(a) Schematic representation of the epitaxial relationship between the cubic MAO substrate (the bottom one) and the tetragonal Mn3O4 film (the top one with 2 × 2 conventional unit cell). (b) Spin structure of the Mn4 tetrahedron of B sites in Mn3O4 shows two different exchange interactions: two AF bonds along the  or  chain (blue) and four bonds [two AF bonds (gray) and two F bonds (pink)] between the two chains. (c), (d) Schematic pictures of the tetragonal Mn3O4 film and the MAO substrate viewing along the  and [00-1] directions, respectively, indicating the same symmetrical characteristic of the two materials.
RHEED patterns of the MAO (001) substrate [(a), (b)] and the Mn3O4 film [(c), (d)]. The electron beam is incident along the  azimuth of the MAO substrate for (a) and (c), while along the  for (b) and (d). The  and  axes of the Mn3O4 film are separately parallel to the  and  axes of the MAO substrate.
(a) X-ray diffraction curve of the Mn3O4 film grown on the MAO (001) substrate. (b) Raman spectra measured at room temperature of the sample and the MAO (001) substrate, the modes of the substrate are indicated by black lines.
Magnetic-field dependence of the magnetizations along the , , and  directions at 5 K. Inset shows whole curves with the field from −5 T to 5 T.
(a) Temperature dependence of the magnetization in a magnetic field of 50 Oe along the  direction measured in the ZFC test mode (black squares) and FCW (field-cooled-warming) test mode (red circles). (b)Absolute value of the derivative curves |dM/dT| plotted with a logarithmic vertical scale and restricted to the transition regime (20 K-60 K).
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