Anisotropy change of the magnetization-direction dependence of the density of states as a function of the electron energy in La$_{\mathrm{2/3}}$Sr$_{\mathrm{1/3}}$MnO$_{\mathrm{3}}$

Recent studies of the tunnel anisotropic magnetoresistance for single-crystal ferromagnetic materials have shown that the magnetic-field direction dependence of the density of states (DOS) is related to the electronic structure via the spin-orbit interaction and can largely change depending on the electron energy. This fact will provide us a novel way to control the magnetic anisotropy. Here, we have investigated the magnetic-field direction dependence of \textit{dI}/\textit{dV} in a tunnel diode consisting of La$_{\mathrm{2/3}}$Sr$_{\mathrm{1/3}}$MnO$_{\mathrm{3}}$ (LSMO, 40 uc)/ LaAlO$_{\mathrm{3}}$ (4 uc) grown on a Nb-doped SrTiO$_{\mathrm{3}}$(001) substrate by molecular beam epitaxy. We applied an in-plane magnetic field of 1 T and a voltage $V$ to the LSMO electrode with respect to the substrate at 4 K. At $V$ ranging from --0.2 to $+$0.4 V, \textit{dI}/\textit{dV} showed two-fold symmetries along the [100] and [110] axes in addition to a weak four-fold symmetry along the \textless 110\textgreater axes. However, when $V$ was decreased from --0.2 V to --0.4 V, these symmetries were gradually rotated by 90 degrees. This large change of the anisotropy is probably induced by the emergence of the $t_{\mathrm{2}}_{g}$ state just below the Fermi level.