Spin susceptibility of the topological superconductor ${\mathbf{UPt}}_3$ from polarized neutron diffraction

Experiment and theory indicate that ${\mathrm{UPt}}_3$ is a topological superconductor in an odd-parity state, based in part from the temperature independence of the NMR Knight shift. However, quasiparticle spin-flip scattering near a surface, where the Knight shift is measured, might be responsible. We use polarized neutron scattering to measure the bulk susceptibility with $H\parallel c$, finding consistency with the Knight shift but inconsistency with theory for this field orientation. We infer that neither spin susceptibility nor a Knight shift are a reliable indication of odd parity.

Figure 1

Schematic of the phase diagram of ${\mathrm{UPt}}_3$ showing the superconducting $A, B$, and $C$ phases for magnetic fields perpendicular (parallel) to the $c$ axis [red (blue dashed) curves], taken in part from Adenwalla et al. [15], adjusted at $H=0$ and for $H(T\approx 50\text{mK})$ from measurements on high-purity crystals in this and earlier work [17].

Figure 2

One minus the flipping ratio $R$ as a function of temperature for the nuclear Bragg reflection $(1,0,0)$ at several magnetic fields: 0.4 T (triangles) and 1.0 T (circles). Black lines show the average value of $1-R$ at each field.

Figure 3

Magnetization as a function of magnetic field. At 0.4 and 1.0 T where the temperature dependence was measured, we show the average for $T<T_c$; for all other fields the results are for $T\approx 50$ mK. The proportionality to the magnetic field indicates that the susceptibility can be taken to be $\chi =M/B$, and that the diamagnetic magnetization from the Meissner screening in the superconducting state is negligible. The arrows indicate the magnetic field for the transition from the B to C phase and the upper critical field.

Figure 4

(a) Magnetic susceptibility measured by polarized neutron diffraction (solid green circles) for $H\perp c$ [36], SQUID measurements (open orange triangles) [36], and susceptibility measurements (open blue circles) [42]. (b) Susceptibility calculated from the Knight shift (open red circles [10, 43] and open purple triangles [44]). The statistical error for the susceptibility measured by neutron scattering is approximately the size of the green circles. (Figure taken from Ref. [36].)

Figure 5

Magnetic susceptibility measured by polarized neutron diffraction for $H\parallel c$ (solid green circles). The symbol notation is the same as for Fig. 4.