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The microstructure and magnetic properties of Nd-Fe-B films with thicknesses from 100 nm to 3 nm have been investigated. All the films show excellent perpendicular magnetic anisotropy with a squareness ratio of 1 in the perpendicular direction and almost zero coercivity in the in-plane direction. Of particular interest is that the initial magnetization curves sensitively depended on the film thickness. Films thicker than 15 nm show steep initial magnetization curve. Although the films have coercivities larger than 21 kOe, the films can be fully magnetized from the thermally demagnetized state with a field as small as 5 kOe. With the decrease of film thickness to 5 nm, the initial magnetization curve becomes flat. The evolution of initial magnetization curves with film thickness can be understood by the microstructure of the films. Films with thickness of 15 nm show close-packed grains without any intergranular phases. Such microstructures lead to steep initial magnetization curves. On the other hand, when the film thickness decreased to 3 nm, the film thickness became nonuniform. Such microstructure leads to flat initial magnetization curves. [ABSTRACT FROM AUTHOR]