Interplay between magnetic order at Mn and Tm sites alongside the structural distortion in multiferroic films of o-TmMnO₃

We employ resonant soft x-ray diffraction to individually study the magnetic ordering of the Mn and the Tm sublattices in single-crystalline films of orthorhombic (o−)TmMnO₃. The same magnetic ordering wave vector of (0q0) with q≈0.46 is found for both ionic species, suggesting that the familiar antiferromagnetic order of the Mn ions induces a magnetic order on the Tm unpaired 4f electrons. Indeed, intensity variations of magnetic reflections with temperature corroborate this scenario. Calculated magnetic fields at the Tm sites are used as a model magnetic structure for the Tm, which correctly predicts intensity variations at the Tm resonance upon azimuthal rotation of the sample. The model allows ruling out a bc-cycloid modulation of the Mn ions as the cause for the incommensurate ordering, as found in TbMnO₃. The structural distortion, which occurs in the ferroelectric phase below T_C, was followed through nonresonant diffraction of structural reflections forbidden by the high-temperature crystal symmetry. The (0q0) magnetic reflection appears at the Mn resonance well above T_C, indicating that this reflection is sensitive also to the intermediate sinusoidal magnetic phase. The model presented suggests that the Tm 4f electrons are polarized well above the ferroelectric transition and are possibly not affected by the transition at T_C. The successful description of the induced order observed at the Tm resonance is a promising example for future element-selective studies in which “spectator” ions may allow access to previously unobtainable information about other constituent ions.