Complex Magnetic Interactions in A-site and B-site Doped Multiferroic TbMnO$_{3}$

Multiferroic materials have been of great interest in recent years due to a number of potential applications in random access memory or spintronics devices. TbMnO$_{3}$ in particular has attracted attention since the discovery of significant magnetoelectric coupling. The possibility of ferroelectricity in rare-earth chromites has also been examined recently through x-ray diffraction and dielectric measurements. Although several studies have looked at Cr-doped LaMnO$_{3}$, the nature of the Mn--Cr interactions is still controversial and no studies have been performed where the parent compound is multiferroic. In the present work, bulk Tb$_{1-x}$A$_{x}$MnO$_{3}$ (A = Ca$^{2+}$ or Sr$^{2+}$) and TbMn$_{1-y}$Cr$_{y}$O$_{3}$ have been synthesized via solution route. The structural evolution as determined through x-ray diffraction and Raman spectroscopy is consistent with a reduction in the orthorhombic distortion. Magnetic properties distinct from the parent compound, including ferrimagnetism and ferromagnetism, have been observed due to the Mn$^{3+}$--Mn$^{4+}$ or Mn$^{3+}$--Cr$^{3+}$ interactions. These complex interactions between the Mn$^{3+}$/Mn$^{4+}$, Cr$^{3+}$, and Tb$^{3+}$ moments will be discussed in detail.