On the atomic orbital magnetism: A rigorous derivation of the Larmor and Van Vleck contributions

42 pages. Revised version: the introduction has been further developed, and a section devoted to the outline of the proof of Theorem 1.1 has been added. A remark (namely Remark 1.3) has been added below the main theorem, and the remark making the connection with the Van Vleck results (Remark 1.4) has been further developed. Accepted for publication in AHP.