Method for the preparation of carbon fiber from fiber precursor, wherein the fiber precursor is subjected to a magnetic field of at least 3 Tesla during a carbonization process. The carbonization process is generally conducted at a temperature of at least 400.degree. C. and less than 2200.degree. C., wherein, in particular embodiments, the carbonization process includes a low temperature carbonization step conducted at a temperature of at least or above 400.degree. C. or 500.degree. C. and less than or up to 1000.degree. C., 1100.degree. C., or 1200.degree. C., followed by a high temperature carbonization step conducted at a temperature of at least or above 1200.degree. C. In particular embodiments, particularly in the case of a polyacrylonitrile (PAN) fiber precursor, the resulting carbon fiber may possess a minimum tensile strength of at least 600 ksi, a tensile modulus of at least 30 Msi, and an ultimate elongation of at least 1.5%.