High magnetic-field evolution of the in-plane angular magnetoresistance of electron-doped ${\mathrm{Sr}}_{1-x}{\mathrm{La}}_x{\mathrm{CuO}}_2$ in the normal state

We studied the in-plane angular magnetoresistance (AMR), in the normal state, of underdoped superconducting ${\mathrm{Sr}}_{1–x}{\mathrm{La}}_x\mathrm{Cu}{\mathrm{O}}_2$, which has the simplest crystal structure among cuprates. The measurements of two underdoped thin films with different dopings were performed in intense magnetic field $H$ (up to 22 T). The longitudinal magnetoresistance at temperature $T$ is negative and scales with $H/T$. For both samples, the AMR is anisotropic and shows an unexpected dependence on $H$ intensity. While at the low magnetic field, one observes essentially twofold AMR oscillations for the more doped sample, fourfold ones start to grow under the high magnetic field, resulting in the coexistence of the two. For the less doped film at the low magnetic field, both twofold and fourfold AMR components exist. With the increase of the magnetic field, the fourfold component survives a π/4 phase shift, during which its amplitude vanishes, at a magnetic field $H_c$ such as $16\mathrm{T}<H_c<17\mathrm{T}$. As a result, at the high magnetic field above $H_c$, the angular dependence of the in-plane magnetoresistance turns out to be the same for both samples. We tentatively ascribe the above features to the presence of antiferromagnetism in the ${\mathrm{CuO}}_2$ planes of underdoped ${\mathrm{Sr}}_{1–x}{\mathrm{La}}_x\mathrm{Cu}{\mathrm{O}}_2$.

Figure 1

Pictures of thin films (a) F1 and (b) F2, patterned by optical lithography. (c) Resistivity ρ of films F1 (dashed black curve, multiplied by 3) and F2 (solid red curve). Arrows indicate resistivity minima $T_{\min }$. Inset shows the crystal structure of SLCO films.

Figure 2

(a) Normalized magnetoresistance $(\rho –{\rho }_0)/{\rho }_0$ of F1 for magnetic field $H$ parallel to ${\mathrm{CuO}}_2$ planes at different temperatures. (b) The same normalized MR as a function of $H/T$. (c) Normalized MR of F2 for magnetic field $H$ parallel to ${\mathrm{CuO}}_2$ planes at different temperatures. (d) The same normalized MR as a function of $H/T$. The ${\rho }_0$ is the zero-field resistivity, curves are smoothed, and measurement error is estimated to ${10}^{-3}\%$.

Figure 3

Polar plots of AMR of F1 (high doping) at 25 K are given in (a) for 10 T, (b) for 15 T, and (c) for 21 T. Polar plots of AMR of F2 (low doping) at 18 K are given in (d) for 10 T, (e) for 16 T, and (f) for 21 T. Solid lines represent fits to experimental data given by Eq. (1), while ${\rho }_{\min }$ is the resistivity corresponding to the minimum of AMR curves. The error could be estimated as the average difference between raw data and the fitted curve.

Figure 4

(a) AMR for film F1 (high doping) at 25 K and 10 T, 15 T (offset by 0.02%), 18 T (offset by 0.04%), 20 T (offset by 0.06%), and 21 T (offset by 0.08%); (b) twofold and (c) fourfold components of the AMR from Eq. (1) [offsets equal to half of the corresponding ones from (a)]. (d) AMR for film F2 (low doping) at 18 K at 10 T, 12 T (offset by 0.02%), 14 T (offset by 0.04%), 15 T (offset by 0.06%), 16 T (offset by 0.08%), 17 T (offset by 0.1%), 18 T (offset by 0.12%), and 21 T (offset by 0.14%); (e) twofold and (f) fourfold components of the AMR from Eq. (1) [offsets equal to half of the corresponding ones from (d)]. Note that the amplitude $A_4/C$ of the fourfold component crosses zero, or equivalently, the phase of the fourfold oscillation shifts by π/4 at the transition (dashed) line at a field $H_c$ between 16 and 17 T. The resistivity ${\rho }_{\min }$ corresponds to the minimum of AMR curves. Inset shows the angle ϕ between the applied current (along $a$ or $b$) and $H$.

Figure 5

(a) AMR of film F1 at 21 T and 25 K (black squares, offset by 0.03%), 31 K (red circles, offset by 0.02%), 41 K (blue diamonds, offset by 0.01%), and 45 K (green triangles). Solid lines represent fits to experimental data given by Eq. (1), while ${\rho }_{\min }$ is the resistivity corresponding to the minimum of AMR curves. (b) Temperature dependence of normalized amplitudes $A_2/C$ and $A_4/C$ of twofold (red solid circles) and fourfold (black open squares) oscillations, respectively, at 21 T obtained from (a) by the use of Eq. (1). Error bars are indicated and lines are guides to the eyes.