Magnetization in the superconducting state of UPt${}_3$ from polarized neutron diffraction

The heavy-fermion superconductor UPt${}_3$ is thought to have odd parity, a state for which the temperature dependence of the spin susceptibility is an important signature. In order to address conflicting reports from two different experiments, the NMR Knight shift and measurements of the anisotropy of the upper critical field, we have measured the bulk susceptibility in a high-quality single crystal using polarized neutron diffraction. A temperature-independent susceptibility was observed for $H\parallel a$ through the transitions between the normal state and the superconducting A, B, and C phases, consistent with odd-parity, spin-triplet superconductivity.

Figure 1

Schematic of the phase diagram of UPt${}_3$ showing the superconducting A, B, and C phases for magnetic fields perpendicular to the $c$ axis (red curves) from Adenwalla et al. (Ref. 7). The upper critical field for fields parallel to the $c$ axis is shown as the blue dashed curve. Black dashed lines correspond to the fields at which the temperature dependence of the magnetization was measured.

Figure 2

The flipping ratio $R$ as a function of temperature for the nuclear Bragg reflection [1,0,0] at three fields: 0.2 T (squares), 0.4 T (triangles), and 1.0 T (circles). Black lines show the average value of $1-R$ at each field.

Figure 3

The average magnetization for $T<T_c$, $\overline{M}$, as a function of applied magnetic field. The left axis shows $\overline{M}$ normalized to the value at 0.2 T. The right axis gives $\overline{M}$ in absolute units. The proportionality to magnetic field indicates that the susceptibility can be taken to be $\chi =M/B$. The zero-field $\overline{M}\left(H\right)/\overline{M}(0.2$ T$)$ intercept of the fit is 0.02.

Figure 4

Magnetic susceptibility measured by polarized neutron diffraction (solid green circles) multiplied by a constant factor of 2.35 (both panels). (a) Comparison to our SQUID measurements (open orange triangles) and the susceptibility measurements from Frings et al. (Ref. 23) (open blue circles). (b) Comparison to the susceptibility calculated from the Knight shift measurements as described in the text. Open red circles are from Refs. 12 and 26. Open purple triangles are from Ref. 4. Statistical error for the susceptibility measured by neutron scattering is approximately the size of the green circles.