Reply to “Comment on ‘No evidence for orbital loop currents in charge-ordered ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ from polarized neutron diffraction”'

The issues raised in the preceding comment of Bourges et al. [Phys. Rev. B 98, 016501 (2018)], are shown to be unfounded. We highlight the complications caused by inhomogeneous beam polarization that can occur when using polarized neutron diffraction to detect small magnetic moments.

Figure 1

(a) Schematic angular flux distributions produced by a polarizing device, normalized by $\max \left[{\varphi }_i\left(\alpha \right)\right]$. The flux of the nominal polarization $\left({\varphi }_{\uparrow }\right)$ is much larger than the other $\left({\varphi }_{\downarrow }\right)$. The flux distributions are sampled by Bragg scattering as illustrated by shaded sample mosaic. (b) Measured flux distributions ${\varphi }_{\uparrow }$ and ${\varphi }_{\downarrow }$ (from Fig. 6 of Ref. [3]) scaled to show the differences in form. (c) SF and NSF intensities of the (020) Bragg peak collected in a “continuous temperature run” in which the spectrometer was not moved. (d) $R^{-1}\left(T\right)$ determined from the data in (c) (“No realignment”) (open circles). The spurious $T$ dependence observed can be removed (closed squares) by using a “realignment” measurement protocol where corrections are made for changing lattice parameter and sample movement (“With realignment”).

Figure 2

Comparison of raw data. Inverse of the measured flipping ratio $R^{-1}$ for detwinned underdoped ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ samples at $\mathbf{Q}=\left(011\right)$. (a) Black diamonds are data of Croft et al. for ortho-II ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.54}\left(p=0.104\right)$. (b) Black squares are ortho-VIII ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.67}\left(p=0.123\right)$. In both cases, $R^{-1}$ is compared with that calculated from the raw data of Fauqué et al. [7] Fig. 1(a), sample C $\left({\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.6},p=0.115\right)$. These data are shown as blue open circles. Bourges et al. [5] state that the raw data do not change appreciably with doping in the range $\left(p=0.1–0.12\right)$. Theory [3, 7] [e.g., Croft et al. [3] Eq. (8)] suggests that changes in $R^{-1}$ are comparable, so the offsets of the left and right axes are different to accommodate different residual instrumental flipping ratios $R_{\mathrm{inst}}^{-1}$. The blue solid line in (b) is that shown schematically in Croft et al. [3] Fig. 9(c).

Figure 3

$T$ dependence of the magnetic cross section ${\sigma }_{\uparrow \downarrow }$ and magnetic structure factor squared ${\left|{\mathbf{M}}_{\perp }\left(\mathbf{G}\right)\right|}^2$ determined using Croft et al. [3] Eqs. (8) and (9) with values of $|F_N{|}_{\mathrm{calc}}^2$ from Table 1 of our SM. The solid blue lines show indicative values of ${\sigma }_{\uparrow \downarrow }$ from Fauqué et al. [7] Figs. 1(c) and 2(b). Note that these values have recently been revised downwards by 15%–20% in Ref. [5] and that the comparison of twinned samples with detwinned samples requires averaging over domains.