If you take leave of absence in the spring semester it will run from 1 February to 31 August the same year. Leave of absence will start from the first day of the semester, or, otherwise, the date of the application. You cannot apply for leave of absence retroactively.
As a general rule, it is not possible to take leave of absence for a part of a semester unless in cases with acute illness where you are reported ill in the end of a semester including the coming semester.
It will usually not be to your advantage to take leave of absence, due to the consequences it has - see for other options