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Register a new userMeasuring the Penetration Depth Anisotropy in MgB$_2$ using Small-Angle Neutron Scattering
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Using small-angle neutron scattering we have measured the misalignment between an applied field of 4 kOe and the flux-line lattice in MgB$_2$, as the field is rotated away from the c axis by an angle $theta$. The measurements, performed at 4.9 K, showed the vortices canting towards the c axis for all field orientations. Using a two-band/two-gap model to calculate the magnetization we are able to fit our results yielding a penetration depth anisotropy, $glam = 1.1 pm 0.1$.
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A study of the pressure effect on the magnetic penetration depth $lambda$ in polycrystalline MgB$_{2}$ was performed by measuring the temperature dependence of the magnetization under an applied pressure of 0.15 and 1.13 GPa. We found that $lambda^{-2}$ at low temperature is only slightly affected by pressure [$frac{Delta lambda^{-2}}{lambda^{-2}} = 1.5(9)%$], in contrast to cuprate superconductors, where, in the same range of pressure, a very large effect on $lambda^{-2}$ was found. Theoretical estimates indicate that most of the pressure effect on $lambda^{-2}$ in MgB$_2$ arises from the electron-phonon interaction.
Spanning a broad range of physical systems, complex symmetry breaking is widely recognized as a hallmark of competing interactions. This is exemplified in superfluid $^3$He which has multiple thermodynamic phases with spin and orbital quantum numbers $S=1$ and $L=1$, that emerge on cooling from a nearly ferromagnetic Fermi liquid. The heavy fermion compound UPt$_3$ exhibits similar behavior clearly manifest in its multiple superconducting phases. However, consensus as to its order parameter symmetry has remained elusive. Our small angle neutron scattering measurements indicate a linear temperature dependence of the London penetration depth characteristic of nodal structure of the order parameter. Our theoretical analysis is consistent with assignment of its symmetry $L=3$ odd parity state for which one of the three thermodynamic phases in non-zero magnetic field is chiral.
The penetration depth lambda of MgB2 was deduced from both the ac susceptibility chi and the magnetization M(H) of sorted powders. The good agreement between the two sets of data without geometric correction for the grain orientation suggests that MgB2 is an isotropic superconductor.
We demonstrate that images of flux vortices in a superconductor taken with a transmission electron microscope can be used to measure the penetration depth and coherence length in all directions at the same temperature and magnetic field. This is particularly useful for MgB$_2$, where these quantities vary with the applied magnetic field and values are difficult to obtain at low field or in the $c$-direction. We obtained images of flux vortices from an MgB$_2$ single crystal cut in the $ac$ plane by focussed ion beam milling and tilted to $45^circ$ with respect to the electron beam about its $a$ axis. A new method was developed to simulate these images which accounted for vortices with a non-zero core in a thin, anisotropic superconductor and a simplex algorithm was used to make a quantitative comparison between the images and simulations to measure the penetration depths and coherence lengths. This gave penetration depths $Lambda_{ab}=100pm 35$ nm and $Lambda_c=120pm 15$ nm at 10.8 K in a field of 4.8 mT. The large error in $Lambda_{ab}$ is a consequence of tilting the sample about $a$ and had it been tilted about $c$, the errors would be reversed. Thus, obtaining the most precise values requires taking images of the flux lattice with the sample tilted in more than one direction. In a previous paper, we obtained a more precise value using a sample cut in the $ab$ plane. Using this value gives $Lambda_{ab}=107pm 8$ nm, $Lambda_c=120pm 15$ nm, $xi_{ab}=39pm 11$ nm and $xi_c=35pm 10$ nm which agree well with measurements made using other techniques. The experiment required two days to conduct and does not require large-scale facilities. It was performed on a very small sample: $30times 15$ microns and 200 nm thick so this method could prove useful for characterising new superconductors where only small single crystals are available.
We present studies of the magnetic field distribution around the vortices in LuNi2B2C. Small-angle neutron scattering measurements of the vortex lattice (VL) in this material were extended to unprecedentedly large values of the scattering vector q, obtained both by using high magnetic fields to decrease the VL spacing and by using higher order reflections. A square VL, oriented with the nearest neighbor direction along the crystalline [110] direction, was observed up to the highest measured field. The first-order VL form factor, |F(q10)|, was found to decrease exponentially with increasing magnetic field. Measurements of the higher order form factors, |F(qhk)|, reveal a significant in-plane anisotropy and also allow for a real-space reconstruction of the VL field distribution.
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