In cgs, the bound surface current due to magnetization M is given by
where c is the speed of light, M is the magnetization, and is the unit normal vector, and in MKS
In addition, bound current densities are also induced in the interior.
Bound Current Density, H, Magnetization, Surface Current
References
Griffiths, D. J. "Bound Currents." §6.2.1 in Introduction to Electrodynamics, 3rd ed. Englewood Cliffs, NJ: Prentice-Hall, pp. 225-227, 1998.