Introduction

Unique properties based on various orderings in complex materials, especially the RFe2O4 system, have drawn great interest recently1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21. Experiments such as x-ray diffraction1,2, neutron scattering4,13, electronic transport measurement8, in situ cooling transmission electron microscopy23, optical spectroscopy6,17, etc. have been carried out and illustrated various types of orderings and properties such as charge ordering5,9, spin ordering1,5, giant magnetocapacitance9, giant room-temperature magnetodielectric response10, giant magnetic anisotropy20, etc in the system. However, there are very few reports on the detailed energy structure of the 2D CO states and optical methods have been less reported in identification of the spin ordering state. In this paper we show clear evidence of observing non-degenerate double 2D CO states and a ferrimagnetic SO state in an electronic ferroelectric material Er0.1Yb0.9Fe2O4 by using temperature-dependent Raman scattering. Furthermore, we have also observed two infrared-active phonon modes besides the full spectrum of Raman-active phonon modes in it. This is a material with which we had for the first time observed the Stark effect in a solid, which confirmed the existence of strong local field and provided a spectroscopic evidence of the ferroelectric nature of the material7.

The Er0.1Yb0.9Fe2O4 crystal belongs to the RFe2O4 type mixed-valence materials, which has been known exhibiting CO composing Fe2+ and Fe3+ ions on a geometrically frustrated triangular lattice. The bulk ferroelectric polarization thus formed (i.e. electronic ferroelectricity) arises from the 3D alternating arrangement of valence-charges, instead of the spatial displacement of cations as in the conventional ferroelectric materials1,23. Among the many investigation methods, Raman and infrared (IR) spectroscopy investigations have been carried out on LuFe2O46,16,17,18, illustrating its structural, magnetic and charge ordering properties. In the IR investigation a transition between the 2D and the 3D CO was observed17. However, so far Raman and IR results have not provided any information on spin ordering in the RFe2O4 system, although neutron diffraction have been used to find the ferrimagnetic order in LuFe2O422.

In this Article, a temperature-dependent Raman scattering study on the phase transition in polycrystalline Er0.1Yb0.9Fe2O4 has been carried out. Unlike available reports on Raman scattering and other optical spectroscopy of the RFe2O4 system, our experiment presents a full spectrum of the excitations and show five distinct new modes. Significantly we observed two non-degenerate 2D CO modes at the temperature range of 300 ~ 400 K. We directly obtained the energy gaps between these 2D double CO states and the 3D CO state. Also we have observed one mode attributed to the ferrimagnetic spin ordering at below 210 K. Furthermore two IR-active modes have also been identified due to the breakdown of inversion symmetry at the crystalline domain boundaries. Our investigation extends or demonstrates the Raman (and optical) investigation capability in identifying the phase transitions and various orderings in such complex quantum materials.

Results

Variable-temperature Raman spectra of our polycrystalline Er0.1Yb0.9Fe2O4 are shown in Fig. 1. The temperature dependences of the frequencies and intensities of all the observed modes are shown in Figs. 2 and 3, respectively. We observed 11 modes altogether, of which the information is summarized in Table 1.

Table 1 Observed active modes in Er0.1Yb0.9Fe2O4 (at room temperature, if not specified)
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Figure 1
figure 1

Raman spectra of Er0.1Yb0.9Fe2O4 at various temperatures.

Raman peaks are numbered and highlighted by dashed lines.

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Figure 2
figure 2

Frequency of the 11 Raman modes highlighted in Fig. 1 as a function of temperature.

The vertical dashed lines highlight the temperatures at which phase transitions occur. The solid lines are guides to the eye.

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Figure 3
figure 3

Integrated intensities of the 11 Raman modes (see Fig. 1) as a function of temperature.

The vertical dashed lines highlight the temperatures at which phase transitions occur. The intensity for each mode is shifted vertically for clarity. The solid curves are guides to the eye. The horizontal dotted lines below each solid curve represent the base line of intensity without offsets.

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Significantly, two high frequency modes (numbered 10 and 11 in Figs. 1–3) begin to emerge when the temperature T is raised to higher than 300 K. These two Raman peaks cannot be assigned to higher-order Raman or IR modes since they appear only when T is higher than 300 K. Various diffraction techniques and theoretical analysis have been applied to the LuFe2O4 systems, which suggested a 3D CO to 2D CO transition that occurs at a similar temperature when temperature is raised5,24. Here we assign these two high frequency modes to the 2D CO states in the Er0.1Yb0.9Fe2O4 crystal. The energy scale of these two modes is at the same order as those observed in other RFe2O4 systems using other methods3,25 (see below discussion). In light of the relatively high frequencies of these two modes we speculate that these two modes are due to in-plane interactions, which is relatively stronger due to closer distance between atoms and consistent with the 2D nature of the CO state.

As expected (see Discussions) all six Raman-active modes (with subscripts g) are observed (highlighted by black dashed lines in Fig. 1 and gray points in Fig. 2). Among them, the three Raman modes of A1g symmetry are due to the out-of-plane vibrations (where atoms move perpendicularly to the Yb-O, Er-O and Fe-O planes, respectively) and the three Eg symmetry Raman modes corresponds to the in-plane vibrations6. A pair of modes (modes 1 and 7) exist in the entire range of temperature (highlighted by red dashed lines in Fig. 1 and red points in Fig. 2), whose frequencies are close to those of the Eu1 and Eu3 vibrations in the RFe2O4 type crystals6. We assign these two modes to the IR-active modes with Eu1 and Eu3 symmetries, respectively. Usually the IR active modes are not expected in Raman measurements for this material. The observation of the Eu1 and Eu3 symmetry modes can be well understood based on the polycrystalline nature of the sample. The rich boundaries and vacancies in the sample break down the inversion symmetry of the crystal at the surfaces and the phonon parity selection rule is largely relaxed in our polycrystalline sample.

In Fig. 2 we can see that the frequencies of three Raman-active modes Eg1, A1g1, A1g2 and the lowest energy IR-active mode Eu1 do not show much variation in the entire temperature range. The Eg2 mode softens from 477 cm−1 to 447 cm−1 when T changes from 78 K to 403 K. The frequencies of the three higher energy vibrational modes Eu3, Eg3 and A1g3 show non-monotonic dependence on T. When T varies from 78 K to 300 K, the Eu3 vibration hardens slightly, whereas the Eg3 vibration redshifts from 626 cm−1 to 593 cm−1. The A1g3 vibrational frequency remains unchanged in this temperature range. For T > 300 K, the Eu3 and Eg3 vibrational frequencies reach a minimum at about 350 K and the A1g3 frequency reaches a maximum at T ~ 350 K. The spin-ordered mode 4 blueshifts slightly when T increases from 78 K to ~ 210 K and it disappears for T higher than 210 K. The two highest frequency modes (numbered 10 and 11) only appear when T is higher than 300 K. The frequency of mode 10 has a minimum value at T ~ 350 K, whereas the frequency of mode 11 has a maximum value at T ~ 350 K.

In Fig. 3 we show that the intensities of modes 1–3 and 5–7 do not display significant changes for T < 300 K. The intensity of mode 8 decreases when T changes from 78 K to 210 K. Between 210 K and 300 K, the intensity of mode 8 does not change. Specifically, at around 150 K, the mode intensity decreases and a transfer of oscillator strength occurs the surrounding background gains weight. For mode number 9, its intensity changes when T changes from 78 K to 300 K. All modes (modes 1 to 11 except mode 4) show their strongest intensities at T ~ 350 K. The intensity of mode 4 which we attribute to spin ordering does not show noticeable changes for the temperature range of 78 K ~ 210 K.

Discussion

Charge ordering phase transition

Since Fe ion has an average valence of 2.5+, equal numbers of Fe2+ and Fe3+ ions co-exist in a lattice unit cell. Compared to the average valence of 2.5+ for the Fe ions, the Fe2+ and Fe3+ ions are practically equivalent to possessing a 0.5− and 0.5+ valence, respectively. In the triangular lattice charge frustration between the 0.5- and 0.5+ ions is thus inevitable, which leads to various forms of charge orders. Most noticeably charge order phase transition has been confirmed by various scattering experiments, such as X-ray scattering, neutron scattering, electron diffraction, etc2,3,22,26,27. For example, LuFe2O4 exhibits a phase transition at 330 K, where a 2D CO emerges and replaces the low temperature 3D CO and persists up to 500 K2,28. It is speculated that the Fe2+ and Fe3+ ions arranges themselves such that a 2D superstructure is formed within each individual W layer, largely owing to the stronger intralayer correlation24, as well as the interlayer correlation between W layers29,30. Here we attribute the phase transition of Er0.1Yb0.9Fe2O4 around 300 K to a 3D-2D CO phase transition with increasing temperature, as marked by the 1372 and 1554 cm−1 peaks. Quantitatively, these Raman shift results provides explicit energy band information that the 2D CO is 170 meV and 193 meV higher that the 3D CO, respectively. Such an energy gap (Fig. 4c) exists at 300 ~ 400 K.

Figure 4
figure 4

Fine structure in energy for the orderings.

The anti-parallel (a) and parallel (b) spin orderings in the material [Ref. 27]. (c) The schematic energy level for the double 2D COs, the SO and the 3D CO with the energy gap values marked explicitly. Note the 3D CO level is very close to the ground state. Schematic lattice structures of the (d) 2D CO states and the (e) 3D CO state, where the polarization is marked by arrows explicitly on the right panel [Ref. 2].

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Double 2D CO states with THz energy

In Fig. 2, the Raman peaks emerge at the temperature above 300 K are attributed to the 3D-2D phase transition. In the 2D CO state the atoms are closer than those in the 3D CO state, so the energy of the 2D CO is higher. Significantly we have observed two separate peaks, which indicated that the 2D CO is indeed composed of non-degenerate double states. The energies are 170 meV (41.2 THz) and 193 meV (46.6 THz) higher than that of the 3D CO state, respectively (Fig. 4c). We speculate that these non-degenerate double 2D CO states might come from two separate and different charge orderings within the W-layer: one comes from the nearest neighbors and the other comes from the next-to-nearest neighbors, thus forming charge orderings along different directions of the crystal lattice. Since collective CO or SO states are very sensitive to distances between atoms, this might explain the non-degeneracy of the double THz states. If this is true, then bi-directional ferroelectricity can be expected, which must co-exist together (although not all the experimental means are sensitive to it).

Alternatively, these double 2D CO states might originate from a predicted fact9 that the W-layer of the iron ions are asymmetric and composes of a Fe2+-rich layer and a Fe3+-rich layer simultaneously. Thus double long-range 2D CO develop within each sub-layer plane, but with non-degenerate energies. If the latter scenario is true, then our result provides direct experimental proof of the theoretical prediction of the bifurcated charge distribution and ordering within the W-layer in Ref. 9.

There is also a third possibility that this double CO state is originated from the doping of Yb atoms. The CO state reflects the properties of the Iron ions of the W layer, whereas the doping of Er/Yb ions does not affect the charges of Iron ions directly. However, from Fig. 2 and 3, for the temperature range accommodating the double CO states (Fig. 2 & 3), it can be seen that all the phonon modes (see below for discussion) show variations (in both frequency and intensity) with temperature, leading us to claim that the emergence of the double THz 2D CO is correlated to a structural softening. Note that both the phonon softening and the 2D CO states are associated to the varying lattice constants with temperature. The effect of doping might be conveyed by charge-lattice interactions. If this is true, then what we have found is a realization of generating double CO states by using chemical doping.

The observation of the double state of CO is unlikely due to slightly different states possibly due to the polycrystalline multi-domains, because we did not observe other multiple peaks and the two Raman peaks are clearly separated. In any case, further investigation is needed to confirm the origin of the double CO states.

Spin Ordering State

Among the various investigations of the magnetic properties of RFe2O4, neutron scattering is most extensively used, with the initial identification of a ferrimagnetic ordering below 240 K in LuFe2O431. Further neutron investigation with single crystal demonstrated that the ferrimagnetic spin ordering is of 3D nature22. Then the results of X-ray absorption spectroscopy suggested that in the W layer the Fe2+ ions all align ferromagnetically and the Fe3+ ions experience triangular frustration, emerging two possible configurations each preserving a 1:2 ferrimagnetic ordering20. So far whether the two configurations are degenerate is not clear and no further evidence has been found to further identify the spin ordering thus formed. Particularly, no Raman scattering or other optical spectroscopy methods have been reported on observing such a spin ordering. Here in our result, when T is below 210 K, a new mode was unambiguously observed (mode 4 in Figs. 1–3), with a characteristic energy of 45 meV (10.7 THz). Comparing with the available neutron and X-ray data we attribute this mode to the ferrimagnetic spin ordering of the system. Such a ground state of the spin structure is of long-range ordering nature and is usually elusive in a typical Raman scattering with linearly polarized probe to the center of the Brillion zone32,33,34. However, we have a polycrystalline sample immersed in the scatterings and breakings of the symmetry, which greatly relaxes the dipole transition restriction. In Fig. 4a–b, we show the suggested 3D spin ordering configuration of the system at temperatures below 210 K20. The fact that we have observed only one such spin ordering state implies that the two suggested configurations are either degenerate or non-degenerate with very small energy difference. From Fig. 3 it can be seen that this spin ordering state might be associated with the Eg3 mode phonon, where the interaction between them greatly modifies the phonon mode energy, especially at the low temperature regime.

Raman- and IR-active phonon modes

The RFe2O4 family crystals share a layered rhombohedral lattice structure (with space group ) at room temperature. It consists of alternating Fe-O double-layers (W layer) and R-O layers (U layer) stacked along the z-axis. In the W layer two sheets of triangular corner-sharing FeO5 trigonal bipyramids constitute a layer of hexagonal Fe2O2.5, where the two sheets are shifted by 1/3 x in the xy plane2. In the U layer the R2O3 atoms form a single flat layer instead. Such a RFe2O4 crystal structure preserves the center inversion symmetry. The lattice vibrations in RFe2O4 is constituted of six Raman-active modes and six infrared (IR)-active modes, i.e., 3A1g + 3Eg for Raman and 3A2u + 3Eu for IR5,6. The displacement symmetry of the A1g mode is along the c-axis, whereby the R-Fe atoms vibrate in opposite directions along the c-axis. The displacement symmetry of the Eg mode is along the xy plane, whereby the atoms vibrate in opposite directions along to the R-O and Fe-O bonds, respectively. Er0.1Yb0.9Fe2O4 has been shown to have a similar structure to that of LuFe2O4 via X-ray experiment7.

In conclusion, we have investigated the orderings and phase transition in the polycrystalline Er0.1Yb0.9Fe2O4 using Raman scattering. We for the first time found the double 2D CO states in the system and directly obtained the energy gap between the 2D and 3D CO states, which is at the THz range. Furthermore, a ferrimagnetic spin ordering mode was also observed, which has not been reported before in Raman scattering. Meanwhile two IR-active modes were also observed due to the symmetry breaking at the domain boundaries. Our investigation adds new feature to the fine structure of RFe2O4 system, which shines light to further investigations of other layered quantum materials.

Methods

Sample preparation

Our sample was synthesized using a conventional solid state reaction method. The details of the growth are described in Ref. 7. In addition, the sample surface was carefully polished mechanically before the Raman measurement. Due to the polycrystalline nature of the sample, the surface displays irregular dents. We measured only at the smooth part of the sample surface.

Variable-temperature Raman spectroscopy

All Raman data shown in this paper were obtained using a near-field con-focal spectrometer. The sample was kept in a continuous flow liquid nitrogen cryostat. The cryostat contains a heating element, making it possible to operate at temperatures ranging from 78 to 403 K. Temperature fluctuation was kept as low as 0.1 K. A 532 nm linearly polarized continuous wave laser beam with a power of 0.9 mW was used. An objective lens with 50× magnification was used to focus the laser light onto a 100 µm slit of the spectrometer which has a spectral resolution of 2 cm-1. X-ray diffraction measurements were carried out to characterize the crystal lattice structure and phase purity. No impurity phase was observed and the lattice constants are described in Ref. 7.