Modulation in charge ordering structure of ferroelectric YbFe₂O₄ by magnetic ordering

The strongly correlated electron system has been attracted much attention in solid state physics. Rare earth ion ferrite RFe₂O₄ (R = Y, Dy, Ho, Er, Tm, Yb, Lu, Sc, or In) is the typical example. This material is composed of doubly stacking iron triangular layers (W-layer) separated by single rare-earth triangular layer.¹ Equal amounts of Fe²⁺ and Fe³⁺ exist on triangular lattices and form charge orders due to the Coulombic interaction between iron ions.^2,3 The charge ordering is confirmed by (n/3 n/3 integer) or (n/3 n/3 half integer) diffraction peak where n is integer.

It has been proposed that each W-layer has microscopic electric spontaneous polarization, and the in-phase and out-of-phase stacking of the polar W-layers generate ferroelectric and antiferroelectric charge orderings respectively (see figure 1).^4–6 Although the existence of the polar W-layer has been questioned recently,⁷ we have proved the existence of the ferroelectricity in YbFe₂O₄ single crystal by macroscopic spontaneous polarization in P-E loop.⁸ The ferroelectricity in YbFe₂O₄ supports the existence of the polar W-layer.

Each W-layer also has the net magnetic moment due to the ordering of the spins on iron ions.⁹ The two kinds of stacking of the magnetic W-layers generate ferrimagnetism and antiferromagnetism in analogy with ferroelectricity and antiferroelectricity. Since both of the electric and magnetic properties arise from the ordering of iron ions, correlation is expected between electric and magnetic properties.

In this letter, we report spin-charge coupling of YbFe₂O₄ single crystal which showed clear P-E loop,⁸ promising the existence of the ferroelectricity. The incommensurate modulation was observed on diffraction signal which corresponds to the charge ordering around magnetic ordering temperature, indicating modulation in the charge ordering structure by magnetic ordering. The modulation was observed only in one of two kinds of charge ordering structure. This selectivity can be explained by ferroelectric and antiferroelectric charge ordering models.

High quality single crystal of YbFe₂O₄ was grown using the floating zone melting method from Yb₂O₃ and Fe₂O₃ without any pre-thermal treatment to head off not only the oxygen but also the iron defects, which change the electric properties strongly.^10,11 The mixture of CO₂/CO gas was flown during the melting. The sample showed spotty super lattice diffraction signal which promises high stoichiometry.¹¹ The sample was cut into 2.0 x 2.0 x 1.1 mm³ size and 1.3 x 1.6 x 1.0 mm³ size for the x-ray diffraction experiments and the magnetic measurement respectively, from the same rod. The x-ray diffraction experiments are performed by Rapid-II VariMax (RIGAKU). CuKα radiation and imaging plate were used. The sample was rotated 20° about [110] during the measurement as shown in Figure 2. The sample temperature was controlled by N₂ flow in a small plastic bag. The magnetic moment was measured along [001] by vibrating sample magnetometer mode using MPMS3 (Quantum Design Co., Ltd.). The sample was cooled down from 400 K to 50 K at 1 K/min rate under 1000 Oe of the magnetic field before the measurement. The thermo remanent magnetic moment was measured during heating from 50 K to 400 K at the same rate without magnetic field.

We performed the wide range reciprocal space mapping. Four kinds of peaks were observed: (n n 3m), (n/3 n/3 3m), (n/3 n/3 3m+3/2) and (n n 3m+3/2) where n and m are integer. (n n 3m) peaks are the fundamental peaks. (n/3 n/3 3m) and (n/3 n/3 3m+3/2) peaks correspond to charge ordering structures. On the other hand, the origin of the (n n 3m+3/2) peaks has not been clarified. The four kinds of peaks show different temperature dependences. While only commensurate peaks were observed at (n n 3m) and (n/3 n/3 3m+3/2) positions, commensurate and incommensurate peaks were observed around (n n 3m+3/2) and (n/3 n/3 3m) positions in the temperature range of 280 K and 260 K.

Figures 3 and 4 show the detail temperature dependences of the signals around (0 0 16.5) and (2/3 2/3 12). Figure 3 shows the development of commensurate peaks from incommensurate peaks. Figure 4 shows temperature dependences of the intensities of commensurate and incommensurate peaks and incommensurate width δ. As for (n n 3m+3/2) position, incommensurate peaks appear at 300 K and get close to commensurate position with decreasing temperature. Below 280 K, the incommensurate peaks lose their intensity while commensurate peak appear and develop absorbing incommensurate peaks. As for (n/3 n/3 3m) position, the incommensurate peaks behave the same as that around (n n 3m+3/2) while the commensurate peak is observed even above 280 K.

As for (n n 3m+3/2) position, the temperature dependences of the commensurate and incommensurate peaks indicate formations of short-range order above 280 K and long-range order below 280 K. The lowest panel in Figure 4 shows temperature dependence of magnetization. The macroscopic magnetic moment is observed below magnetic ordering temperature, 280 K, indicating the existence of the long-range order below 280 K. On the other hand, the existence of short-range order has been reported above the magnetic transition temperature from x-ray magnetic circular dichroism experiments.¹² These magnetic properties are consistent with the temperature dependences of the commensurate and incommensurate peaks at (n n 3m+3/2) position. Therefore the magnetic origin of the (n n 3m+3/2) signal is strongly suggested. Moreover, (n n 3m+3/2) signal is observed by neutron diffraction experiments, supporting the magnetic origin of the signal.

(n/3 n/3 3m) peaks also have the incommensurate modulation which shows quite similar temperature dependence to that of (n n 3m+3/2) peaks. Therefore the origin of the modulation should be the same as that of (n n 3m+3/2), i.e. the magnetic ordering. Since the commensurate (n/3 n/3 3m) peaks arise from the charge ordering, our data indicate the correlation between charge and magnetic orders. Similar results are reported by M. Angst et al.⁶ They suggest the incommensuration is an important factor in stabilizing charge order. According to their hypothesis, our data indicate cooperative formations of charge and magnetic orders.

The incommensurate modulation in the charge ordering structure was observed only in (n/3 n/3 3m) type charge order while (n/3 n/3 3m+3/2) type charge order show only commensurate signal. This selectivity can be explained by ferroelectric and antiferroelectric charge ordering models. The balloon in the figure 1 shows ferroelectric and antiferroelectric clusters centering on Yb³⁺ ion. The Yb³⁺ ion is in sixfold coordination. Taking into account the arrangement of Fe²⁺ and Fe³⁺ ions, the Yb³⁺ positions are center-asymmetric and center-symmetric in ferroelectric and antiferroelectric clusters, respectively. When the difference exists in bond lengths between Fe²⁺ - O^2- and Fe³⁺ - O^2-, Yb³⁺ ion can displace in ab-plane in center-asymmetric ferroelectric cluster. On the other hand, Yb³⁺ ion in antiferroelectric cluster cannot displace even with the difference in bond lengths since Yb³⁺ ion is at center-symmetric position. The scenario of the displacements of Yb³⁺ and O^2- ions is supported by transmission electron microscopy experiments and synchrotron x-ray diffraction experiments.^13,14

The displacement of Yb ion is likely to be induced by the development of the magnetic order since the incommensurate signals develop into commensurate signals with magnetic order. Since the hybridization is proposed in Fe 3d and O 2p orbitals,^15,16 the difference can be arisen in correlation between Fe²⁺ - O^2- and Fe³⁺ - O^2- by the spin ordering via spin-orbital coupling which is proposed in ref. 17. Although the detail mechanism is unclear, our results indicate the spin-charge coupling and support the ferroelectric and antiferroelectric charge ordering models.

In summary, we report the modulation in charge ordering structure by magnetic ordering on ferroelectric YbFe₂O₄ from x-ray diffraction experiments. The incommensurate modulation was observed on diffraction signals which corresponds to the charge ordering. The incommensurate signals develop into commensurate signals with magnetic order. The modulation was observed only on one type charge ordering signal. This selectivity can be explained by ferroelectric and antiferroelectric charge ordering models. Our results indicate the spin-charge coupling and support ferroelectric and antiferroelectric charge ordering models. The spin-charge coupling in this material can induce novel phenomena or applications if the ferroelectricity arises from the electronic origin in this material.