Fermi Surface Topology and the Superconducting Gap Function in ${\mathrm{UPd}}_2{\mathrm{Al}}_3$: A Neutron Spin-Echo Study

We report on a single crystal neutron spin-echo investigation of the low-energy dynamic response in the heavy-fermion superconductor ${\mathrm{UPd}}_2{\mathrm{Al}}_3$ in the vicinity of the antiferromagnetic wave vector ${\mathbf{Q}}_0=(000.5)$. Well inside the superconducting phase, antiferromagnetic quasielastic scattering, which is present in the normal state, is absent for relaxation times up to 10 ns, equivalent to an energy resolution of $\sim 1\mu \mathrm{eV}$. This places strong constraints on possible models for this magnetic superconductor.

Figure 1

(a) Intensity observed on rotating the sample in the scattering plane at a fixed scattering angle $2\theta$ corresponding to the $(000.5)$ magnetic Bragg peak at $T=50\mathrm{mK}$. The arrows indicate the positions of the echo groups measured as a function of coil current at (b) ${\mathbf{Q}}_0=(000.5)$, $t=0.49\mathrm{ns}$ with 5 s per point, and (c) ${\mathbf{Q}}^{\prime }=(0.01500.5)$, $t=7.7\mathrm{ns}$ with 15 min per point (intensities normalized to counts per second). The abscissa values of the coil current were chosen to illustrate different numbers of periods in the two cases.

Figure 2

(a) Momentum and time-dependent intermediate scattering function $I({\mathbf{Q}}_0,t)$ normalized to $I({\mathbf{Q}}_0,0)$ as a function of Fourier time at 50 mK (solid circles). (b) Momentum and time-dependent intermediate scattering function $S({\mathbf{Q}}^{\prime },t)$ normalized to $S({\mathbf{Q}}^{\prime },0)$ and corrected for resolution using the measurements in panel (a) as a function of Fourier time at 50 mK (solid circles), 2 K (open circles), and 15 K (solid triangles). The dotted lines mark $I(\mathbf{Q},t)/I(\mathbf{Q},0)=1$ and $S({\mathbf{Q}}^{\prime },t)/S({\mathbf{Q}}^{\prime },0)=1$. The black lines are simple exponential fits described in the text and summarized in Table . The gray lines are possible extremal decay curves at 2 K, illustrating the uncertainty at this temperature. The dash-dotted gray line is a numerical calculation of the predicted scattering at 50 mK assuming a quasielastic response with $\Gamma =0.03\mathrm{meV}$.

Figure 3

The panels superpose, on a common $c^{*}$ axis, an even parity energy gap function (left-hand ordinate) and schematics of (a) the itinerant model Fermi sheets [14] and (b) the dual model Fermi sheets [21]. In both cases, the party-hat sheet is omitted. The gray area marks the first Brillouin zone. Based on Fig. 4 from Ref. 17.