One-magnon Raman scattering in ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$: The origin of the field-induced mode

We investigate the one-magnon Raman scattering in the layered antiferromagnetic ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$ compound. We find that the Raman signal is composed by two one-magnon peaks: one in the $B_{1g}$ channel, corresponding to the Dzyaloshinskii-Moryia mode, and another in the $B_{3g}$ channel, corresponding to the $XY$ mode. Furthermore, we show that a peak corresponding to the $XY$ mode can be induced in the planar $\left(RR\right)$ geometry when a magnetic field is applied along the easy axis for the sublattice magnetization. The appearance of such a field-induced mode signals the existence of a magnetic state above the Néel temperature $T_N$, where the direction of the weak-ferromagnetic moment lies within the $\mathrm{Cu}{\mathrm{O}}_2$ planes.

Figure 1

(Color online) Left: LTO coordinate system with respect to a single $\mathrm{Cu}{\mathrm{O}}_2$ layer. Right: direction of the staggered magnetization, $⟨\mathbf{n}⟩$, of the DM vector, ${\mathbf{D}}_{+}$, and of the WFM, $⟨\mathbf{L}⟩\propto ⟨\mathbf{n}⟩\times {\mathbf{D}}_{+}$, for $\mathbf{B}=0$. In the scattering geometry of Ref. 4, the electric field vector of the light, ${\mathbf{E}}_{I,F}$, is always parallel to the $ab$ plane.

Figure 2

(Color online) Orientation of the staggered magnetization $⟨\mathbf{n}⟩$ and of the WFM $⟨\mathbf{L}⟩$ for: (a) zero field $\mathbf{B}=0$; (b) $\mathbf{B}<{\mathbf{B}}_c$ and $T<T_N$ ($\theta$ and $⟨\mathbf{n}⟩$ are functions of $T$); and (c) $\mathbf{B}<{\mathbf{B}}_c$ and $T>T_N$. Observe that (c) is also realized at any $T$ for $\mathbf{B}>{\mathbf{B}}_c$.

Figure 3

(Color online) $T$ dependence of ${\sigma }_b$ and ${\sigma }_c$ at $H=10T$, from Eqs. (12, 13). Inset: $T$ dependence of the angle $\theta$, from Eq. (14).