Probing Momentum-Dependent Scattering in Uniaxially Stressed ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ through the Hall Effect

The largest Fermi surface sheet of the correlated metal ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ can be driven through a Lifshitz transition between an electronlike and an open geometry by uniaxial stress applied along the [100] lattice direction. Here, we investigate the effect of this transition on the longitudinal resistivity ${\rho }_{xx}$ and the Hall coefficient $R_H$. ${\rho }_{xx}(T)$, when ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ is tuned to this transition, is found to have a $T^2\log T$ form, as expected for a Fermi liquid tuned to a Lifshitz transition. $R_H$ is found to become more negative as the Fermi surface transitions from an electronlike to an open geometry, opposite to general expectations from this change in topology. The magnitude of the change in $R_H$ implies that scattering changes throughout the Brillouin zone, not just at the point in $k$ space where the transition occurs. In a model of orbital-dependent scattering, the electron-electron scattering rate on sections of Fermi surface with $xy$ orbital weight is found to decrease dramatically.

Figure 1

(a) Model Fermi surfaces of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$, colored by orbital weight, from Ref. [15]. (b) Fermi surfaces calculated with a simple tight-binding model, presented later in this Letter, under uniaxial stresses along [100] of 0, $-0.75$, and $-1.1\mathrm{GPa}$. (c),(d) Photographs of samples 1 and 2.

Figure 2

(a) $[{\rho }_{xx}(B=0)/\mathrm{\Delta }{\rho }_{xx}{]}^{0.5}$, where $\mathrm{\Delta }{\rho }_{xx}$ is the change in ${\rho }_{xx}$ between 0 and 1.5 T, against $T^2$ for sample 2 at various stresses. The dashed lines are linear fits. (b) ${\rho }_{xx}(T)$ of sample 2 at $\sigma ={\sigma }_L=-0.75\mathrm{GPa}$ and $B=0$ and 1.5 T. The black line is an estimate of the ${\rho }_{xx}(T)$ that would be obtained at $B=0$ without superconductivity; it is an average of ${\rho }_{xx}$ at $+$ and $-1.5\mathrm{T}$ with the magnetoresistivity subtracted as described in the text. (c) The difference between various fitting models and the black line in panel (b). For the $T^2\log T$ form, the fit yields $T_0=95\mathrm{K}$.

Figure 3

(a) $V_{H}t/I$, where $t$ is sample thickness and $I$ the applied current, versus $B$ for sample 2 at various temperatures and at zero stress. The dotted lines are extrapolations of linear fits over $0<B<0.35\mathrm{T}$. Equivalent data for sample 1 are shown in Ref. [29]. (b) $R_H(T)$ of both samples at zero stress, and $B$ up to $\pm 0.5\mathrm{T}$ for sample 1 and $\pm 0.35\mathrm{T}$ for sample 2. Data from Ref. [32] are also shown.

Figure 4

(a) $R_H(\sigma )$ of sample 2 at various temperatures, measured at $B=\pm 0.35\mathrm{T}$. Data that are clearly affected by superconductivity are excluded. The expected $R_H(\sigma )$ for isotropic mean free path and $T\to 0$, calculated using a simple tight-binding model, is also shown. (b) $R_H(\sigma )$ of sample 2 at $B=\pm 1.5\mathrm{T}$, a strong enough field to fully suppress the superconductivity. (c) ${\rho }_{xx}(\sigma )$ of sample 2 at $B=0$ and 0.35 T. (d) ${\rho }_{xx}(\sigma )$ of sample 2 at $B=1.5\mathrm{T}$. (e) $R_H(\sigma )$ of sample 1 at $B=\pm 1\mathrm{T}$. (f) The phase boundary of the magnetic order, taken as the stresses where $d{{}^{2}R}_H/d{\sigma }^2$ in panel (b) is maximum. The error bars are the FWHM of the peaks in $d{{}^{2}R}_H/d{\sigma }^2$. Also shown is the phase boundary found in elastocaloric effect (ECE) data [34], with the Lifshitz stress normalized to $-0.75\mathrm{GPa}$.

Figure 5

(a) $R_H$ calculated within the orbital-dependent scattering model described in the text, as a function of the ratio of $xy$ and $xz$, $yz$ scattering rates, ${\eta }_{xy}/{\eta }_{xz,yz}$. The calculation employs a simple tight-binding model of the Fermi surfaces of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$. (b) ${\eta }_{xy}/{\eta }_{xz,yz}$ versus stress at 5 and 10 K, determined from $R_H$ of sample 2 at $\pm 0.35\mathrm{T}$ and the calculation results shown in panel (a).