Statics and dynamics of “soft” impurities in a crystal

We investigate the effect of an impurity on the local static and dynamic behaviour of a crystal undergoing a displacive phase transition. It is shown that in mean-field approximation there may occur a freezing-out of local order driven by a soft local mode above the phase transition of the host. For a crystal containing a dilute impurity concentration, the impurity contribution to the static structure factor is calculated. The results are discussed in detail for the specific cases of a displacive and an Ising-type impurity.Work supported by the Swiss National Science FoundationThe results of this paper were presented at the Spring Meeting of the German Physical Society, Münster 1977 (Verhandlungen DPG (VI) 12, 1977)     

The behaviour of an isolated impurity near a phase transition in a spherical-like model

The behaviour of an isolated impurity in a crystal undergoing a displacive phase transition is investigated in an exactly soluble spherical-like model. We find, depending on the parameter of the impurity, either a global phase transition at the bulkT _c or a freezing-out of local order at a temperatureT _c ^loc >T _c driven by a soft local mode. We furthermore discuss the dynamic autocorrelation function of the impurity by introducing a phenomenological damping.Work Supported by The Swiss National Science Foundation     

Discontinuous freezing-out of local order

A soft impurity in a host crystal undergoing a second-order displacive phase transition may induce a freezing-out of local order at temperatures above the bulk transition temperature [1]. We show that in MFA this local phase transition is of first order, i.e. the local order appears discontinuously, and the stability limit of the disordered phase against local ordering lies below the stability limit of the locally ordered phase, if the representation of the impurity coordinate contains a third-order invariant, but the space-group representation of the soft optical phonon does not. This situation occurs for example for anE _g -type impurity coordinate coupling to a soft zone-edge or zone-corner phonon driving an antiferrodistortive transition. The theory is applied to the specific case of a Jahn-Teller impurity in a non-Jahn-Teller host crystal.     

Sound attenuation in doped displacive ferroelectrics

An expression is obtained for the sound attenuation constant in a doped displacive ferroelectrics in the presence of an external electric field, using double-time temperature-dependent Green’s function technique. The mass and force constant changes due to impurity atoms, are taken into account along with higher order anharmonic and electric dipole moment terms, in the Silverman-Joseph Hamiltonian. The attenuation constant increases with an external electric field. The soft mode is responsible for the anomalously increasing behaviour of the attenuation constant in the vicinity of the Curie temperature. The results agree with those attained by Tani and Tsuda and Heuter and Neuhaus.     

Abelian Bosonization Approach,to a Magnetic Impurity Model

Abelian bosonization is applied to a magnetic impurity model, the so-called Wolff impurity model. The resulting bosonized version of the model can be solved exactly. We calculate the local dynamic spin and charge density-density correlations of the conduction electrons, and show that a quasi-particle peak in the spin-density excitations appears and becomes sharp significantly as the local interaction U grows up. The local static spin and charge susceptibilities and specific heat of the interacting electrons are also obtained, explicitly displaying a local Fermi liquid behavior.     

Spatial distribution of local density of states in vicinity of impurity on semiconductor surface

We present the results of detailed theoretical investigations of changes in local density of total electronic surface states in 2D anisotropic atomic semiconductor lattice in vicinity of impurity atom for a wide range of applied bias voltage. We have found that taking into account changes in density of continuous spectrum states leads to the formation of a downfall at the particular value of applied voltage when we are interested in the density of states above the impurity atom or even to a series of downfalls for the fixed value of the distance from the impurity. The behaviour of local density of states with increasing of the distance from impurity along the chain differs from behaviour in the direction perpendicular to the chain. The article is published in the original.     

Deuterium and Impurity Flux Measurements in the Boundary Plasma of T-10

Time resolved measurements of deuterium and impurity fluxes in the boundary layer of T-10 tokamak were carried out using carbon strips as deposition probes. Analysing these probes by RBS and ERD deuterium impact energies of 25–40 eV could be estimated from the saturation behaviour of deuterium in carbon. The high impurity concentration level and it's time behaviour give indications for local impurity producing sources playing an important role for the impurity transport in the near wall plasma.     

The influence of magnetic impurities on thermodynamic characteristics of antiferromagnets

The thermodynamic behaviour of an impurity spin interacting with both one and another sublattice of an antiferromagnet with the “easy axis” anisotropy type is considered in the framework of phenomenological theory. The direct interaction between impurity magnetic moments is assumed to be negligible. The ground (pure Neel) state of the host lattice is shown to become unstable in the presence of an impurity. At this condition a local magnetic distortion being “frozen” in the vicinity of an impurity takes place and gives rise to appearance of a local ferromagnetism vector perpendicular to the anisotropy axis. Such phenomenon may be described as a local phase transition within the host lattice.     

Electronic transmission through a ladder with a single side-attached impurity

We study the electronic transmission of a model system composed by two coupled chains with an impurity attached to one of them. Analytical espressions for the transmittivity and for the diagonal and the off-diagonal Green’s function matrix elements are derived. Green’s function behaviour as function of the charge carrier energy is exploited to interpret the system transmittivity calculated by the scattering matrix formalism. We find that while a single substitutional impurity in the ladder may generate a Fano resonance in the transmittivity in the lower or in the higher energy part of the spectrum, in the case of a single side-attached impurity to the ladder, a resonance is found in each energy region. We interpret such resonances in terms of local density of states and off-diagonal Green’s function matrix elements.     

Impurity pair modes in a diatomic linear chain: nearest neighbour pair

The behaviour of the impurity modes due to a pair of substitutional impurities characterized by both mass as well as force-constant changes and occupying nearest neighbour positions in a diatomic linear chain, is studied. The results are compared with those for the case of impurity pairs occupying next nearest neighbour sites discussed earlier as well as the existing three dimensional calculations of Elliott and Pfeuty. The nearest neighbour impurity pair gap and local modes can be interpreted in terms of two single impurities substituted in the two different sublattices unlike the next nearest neighbour pair modes. The inband resonant modes are totally new features characteristic of the pair. Finally, the predictions of the theory are compared with the available experimental data for Si-impurity-pair-complexes and qualitative agreement is shown.     

Local impurity phase pinning and pinning force in charge density waves

Starting from the static Fukuyama-Lee-Rice equation for a three-dimensional incommensurate charge density wave (CDW) in quasi one-dimensional conductors a solvable model for local phase pinning by impurities is defined and studied. We find that average CDW energy and average pinning force show critical behaviour with respect to the pinning parameter h. Specifically the pinning force exhibits a threshold at h=1 with exponent . Our model exemplifies a general concept of local impurity pinning in which the force exerted by the impurity on the periodic CDW structure becomes multivalued and metastable states appear beyond a threshold. It is found that local impurity pinning becomes less effective at low temperatures and may eventually cease completely. These results are independent of spatial dimensionality as expected for local impurity pinning. Comparison with Larkin's model is also made. Received 8 July 1998     

Tunneling conductance of Al-oxide-Al junctions doped with Ni at the oxide-Al interface

The effect of a Ni impurity layer at the Oxide-Al interface has been studied for thickness in the range between 0.3 nm and 100 nm. The results obtained from the temperature dependence of the zero bias conductance and the voltage dependence of the dynamic resistance exhibit structures being due to the dynamics of spin-flip scattering and impurity interaction. We show that at a layer thickness of 1.5 nm Ni the behaviour of the tunnel junctions changes drastically because of the occurence of the magnetic interaction between the impurity atoms.     

The two-dimensional Ising model with isolated impurity

We study the behaviour of a single impurity in a two-dimensional Ising model. Local properties in the neighbourhood of the impurity are calculated exactly. The results show that the critical exponents remain unchanged, but the critical amplitudes undergo pronounced changes. Furthermore, we develop a real-space renormalisation group for the perturbed system and calculate by means of two different approximate realisations the correlation functions near the impurity. In all cases we find that an ordered cluster forms around the impurity at temperatures well above the critical temperature. We discuss the relation of this effect to the local freezing-out phenomenon.     

Sound velocity change in doped displacive ferroelectrics

An expression is obtained for the sound velocity change in doped displacive ferroelectrics, in the presence of an electric field by considering higher order anharmonic terms in the modified Silverman-Joseph Hamiltonian. The mass and force constant changes due to impurity may give cancellation effects. The presence of higher order anharmonicity decreases the sound velocity which in turn varies with the applied electric field. The sound velocity decreases anomalously near the Curie temperature.     

Reaction of a dislocation-impurity system to an electromagnetic excitation

In experiments on indium antimonide single crystals, the dynamic behavior of a screw dislocation-impurity ambient system was studied. It was found that local absorption of electromagnetic energy takes place in this system, leading to development of relaxation processes which change the system energy and, consequently, its dynamic properties. It is remarkable that the system can be activated by an electromagnetic field due to the presence of impurity ambient around otherwise inactive screw dislocations.     

一维单原子链中杂质引起的局域振动模

讨论了一维单原子链中杂质引起的晶格局域振动模和局域振动图像,分析了杂质质量和杂质近邻力常数对振动模的影响,通过数值求解晶格振动运动方程组．给出了局域振动模关于杂质质量和杂质近邻力常数分布的相图;分析了含杂质晶格振动模频率相对于完整晶格振动模频率的变化。     

Character of order-disorder and displacive components in barium titanate

Reconciling the apparently contradictory results of NMR and x-ray absorption fine structure measurements on the ferroelectric perovskite BaTiO3 gives insight into the character of the displacive and order-disorder components of the phase transitions of this material. The order-disorder component in the transition consists of local atomic displacements from cubic symmetry of constant magnitude that partially lose long-range order, while the displacive component consists of reorientation of these displacements.     

Displacive and order-disorder behavior of KDP-type ferroelectrics on the local scale

The modified strong dipole-proton coupling (MSDPC) model, which predicted several static and dynamic dielectric properties of KH₂PO₄ or KDP-type ferroelectrics, was used to investigate the properties of these crystals on the local scale. Results calculated by molecular dynamics (MD) simulation show that both order-disorder and displacive characteristics of one PO₄ dipole are present in KDP and KD₂PO₄ (DKDP). These results correlate with experimental data from NMR and neutron scattering studies of local properties.     

Intermediate valence impurity with a local boson field. Response to external probes

The spinless Anderson impurity model accomplished by the coupling with local bosons is considered in the context of the response to external probes. The influence of the electron-boson coupling on the behaviour of the spectral functions is analysed with the help of the method of equations of motion for Green functions within the approximation scheme, leading to analytical expressions. With the increase of electron-boson coupling the boson satellite appears in the spectra whose structure is then smeared.     

Mode-locking of self-generated oscillations in a semiconductor model for low-temperature impurity breakdown

The nonlinear dynamic behaviour of a model for self-generated, spatially coupled current oscillations in two separated parts of a semiconductor is analysed. The model involves impurity impact ionization, nonlinear energy relaxation of hot carriers, and energy exchange between the two subsystems. Quasiperiodicity and mode-locking are obtained, and characterized by a suitably defined rotation number and a spectral bifurcation diagram. The mode-locking structure is found to obey the Farey tree ordering, and can be understood on the basis of the circle map theory, assuming a particular path in the two-dimensional phase diagram of the circle map.