₁₃Si has been measured between 4.2 and 295 K under an applied magnetic field of between zero and 23 T. Isofield magnetization measurements at 1, 10, 15 and 20 T have also been carried out between 4.2 and 295 K. The magnetic phase diagram of Nd₆Fe₁₃Si contains three regions. Between 4.2 and 110 K, the magnetic moments are aligned within the basal plane of the tetragonal unit cell and two critical fields are observed. Between 160 and 295 K, the magnetic moments are aligned along the c-axis and one critical field is observed. Finally, between 110 and 160 K, a complex intermediate or mixed magnetic phase with up to three critical fields is observed. At 4.2 K and 23 T a hysteresis with a substantial coercive field of 0.4 T is observed. The presence of both two critical fields and hysteresis at low temperatures indicates a strong magnetic anisotropy within the basal plane. At 295 K an applied field of 23 T does not yield a complete spin flop of the axial magnetic moments, which remain canted. The critical field in the high temperature region is smaller than that observed in the low temperature region, indicating that the uniaxial antiferromagnetic exchange is weaker than the basal exchange. The temperature dependence of the magnetization under applied fields of 15 and 20 T shows the overall expected decrease with increasing temperature but with a break between 80 and 110 K in the spin reorientation region. Finally, the temperature dependence of the magnetization under applied fields of 10 T or less is very complex and results from a field induced canting of the magnetic moments below 30–40 K and a minimum in magnetic anisotropy around the spin reorientation at 110 K.

Ultrafine magnetic nickel ferrite NiFe₂O₄ particles of high crystallinity were directly prepared by forced hydrolysis of ionic iron (III) and nickel (II) solutions in 2-hydroxyethyl ether at about 478 K under atmospheric pressure. The resulting nickel ferrite particles exhibit very interesting magnetic properties: they are superparamagnetic at room temperature and have a saturation magnetization close to that of the bulk at low temperature. An in-field Mössbauer study shows clearly that this surprising behaviour is mainly due to: (i) a departure of the cation distribution from the classical distribution encountered in the bulk material and (ii) the absence of spin canting for both tetrahedral and octahedral cations.

Cluster beam experiments using Stern–Gerlach type measurements yield information about the magnetic properties of transition metal clusters. One of the intriguing results to have come out of such measurements is the observation of a magnetic moment in cobalt clusters that increases with temperature up to about 500 K, before decreasing as the bulk Curie temperature is approached. We argue in this paper that this behaviour can be understood as an artifact of the method of extracting results from raw experimental data, and that the origin of the anomalous behaviour lies in the neglect of the magnetic anisotropy in the analysis.

Temperature-dependent Brillouin scattering studies have been carried out on La_0.77Ca_0.23MnO₃ across the paramagnetic insulator–ferromagnetic metal (I–M) transition ( K). The spectra show modes corresponding to a surface Rayleigh wave (SRW) and a high velocity pseudo-surface wave (HVPSAW) along with bulk acoustic waves (B1 and B2). The Brillouin shifts associated with the SRW and HVPSAW increase, whereas the B1 and B2 frequencies decrease, below T_C. The temperature dependence of the SRW and HVPSAW modes is related to the increase in the elastic constant C₁₁ across the I–M transition. The decrease in frequency across the I–M transition of the bulk modes is understood to be due to enhanced self-energy corrections as a result of increased magnon–phonon interaction across the I–M transition. Correspondingly, these modes show a large increase in the full width at half maximum (FWHM) as the temperature decreases. We also observe a central peak whose width is maximum at T_C.

We present neutron scattering measurements of Bose–Einstein condensation (BEC) in liquid ⁴He adsorbed in thick layers on an MgO substrate to study whether the condensate fraction, n₀, is increased near a free surface of liquid ⁴He. The data show that there is definitely a condensate in the layers adsorbed on the substrate with a condensate fraction comparable to that of bulk liquid ⁴He. Two methods of analysis are employed to cross-check the results. The data indicate that the condensate fraction increases significantly when the number of adsorbed layers is reduced. This effect is independent of the analysis technique used. In addition, a significant increase in the kinetic energy of the ⁴He atoms is observed when the number of adsorbed layers is reduced.