Scanning Tunneling Microscopy Observation of a Square Abrikosov Lattice inLuNi2B2C

Abstract

We present scanning tunneling microscopy measurements of the (001) surface of a LuNi 2 B 2 C borocarbide single crystal at 4.2 K. In zero field, the conductance versus voltage characteristics recorded at various locations on the sample reproducibly provide a gap value of 2.2 meV. In a magnetic field of 1.5 and 0.375 T, the recordings of the conductance as a function of position reveal a regular square vortex lattice tilted by 45 ± with respect to the crystalline a axis. This unusual result is correlated with an in-plane anisotropy of the upper critical field H k c2 ͑45 ± ͒͞H k c2 ͑0͒ 0.92 at 4.2 K and is analyzed within the framework of Ginzburg-Landau theory.[S0031-9007 (97)03335-8] PACS numbers: 74.60.Ge The scanning tunneling microscope (STM) is a powerful probe of the real space structure of the vortex lattice (VL) of type-II superconductors. Most other techniques, such as magnetic force microscopy [1], Bitter decoration [2], and neutron scattering [3], are sensitive to magnetic contrast on the scale of the London penetration depth l and are therefore limited to low magnetic fields. STM, in contrast, is sensitive to the local density of states on the much smaller scale of the coherence length j and can image vortices even at high fields, where the vortex spacing is smaller than l. So far, surface quality has limited the observation of vortices by STM to two materials: NbSe 2 , which presents clean atomically flat surfaces [4][5][6][7], and crystals of YBCO grown in special BaZrO 3 crucibles [8].Although the VL forms a hexagonal structure for isotropic superconductors in the absence of pinning [9,10], many deviations from this symmetry have been found, generally associated with anisotropic uniaxial character or pinning by extrinsic defects. A distorted hexagonal symmetry and vortex chains were predicted and observed by Bitter decoration [11], neutron scattering [12], and STM [8] in YBCO and BSCCO along with sawtooth VLs, hexatic lattices, order-disorder transitions, intrinsic pinning, and pinning by twin boundaries. Analogous features were found in NbSe 2 by STM [5,7] and Bitter decoration [11].On the low T c materials Nb and Pb-Tl, hexagonal, distorted hexagonal, and square VLs, depending on the crystal orientation, were observed by Bitter decoration [13,14] and neutron scattering experiments [15]. A gradual phase transition in Pb-Tl(111) of the VL from hexagonal to square for increasing field was observed and explained by an attractive interaction between the vortices when the vortex spacing is of the order of the coherence length in this low k material [16,17]. In recent neutron scattering experiments [3] a square VL which transforms to hexago-nal at very low fields [18] was observed in an ErNi 2 B 2 C single crystal. This compound belongs to the recently discovered borocarbide family [19,20] and exhibits an antiferromagnetic ordering which was shown to directly influence the VL [3].To avoid any possible coupling between magnetic ordering and the VL, we performed STM investigations on LuNi 2 B 2 C which has...

Field dependence of the vortex structure ind-wave ands-wave superconductors

“…The gradual transition from the triangular to the square vortex lattice is also observed with increasing field. 23,43 As µSR and SANS experiments have begun on these materials, we expect that the d x 2 −y 2 -wave-like nature will be detected there.…”

“…As for the orientation of the triangular lattice, the case θ 0 = 45 • has a smaller F than the case θ 0 = 0 • , but the difference is very small. Some theoretical calculations considered the vortex lattice configuration near H c2 , [21][22][23] or based on the London theory. [24][25][26] These theories suggested that the vortex lattice configuration gradually changes from the triangular lattice to the square lattice with increasing field, and the oblique lattice is realized at a lower field before settling into the square lattice.…”

Hall effect inLuNi2B2Cand<

“…One of the interesting features of some borocarbides (R=Er, Lu, Y) is the vortex lattice (VL) with unusual square symmetry [11][12][13][14] observed in the mixed state for magnetic fields H directed along tetragonal c-axis at H > ∼ 1 kOe. Square symmetry of VL can be connected 11,8 with the anisotropy of the upper critical magnetic field H c2 (T ) observed in the ab-plane for LuNi 2 B 2 C. 8,9 Practically no anisotropy of H c2 (T ) was found for YNi 2 B 2 C, 6,9 although this compound is very similar to LuNi 2 B 2 C. The reason for the difference in the behavior of these two borocarbides is still unclear.…”

Anomalous paramagnetic effects in the mixed state ofLuNi2B2C

“…According to the Gurevich-Kogan non-local London model, 14 the anisotropic nonlocal potential, which is responsible for the low-field FLL transition observed in SANS, 9 is averaged out by thermal vortex fluctuations near H c2 . Since the interaction becomes isotropic, the hexagonal Abrikosov lattice is preferable, leading to the second FLL transition from square back 28,29 The diamonds are SANS data, where the numbers next to the data indicate the degrees of the azimuthal splitting with which the transition line is determined. 9 The square and rhombic shapes are forms of vortex lattices.…”