Negative hopping magnetoresistance and dimensional crossover in lightly doped cuprate superconductors

We show that, due to the weak ferromagnetism of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$, an external magnetic field leads to a dimensional crossover from two to three dimensions for the in-plane transport. The crossover results in an increase of the hole’s localization length and hence in a dramatic negative magnetoresistance in the variable range hopping regime. This mechanism quantitatively explains puzzling experimental data on the negative magnetoresistance in the Néel phase of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$.

Figure 1

(Color online) Spin structure of LSCO. Red arrows correspond to $H<H_f$; the blue arrows in the middle layer show the spin reversal for $H>H_f$.

Figure 2

(Color online) The MR jump $\mid \Delta \rho ∕\rho \mid$ (solid blue line) across the spin-flop transition for $H\parallel \widehat{c}$. Here, $Z{t}_{\perp }∕{ϵ}_0=0.057$ and $T_0=3.6\times {10}^4\mathrm{K}$. The circles are data from Ref. 11. Inset: zero field in-plane resistivity fit to 2D VRH form (solid, red line) with $T_0=3.6\times {10}^4\mathrm{K}$.

Figure 3

(Color online) The MR $\rho \left(H\right)∕\rho \left(0\right)$ (solid, blue line) for in-plane field $H\parallel \widehat{b}$, with $Z{t}_{\perp }∕{ϵ}_0=0.047$. The squares are data from Ref. 12. Inset: evolution of the angle [Eq. (13)] with field.