• Exact property estimation from diffusion Monte Carlo with minimal stochastic reconfiguration /

      Bosá, Ivana.; Department of Earth Sciences (Brock University, 2004-07-14)
      Our objective is to develop a diffusion Monte Carlo (DMC) algorithm to estimate the exact expectation values, ($o|^|^o), of multiplicative operators, such as polarizabilities and high-order hyperpolarizabilities, for isolated atoms and molecules. The existing forward-walking pure diffusion Monte Carlo (FW-PDMC) algorithm which attempts this has a serious bias. On the other hand, the DMC algorithm with minimal stochastic reconfiguration provides unbiased estimates of the energies, but the expectation values ($o|^|^) are contaminated by ^, an user specified, approximate wave function, when A does not commute with the Hamiltonian. We modified the latter algorithm to obtain the exact expectation values for these operators, while at the same time eliminating the bias. To compare the efficiency of FW-PDMC and the modified DMC algorithms we calculated simple properties of the H atom, such as various functions of coordinates and polarizabilities. Using three non-exact wave functions, one of moderate quality and the others very crude, in each case the results are within statistical error of the exact values.
    • An experimental investigation of dechanneling in copper single crystals

      Tulonen, Paul V. G.; Department of Physics (Brock University, 1984-07-09)
      This investigation comprises a comparison of experimental and theoretical dechanneling of MeV protons in copper single crystals. Dechanneling results when an ion's transverse energy increases to the value where the ion can undergo small impact parameter collisions with individual atoms. Depth dependent dechanneling rates were determined as functions of lattice temperature, ion beam energy and crystal axis orientation. Ion beam energies were IMeV and 2MeV,temperatures ranged from 35 K to 280 K and the experiment was carried out along both the (lOa) and <110) axes. Experimental data took the form of aligned and random Rutherford backscattered energy spectra. Dechanneling rates were extracted from these spectra using a single scattering theory that took explicit account of the different stopping powers experienced by channeled and dechanneled ions and also included a correction factor to take into account multiple scattering effects along the ion's trajectory. The assumption of statistical equilibrium and small angle scattering of the channeled ions allows a description of dechanneling in terms of the solution of a diffusion like equation which contains a so called diffusion function. The diffusion function is shown to be related to the increase in average transverse energy. Theoretical treatments of increase in average transverse energy due to collisions of projectiles with channel electrons and thermal perturbations in the lattice potential are reviewed. Using the diffusion equation and the electron density in the channel centre as a fitting parameter dechanneling rates are extracted. Excellent agreement between theory and experiment has been demonstrated. Electron densities determined in the fitting procedure appear to be realistic. The surface parameters show themselves to be good indicators of the quality of the crystal.
    • Extracting Ramachandran torsional angle distributions from 2D NMR data using Tikhonov regularization /

      Keyvanloo Shahrestanaky, Amirmohamad.; Department of Physics (Brock University, 2004-06-29)
      Solid state nuclear magnetic resonance (NMR) spectroscopy is a powerful technique for studying structural and dynamical properties of disordered and partially ordered materials, such as glasses, polymers, liquid crystals, and biological materials. In particular, twodimensional( 2D) NMR methods such as ^^C-^^C correlation spectroscopy under the magicangle- spinning (MAS) conditions have been used to measure structural constraints on the secondary structure of proteins and polypeptides. Amyloid fibrils implicated in a broad class of diseases such as Alzheimer's are known to contain a particular repeating structural motif, called a /5-sheet. However, the details of such structures are poorly understood, primarily because the structural constraints extracted from the 2D NMR data in the form of the so-called Ramachandran (backbone torsion) angle distributions, g{^,'4)), are strongly model-dependent. Inverse theory methods are used to extract Ramachandran angle distributions from a set of 2D MAS and constant-time double-quantum-filtered dipolar recoupling (CTDQFD) data. This is a vastly underdetermined problem, and the stability of the inverse mapping is problematic. Tikhonov regularization is a well-known method of improving the stability of the inverse; in this work it is extended to use a new regularization functional based on the Laplacian rather than on the norm of the function itself. In this way, one makes use of the inherently two-dimensional nature of the underlying Ramachandran maps. In addition, a modification of the existing numerical procedure is performed, as appropriate for an underdetermined inverse problem. Stability of the algorithm with respect to the signal-to-noise (S/N) ratio is examined using a simulated data set. The results show excellent convergence to the true angle distribution function g{(j),ii) for the S/N ratio above 100.
    • Far infared reflectance along the C-axis of the charge stripe superconductor La1.875Ba0.125CuO4.

      Dempsie, Brad; Department of Physics (Brock University, 2011-03-08)
      Reflectance measurements along the c-axis of La1.875 Bao.125CU04 at temperatures above(6K) and below(O.5K) the bulk superconducting transition temperature(3K) were performed using a Bruker rapid scan spectrometer and a Martin-Puplett polarizing spectrometer. It was found that when polarized light reflected from a sample the Bruker rapid scan spectrometer has a low frequency cutoff of lOcm-1 while the Martin-Puplett polarizing spectrometer has a low frequency cutoff of 6cm-1 A superconducting pla ma edge was absent in all measurements taken. It was concluded that if a superconducting plasma edge exists in La1.875Bao.125CU04 it is below 6cm-1.
    • Far infrared optical properties of V and Cr doped Sb2Te3 /

      Madubuonu, Anthony.; Department of Physics (Brock University, 2009-06-15)
      The far infrared reflectance of Sb2Te3 , Sbi.97Vo.o3Te3 and Sbi.94Cr .o6Te3 was measured near normal incidence at different temperatures (between 45K and 300K). The direct current resistivities of the above samples were also measured between the temperatures of 4K and 300K. Also Kramers Kronig (KK) analyses were performed on the reflectance spectra to obtain the optical conductivities. In the doped samples, it was observed that a phonon at 62cm-1 softens to about 55cm-1 on decreasing the temperature from 295K to 45K. Also, it was observed that the plasma frequency of the doped samples is independent of doping. The scattering rate for the vanadium doped sample was seen to be greater than that for the chromium doped sample despite the fact that vanadium impurity density is less than that of chromium. The Drude-Lorentz model fits to the KK optical conductivity show that the samples used in this work are conventional metals. Definitive measurements of the temperature dependence of the scattering rate across the ferromagnetic transition await equipment changes allowing measurements at low temperature using the mercury cadmium telluride (MCT) detector.
    • Far infrared reflectance and optical properties of organic superconductor (TMTSF)2ClO4 /

      Ellison, Rodica.; Department of Physics (Brock University, 2001-05-21)
      Polarized reflectance measurements of the quasi I-D charge-transfer salt (TMTSFh CI04 were carried out using a Martin-Puplett-type polarizing interferometer and a 3He refrigerator cryostat, at several temperatures between 0.45 K and 26 K, in the far infrared, in the 10 to 70 cm- 1 frequency range. Bis-tetramethyl-tetraselena-fulvalene perchlorate crystals, grown electrochemically and supplied by K. Behnia, of dimensions 2 to 4 by 0.4 by 0.2 mm, were assembled on a flat surface to form a mosaic of 1.5 by 3 mm. The needle shaped crystals were positioned parallel to each other along their long axis, which is the stacking direction of the planar TMTSF cations, exposing the ab plane face (parallel to which the sheets of CI04 anions are positioned). Reflectance measurements were performed with radiation polarized along the stacking direction in the sample. Measurements were carried out following either a fast (15-20 K per minute) or slow (0.1 K per minute) cooling of the sample. Slow cooling permits the anions to order near 24 K, and the sample is expected to be superconducting below 1.2 K, while fast cooling yields an insulating state at low temperatures. Upon the slow cooling the reflectance shows dependence with temperature and exhibits the 28 cm- 1 feature reported previously [1]. Thermoreflectance for both the 'slow' and 'fast' cooling of the sample calculated relative to the 26 K reflectance data indicates that the reflectance is temperature dependent, for the slow cooling case only. A low frequency edge in the absolute reflectance is assigned an electronic origin given its strong temperature dependence in the relaxed state. We attribute the peak in the absolute reflectance near 30 cm-1 to a phonon coupled to the electronic background. Both the low frequency edge and the 30 cm-1 feature are noted te shift towards higher frequcncy, upon cntering the superconducting state, by an amount of the order of the expected superconducting energy gap. Kramers-Kronig analysis was carried out to determine the optical conductivity for the slowly cooled sample from the measured reflectance. In order to do so the low frequency data was extrapolated to zero frequency using a Hagen-Ru bens behaviour, and the high frequency data was extended with the data of Cao et al. [2], and Kikuchi et al. [3]. The real part of the optical conductivity exhibits an asymmetric peak at 35 cm-1, and its background at lower frequencies seems to be losing spectral weight with lowering of the temperature, leading us to presume that a narrow peak is forming at even lower frequencies.
    • Far infrared spectroscopy of heavy fermion superconductor CeCoIn5

      Ocadlík, Stanislav.; Department of Physics (Brock University, 2004-07-09)
      The optical response to far infrared radiation has been measured on a mosaic of heavy fermion CeColnssingle crystals. The superconducting transition temperature of the crystals has been determined by van der Pauw resistivity and ac-susceptibility measurements as Tc = 2.3 K. The optical measurements were taken above and below the transition temperature using a 3He cryostat and step and integrate Martin-Puplett type polarizing interferometer. The absolute reflectance of the heavy fermion CeColns in the superconducting state in range (0, 100)cm-1 was calculated from the measured thermal reflectance, using the normal state data of Singley et al and a low frequency extrapolation for a metallic material in the Hagen-Rubens regime. By means of Kramers-Kronig analysis the absolute reflectance was used to calculate the optical conductivity of the sample. The real part of the calculated complex conductivity 0-(w) ofCeColns indicates a possible opening of an energy gap close to 50 em-I.
    • Far infrared spectroscopy of heavy fermion superconductor CeCoIn5 /

      Ocadlík, Stanislav.; Department of Physics (Brock University, 2004-07-14)
      The optical response to far infrared radiation has been measured on a mosaic of heavy fermion CeCoIns single crystals. The superconducting transition temperature of the crystals has been determined by van der Pauw resistivity and ac-susceptibility measurements as Tc = 2.3 K. The optical measurements were taken above and below the transition temperature using a ^He cryostat and step and integrate Martin-Puplett type polarizing interferometer. The absolute reflectance of the heavy fermion CeCoIns in the superconducting state in range (0, 100)cm~^ was calculated from the measured thermal reflectance, using the normal state data of Singley et al and a low frequency extrapolation for a metallic material in the Hagen-Rubens regime. By means of Kramers-Kronig analysis the absolute reflectance was used to calculate the optical conductivity of the sample. The real part of the calculated complex conductivity a{u)) of CeCoIns indicates a possible opening of an energy gap close to 50 cm~^.
    • Far-infrared optical properties of the heavy fermion superconductor UB[E13]

      Brown, Adán.; Department of Physics (Brock University, 2001-07-09)
      Temperature dependent resistivity, p, magnetic susceptibility, X, and far-infrared reflectance measurements were made on the low Tc superconductor UBe13. Two variants of UBe13 have been proposed, named 'L'- (for low Tc ) and 'H'-type (for high Tc ). Low temperature resistivity measurements confirmed that our sample was of H-type and that the transition temperature was at 0.9 K. This was further confirmed with the observation of this transition in the AC-susceptibility. Low temperature reflectance measurements showed a decrease in the reflectivity as the temperature is lowered from 300 to 10 K, which is in qualitative agreement with the increasing resistivity in this temperature range as temperature is lowered. No dramatic change in the reflectivity was observed between 10 and 0.75 K. A further decrease of the reflectance was observed for the temperature of 0.5 K. The calculated optical conductivity shows a broad minimum near 80 cm-1 below 45 K. Above 45 K the conductivity is relatively featureless. As the temperature is lowered, the optical conductivity decreases. The frequency dependent scattering rate was found to be flat for temperatures between 300 and 45 K. The development of a peak, at around 70 cm-1 was found for temperatures of 45 K and below. This peak has been associated with the energy at which the transition to a coherent state occurs from single impurity scattering in other heavy fermion systems. The frequency dependent mass enhancement coefficient was found to increase at low frequencies as the frequency decreases. Its' magnitude as frequency approaches zero also increased as the temperature decreased.
    • The finite bandwidth model for spin fluctuations in Pd

      Longo, Janice P.; Department of Physics (Brock University, 1988-07-09)
      The frequency dependence of the electron-spin fluctuation spectrum, P(Q), is calculated in the finite bandwidth model. We find that for Pd, which has a nearly full d-band, the magnitude, the range, and the peak frequency of P(Q) are greatly reduced from those in the standard spin fluctuation theory. The electron self-energy due to spin fluctuations is calculated within the finite bandwidth model. Vertex corrections are examined, and we find that Migdal's theorem is valid for spin fluctuations in the nearly full band. The conductance of a normal metal-insulator-normal metal tunnel junction is examined when spin fluctuations are present in one electrode. We find that for the nearly full band, the momentum independent self-energy due to spin fluctuations enters the expression for the tunneling conductance with approximately the same weight as the self-energy due to phonons. The effect of spin fluctuations on the tunneling conductance is slight within the finite bandwidth model for Pd. The effect of spin fluctuations on the tunneling conductance of a metal with a less full d-band than Pd may be more pronounced. However, in this case the tunneling conductance is not simply proportional to the self-energy.
    • Generalization of the BTK Theory to the Case of Finite Quasiparticle Lifetimes

      Rohanizadegan, Yousef; Department of Physics (Brock University, 2013-01-24)
      A generalization to the BTK theory is developed based on the fact that the quasiparticle lifetime is finite as a result of the damping caused by the interactions. For this purpose, appropriate self-energy expressions and wave functions are inserted into the strong coupling version of the Bogoliubov equations and subsequently, the coherence factors are computed. By applying the suitable boundary conditions to the case of a normal-superconducting interface, the probability current densities for the Andreev reflection, the normal reflection, the transmission without branch crossing and the transmission with branch crossing are determined. Accordingly the electric current and the differential conductance curves are calculated numerically for Nb, Pb, and Pb0.9Bi0.1 alloy. The generalization of the BTK theory by including the phenomenological damping parameter is critically examined. The observed differences between our approach and the phenomenological approach are investigated by the numerical analysis.
    • High Temperature Method Of Measuring Electrical And Magnetic Properties Of Europium Doped Nickel Oxide

      Torabi, S. Parisa; Department of Physics
      The measurement of the magnetic moment of materials as a function of temperature in modern AC or DC magnetometers normally has a limited high temperature range up to 400 K. To overcome this problem one needs to design ovens which can handle high temperatures. The highest Curie temperature observed in materials is in pure Co which is about 1400 K. However, most materials and compounds show Tc below 800 K. My thesis research topic is to study the substitution of Ni ions by rare earth ions in NiO. The NiO is a semiconductor which exhibits antiferromagnetism below 520 K, which makes it suitable for applications; to name a few, rechargeable batteries, and p-type transport conducting lms. In this study, Ni ions were substituted by 2, 5, and 8 percent of Eu ions. The effect of substitution on the semiconducting properties of Ni1-xEuxO was studied as function of temperature from room temperature to 1000 K. To study the magnetic properties and the effect of Eu substitution on the Neel temperature of Ni1-xEuxO we adapted two ovens for high temperature measurements of AC susceptibility by using the ac modulation technique implementing a lock-in ampli er and the DC susceptibility using the SQUID magnetometer. To check the reliability of these two ovens we also examined the ferromagnetic transition temperatures of Bismuth Ferrite samples as function of Co substitutions for Fe.
    • Histogram filtering as a tool in variational Monte Carlo optimization

      Å najdr, Martin.; Department of Physics (Brock University, 1999-07-09)
      Optimization of wave functions in quantum Monte Carlo is a difficult task because the statistical uncertainty inherent to the technique makes the absolute determination of the global minimum difficult. To optimize these wave functions we generate a large number of possible minima using many independently generated Monte Carlo ensembles and perform a conjugate gradient optimization. Then we construct histograms of the resulting nominally optimal parameter sets and "filter" them to identify which parameter sets "go together" to generate a local minimum. We follow with correlated-sampling verification runs to find the global minimum. We illustrate this technique for variance and variational energy optimization for a variety of wave functions for small systellls. For such optimized wave functions we calculate the variational energy and variance as well as various non-differential properties. The optimizations are either on par with or superior to determinations in the literature. Furthermore, we show that this technique is sufficiently robust that for molecules one may determine the optimal geometry at tIle same time as one optimizes the variational energy.
    • The infared optical properties of Sr2RuO4 and SmTiO3 including an object-oriented resistivity interface /

      Hildebrand, Mylo George.; Department of Physics (Brock University, 1999-05-21)
      The perovskite crystal structure is host to many different materials from insulating to superconducting providing a diverse range of intrinsic character and complexity. A better fundamental description of these materials in terms of their electronic, optical and magnetic properties undoubtedly precedes an effective realization of their application potential. SmTiOa, a distorted perovskite has a strongly localized electronic structure and undergoes an antiferromagnetic transition at 50 K in its nominally stoichiometric form. Sr2Ru04 is a layered perovskite superconductor (ie. Tc % 1 K) bearing the same structure as the high-tem|>erature superconductor La2_xSrrCu04. Polarized reflectance measurements were carried out on both of these materials revealing several interesting features in the far-infrared range of the spectrum. In the case of SmTiOa, although insulating, evidence indicates the presence of a finite background optical conductivity. As the temperature is lowered through the ordering temperature a resonance feature appears to narrow and strengthen near 120 cm~^ A nearby phonon mode appears to also couple to this magnetic transition as revealed by a growing asymmetry in the optica] conductivity. Experiments on a doped sample with a greater itinerant character and lower Neel temperature = 40 K also indicate the presence of this strongly temperature dependent mode even at twice the ordering temperature. Although the mode appears to be sensitive to the magnetic transition it is unclear whether a magnon assignment is appropriate. At very least, evidence suggests an interesting interaction between magnetic and electronic excitations. Although Sr2Ru04 is highly anisotropic it is metallic in three-dimensions at low temperatures and reveals its coherent transport in an inter-plane Drude-like component to the highest temperatures measured (ie. 90 K). An extended Drude analysis is used to probe the frequency dependent scattering character revealing a peak in both the mass enhancement and scattering rate near 80 cm~* and 100 cm~* respectively. All of these experimental observations appear relatively consistent with a Fermi-liquid picture of charge transport. To supplement the optical measurements a resistivity station was set up with an event driven object oriented user interface. The program controls a Keithley Current Source, HP Nano-Voltmeter and Switching Unit as well as a LakeShore Temperature Controller in order to obtain a plot of the Resistivity as a function of temperature. The system allows for resistivity measurements ranging from 4 K to 290 K using an external probe or between 0.4 K to 295 K using a Helium - 3 Cryostat. Several materials of known resistivity have confirmed the system to be robust and capable of measuring metallic samples distinguishing features of several fiQ-cm.
    • Infrared Spectroscopy of (Nb+In) Co-Doped Rutile

      Yee, Susan; Department of Physics
      This work studied rutile TiO2 in pure form and co-doped with In (e􀀀 acceptor) and Nb (e􀀀 donor) at 5% and 10% to explore the effect of co-doping on the infrared active (IR) modes and the complex dielectric response function between 50 and 8000 cm􀀀1 (1.5 - 240 THz, 0.00620 - 0.993 eV). Ceramic pellets of pure, 5% and 10% co-doped TiO2 were prepared using a standard technique. Infrared reflectance (IR) measurements were taken and these data are supplemented with data from the literature to extend the range of frequencies beyond infrared. The dielectric function was determined two ways: (i) by fits of the reflectance to the factorized model of the dielectric function and (ii) by Kramers- Kronig analysis. Co-doping rutile appears to decrease the permittivity at frequencies just below the mode that softens. It is possible that this is due to an increase in porosity resulting from codoping. It appears that the increase in permittivity recently observed elsewhere [1] is not caused by doping induced changes to the phonon modes. The overall effect of co-doping is to make the sample less reflective. The spectrum is composed of three wide, high-reflectance bands. For all levels of co-doping the first band is a mode that softens. The amount of doping does not affect the frequency of the mode that softens. The second and third bands are hard modes. Co-doping appears to introduce four new, impurity, phonon modes that increase in oscillator strength with increasing co-doping level. These modes are centered near w 136, 447, 654 and 793 cm􀀀1 which are close to four, previously observed, Raman active modes in rutile. It is possible that the co-doping process causes the Raman modes to develop a dipole moment and become weakly IR active.
    • Infrared Spectroscopy Of Ba_3+y Co_1+xNb_2O_9 Ceramics

      Ibrahim, Samia; Department of Physics
      The dielectric properties of ceramic Ba3+y Co1+xNb2O9 where x= 0,-0.07,0.03 and y = 0, -0.03 were characterized because it might used for a wide range of applications including wireless communication used in mobile communication, ultra high speed local area networks, intelligent transport system and satellite communications. Room temperature optical re ectivity measurements of ceramics sintered at di erent temperatures between 1200 C to 1500 C were made covering the spectral range between 70-8000 cm􀀀1. The Lorentz model was used to t the re ectance data to make extrapolations for Kramers Kronig (K-K) analysis and to estimate the microwave properties. K -K analysis was applied to extract the other optical response functions from the re ectance data ( optical conductivity and dielectric permittivity). Powder X-Ray di raction measurements were done with 2 in the range between 10 to 80 degree for all samples. Most samples exhibit some degree of 1:2 ordering which appears as small superlattice peaks at 17.6 and 12 degree. All samples exhibit a small amount of impurity phases. The main purpose of this work is to study the e ect of the density, 1:2 ( Co:Nb) ordering and concentration of Cobalt on the dielectric properties. It was shown that density has a clear e ect on the dielectric properties. For example 1 (50 cm􀀀1) decreased if the densjhfnadfity decreased. On the other hand the change of the concentration of Cobalt does not have any real e ect on the dielectric properties. 1:2 order also has an e ect on the dielectric properties. It was observed that the scattering rate of the optical phonon was smaller in sample exhibiting more 1:2 order.
    • Infrared Spectroscopy of Gadolinium

      Obied, Laila; Department of Physics (2013-04-10)
      Measurements of the optical reflectivity of the normal incident light along c-axis [0001] have been made on a Gadolinium single crystal, for temperatures between 50 K and room temperature just above the Curie temperature of Gd, which is 293 K. And covering the spectrum range between 100 -11000 cm-I . This work is the first study of Gd in the far infrared range. In fact it fills the gap below 0.2 eV which has never been measured before. Extreme attention was paid to the fact that Gadolinium is a very reactive metal with air. Thus, the sample was mechanically polished and carefully handled during the measurement. However, temperature dependent optical measurements have been made in the same frequency range for a sample of Gd2O3. For comparison, both samples of Gd and Gd2O3 were examined by X-Ray diffraction. XRD analysis showed that the sample was pure gadolinium and the oxide layer either does not exist, or is very thin. Furthermore, this fact was supported by the absence of any of Gd2O3 features in the Gd sample reflectivity. Kramers Kronig analysis was applied to extract the optical functions from the reflectance data. The optical conductivity shows a strong temperature dependence feature in the mid-infrared. This feature disappears completely at room temperature which supports a magnetic origin.
    • Infrared spectroscopy of Mg-doped SrRuO3 thin films /

      Eftekhari, Fatemeh.; Department of Physics (Brock University, 2006-06-01)
      The reflectance of thin films of magnesium doped SrRu03(Mg-SR0) produced by pulsed laser deposition on SrTiOa (100) substrates has been measured at room temperature between 100 and 7500 cm~^. The films were chosen to have wide range of thickness, stoichiometry and electrical properties. As the films were very thin (less than 300 nm), and some were insulating the reflectance data shows structures due to both the film and the substrate. Hence, the data was analyzed using Kramers-Kronig constrained variational fitting (VDF) method to extract the real optical conductivity of the Mg-SRO films. Although the VDF technique is flexible enough to fit all features of the reflectance spectra, it seems that VDF could not eliminate the substrate's contribution from fllm conductivity results. Also the comparison of the two different programs implementing VDF fltting shows that this technique has a uniqueness problem. The optical properties are discussed in light of the measured structural and transport properties of the fllms which vary with preparation conditions and can be correlated with differences in stoichiometry. This investigation was aimed at checking the VDF technique and also getting answer to the question whether Mg^"*" substitutes in to Ru or Sr site. Analysis of our data suggests that Mg^+ goes to Ru site.
    • Interaction between vortices and impurities in a d-wave superconductor /

      Farhoodfar, Avid.; Department of Physics (Brock University, 2005-06-15)
      High temperature superconductors were discovered in 1986, but despite considerable research efforts, both experimental and theoretical, these materials remain poorly understood. Because their electronic structure is both inhomogeneous and highly correlated, a full understanding will require knowledge of quasiparticle properties both in real space and momentum space. In this thesis, we will present a theoretical analysis of the scanning tunneling microscopy (STM) data in BSCCO. We introduce the Bogoliubov-De Gennes Hamiltonian and solve it numerically on a two-dimensional 20 x 20 lattice under a magnetic field perpendicular to the surface. We consider a vortex at the center of our model. We introduce a Zn impurity in our lattice as a microscopic probe of the physical properties of BSCCO. By direct numerical diagonalization of the lattice BogoliubovDe Gennes Hamiltonian for different positions of the impurity, we can calculate the interaction between the vortex and the impurity in a d-wave superconductor.
    • Investigation into the Magnetoelectric Effect and Magnetic Properties of Iron-doped Cobalt Molybdate

      Pula, Mathew; Department of Physics
      The plausibility of revealing linear magnetoelectric coupling is investigated in the cobalt molybdate (Co2Mo3O8). Recently, Wang et al.[Scientific Reports. 2015;Vol. 5:Article 12268] showed that iron molybdate(Fe2Mo3O8) can be induced into a ferrimagnetic state from a nominal antiferromagnetic state via application of a magnetic field. As such, it may be possible that cobalt molybdate exhibits a similar effect intrinsically or with addition of iron dopant. Single crystals of the hexagonal molybdate (Co(1-x)Fe(x))2Mo3O8 (x=0, 0.25, 0.5, 0.75, 1) were synthesized via chemical vapour transport. The magnetic properties were investigated along the polar axis and in the basal plane. Despite doping with iron, no metamagnetic phase transition was present in (Co(1-x)Fe(x))2Mo3O8 (x=0.25, 0.5, 0.75). Low field measurements of the susceptibility reveal the presence of an anisotropic ferromagnetic-like moment, which is suppressed at moderate fields. This is believed to be a product of an exchange-bias-like phenomena, which is not fully understood. The magnetocapacitance was measured along the c-axis for x=(0.25, 0.5). Co1.5Fe0.5Mo3O8 exhibits the conventional magnetodielectric effect, with a proportionality constant of 5.1(0.3) x10^(-14) Oe^(-2) at 40K, while the capacitance of Co1Fe1Mo3O8 shows linear dependency on H, with slope -6.99(0.07) x10^(-9) Oe^(-1) at 49K.