  The "devil's staircase" type phase transition in the quarter-filled
spin-ladder compound NaV2O5 has been discovered at low temperature and high
pressure by synchrotron radiation x-ray diffraction. A large number of
transitions are found to successively take place among higher-order
commensurate phases with 2a * 2b * zc type superstructures. The observed
temperature and pressure dependence of modulation wave number qc, defined by
1/z, is well reproduced by the Axial Next Nearest Neighbor Ising (ANNNI) model.
The qc is suggested to reflect atomic displacements coupled with charge
ordering in this system. The experimental fact implies that two competitive
inter-layer interactions between the Ising spins, i.e., the nearest neighbor
J1>0 (ferro) and the next nearest neighbor J2<0 (antiferro) along the c-axis,
are intrinsic in this compound. A microscopic origin of the inter-layer
interaction is not yet known; however, the nearest neighbor interaction J1>0
between the V2O5 layers is especially interesting. It is very surprising that
the phase transition of such a complicated charge-lattice-spin coupled system
NaV2O5 can be described by the simple ANNNI model.
