Are Polarization and Magnetization Really Bulk Properties?

Raffaele Resta
Dipartimento di Fisica,  Università di Trieste, Italy

Textbooks typically attempt microscopic definitions in terms of the dipole moment per cell: this
is only correct for the spin contribution to magnetization M, but is incorrect for both polarization
P and for the orbital contribution to M. The microscopic quantities well defined inside a polarized material are the microscopic charge and current densities: these trivially determine the dipole
(electric and magnetic) of a finite sample, but the sample boundary yields an extensive contribution
to such dipoles.

Contrary to what textbooks pretend, the microscopic charge and current densities in the bulk of a
sample do not determine the values of P and M. The problem has been solved in 1993 for P and in
2005-6 for M. In the latter case, there have been recent developments at the fundamental level[1].
In this talk I will outline the state of the art about P and M.

[1] R. Bianco and R. Resta, ?Orbital Magnetization as a Local Property?, Phys. Rev. Lett. 110, 087202
(2013).