Prominent role of oxygen in the multiferroicity of ${\mathrm{DyMnO}}_3$ and ${\mathrm{TbMnO}}_3$: A resonant soft x-ray scattering spectroscopy study

Oxygen is known to play an important role in the multiferroicity of rare earth manganites; however, how this role changes with rare earth elements is still not fully understood. To address this question, we have used resonant soft x-ray scattering spectroscopy to study the $F$-type $(0,\tau ,0)$ diffraction peak from the antiferromagnetic order in ${\mathrm{DyMnO}}_3$ and ${\mathrm{TbMnO}}_3$. We focus on the measurements at O $K$ edge of these two manganites, supplemented by the results at Mn $L_2$ and Dy $M_5$ edge of ${\mathrm{DyMnO}}_3$. We show that the electronic states of different elements are coupled more strongly in ${\mathrm{DyMnO}}_3$ than in ${\mathrm{TbMnO}}_3$, presumably due to the stronger lattice distortion and the tendency to develop E-type antiferromagnetism in the ferroelectric state that promote the orbital hybridization. We also show that the anomaly in the correlation length of $(0,\tau ,0)$ peak in ${\mathrm{DyMnO}}_3$ signifies the exchange interaction between Mn and rare earth spins. Our findings reveal the prominent role of oxygen orbitals in the multiferroicity of rare earth manganites and the distinct energetics between them.

Figure 1

(a) The schematic plot showing the characteristic temperatures of Mn and Dy spin orders and the electric properties of ${\mathrm{DyMnO}}_3$. (b) and (c) Normalized $q$ scans about the $(0,{\tau }^{\text{(D)}},0)$ wave vector measured at selected temperatures at (b) Mn $L_2$ edge (645.4 eV) and (c) O $K$ edge (523.75 eV). Spectra are shifted vertically for clarity. (d) The schematic plot showing the experimental setup.

Figure 2

(a)–(e) Lorentzian fitting results of $q$ scans from ${\mathrm{DyMnO}}_3$ showing the temperature dependence of (a) ${\tau }^{\text{Mn(D)}},{\tau }^{\text{Dy(D)}}$, and ${\tau }^{\text{O(D)}}$, (b) $I^{\text{O(D)}}$, (c) ${\lambda }^{\text{O(D)}}$, (d) $I^{\text{Dy(D)}}$, and (e) $I^{\text{Mn(D)}}$. Black filled circles, blue open circles, and red filled diamonds are data recorded at O $K$ (523.75 eV), Mn $L_2$ (645.4 eV), and Dy $M_5$ edge (1290 eV), respectively. The difference in wave vector $\mathrm{\Delta }\tau ={\tau }^{\text{Dy(D)}}-{\tau }^{\text{Mn(D)}}$ is shown on top of (a) (right axis). (f) Selected $q$ scans at O $K$ edge. The $q$ scans are scaled in height and shifted in $\vec{k}$ to align the peak centroids for comparison. (g)–(i) Lorentzian fitting results of $q$ scans from ${\mathrm{TbMnO}}_3$ at O $K$ edge (523.75 eV) showing the temperature dependence of (g) ${\tau }^{\text{O(T)}}$, (h) $I^{\text{O(T)}}$, and (i) ${\lambda }^{\text{O(T)}}$. Red arrow in (g) marks the lock-in temperature. Light blue regions indicate the ferroelectric state below 19 K $T_{\text{FE}}^{\text{(D)}}$ (a)–(e) or 28 K $T_{\text{FE}}^{\text{(T)}}$ (g)–(i). Thin solid lines in (b), (d), (e), and (h) are guides for eyes. The gray dashed line in (c) denotes our conjectured baseline value of ${\lambda }^{\text{O(D)}}$.

Figure 3

(a) Mn (top) and Dy (bottom) spin partial density of states (pDOS) from first-principles calculations. The $s$ (black curves) and $p$ bands (red curves) are magnified by a factor of 5 for clarity. (b) X-ray absorption spectrum of ${\mathrm{DyMnO}}_3$ around O $K$ edge recorded in the total electron yield mode at 13 K. The Mn and Dy electronic states that hybridize with oxygen $2p$ orbitals are also labeled in this panel. (c) Resonance profiles of $(0,{\tau }^{\text{O(D)}},0)$ (red line with filled circles) and $(0,{\tau }^{\text{O(T)}},0)$ (blue line with open circles) peaks measured at 13 K.

Figure 4

Iso-charge surface of ${\mathrm{DyMnO}}_3$ with (a) and (c) A-type and (b) and (d) E-type antiferromagnetism using relaxed crystal structures. The in-plane and out-of-plane results are shown in (a) and (b) and (c) and (d), respectively. The iso-charge surface is produced by integrating the DFT density of states (summed over spins) over $[-0.74$ eV, 0 eV] energy window. The magnetic orders are illustrated by the color arrows. The calculated Mn-O bond lengths are listed in (a) and (b), and also summarized in Table 1. (e)–(h) Iso-charge surface of ${\mathrm{DyMnO}}_3$ with (e) and (f) A-type and (g) and (h) E-type antiferromagnetism without relaxing the crystal structures (frozen structure). The Mn-O bond lengths are also summarized in Table 1. ${\mathrm{O}}_1$ and ${\mathrm{O}}_2$ denote the out-of-plane and in-plane oxygens, respectively.

Figure 5

Lorentzian fitting results of $q$ scans from ${\mathrm{DyMnO}}_3$ showing the temperature dependence of (a) ${\lambda }^{\text{Mn(D)}}$ and (b) ${\lambda }^{\text{Dy(D)}}$. (c) Selected $q$ scans at Mn $L_2$ edge. (d) The schematic plot illustrating the symmetric exchange coupling $H_{df}$ between Dy (red arrows) and Mn (blue arrows) spins below (left panel) and above $T_{\text{FE}}^{\text{(D)}}$ (right panel).