In-Plane Anisotropy of the Electronic Structure for the Charge- and Orbital-Ordered State in Half-Doped Manganite with Layered Structure

We report on the in-plane anisotropy of the electronic response in the spin-, charge-, and orbital-ordered phase of a half-doped layered-structure manganite. The optical conductivity spectra for a single domain of ${\mathrm{Eu}}_{1/2}{\mathrm{Ca}}_{3/2}{\mathrm{MnO}}_4$ unambiguously show the anisotropic charge dynamics which well corresponds to the theoretical calculation: the optical conductivity with the polarization along the zigzag ferromagnetic chain direction exhibits a smaller gap and a larger intensity at lower energies than that of the perpendicular polarization mostly due to the charge and orbital ordering and the associated quantum interference effect.

Figure 1

(a) Optical conductivity spectra along the chain and the stripe directions from (a) the calculation using the Hartree-Fock method and (b) the experiment for the single domain of ECMO. The optical gap in the calculated optical conductivity is estimated to be 0.37 eV and 0.6 eV for $t=0.25\mathrm{eV}$ along the chain and stripe directions, respectively. These values are reasonably compared with the experimental result at 10 K, 0.68 eV, and 0.8 eV. In the inset of (a) the result of the exact-diagonalization study is displayed. In the inset of (b) two Jahn-Teller modes, $u$ and $v$, are drawn with a ${\mathrm{MnO}}_6$ octahedron. (c) Schematic diagram for the charge- and orbital-ordered state at half doping. Right bottom panels depict difference in the phases for the local hopping and current matrix elements from the $d_{3x^2-r^2}/d_{3y^2-r^2}$ orbitals at the electron-rich sites to (d) the $d_{x^2-y^2}$ and (e) the $d_{3z^2-r^2}$ orbitals at the electron-poor ones.

Figure 2

Reflectivity spectra (left panels) and optical conductivity spectra (right panels) of ${\mathrm{Eu}}_{1/2}{\mathrm{Ca}}_{3/2}{\mathrm{MnO}}_4$ along the $a^{\prime }$ and $b^{\prime }$ axes. The panels at each temperature are shifted up in sequence. The 335 K data are included in the top panels to clarify the temperature dependence. The dotted line in the right panels is for guidance.

Figure 3

(a) Optical gap, $2{\Delta }_{\mathrm{opt}}$ and (b) absorption peak below 2 eV, ${\omega }_{\mathrm{peak}}$ along the $a^{\prime }$ and $b^{\prime }$ axes. (c) Differential conductivity $\Delta \sigma (\omega )={\sigma }_{a^{\prime }}(\omega )-{\sigma }_{b^{\prime }}(\omega )$ at various temperatures. Inset displays the temperature dependence of $\Delta N_{\mathrm{eff}}(\omega =1.3\mathrm{eV})$. The unit is ${\Omega }^{-1}{\mathrm{cm}}^{-2}$.