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LuNi2B2C has the crystal structure illustrated in Figure 3.1 with lattice parameters $a = 3.4639(1)\,\textrm{\AA}$ and $c = 10.6313(4)\,\textrm{\AA}$ at temperature $T = 2.3\,\mathrm{^{\circ}C}$, leading to a calculated density of $8.488\,\mathrm{g}\,\mathrm{cm}^{-3}$ [35]. Table 3.1 lists the interatomic distances.

Table: Interatomic distances within the LuNi2B2C structure [35].
Atom pair Separation ( $\textrm{\AA}$)
B - C 1.47
Lu - C 2.449
Lu - B 2.855
B - B 2.94
Ni - B 2.10
Ni - Ni (in Ni plane) 2.449

The slightly shorter in-plane nickel separation, in comparison to that of metallic nickel ( $2.50\,\textrm{\AA}$), implies a strong metallic bond. Covalent [36] B - C bonds link the LuC and Ni2B2 layers together. As previously mentioned, the electronic properties of LuNi2B2C are of a strongly 3D metallic character. Band structure calculations indicate an average Fermi velocity $v_F = 2.3 \times 10^7\,\mathrm{cm}\,\mathrm{s}^{-1}$ [37] and a sharp local maximum in the electronic density of states N(E) near the Fermi surface EF. Normal state heat capacity  CP = Ce + Cph measurements [38] yield a Debye temperature of $\Theta_D = 360(3)\,\mathrm{K}$, related to the phononic contribution $C_{ph}
\propto T^3$, and a Sommerfeld constant $\gamma_N = 19.5(3)\,\mathrm{mJ}\,\mathrm{mol}^{-1}\,\mathrm{K}^{-2}$, the coefficient of the electronic term $C_e = \gamma_N T$. The Sommerfeld constant gives rise to an estimated Fermi surface density of states $N(E_F) = 11.8\,\mathrm{mJ}\,\mathrm{mol}^{-1}\,{k_B}^{-2}\,
\mathrm{K}^{-2}$ [39]. This, together with an experimentally determined plasma energy of $\hbar\omega_{pl} = 4.0\,\mathrm{eV}$, leads to a Fermi velocity $v_F = \sqrt{\smash[b]{3}} \hbar \omega_{pl} / [e \sqrt{\smash[b]{4 \pi N(0)}}]
= 2.76 \times 10^7\,\mathrm{cm}\,\mathrm{s}^{-1}$, in near agreement with band theory. In addition to these normal state properties, LuNi2B2C also exhibits various superconducting characteristics.

The superconducting properties of LuNi2B2C are intriguing. There exists much experimental evidence both for and against an s-wave pairing state [40]. Scanning tunneling microscopy [41] discloses a bulk energy gap of $\Delta = 2.2\,\mathrm{meV}$, and thermal conductivity measurements [42] detect a large gap anisotropy $\Delta_{max}/\Delta_{min} \ge 10$. The average out of plane upper critical field anisotropy holds constant with temperature at $0.5(H_{c2}^{\langle 100 \rangle} + H_{c2}^{\langle 110
\rangle})/H_{c2}^{\langle 001 \rangle} = 1.16$, as found from magnetisation studies [37]. The slight basal plane anisotropy falls from $H_{c2}^{\langle 100 \rangle}/H_{c2}^{\langle 110 \rangle} = 1.1$ at temperature $T = 4.5\,\mathrm{K}$ to $H_{c2}^{\langle 100
\rangle}/H_{c2}^{\langle 110 \rangle} = 1.0$ by the critical temperature Tc. The initial slope of the upper critical field gives an estimated coherence length $\xi_{BCS} = 130\,\textrm{\AA}$. On the other hand small angle neutron scattering (SANS) [43] extracts a coherence length $\xi_{BCS} = 82(2)\,\textrm{\AA}$ and a penetration depth $\lambda = 1060(30)\,\textrm{\AA}$ at temperature $T = 2.2\,\mathrm{K}$.

One of the most fascinating aspects of the superconducting behaviour of LuNi2B2C is the occurrence of field driven transitions in its vortex lattice geometry. The evolution of the flux line lattice symmetry in LuNi2B2C, as a function of external field H, is clearly evident through Bitter decoration and SANS. Under weak fields H applied parallel to the crystal $\hat{c}$ axis, the decoration method images a hexagonal to square vortex lattice transition [44][45]. As the magnetic field H climbs from $H = 0.002\,\mathrm{T}$ to $H = 0.02\,\mathrm{T}$, triangular flux line domains enlarge and one of their nearest neighbour directions becomes parallel with the $\langle 110 \rangle$ or $\langle 100 \rangle$ orientations. Raising the magnetic field H distorts the hexagonal configuration and local regions of square geometry appear above $H = 0.06\,\mathrm{T}$. Further magnetic field increase up to $H = 0.1\,\mathrm{T}$ reveals an expanding square proportion co-existing with a heavily distorted triangular phase. At fields H upwards of $H = 0.2\,\mathrm{T}$, SANS records [43] a square vortex lattice which slowly becomes completely amorphous by $H = 6\,\mathrm{T}$. SANS also shows another vortex lattice symmetry transition occurring at an external field of $\mathbf{H} = 0.3\,\mathrm{T}\,\mathbf{\hat{a}}$ [46]. The hexagonal lattice reorients from having a nearest neighbour direction along the $\mathbf{\hat{b}}$ axis at lower fields H to having one along the $\mathbf{\hat{c}}$ axis at higher fields H. Whereas the geometrical transitions taking place in LuNi2B2C for applied fields  $\mathbf{H} \parallel \mathbf{\hat{c}}$ arise from nonlocal interactions, those for fields $\mathbf{H} \parallel \mathbf{\hat{a}}$ stem from energy gap $\Delta$ anisotropy [46].

The LuNi2B2C sample examined in this $\mu $SR experiment was a single crystal $1.3\,\mathrm{cm}$ in diameter and $1\,\mathrm{g}$ in mass. The crystal grew from a mixture of Ni2B flux and arcmelted and annealed polycrystalline LuNi2B2C as the solution cooled from $1500\,^{\circ}\mathrm{C}$ to $1200\,^{\circ}\mathrm{C}$ over several days [47][48][33]. The sample formed as a plate, with the crystalline $\hat{c}$ axis perpendicular to the plate plane. Thermal conductivity measurements [42] performed on this sample find an upper critical field $H_{c2}(0) \approx 7\,\mathrm{T}$. Its residual resistivity is $\rho_0 = 1.30\,\mu\Omega\,\mathrm{cm}$ and its electron mean free path is $l \approx 500\,\textrm{\AA}$. Resistivity data [48] from similarly grown crystals indicate that this sample should have a critical temperature $T_c =

The expected Kramer-Pesch effect for the sample studied in this experiment is that the vortex core radius $\rho $ should contract linearly with temperature T on cooling from $T \ll 16.0\,\mathrm{K}$ (= Tc) down to $T \gg 0.7(1)\,\mathrm{K}$ [= T0, assuming $\xi_{BCS} = 100(20)\,\textrm{\AA}$]. Below the quantum limit temperature $T_0 \approx 0.7\,\mathrm{K}$, the core radius $\rho $ should stay constant at $\rho \sim 4\,\textrm{\AA}$ (=1/kF). The experimental setup employed to investigate this effect in LuNi2B2C is described in the following chapter.

next up previous contents
Next: Experiment Up: Material Properties of LuNiBC Previous: The Nickel Borocarbide Family
Jess H. Brewer