Low-Cost Experiments with Everyday Objects for Homework Assignments

We describe four classical undergraduate physics experiments that were done with everyday objects and low-cost sensors: mechanical oscillations, transmittance of light through a slab of matter, beam deformation under load, and thermal relaxation due to heat loss. We used these experiments to train students for experimental homework projects but they could be used and expanded in a variety of contexts: lecture demonstrations, low cost students' labs, science projects, distance learning courses...Comment: details on students where added : a section dedicated to the student difficulties and general feedback on this teaching unit. Minor typos were fixed. Published in Physics Educatio

Atomic coexistence of superconductivity and incommensurate magnetic order in the Ba(Fe1-xCox)2As2 pnictide

75As NMR and susceptiblity were measured in a Ba(Fe1-xCox)2As2 single crystal for x=6%. Nuclear Magnetic Resonance (NMR) spectra and relaxation rates allow to show that all Fe sites experience an incommensurate magnetic ordering below T=31K. Comparison with undoped compound allows to estimate a typical moment of 0.05 muB. Anisotropy of the NMR widths can be interpreted using a model of incommensurability with a wavevector (1/2-eps,0,l) with eps of the order of 0.04. Below TC=21.8K, a full volume superconductivity develops as shown by susceptibility and relaxation rate, and magnetic order remains unaffected, demonstrating coexistence of both states on each Fe site.Comment: 4 pages, 4 figure

Study of one-dimensional nature of (Sr,Ba)_2Cu(PO_4)_2 and BaCuP_2O_7 via 31P NMR

The magnetic behavior of the low-dimensional phosphates (Sr,Ba)_2 Cu(PO_4)_2 and BaCuP_2O_7 was investigated by means of magnetic susceptibility and ^{31}P nuclear magnetic resonance (NMR) measurements. We present here the NMR shift K(T), the spin-lattice 1/T_1 and spin-spin 1/T_2 relaxation-rate data over a wide temperature range 0.02 K < T < 300 K. The T-dependence of the NMR K(T) is well described by the S=1/2 Heisenberg antiferromagnetic chain model with an intrachain exchange of J/k_B = 165 K, 151 K, and 108 K in Sr_2Cu(PO_4)_2, Ba_2Cu(PO_4)_2, and BaCuP_2O_7, respectively. Our measurements suggest the presence of magnetic ordering at 0.8 K in BaCuP_2O_7 (J/k_B = 108 K). For all the samples, we find that 1/T_1 is nearly T-independent at low-temperatures (1 K < T < 10 K), which is theoretically expected for 1D chains when relaxation is dominated by fluctuations of the staggered susceptibility. At high temperatures, 1/T_1 varies nearly linearly with temperature

Hall effect in the normal state of high Tc cuprates

We propose a model for explaining the dependence in temperature of the Hall effect of high Tc cuprates in the normal state in various materials. They all show common features: a decrease of the Hall coefficient RH with temperature and a universal law, when plotting RH(T)/RH(T0) versus T/T0, where T0 is defined from experimental results. This behaviour is explained by using the well known electronic band structure of the CuO2 plane, showing saddle points at the energies ES in the directions (0,+/-pi) and (+/-pi,0). We remark that in a magnetic field, for energies E>ES the carrier orbits are hole-like and for E<ES they are electron-like, giving opposite contributions to RH. We are abble to fit the experimental results for a wide range of hole doping, and to fit the universal curve. For us kb*T0 is simply EF-ES, where EF is the Fermi level varying with the doping.Comment: 7 pages, 11 figure

Far-infrared measurements of oxygen-doped polycrystalline La2CuO4.0315 superconductor under slow-cooled and fast-cooled conditions

We have studied the far-infrared (far-IR) charge dynamics of an equilibrated pure oxygen doped La2CuO4+0.0315 under slow-cooled and fast-cooled conditions. The superconducting transition temperature (Tc) for the slow-cooled and that for the fast-cooled processes were respectively found to be close to the two intrinsic Tc's: One at 30 K and the other at 15 K. Direct comparison with our previous results and other far-IR and Raman studies on single crystalline La2-xSrxCuO4, we conclude that the topology of the pristine electronic phases that are responsible for the two intrinsic Tc's is holes arranged into two-dimensional (2D) square lattices.Comment: Submitted to PR

Mn local moments prevent superconductivity in iron-pnictides Ba(Fe 1-x Mn x)2As2

75As nuclear magnetic resonance (NMR) experiments were performed on Ba(Fe1-xMnx)2As2 (xMn = 2.5%, 5% and 12%) single crystals. The Fe layer magnetic susceptibility far from Mn atoms is probed by the75As NMR line shift and is found similar to that of BaFe2As2, implying that Mn does not induce charge doping. A satellite line associated with the Mn nearest neighbours (n.n.) of 75As displays a Curie-Weiss shift which demonstrates that Mn carries a local magnetic moment. This is confirmed by the main line broadening typical of a RKKY-like Mn-induced staggered spin polarization. The Mn moment is due to the localization of the additional Mn hole. These findings explain why Mn does not induce superconductivity in the pnictides contrary to other dopants such as Co, Ni, Ru or K.Comment: 6 pages, 7 figure

Antiferromagnetic correlations and impurity broadening of NMR linewidths in cuprate superconductors

We study a model of a d-wave superconductor with strong potential scatterers in the presence of antiferromagnetic correlations and apply it to experimental nuclear magnetic resonance (NMR) results on Zn impurities in the superconducting state of YBCO. We then focus on the contribution of impurity-induced paramagnetic moments, with Hubbard correlations in the host system accounted for in Hartree approximation. We show that local magnetism around individual impurities broadens the line, but quasiparticle interference between impurity states plays an important role in smearing out impurity satellite peaks. The model, together with estimates of vortex lattice effects, provides a semi-quantitative description of the impurity concentration dependence of the NMR line shape in the superconducting state, and gives a qualitative description of the temperature dependence of the line asymmetry. We argue that impurity-induced paramagnetism and resonant local density of states effects are both necessary to explain existing experiments.Comment: 15 pages, 23 figures, submitted to Phys. Rev.