Interplay between magnetic order at Mn and Tm sites alongside the structural distortion in multiferroic films ofo−TmMnO3

Abstract

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 $(o\text{\ensuremath{-}})\phantom{\rule{0.16em}{0ex}}\mathrm{TmMn}{\mathrm{O}}_{3}$. The same magnetic ordering wave vector of $(0\phantom{\rule{0.16em}{0ex}}q\phantom{\rule{0.16em}{0ex}}0)$ with $q\ensuremath{\approx}0.46$ 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 $\mathrm{TbMn}{\mathrm{O}}_{3}$. 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 $(0\phantom{\rule{0.16em}{0ex}}q\phantom{\rule{0.16em}{0ex}}0)$ 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.