Impurity susceptibility and the fate of spin-flop transitions in lightly doped ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$

We investigate the occurrence of a two-step spin-flop transition and spin reorientation when a longitudinal magnetic field is applied to lightly hole doped ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$. We find that for large and strongly frustrating impurities, such as Sr in ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$, the huge enhancement of the longitudinal susceptibility suppresses the intermediate flop and the reorientation of spins is smooth and continuous. Contrarily, for small and weakly frustrating impurities, such as O in ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_{4+y}$, a discontinuous spin reorientation (two-step spin-flop transition) takes place. Furthermore, we show that for ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$ the field dependence of the magnon gaps differs qualitatively from the ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$ case, a prediction to be verified with Raman spectroscopy or neutron scattering.

Figure 1

(Color online) Magnetic structure of ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$ for a small longitudinal field, $H\Vert b$. Solid (red) arrows represent ${\mathrm{Cu}}^{++}$ moments and for $H=0$ we have $\theta =0$.

Figure 2

(Color online) Field dependence of the rotation angle $\theta \left(H\right)$ for 1% doped $\mathrm{LCO}y$ (left) and LSCO (right). Observe that for $\mathrm{LCO}y$ a kink at the intermediate spin-flop transition at $H_c^1$ is observed, as indicated by the arrow.

Figure 3

(Color online) Field dependence of the in-plane (DM) gap for undoped LCO and for doped $\mathrm{LCO}y$ and LSCO. In the first two cases ${\chi }_{\mathit{imp}}=0$ and ${\chi }_{\mathit{imp}}=5$, so that the low-field susceptibility has approximately the same value (see inset), and an intermediate spin flop occurs at $H_c^1$ given by Eq. (12), where the gap vanishes. Instead, for doped LSCO ${\chi }_{\mathit{imp}}=80$, ${\chi }_b$, is strongly enhanced (see inset), no intermediate spin flop occurs, and the in-plane gap never vanishes. Inset: low-field susceptibility data taken from Ref. 2.