Hall coefficient anomaly in the low-temperature high-field phase of Sr${}_3$Ru${}_2$O${}_7$

We report a study of the Hall effect of high-purity Sr${}_3$Ru${}_2$O${}_7$ single crystals. We establish an empirical correlation between the onset of its unusual low-temperature, high-field phase and a pronounced dip in the field-dependent Hall coefficient. Unlike the order parameter obtained from measurements of anisotropic resistivity, which is affected by the formation of domains, the Hall effect feature seems to reflect the nature of the ordering within a single domain. We checked for violations of the Onsager relations for the off-diagonal components of the resistivity tensor but do not detect any. We compare our observations to those on materials that have long-wavelength spin structures, and discuss them in relation to a growing body of theoretical work on the nature of the low-temperature phase in Sr${}_3$Ru${}_2$O${}_7$.

Figure 1

Magnetotransport of Sr${}_3$Ru${}_2$O${}_7$ for field applied within $3^{\circ }$ of the $c$ axis, measured in a needle-shaped sample. (a) Magnetoresistance as a function of field. At low temperatures a sharp peak develops within the novel phase. (b) Corresponding Hall resistivity. The linear term at low field is followed by a pronounced upturn, following the behavior of the magnetisation. At higher fields the traces show evidence of quantum oscillations. The most striking feature is the sharp and pronounced dip at low temperatures that takes place in the field and temperature region where the anisotropic phase exists.

Figure 2

Magnetotransport at 100 mK measured on octagonal single-crystal plates at different field angles $\theta$. The field is always perpendicular to the $b$ axis, and $\theta$ is measured from the $a$ axis. (a) Schematic view of the four different transport configurations we used to measure Hall effect and magnetoresistance for different combinations of in-plane current-field angle $\phi$ (the color of the arrows in the octagons correlates with the color of the traces in the other panels). The octagonal shape minimizes the extrinsic anisotropy when commuting the current and voltage contacts. (b) Near the $c$ axis ($\theta ={90}^{\circ }$) and above $\approx {60}^{\circ }$ the resistivity (${\rho }_{ii}$, with $i=x,y,\text{or}\pm$45) is quite similar along the four directions explored, in a wide field range (Ref. 32). However, within this angular range, there is a narrow field region where the resistivity in configurations $I_x$(black) and $I_y$ (red) differs markedly. This defines the hard and easy directions, respectively, within the nematic phase. The resistivity along the remaining configurations ($I_{\pm 45}$, green and blue) is approximately the average of the hard and easy resistivities. (c) There is a sharp dip in the Hall signal ${\rho }_{xy}$ that coincides with the position where nematicity is observed; the feature fades away at low angles, where we measure little anisotropy in ${\rho }_{ii}$. The dip is most noticeable near the $c$ axis; here, the intrinsic anisotropy in the resistivity is suspected to be masked by domain formation. The traces at different angles have been shifted vertically for clarity.

Figure 3

Comparison between $|{\rho }_{xy}|$ and $|{\rho }_{yx}|$, with current parallel ($I_x$, black) and perpendicular ($I_y$, red) to the in-plane field, at different applied field angles $\theta$. The curves overlap within experimental error in both configurations at all fields, and for all angles explored. The Onsager relations are obeyed even at angles where the resistivity becomes highly anisotropic within the nematic phase (see the black and red resistivity curves in Panel a of Fig. 2). The traces at different angles have been shifted vertically for clarity. The inset shows a photograph of one of the samples, with eight gold wires attached with silver paint.