We systematically investigate the weakly trapped spin-1 Bose-Einstein condensates with spin-orbit coupling in an external Zeeman field. We find that the mean-field ground state favors either a magnetized standing wave phase or plane wave phase when t
he strength of Zeeman field is below a critical value related to the strength of spin-orbit coupling. Zeeman field can induce the phase transition between standing wave and plane wave phases, and we determine the phase boundary analytically and numerically. The magnetization of these two phases responds to the external magnetic field in a very unique manner, the linear Zeeman effect magnetizes the standing wave phase along the direction of the magnetic field, but the quadratic one demagnetizes the plane wave phase. When the strength of Zeeman field surpasses the critical value, the system is completely polarized to a ferromagnetic state or polar state with zero momentum.
The interface and electronic structure of thin (~20-74 nm) Co3O4(110) epitaxial films grown by oxygen-assisted molecular beam epitaxy on MgAl2O4(110) single crystal substrates have been investigated by means of real and reciprocal space techniques. A
s-grown film surfaces are found to be relatively disordered and exhibit an oblique low energy electron diffraction (LEED) pattern associated with the O-rich CoO2 bulk termination of the (110) surface. Interface and bulk film structure are found to improve significantly with post-growth annealing at 820 K in air and display sharp rectangular LEED patterns, suggesting a surface stoichiometry of the alternative Co2O2 bulk termination of the (110) surface. Non-contact atomic force microscopy demonstrates the presence of wide terraces separated by atomic steps in the annealed films that are not present in the as-grown structures; the step height of ~ 2.7 A corresponds to two atomic layers and confirms a single termination for the annealed films, consistent with the LEED results. A model of the (1 * 1) surfaces that allows for compensation of the polar surfaces is presented.
