Melting of incommensurate-ferroelectric phase with magnetic field in multiferroic ${\mathrm{TbMnO}}_3$

We have investigated the reentrant ferroelectric behavior of ${\mathrm{TbMnO}}_3$ under a $c$-axis-aligned magnetic field $(H\parallel c)$ using neutron and x-ray single-crystal diffraction. We find that below $T_N=41\mathrm{K}$ and at high field the incommensurate ordering of Mn spins melts and coincides with the disappearance of ferroelectricity. The paraelectric phase which emerges is characterized by a simple commensurate antiferomagnetic ordering. We suggest that the reentrance of ferroelectricity at low temperatures and high magnetic field coincides with the development of incommensurate Mn- and Tb-spin ordering.

Figure 1

(Color online) Magnetoelectric phase diagram of ${\mathrm{TbMnO}}_3$ for $H\parallel c$, reproduced from Ref. 6. The $H$-$T$ phase diagram shows the high-temperature paramagnetic, lower-temperature sinusoidal antiferromagnetic (AF) regions. The onset of ferroelectric polarization at $T_{\mathrm{C}}$ as a function of $H$ and $T$ is also shown. The two lines at the phase boundary to the high-field paraelectric phase represent hysteresis. The observation of $T_N^{\mathrm{Tb}}$ from neutron diffraction is also indicated in the figure as solid circles $(•)$. The dashed and dot-dashed lines indicate the direction of the neutron and x-ray diffraction measurements, respectively.

Figure 2

(Color online) A two-dimensional plot representing neutron diffraction scans measured on the FLEX spectrometer along $(0,k,0)$ and $(1,k,0)$ (a)–(c) as a function of magnetic field $H\parallel c$ at $15\mathrm{K}$ and (d), (e) as a function of temperature in a magnetic field $H\parallel c=12\mathrm{T}$. Indicative magnetic reflections for Mn and Tb spin order are labeled. For (b) the scan range is (0,1$\pm$0.07,0). Transitions to paraelectric and ferroelectric states from Fig. 1 are also represented here.

Figure 3

(Color online) Results of neutron diffraction measurements at $T=15\mathrm{K}$ as a function of $H\parallel c$. (a) Field dependence of the integrated intensity of characteristic magnetic and structural reflections arising from Mn- and Tb-spin ordering as well as the (0,1,0) reflection. The $F$- and $C$-type $3{\delta }^{\mathrm{Mn}}$, $2{\delta }^{\mathrm{Mn}}$, and ${\delta }^{\mathrm{Tb}}$ labels in the figure correspond, respectively, to $(1,1+{\delta }^{\mathrm{Mn}},0)$, $(1,2-{\delta }^{\mathrm{Mn}},0)$, $(1,2-3{\delta }^{\mathrm{Mn}},0)$, $(1,2{\delta }^{\mathrm{Mn}},0)$, and $(1,{\delta }^{\mathrm{Tb}},0)$. (b), (c) Field dependence of the wave vector ${\delta }^{\mathrm{Mn}}$ and full width at half maximum (FWHM) of the $(1,1+{\delta }^{\mathrm{Mn}},0)$ reflection at $T=15\mathrm{K}$.

Figure 4

(Color online) Results of field-cooled neutron diffraction measurements with $H\parallel c=12\mathrm{T}$. (a) Temperature dependence of ${\delta }^{\mathrm{Mn}}$ and ${\delta }^{\mathrm{Tb}}$. (b) Temperature dependence of the integrated intensity of characteristic magnetic and structural reflections arising from Mn- and Tb-spin ordering as well as the (0,1,0) reflection. The labels here are as in Fig. 3a. (c) Temperature dependence of the FWHM of the (0,1,0) reflection. The brief region in which ferroelectricity appears at high temperature is highlighted, while $T_{\mathrm{C}}=5\mathrm{K}$ indicates the reentrance of ferroelectrocity at lower temperatures.

Figure 5

(Color online) (a) Neutron diffraction scans measured on the FLEX spectrometer along the $(1,k,0)$ direction at constant field $(H\parallel c=12\mathrm{T})$. (b)–(d) X-ray diffraction scans at constant temperature $(T=2\mathrm{K})$ along the $(0,k,5)$ direction for different fields $(H\parallel c)$.