Orbital order and fluctuations in the two-leg ladder materials BaFe$_2X_3$ ($X$ = S and Se) and CsFe$_2$Se$_3$

TL;DR

This study investigates the electronic structure and orbital order in two-leg ladder iron-based materials BaFe$_2X_3$ ($X$ = S, Se) and CsFe$_2$Se$_3$ using x-ray spectroscopy, revealing coexistence of itinerant and localized electrons and distinct magnetic and orbital orders.

Contribution

It provides new insights into the orbital order and fluctuations in Fe-ladder materials, highlighting the role of direct exchange interactions in stabilizing magnetic and orbital states.

Findings

Coexistence of itinerant and localized Fe 3d electrons in BaFe$_2X_3$.

Presence of orbital order or fluctuations above the N{é}el temperature.

Different magnetic interactions stabilize orbital and magnetic orders in BaFe$_2$S$_3$ and CsFe$_2$Se$_3$.

Abstract

The electronic structure of BaFe$_2X_3$ ($X$ = S and Se) and CsFe$_2$Se$_3$ in which two-leg ladders are formed by the Fe sites are studied by means of x-ray absorption and resonant inelastic x-ray scattering spectroscopy. The x-ray absorption spectra at the Fe L edges for BaFe$_2X_3$ exhibit two components, indicating that itinerant and localized Fe 3$d$ sites coexist. Substantial x-ray linear dichroism (XLD) is observed in polarization dependent spectra, indicating the existence of orbital order or fluctuation in the Fe-ladder even above the N\'{e}el temperature $T_N$. Direct exchange interaction along the legs of the Fe-ladder stabilizes the orbital and antiferromagnetic orders in BaFe$_2$S$_3$, while the ferromagnetic molecular orbitals are realized between the rungs in CsFe$_2$Se$_3$.

Full text

I Introduction

The magnetic-orbital fluctuations and their anisotropies in iron-based superconductors have been attracting much attention. The parent compounds of the iron-based superconductors show antiferromagnetic (AF) transitions at low temperatures, typically exhibiting striped-type magnetic ordering.Cruz08 ; Huang08 ; Dai15 On the basis of theoretical analyses on multiband models with hole and electron Fermi pockets, the striped-type magnetic ordering is stabilized by Fermi-surface nesting, and the associated AF and orbital fluctuations are proposed to induce the superconductivity.Mazin ; Kuroki ; Lee09 ; Dai15 ; Yamakawa ; Chubukov However, there are some iron-based superconductors showing significant disagreement with the Fermi-surface nesting scenario. For example, superconductivity with $T_{\rm c}\sim$30 K in 245 system ($A_{2}$Fe4Se5, $A$ = K, Rb, and Cs)Guo ; Ye ; Shermadini appears in the vicinity of the Mott insulating state with block-type AF ordering. In this context, it is very important to study the nature of the Mott insulating state in the parent compounds of iron-based superconductors.

Recently, another insulating Fe chalcogenide $A$Fe${}_{2}X_{3}$ ($A$ = Cs and Ba, $X$ = S and Se) has been attracting attention due to the specific quasi-one-dimensional crystal structure and magnetism.Hong ; Krzton ; Caron11 ; Caron12 ; Nambu ; Du ; Chi ; Takahashi ; Yamauchi ; Lei ; Hirata ; Monney ; Ootsuki ; Popovic ; Luo ; Dong In this family of compounds, Fe(S,Se)4 tetrahedra share their edges and form a two-leg ladder of Fe sites as shown in Fig. 1 (a). These compounds all exhibit unique magnetic ordering. The magnetic structure of BaFe2Se3 ($Pnma$ space group) is a one-dimensional analog of the block magnetism observed in $A_{2}$Fe4Se5, in that four Fe spins in the two-leg ladder form a ferromagnetic block and the neighboring blocks are antiferromagnetically coupled as illustrated in Fig. 1 (f).Krzton ; Caron11 ; Caron12 ; Nambu In contrast, the magnetic structures of BaFe2S3 and CsFe2Se3 ($Cmcm$ space group), are of the stripe-type, in which the magnetic moments couple ferromagnetically along the rung, and antiferromagnetically along the leg direction.Du ; Chi However, the magnetic moments in CsFe2Se3 point toward the layers, while those in BaFe2S3 point toward the rungs.

Moreover, recent works under high-pressures revealed that BaFe2S3, which is the most conductive compound among these compounds, shows an appearance of the superconducting phase at T_{\rm c}$$\sim14 K under 11 GPa without major crystal structure change.Takahashi Also it has been clarified that the superconducting phase is in the vicinity of bandwidth-control type Mott transition.Yamauchi In addition, the magnetic transition temperature and resistivity of BaFe${}_{2}X_{3}$ (Fe2+) depend on the sample stoichiometry. Lei et al. reported the activation-type temperature dependence for BaFe2Se3 with a band gap of 0.18 eV.Lei On the other hand, one-dimensional variable range hopping was reported, indicating that some carriers are localized due to strong scattering effects in the quasi-one-dimensional structure.Nambu ; Yamauchi ; Hirata Moreover, coexistence of the itinerant and localized electrons was indicated by the resonant inelastic x-ray scattering (RIXS),Monney and x-ray photoemission spectroscopy (XPS).Ootsuki These observations suggest that the itinerant electrons introduced by small Fe vacancies or some other effects would be responsible for the variable range-hopping behavior of the resistivity.Nambu ; Hirata ; Yamauchi In contrast to BaFe${}_{2}X_{3}$, CsFe2Se3 with formal Fe valence of +2.5 is much more insulating. Usually, Mott insulators with integer number of valence are expected to be more insulating than the mixed valence systems. Such puzzling mismatch between the formal valence and the transport behavior indicates unusual electronic states in the vicinity of the superconducting phase of $A$Fe${}_{2}X_{3}$. The x-ray linear dichroism (XLD) for x-ray absorption spectroscopy (XAS) and RIXS are ideal tools to detect electronic anisotropy in such systems with charge and orbital degrees of freedom of transition-metal 3$d$ electrons.

In other families of the iron-based superconductors, 122 ($A$Fe2As2, $A$ = alkaline-earth) and 1111 ($R$FeAsO, $R$ = rare earth) systems, the Néel temperature ($T_{\rm N}$) and structural transitions ($T_{\rm s}$) are split, which have recently been considered as a manifestation of electronic nematic order.Fernandes14 These orders have been inferred from the unusual anisotropy in resistivity,Chu10 ; Ying11 ; Chu12 optical conductivity,Dusza11 and orbital occupancyYi11 ; Kim observed at the temperatures above $T_{\rm s}$ and $T_{\rm N}$. In the present paper, we investigate the electronic structure of BaFe2S3, BaFe2Se3, and CsFe2Se3 in the Fe sites by means of XAS and RIXS at the Fe $L_{2,3}$ absorption edges. An opposite XLD, namely the electronic anisotropy, is observed for BaFe${}_{2}X_{3}$ and CsFe2Se3 at room temperature, indicating the existence of the orbital order or fluctuation above $T_{\rm N}$. The orbital and AF order along the legs of Fe ladder is emerged via the direct exchange interaction between the Fe sites in BaFe2S3. On the other hand, the molecular orbital formation along the rung is associated in CsFe2Se3.

II Experiment

Single crystals of BaFe2S3, BaFe2Se3, and CsFe2Se3 were grown by the melt-growth method.Hirata ; Du XAS and RIXS measurements were performed at the REIXS beamline of the Canadian Light Source.Hawthorn The single crystals were cleaved at room temperature (300 K) under the base pressure of 5$\times$10*-6* Pa for the XAS and RIXS measurements. The cleaved surfaces were oriented to the (110) planes for BaFe2S3 and CsFe2Se3, and (100) plane for BaFe2Se3, parallel to the legs of ladder. Although the crystals of BaFe2Se3 consist of some blocks misaligned by a rotation along the ladder direction,Krzton ; Monney this fact does not seriously affect the main conclusion of XLD for $E//{\rm leg}$ or $E\perp{\rm leg}$ discussed later. The XAS spectra were recorded both in the total-electron-yield (TEY) and total-fluorescence-yield (TFY) modes. At the RIXS measurement, the samples were measured at the incident angle of 60∘ and the emissions were detected at $\theta$=90∘ for the x ray [see inset of Fig. 5 (d) about the experimental geometry]. The beamline slit was set to 25 ${\mu}$m, which resulted in an effective combined resolution of both the incoming beam and spectrometer of $\sim$0.8 eV for RIXS measurements at the Fe $L_{3}$ edge. The energy of outgoing photons was calibrated by a reflection from a copper plate.

III Results and Discussion

Figure 2 shows the XAS spectra at the Fe $L_{2,3}$ absorption edge of BaFe2S3, BaFe2Se3, and CsFe2Se3 taken with the (a) TEY and (b) TFY modes at room-temperature. Spectral difference between the less-distorted TEY and bulk-sensitive TFY spectra is barely observed, indicating the clean ordered surface for these samples. The two white lines in the spectra result from 2$p$ to 3$d$ dipole transitions ($2p^{6}3d^{6}\rightarrow 2p^{5}3d^{7}$) with the well-separated spin-orbit-split 2$p$ states $2p_{3/2}$ ($L_{3}$) and $2p_{1/2}$ ($L_{2}$), appearing respectively at around $\sim$708 and $\sim$721 eV. No sharp multiplet is observed in the spectra, that exhibits a similar spectral shape as chalcogenides of Fe(Se,Te)Saini and Fe-pnictide materials.Yang ; ParksCheney ; Bondino08 ; Bondino10 ; Kim Additionally, some spectral weights can be seen in the energy range of 3-5 eV above the white lines. These features are an indication of interaction of the chalcogen sites with the Fe 3$d$ statesSaini and is notably well-separated in the sharp spectrum for CsFe2Se3, which are indicated in the red arrows in Fig. 2(a). Despite the formal Fe valence of +2.5 for CsFe2Se3, the spectrum of CsFe2Se3 is very sharp but consistent with the observation of a previous Fe 2$p$ XPS study,Ootsuki indicating a localized Mott insulating nature with Fe2+. If all the Fe sites in CsFe2Se3 take the high-spin Fe2+ configuration, the extra positive charge (+0.5 per Fe) should be located at the Se sites. Since the charge-transfer energy from Se 4$p$ to Fe 3$d$ is small, if Fe3+ exists in CsFe2Se3, it should take the $d^{6}\underline{L}$ configuration instead of $d^{5}$.Ootsuki In this ligand hole picture, the two-leg ladder in CsFe2Se3 accommodates the $d^{6}$-like and $d^{6}\underline{L}$-like sites. Assuming that the $d^{6}$-like and $d^{6}\underline{L}$-like sites are aligned along the rung, the Se 4$p$ hole should be located at the Se sites sandwiched by the two legs as schematically shown in Fig. 1(e).

On the other hand, some shoulder structures below the white lines are observed in the spectra of BaFe2S3 and BaFe2Se3, that are also similar to the Fe 2$p$ XPS spectra and corresponding to rather electron doping compared to the case of CsFe2Se3. In Fig. 2(a), the results of Mahan’s-line shape fitting are indicated by the dashed curves. The weak but significant components are observed at the pre-edge region $\sim$1.0 eV below the white lines for BaFe2Se3 and BaFe2S3. On the XPS study, these two components have been ascribed as the contribution from itinerant and localized electrons. Since the pre-edge region of XAS for transition-metal $L_{2,3}$ edges corresponds to the transition to unoccupied $d$ state near the Fermi-level, these low energy structures originate from the itinerant $e_{g}$ empty state of the Fe2+ high-spin state [see Fig.1 (b)]. The itinerant and localized electrons will coexist in BaFe2Se3 and BaFe2S3. Namely, self-dopings from the Se 4$p$ and S 3$p$ to Fe 3$d$ states arise from smallness of the charge transfer and cause partial delocalization of the electrons in these systems. On the other hand, the Fe 3$d$ electrons with the Fe2+ high-spin configuration and the Se 4$p$ holes are localized in CsFe2Se3.

In addition to these features, the XAS spectra at the Fe edges exhibit unique anisotropies. Figure 3 gives the XLD spectra of BaFe${}_{2}X_{3}$ ($X$ = S and Se) and CsFe2Se3 at room temperature. The spectra are normalized by the area between 700 eV and 718 eV. The substantial XLD ($I_{E//{\rm leg}}-I_{E\perp{\rm leg}}$) are observed for all samples and exhibit an opposite behavior for BaFe${}_{2}X_{3}$ and CsFe2Se3. The sign of XLD is minus for BaFe2S3 below the $L_{3}$ main peak of 708.1 eV in the overall pre-edge region and plus in the higher energy region. XLD observed in the spectra for BaFe2S3 is fairly similar to that obtained for BaFe2As2 ($I_{AF}-I_{ferromagnetic}$) below $T_{\rm s}$.Kim XLD for BaFe2As2 was consistent with the existence of an orbital order along their AF direction and an opposite to tendency of their local structural distortion of $a_{AF}>b_{ferromagnetic}$.Kim ; Chen The spectrum for BaFe2S3 in the pre-edge region taken with the $E//{\rm leg}$ ($E\perp{\rm leg}$) polarization detects the empty $e_{g}$ state of the $d_{3z^{2}-r^{2}}$ ($d_{x^{2}-y^{2}}$) orbital as discussed earlier. Here, $z$ is defined to be parallel to the leg direction, or $c$ for BaFe2S3 and CsFe2Se3, and $b$ for BaFe2Se3, respectively. Therefore, $d_{3z^{2}-r^{2}}$ will be occupied and the orbital order along the leg direction is indicated in BaFe2S3.

In the case of BaFe2Se3, most of the $d_{3z^{2}-r^{2}}$ orbitals should be occupied, since XLD in the pre-edge region of $\sim$707 eV is essentially similar to that of BaFe2S3. However, a dip-hump like shape is observed at the pre-edge region and the sign of XLD is still minus at the main-peak region of $\sim$708 eV. Since the crystals of BaFe2Se3 has many twins at room temperature compared to BaFe2S3 and CsFe2Se3,Hirata it is possible that the crystal of BaFe2Se3 contains many defects. The small Fe vacancy will affects the electronic configuration for BaFe2Se3 and the orbital order may become more complicated, corresponding to their block-type magnetism and lattice distortion below $T_{\rm N}$.

On the other hand, there is a peak in the pre-edge region of XLD for CsFe2Se3 and it exhibits a dip at the main-peak structure around 708.4 eV. Therefore, more holes are suggested in the $d_{3z^{2}-r^{2}}$ orbital rather than in the $d_{x^{2}-y^{2}}$. Namely, the orbital order perpendicular to the leg direction is indicated in CsFe2Se3, in contrast to BaFe2S3 [see also Fig. 1(e)]. However, the very sharp Fe peaks with the satellite-like structures of CsFe2Se3 cannot be simply understood for the formal valence of 2.5+ with any kind of the orbital order in the Fe sites, whereas this observation is still consistent with the insulating nature of this compound.

One may consider that the anisotropic spectra discussed above are naturally expected on the basis of their local structural distortions in the two-leg ladder of $A$Fe2X3, and do not link to the existence of orbital orders. However, the present tendency of XLD for BaFe2S3 is opposite to its local distortion, which was theoretically clarified by Chen et al. for BaFe2As2.Chen The local distortions around the Fe sites can be described by the elongation or compression for the FeS4 tetrahedra. The FeS4 tetrahedra of BaFe2S3 are elongated along the leg direction ($u/w\sim$1.03)Hong [see Fig. 1(d)], which corresponds to the AF direction for BaFe2As2. In this case, the dip-like structure would be observed in XLD of the higher energy region and hump would be observed in the lower energy region of the Fe $L_{3}$ edge.Chen However, the observed XLD for BaFe2S3 is opposite to these tendencies. On the other hand, the FeSe4 tetrahedra of CsFe2Se3 are compressed ($u/w\sim$0.98) along the leg.Du Moreover, the orbital order in many iron-based superconductors including BaFe2As2 were unable to be reproduced by simple first-principle calculations based on the structural data and still has been a controversial problem. Actually, a recent first-principle calculation for paramagnetic metallic state of BaFe2S3 indicates the different orbital filling in the Fe 3$d$ states ($n_{d_{x^{2}-y^{2}}}>n_{d_{3z^{2}-r^{2}}}$).Arita15 ; Suzuki15 Therefore, the observed XLD for BaFe2S3 and CsFe2Se3 cannot be explained from their structural distortions, indicating the existence of orbital order or fluctuation at room temperature.

Furthermore, the tendency of XLD in the lower energy region of the Fe $L$ edges show scarcely any temperature dependence as shown in Fig. 4. While the higher energy structures of $L_{3}$ around $\sim$709 eV show some cleavage dependences owing to the defects and/or contaminations, the tendency and magnitude of XLD are essentially similar to those obtained at Fig. 3. As the temperature decreases, the magnitudes of XLD for all samples steadily increase but irrelevant to $T_{\rm N}$. Those for BaFe2S3 and BaFe2Se3 at $T$=100 K (and $T$=200 K) are $\sim$ 30$\%$ (and $\sim$ 10$\%$) larger than those at $T$=300 K. On the other hand, that for CsFe2Se3 at $T$=150 K (and $T$=200 K) is $\sim$ 30$\%$ (and $\sim$ 0$\%$) larger than that at $T$=300 K. Therefore, the present temperature dependence of XLD strongly supports the scenario of the orbital order or fluctuation in these systems even above $T_{\rm N}$.

In order to examine the energy levels in the Fe sites with unique anisotropies discussed above, polarization dependent RIXS spectra have been acquired for incident energies $h\nu_{i}$ across the Fe $L_{3}$-edge XAS spectra as indicated by the arrows in Fig. 2(a). The data are shown in Fig. 5 for (a) BaFe2S3, (b) BaFe2Se3, and (c) CsFe2Se3, respectively, on an energy loss scale $\hslash\Omega　=h\nu_{f}-h\nu_{i}$, where $h\nu_{f}$ is the energy of outgoing photons. Although some elastic lines are observed at zero energy loss taken with the vertical polarization, these are barely observed on the spectra with horizontal polarization owing to the experimental geometry given in the inset of Fig. 5(d). The strong fluorescence indicated by the blue arrows are observed on the spectra with $h\nu_{i}>$706.8 eV and disperses from 1 eV energy loss to higher energy losses, which was ascribed by the hybridization effects between Fe 3$d$ states and Se 4$p$ states in the high-resolutional study for BaFe2Se3 by Monney et al.Monney The fluorescence contributions shift to higher energy losses for increasing incident energies, as fluorescence in RIXS typically occurs at fixed x-ray emission energy. Monney et al. also suggested two Raman-like peaks labeled as A and B, not moving in energy position with variation of incident photon energy, superimposed on top of the fluorescence, which are clearly seen in the spectra with $h\nu_{i}$ = 705.5 eV zoomed in Fig. 5 (d). These two Raman-like peaks A and B are corresponding to the energy of $d$-$d$ excitations in the Fe sites [see Fig. 1(c)]. The peak energies of A roughly correspond to the magnitude of band gap and increase in going from 0.4 eV for BaFe2S3, 0.8 eV for BaFe2Se3, to 1.3 eV for CsFe2Se3, which are more or less consistent with the order for the activation energiesLei ; Hirata and threshold energies of the photoemission spectroscopy.Ootsuki

The relatively large band gap observed in RIXS and orbital order along the rung direction clarified by XLD for CsFe2Se3 can be explained by the molecular orbital formation between the two Fe sites of the rung, namely ferromagnetic dimer formation.Pardo08 ; Mazin12 In this scenario, the bonding orbital accommodates two electrons of the $e_{g}$ states in the two Fe sites across the rung in CsFe2Se3 and the gap is opened between the bonding and antibonding states. Since the $d_{x^{2}-y^{2}}$ orbitals along the rung become a bonding localized state, the $d$-$d$ excitation of A on RIXS with the vertical polarization and $I_{E//{\rm leg}}$ of the pre-edges on XLD are enhanced. On the other hand, the ferromagnetic dimers are destabilized partially in BaFe2Se3 and completely in BaFe2S3 and then $I_{E\perp{\rm leg}}$ of XLD are enhanced. The gap sizes depend on the transfer between the dimers and therefore become very small in BaFe${}_{2}X_{3}$. This scenario seems to be consistent with a recent inelastic neutron scattering study for BaFe2S3.Wang It indicates a strong intraladder ferromagnetic exchange interaction along the rung direction, although BaFe2S3 still exhibits the commonly striped AF spin excitations. In addition, the importance of Hund’s rule coupling has generally been suggested in iron-based superconductors, which leads to ferromagnetic interaction between the itinerant electrons and local moments.Haule

IV Summary

We have studied the electronic structures of BaFe${}_{2}X_{3}$ ($X$ = S and Se) and CsFe2Se3 using x-ray absorption and resonant inelastic x-ray scattering spectroscopy. XAS peak structure at the Fe $L$ edges consists of the two components in BaFe${}_{2}X_{3}$, indicating that the itinerant and localized Fe 3$d$ electrons coexist. On the other hand, the sharp peak at the Fe $L$ edges for CsFe2Se3 exhibit the single component accompanied with the well separated charge-transfer like satellite. The distinct electronic anisotropies in the Fe 3$d$ states are inferred from the XLD spectra. Different types of the orbital order or fluctuation exist in BaFe${}_{2}X_{3}$ and CsFe2Se3 even at room temperature far above $T_{\rm N}$, which originate from the direct exchange between the $d_{3z^{2}-r^{2}}$ orbitals and molecular orbital formation bridging the rungs, respectively. The similarity between these findings and the electronic nematic order observed in other families of the iron-based superconductors having square lattices suggests that the similar exotic phases can be realized in the quasi-one-dimensional structure.

Acknowledgements

The authors thank Dr. D. Ootsuki and Dr. Y. Hirata for valuable discussions. Research described in this paper was performed at the Canadian Light Source, which is supported by the Canada Foundation for Innovation, Natural Sciences and Engineering Research Council of Canada, the University of Saskatchewan, the Government of Saskatchewan, Western Economic Diversification Canada, the National Research Council Canada, and the Canadian Institutes of Health Research. This works was supported by the Japan Society for the Promotion of Science (JSPS) of Grant-in-Aid for Young Scientists (B) (No. 16K20997) and for Scientific Research (B) (No. 16H04019). This work was also partially supported by Ministry of Education, Culture, Sports, Science, and Technology of Japan (X-ray Free Electron Laser Priority Strategy Program) and Mitsubishi Foundation.