  The present manuscript completes the study presented in two recent research
articles [K. Koumpouras and I. Galanakis, \textit{J. Magn. Magn. Mater.} 323,
2328 (2011); \textit{ibid}, \textit{J. Spintron. Magn. Nanomater.} 1, in
press]. Preliminary first-principles calculations using the QUANTUM-espresso
package [P. Giannozzi et al \textit{J. Phys.:Condens. Matter} 21, 395502
(2009)] on the magnetic behavior of ultra-thin epitaxial multilayers between
the BiFeO$_3$ magnetoelectric compound and various types of spacers are
presented. As spacer we have considered i) InP semiconductor, ii) Fe which is a
ferromagnet, and iii) metallic V. In all cases under study the growth axis of
the multilayer was the [001]. Our results indicate that the magnetic properties
are seriously downgraded for the ultrathin BiFeO$_3$ multilayers independent of
the nature of the spacer and in some cases under study magnetism even vanishes.
More extensive calculations are needed to establish a more clear view of the
physical properties of the interfaces involving the BiFeO$_3$ compound.
