This study inquires into the relationships between the initial magnetization curve and the magnetic domain pattern in the demagnetized states for amorphous TbFeCo as well as multilayered Co/Pd thin film samples. This was done specifically through an investigation of different demagnetized states of samples demagnetized by a variety of methods. The magnetic domain pattern for the sample demagnetized by an in-plane magnetic field and for the sample demagnetized by a perpendicular magnetic field was found to be quite different even though both states have zero magnetization. The former state has denser and finer domains than the latter. In addition, both states were studied in light of the initial magnetization curves obtained by measurements of the magneto-optic Kerr effect and the extraordinary Hall effect. Moreover, the initial magnetization for the fine domains increases with an increase in magnetic field, while for the coarse domains, the initial magnetization remains at zero for magnetic field below coercivity Hc, then rises sharply to saturated magnetization when magnetic field is nearly equal to Hc.