Measurement of the Planckian Scattering Rate

A variety of exhibit resistivity that is perfectly linear in temperature as $T\rightarrow 0$, in contrast with conventional metals where resistivity increases as $T^2$. This $T$-linear resistivity has been attributed to a scattering rate $1/\tau$ of the charge carriers given by $\hbar/\tau=\alpha k_{\rm B} T$, with $\alpha$ of order unity. It has been suggested that this is a fundamental upper on the scattering rate -- the limit -- but a Planckian transport scattering rate has not been measured. Here we report a measurement of the angle-dependent magnetoresistance (ADMR) of Nd-LSCO, a hole-doped cuprate that displays $T$-linear resistivity just above its pseudogap critical point at $p^*=0.23$. The ADMR unveils a well-defined Fermi surface that agrees perfectly with that measured by angle-resolved photoemission spectroscopy and reveals a $T$-linear scattering rate that satisfies the Planckian limit, namely $\alpha = 1.4 \pm 0.3$. Remarkably, we find that this Planckian scattering rate is isotropic on the Fermi surface. From our fits to the ADMR we are able to quantitatively predict the measured resistivity and Hall coefficient, demonstrating that our model captures all aspects of the electrical transport. Our findings suggest that $T$-linear resistivity in strange metals emerges from a momentum-independent inelastic scattering rate that reaches the Planckian limit.