  We study the native charge compensation effect in Mg doped GaN nanorods
(NRs), grown by Plasma Assisted Molecular Beam Epitaxy (PAMBE), using Raman,
photoluminescence (PL) and X-ray photoelectron spectroscopies (XPS). The XPS
valence band analysis shows that upon Mg incorporation the E$_F$-E$_{VBM}$
reduces, suggesting the compensation of the native n-type character of GaN NRs.
Raman spectroscopic studies on these samples reveal that the line shape of
longitudinal phonon plasmon (LPP) coupled mode is sensitive to Mg concentration
and hence to background n-type carrier density. We estimate a two order of
native charge compensation in GaN NRs upon Mg-doping with a concentration of
10$^{19}$-10$^{20}$ atoms cm$^{-3}$. Room temperature (RT) PL measurements and
our previous electronic structure calculations are used to identify the
atomistic origin of this compensation effect.
