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.
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