Single-parameter scaling in the magnetoresistance of optimally doped La$_{2-x}$Sr$_{x}$CuO$_4$

We show that the recent magnetoresistance data on thin-film La$_{2-x}$Sr$_{x}$CuO$_4$ (LSCO) in strong magnetic fields ($B$) obeys a single-parameter scaling of the form MR$(B,T)=f(\mu_H(T)B)$, where $\mu_H^{-1}(T)\sim T^{\alpha}$ ($1\le\alpha\le2$), from $T=180$K until $T\sim20$K, at which point the single-parameter scaling breaks down. The functional form of the MR is distinct from the simple quadratic-to-linear quadrature combination of temperature and magnetic field found in the optimally doped iron superconductor BaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$. Further, low-temperature departure of the MR in LSCO from its high-temperature scaling law leads us to conclude that the MR curve collapse is not the result of quantum critical scaling. We examine the classical effective medium theory (EMT) previously used to obtain the quadrature resistivity dependence on field and temperature for metals with a $T$-linear zero-field resistivity. It appears that this scaling form results only for a binary, random distribution of metallic components. More generally, we find a low-temperature, high-field region where the resistivity is simultaneously $T$ and $B$ linear when multiple metallic components are present. Our findings indicate that if mesoscopic disorder is relevant to the magnetoresistance in strange metal materials, the binary-distribution model which seems to be relevant to the iron pnictides is distinct from the more broad-continuous distributions relevant to the cuprates. Using the latter, we examine the applicability of classical effective medium theory to the MR in LSCO and compare calculated MR curves with the experimental data.