Giant Optical Polarization Rotation Induced by Spin-Orbit Coupling in Polarons

We have uncovered a giant gyrotropic magneto-optical response for doped ferromagnetic manganite ${\mathrm{La}}_{2/3}{\mathrm{Ca}}_{1/3}{\mathrm{MnO}}_3$ around the near room-temperature paramagnetic-to-ferromagnetic transition. At odds with current wisdom, where this response is usually assumed to be fundamentally fixed by the electronic band structure, we point to the presence of small polarons as the driving force for this unexpected phenomenon. We explain the observed properties by the intricate interplay of mobility, Jahn-Teller effect, and spin-orbit coupling of small polarons. As magnetic polarons are ubiquitously inherent to many strongly correlated systems, our results provide an original, general pathway towards the generation of magnetic-responsive gigantic gyrotropic responses that may open novel avenues for magnetoelectric coupling beyond the conventional modulation of magnetization.

Figure 1

(a) Magneto-optical effects involve changes in the polarization state of light, causing a gyrotropic response. In the presence of a magnetic state ($M$), polarized light acquires an orthogonal polarization state after reflection. In contrast, magnetoreflectance is nongyrotropic and is caused by changes in the intensity of light reflected from magnetized surfaces, without mixing its polarization. (b) Both MO and MR can be detected simultaneously in hysteretic loops of the transverse magneto-optical effect, which is caused by the modulation of $p$-polarized light reflected from surfaces. (c) The temperature dependence of MO and MR mimics the behavior of magnetism and colossal magnetoresistance, respectively.

Figure 2

(a) The different parity of transverse $\mathfrak{J}({\delta }_K)$ hysteresis loops measured at $T\approx 256\mathrm{K}$ and $\lambda =475\mathrm{nm}$ is used to disentangle the MO and MR curves. The spectral responses of MR [$\mathfrak{J}{({\delta }_K)}_{\mathrm{MR}}$] and MO [$\mathfrak{J}{({\delta }_K)}_{\mathrm{MO}}$] are plotted in (b), while those of the dielectric function $\tilde{\epsilon }={\epsilon }_1+i{\epsilon }_2$ are shown in (c). The spin-dependent photoinduced polaron-hopping is schematically drawn in (d): for wavelengths in spin-preserving spectral region SP, electrons in $e_g$ states of ${\mathrm{M}\mathrm{n}}^{3+}$ jump into an empty state of a neighboring ${\mathrm{M}\mathrm{n}}^{4+}$ site, with their spin unchanged. Contrarily, spins are flipped in transitions induced by higher energy photons in region SF.

Figure 3

(a) The temperature dependence of the gyrotropic $\mathfrak{J}{({\delta }_K)}_{\mathrm{MO}}$ response measured at $H\sim 12\mathrm{kOe}$ is shown normalized to the values recorded at $T=230\mathrm{K}$. The areas shaded under the bumps correspond to the difference between the curves measured at different wavelengths and that measured at $\lambda =700\mathrm{nm}$. Close to $T_C$ these shaded areas are used to estimate the enhancement of the MO signal. In (b), the MR response is mapped as a function of wavelength and temperature. Peaks corresponding to photoinduced small polaron hopping are identified as spin preserving as well as spin flipping. In (c) we chart as a function of wavelength and temperature the gyrotropic enhancement estimated from the shaded areas in (a).

Figure 4

(a) Temperature dependence of the ellipticity $ϵ$ measured at $\lambda =402\mathrm{nm}$ for different magnetic fields. Around $T_C$ an outstanding gyrotropic enhancement is visible for decreasing fields. (b) The gyrotropic response at $H$ $\sim 12\mathrm{kOe}$ is shown for three selected wavelengths. A large increase of $ϵ$ develops at $\lambda =402\mathrm{nm}$ [inside the SF region defined in Figs. 2, and 3], whereas it is suppressed for longer wavelengths in the SP region ($\lambda =632$ and 700 nm). The inset in (b) shows the loops measured at $\lambda =402\mathrm{nm}$ and at three different temperatures around $T_C$. Panel (c) displays the ratio between the gyrotropic responses measured at $\lambda =402$ and $\lambda =700\mathrm{nm}$, and gives an accurate estimation of the gyrotropic enhancement for a manifold of applied fields. Enhancements upward of $\cong 60$-fold are observed at low fields.

Figure 5

(a) Scheme of the main process describing the polaron hopping in ${\mathrm{La}}_{2/3}{\mathrm{Ca}}_{1/3}{\mathrm{MnO}}_3$ close to the magnetic transition. A spin-up self-trapped electron moves from the $z^2$ orbital in an elongated ${\mathrm{Mn}}^{\mathrm{III}}{\mathrm{O}}_6$ complex into the $z^2$ orbital of a ${\mathrm{Mn}}^{\mathrm{IV}}{\mathrm{O}}_6$ complex that can have the same spin-up (blue box) or spin-down (green box). (b) Local $d$ levels in ${\mathrm{Mn}}^{\mathrm{III}}$ and ${\mathrm{Mn}}^{\mathrm{IV}}$ complexes where the effect of the Jahn-Teller distortion, ${\mathrm{Q}}_{\mathrm{JT}}$, is seen, effectively reducing the energy spacing between the $z^2$ levels and those of $xz$ and $yz$ states in tetragonal symmetry. This distortion helps the mixing of occupied and unoccupied levels due to the spin-orbit coupling (shown in purple). (c) Electrons with a particular spin polarization can only absorb circular polarized light that rotates in a specific direction to invert the spin upon hopping.