Unexpected phase locking of magnetic fluctuations in the multi-k magnet USb

The spin waves in the multi-k antiferromagnet USb soften and become quasielastic well below the antiferromagnetic ordering temperature $T_N$. This occurs without a magnetic or structural transition. It has been suggested that this change is in fact due to dephasing of the different multi-k components: a switch from 3-k to 1-k behavior. In this work, we use inelastic neutron scattering with tridirectional polarization analysis to probe the quasielastic magnetic excitations and reveal that the 3-k structure does not dephase. More surprisingly, the paramagnetic correlations also maintain the same clear phase correlations well above $T_N$ (up to at least $1.4T_N$).

Figure 1

Typical inelastic polarized neutron spectra from USb at low temperatures (50 K), along the $x$, $y$, and $z$ neutron polarization axes (defined in text), adapted from Ref. 8. The ySF and zSF channels are able to pick out the acoustic and optical modes, respectively. The total magnetic signal is measured in the xSF channel. Inset: a schematic of the sample-polarization geometry.

Figure 2

(Upper panel) (1, 1, 0) Bragg integrated intensity (blue circles) and the extracted elastic intensities from fitted spectra (red squares) serve as a proxy for the AFM order parameter (fitted with critical exponent—black curve). Inset: plot of the (1, 1, 0) intensity against reduced temperature. (Lower panel) Spectra were fitted with elastic and quasielastic components and the ySF:zSF ratio for these integrated intensities is plotted vs temperature. The ratio of the elastic components exactly follows the expected behavior for the ordered 3-k state, whereas a value of the ratio between the quasielastic channels greater than $\sqrt{2}$ indicates 3-k correlations.

Figure 3

Inelastic polarized neutron spectra from the (1, 1, 0) reflection at different temperatures with the experimental data as solid points (with error bars) and lines showing fits to the data. (a) and (b) show the spin waves in the xSF and ySF channels only, which broaden and collapse towards the elastic line with increasing temperature. (c) and (d) show that the Fourier components do not fully dephase above $T^{*}$ and $T_N$, respectively. The black dashed-dotted line shows an estimate of the polarization leakthrough (calculated from the flipping ratio) from the $xSF$ into the $zSF$ channel, showing there is a finite quasielastic component above 40 K.

Figure 4

(Upper panel) Extracted quasielastic integrated intensities. The quasielastic signal develops only above $T^{*}$ and shows divergent behavior as expected around $T_N$ in the $\mathit{ySF}$ channel; however this is not seen in the $\mathit{zSF}$ intensity. (Lower panel) Half-width at half maximum (HWHM) of the quasielastic signal, where again critical behavior is seen in the $\mathit{ySF}$ but not in the $zSF$ channel (the instrumental resolution is shown by the dashed horizontal line).