Strong coupling between the spin polarization of Mn and Tb in multiferroic $\mathrm{Tb}\mathrm{Mn}{\mathrm{O}}_3$ determined by x-ray resonance exchange scattering

We report on an x-ray resonance exchange scattering (XRES) study of multiferroic $\mathrm{Tb}\mathrm{Mn}{\mathrm{O}}_3$. Magnetic scattering is observed close to the $\mathrm{Mn}K$ edge and the $\mathrm{Tb}{L}_{\mathrm{III}}$ and $L_{\mathrm{II}}$ edges. Surprisingly, Tb shows XRES also in the paraelectric phase, where neutron diffraction results suggested the $4f$ moments to be disordered. The temperature dependence of the XRES intensities shows a distinct kink close to the ferroelectric transition temperature $T_C$ for all absorption edges. We were able to model the temperature dependence for all edges, assuming a strong coupling of Mn and Tb magnetism via the spin polarized $5d$ conduction band. We argue that the hybridization between Mn and Tb states is a prerequisite for the multiferroic effect in this material.

Figure 1

(Color online) Linear $\mathit{Q}$ scans along $\left(0k1\right)$ normalized to monitor counts. The data without polarization analysis were taken at an energy $E=7.5\mathrm{keV}$ and $T=32\mathrm{K}$. The $\sigma \to {\pi }^{\prime }$ data were taken at the maximum of the $\mathrm{Tb}{L}_{\mathrm{III}}$ resonance (see Fig. 2), $E=7.518\mathrm{keV}$ and $T=7\mathrm{K}$. The peaks denoted with A and B are background features.

Figure 2

(Color online) Energy dependence of the peak intensity $(04-q_{m}1)$ for the different absorption edges at different temperatures. The data are corrected for absorption. The zero of the energy scale is given by the point of inflection from the fluorescence at the different absorption edges, respectively (not shown): $E_{\mathrm{Mn},K}=6.549\mathrm{keV}$, $E_{\mathrm{Tb},L_{\mathrm{III}}}=7.515\mathrm{keV}$, and $E_{\mathrm{Tb},L_{\mathrm{II}}}=8.253\mathrm{keV}$. The insets show the energy range $0.006<E_{\mathrm{Ph}}-E_{\mathit{\text{edge}}}<0.035\mathrm{keV}$ on a reduced scale.

Figure 3

(Color online) Temperature dependence of the XRES at the different absorption edges. The solid lines are refinements to the data using a molecular field model. The data were normalized to the maximum values of each set and offset for clarity.

Figure 4

(Color online) Temperature dependence of the magnetic and lattice modulation vectors at the different edges. The data are corrected for the temperature dependence of the $b$ lattice constant.

Figure 5

(Color online) Azimuthal dependence for the $(03+q_{m}0)$ ($C$ type) and $(04-q_{m}0)$ ($F$ type) reflections. The integrated intensity was obtained from rocking curves across the reflections and normalized to the integrated intensity of the (040) Bragg peak. The azimuthal scan was performed at base temperature $T\approx 6\mathrm{K}$ and $E=8.255\mathrm{keV}$. The inset illustrates the scattering geometry and the definition of $\Psi$. $\Psi$ is measured with respect to the reference direction [100].

Figure 6

(Color online) (a) Partial density of states for $\mathrm{Mn}3d$ and $4p$ states and $\mathrm{Tb}4f$ and $5d$ states from density functional theory, calculated from a model assuming disordered $\mathrm{Tb}4f$ moments. The $\mathrm{Mn}4p$ and the Tb density of states have been multiplied by a factor 50 and 10 for clarity, respectively. (b) Magnetization density of the first unoccupied Mn peak $(0<E-E_F<2\mathrm{eV})$. Dark gray color represents higher magnetization density. Slice through a Tb atom in a plane normal to the [010] direction. Small gray sphere, Tb; red (dark gray) spheres, O; and big light blue (light gray) spheres, Mn.