Formation of local electric dipoles with no unique polar axis in ${\text{Tb}}_3{\text{Fe}}_5{\text{O}}_{12}$

Using neutron scattering and the pair-density-function analysis, we investigated, the local atomic structure of the ferrimagnetic dielectric ${\text{Tb}}_3{\text{Fe}}_5{\text{O}}_{12}$ garnet. Pronounced magnetic diffuse scattering is observed at high temperatures that gradually decreases with cooling as the Tb spins take on an ordered structure at about 50 K. In the temperature range where the dielectric $\left(\epsilon \right)$ constant is enhanced, a volume striction is observed from the diffraction measurements under a magnetic field that couples the magnetic response to the dielectric properties. At the same time, large oxygen displacements, on the order of $0.1–0.2\text{Å}$, are observed starting first at 90 K that persist up to 550 K, resulting in the formation of electric dipoles. However, they are not ordered and the lack of a unique polar axis in the hyperkagome structure may be linked to the absence of a polarized phase in this system. If it were present, the system could have a high ferroelectric transition temperature.

Figure 1

(Color online) The FC and ZFC bulk magnetic susceptibilities, $\chi$, at 200 Oe. The ferrimagnetic transition, $T_N$, is at $\sim 550\text{K}$. A compensation point is reached at 250 K. On cooling, the ZFC and FC curves start to split, $\sim 140\text{K}$. (Inset) The temperature dependence of $T_N$ and $T_{SG}$. When Ga is substituted for Fe, $T_N$ is suppressed down to zero and so is the split between FC and ZFC.

Figure 2

(Color online) The temperature dependence of the structure function, $S\left(Q\right)$, as a function of momentum transfer, $Q$. Diffuse scattering that appears as background (different from instrumental background) is observed starting at 550 K, with little or no change with cooling down to 90 K. Below this temperature, the background is reduced by 50 K, magnetic Bragg peaks appear. By 15 K, the magnetic Bragg peaks become stronger where little or no diffuse scattering is present.

Figure 3

(Color online) (a) A plot of the intensity at $1.6{\text{Å}}^{-1}$ Bragg peak as a function of temperature. The intensity increases at the magnetic transition of 50 K. (b) The inelastic intensity as a function of temperature at $Q=1.1{\text{Å}}^{-1}$. The scattering intensity is centered around $E=0\text{meV}$ and increases with cooling. By $\sim 50\text{K}$, it reaches a maximum and then decreases with further cooling. (c) The intensity measured at three constant energy transfers. At $E=0\text{meV}$, a maximum is reached at 50 K, which corresponds to the intensity reaching a maximum of Fig. 3a. At higher energy transfers, the maximum shifts to higher temperatures and becomes broad. Thus 50 K corresponds to the characteristic temperature of spin freezing. This temperature coincides with the magnetic transition temperature. At the same time, spins weakly fluctuate at higher temperatures.

Figure 4

(Color online) (a) A comparison of the PDF determined from data collected at 15 K (symbols) with a model PDF (solid line) calculated assuming the crystal model at 300 K. Also shown are the partial PDF’s corresponding to the different pairs of atoms. (b) The PDF’s are plotted in an expanded range that includes the Fe-O and Tb-O peaks only as a function of temperature.

Figure 5

(Color online) The temperature dependence of the Tb-O and Fe-O bond lengths. According to the cubic symmetry, only two Fe-O bonds and one Tb-O bond should be present, but locally, there are three Fe-O and two Tb-O bonds starting at $\sim 90$ all the way to 550 K.