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We report on a nitride interface structure formed between epitaxial graphene and SiC (0001). The nitride interface can be obtained by the pretreatment of SiC in an $\mathrm{Ar}/{\mathrm{N}}_{2}$ atmosphere at 1600 \ifmmode^\circ\else\textdegree\fi{}C, followed by graphene growth in Ar at 1700 \ifmmode^\circ\else\textdegree\fi{}C. Our detailed high-resolution transmission electron microscopy revealed a nitride atomic layer between the 0th carbon layer and the SiC substrate. Due to the nitride interface, the interface carrier scattering was reduced, which resulted in an improvement of the room temperature mobility of graphene, indicating that this is another technique to modify the electronic properties of graphene.

The formation of large-area homogeneous graphene on a C-terminated SiC (000$\overline{1}$) surface was achieved via decomposition of the SiC (000$\overline{1}$) surface covered with an ultrathin but much more stable TiC layer than the reactive SiC(000$\overline{1}$). By heating the SiC (000$\overline{1}$) surface with a mixed powder of TiO${}_{2}$ and carbon at 1500--1550 \ifmmode^\circ\else\textdegree\fi{}C in vacuum, an extremely homogeneous, epitaxial 0.75-nm-thick TiC(111) layer was grown on the SiC(000$\overline{1}$) surface over a millimeter-scale area. Graphitization of the TiC-masked SiC surface led to the growth of high-quality graphene layers, which consist of TiC- and SiC-derived carbon. High-resolution transmission electron microscopy revealed the presence of disordered stacking of graphene layers on SiC through an amorphous layer at the interface. This unique method will promise further progress of relatively high carrier mobility of graphene formed on the SiC (000$\overline{1}$) surface.

Graphene layers were grown on a C-terminated SiC (000$\overline{1}$) surface in a high-pressure Ar atmosphere. Their growth mechanism was investigated using high-resolution transmission electron microscopy (TEM). First at a low temperature, local areas of SiC surface are decomposed, and several layers of graphene nucleus are formed in the resulting craters. Then graphene layers grow in all directions laterally, keeping their number of layers invariant. These results indicate that control of the number of graphene layers require precise control of the first stage of decomposition. After the graphene layers cover the surface completely, SiC decomposition occurs at a higher temperature along the [0001]${}_{\mathit{SiC}}$ direction, and the number of graphene layers increase. The formation of local wrinkles accompanies the increase of the number of layers. In addition we propose that the formation mechanism strongly affects the rotational stacking, which is characteristic of multilayer graphene on the C-face of SiC.

An investigation using high-resolution transmission electron microscopy of the stacking sequence of several layers of graphene formed on SiC(0001) shows that graphene layers selectively exhibit an ABC-type stacking. Using the well-known Slonczewski-Weiss-McClure model based on the tight-binding method, we suggest that a ${\ensuremath{\gamma}}_{5}$-like interatomic interaction, which corresponds to the formation of a linear trimer of ABA type stacking, is spontaneously weakened by the interaction between graphene and SiC. This can lead to the destabilization of the ABA stacking and to the formation of the ABC stacking, indicating the possibility of bandgap tuning by an electric field in more than three layers of graphene on SiC.

The crystallographic features of the orbital-ordered and charge-and-orbital-ordered states in ${\mathrm{Sr}}_{2\ensuremath{-}x}{\mathrm{Nd}}_{x}\mathrm{Mn}{\mathrm{O}}_{4}$ have been investigated by in situ observations, using a transmission electron microscope, in an attempt to understand the distinct characteristics of their electronic states. In the orbital-ordered state with orthorhombic symmetry, there exist four banded-domain-structure states, that is, two orthorhombic variant states $({O}_{I}+{O}_{II})$ accompanying the $C$-type antiferromagnetic ordering at lower temperatures and $(\mathrm{DT}+{O}_{I})$ coexistence and $({O}_{I}+{O}_{II})$ states lacking magnetic ordering at higher temperatures, where DT represents the disordered tetragonal state and ${O}_{I}$ and ${O}_{II}$ the two orthorhombic variants. On the other hand, the stability of the charge-and-orbital-ordered state present for $0.25\ensuremath{\leqslant}x\ensuremath{\leqslant}0.43$ is strongly suppressed when $xg0.38$. As a result of the strong suppression, the charge-exchange-type charge-and-orbital-ordered state is absent for $x=0.5$. The important features of the charge-and-orbital-ordered state are that it is basically characterized by incommensurate structural modulations and that round-shaped domains separated by disordered regions appear for $0.38lx\ensuremath{\leqslant}0.43$ near the DT state. On the basis of these data, the origin of the appearance of the four banded-structure states in the orbital-ordered state was attributed to a coupling between the local Jahn-Teller distortion and the long-range distortions, including a dilational one. In addition, we propose a model for the ground-state change between the orbital-ordered and charge-and-orbital-ordered states in terms of orbital degree of freedom.

An in situ observation of the tetragonal-to-orthorhombic phase transition in Fesubstituted Sr1.8La0.2MnO4 by transmission electron microcopy revealed that the domainstructure changes, as a relaxation phenomenon, took place during the aging for the formation of the orbital ordered state. At each aging temperature, the final banded domain structure could be produced from any starting state. The characteristic features of the domain-structure relaxation found in this study are also discussed in terms of a coupling between the local JT and long-range dilational distortions.

When ${\mathrm{Sr}}^{2+}$ ions in ${\mathrm{Sr}}_{2}\mathrm{Mn}{\mathrm{O}}_{4}$ containing only ${\mathrm{Mn}}^{4+}$ ions were partially replaced by ${\mathrm{La}}^{3+}$, a new phase having orthorhombic symmetry appeared around an La content of $x=0.15$ between the tetragonal $I4∕mmm$ $(T)$ phase and the charge and orbital ordered (COO) phase, accompanying the introduction of ${\mathrm{Mn}}^{3+}$ ions. Our in situ observation using a transmission electron microscope revealed that the orthorhombic (O) phase could be identified as an orbital ordered state without charge ordering, and that its microstructure is characterized by an alternating array of two banded-shape variants with different orthorhombicities, ${\mathrm{O}}_{I}$ and ${\mathrm{O}}_{II}$. It was also found that the $T$-to-O phase transition exhibited a unique evolution of domain structures, which resulted in the above-mentioned banded microstructure. In particular, the domain-structure evolution consisted of three steps: the appearance of the $(T+{\mathrm{O}}_{I})$ and then the $({\mathrm{O}}_{I}+{\mathrm{O}}_{II})$ coexisting states, followed by the annihilation of the interface between the ${\mathrm{O}}_{I}$ and ${\mathrm{O}}_{II}$ variants. The evidence suggests that this unique pattern of evolution is due to coupling between the short-wavelength Jahn-Teller (JT) distortion, associated with the ${\mathrm{Mn}}^{3+}$ ion, and the long-wavelength O distortion.