Spin-state order/disorder and metal–insulator transition in GdBaCo₂O_5.5: experimental determination of the underlying electronic structure

The layered cobaltates RBaCo₂O_5.5 (R = rare earth) have attracted considerable attention of the scientific community in recent years because of their peculiar magnetic and transport properties, showing giant magneto-resistance as well as metal–insulator (MIT) and antiferro–ferro-para-magnetic transition phenomena [1–27]. Moreover, these compounds possess the so-called spin-state degree of freedom, i.e. the possibility of the Co³⁺ ions to be in a low spin (LS, S = 0), high spin (HS, S = 2) and even intermediate spin (IS, S = 1) state [28, 29]. This spin-state degree of freedom is generally considered to play a key role for the unconventional transport properties of the cobaltates, and a spin-blockade mechanism [13, 30] has recently been proposed [13, 16] as the driving force for the MIT in RBaCo₂O_5.5.

The crystal lattice of RBaCo₂O_5.5 is composed of an equal number of CoO₆ octahedra and CoO₅ pyramids and the valence of all the Co ions is 3 + . These materials exhibit a series of magnetic orders, namely, a ferromagnetic-like phase below T_C ∼ 290 K, an antiferromagnetic phase below T_N1 ∼ 260 K which is accompanied by the appearance of strong magneto-resistive effects and a second antiferromagnetic phase below T_N2 ∼ 200 K. Despite a large number of neutron diffraction studies, the nature of these magnetic orderings is still unresolved [7, 18–20, 22]. One main reason for the disagreement is the confusion about the spin state of the Co³⁺ ions in both octahedral (Co³⁺_oct) and pyramidal (Co³⁺_pyr) coordination. This is particularly evident in the discussion about the sharp drop in the resistivity, the so-called MIT, occurring in the paramagnetic phase at T_MI ∼ 360 K. This MIT is commonly attributed to a sudden spin-state switch of Co³⁺_oct, but its modality is controversial and intensely debated. Contradictory scenarios have been proposed, including full or partial LS → IS or LS → HS state transitions for the Co³⁺_oct and IS or HS configurations for the Co³⁺_pyr [1–6–26]. It is noteworthy that at present there is, in fact, no direct evidence for any of the claimed spin-state transitions. There is therefore a pressing need to address the issue of the spin state of the Co ions and its evolution as a function of temperature. We have performed experiments utilizing soft x-ray absorption spectroscopy (XAS) at the Co-L_2,3 and O-K edges, a method proven to be extremely sensitive to the spin state of transition metal ions in general [31, 32] and 3d⁶ systems in particular [30, 33–35]. We have also carried out valence band photoelectron spectroscopy (PES) measurements in order to determine the changes of the band width and band gap in relationship to the temperature evolution of the spin state.

Twinned single crystals of GdBaCo₂O_5.5 were grown from a high-temperature flux melt. The purity and cation composition of the crystals were checked by x-ray diffraction and fluorescence analysis, respectively. The oxygen content was determined by iodometric titration to be 5.48(2). Co-L_2,3 spectra in the total-electron-yield mode and O-K XAS spectra in the total-fluorescence-yield mode were measured at the Dragon beamline of the NSRRC in Taiwan with a photon-energy resolution of 0.45 and 0.25 eV, respectively. XAS spectra of CoO were measured simultaneously as energy calibration for the Co-L_2,3 and O-K edges, respectively. The O-K and Co-L_2,3 XAS spectra of two reference compounds LaCoO₃ and Sr₂CoO₃Cl were collected under the same conditions. The PES spectra were recorded at the ID08 beamline of the ESRF in Grenoble, using a photon energy of 700 eV and a Scienta SES200 electron analyser. The overall experimental resolution was 110 meV and the Fermi level was calibrated using polycrystalline silver.

Figure 1(a) displays the isotropic O-K XAS measured on GdBaCo₂O_5.5 at different temperatures. The spectral structures from 528 to 532 eV are due to transitions from the O 1s core level to the O 2p orbitals that are mixed with the unoccupied Co 3d t_2g and e_g states. In the XAS of GdBaCo₂O_5.5 we observe a very modest spectral weight transfer from the broad feature at 530 eV to the dominant peak at 528.4 eV. These spectra are the sum of two contributions related to the Co³⁺_pyr and Co³⁺_oct sites. To explain their line shapes we will make use of Sr₂CoO₃Cl as a reference compound containing Co³⁺_pyr ions [34, 37], and of LaCoO₃ as a reference material having Co³⁺_oct ions which undergo a spin-state transition as a function of temperature [35, 38].

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The O-K XAS of Sr₂CoO₃Cl is reported in figures 1(b) and (c) as the curve of blue dots. The Co³⁺_pyr ions here have the HS configuration [34, 37]. The O-K spectra of LaCoO₃ are displayed in figure 1(d) for T = 20 K (black), 300 K (blue) and 650 K (red). Figure 1(d) shows a significant spectral-weight transfer from the higher energy structure at around 529.4 eV to the lower energy one at around 528.4 eV when going from 20 to 300 K and further to 650 K. The LaCoO₃ data demonstrate that O-K XAS is also very sensitive to the spin-state transition of Co³⁺ ions, which can be explained as follows. At low temperatures, the LS Co³⁺_oct has its t_2g shell completely occupied [35] and only transitions to the higher lying empty e_g states are possible. At higher temperatures, with part of the Co ions in the HS state [35], the t_2g states become partially unoccupied; then transitions to lower lying t_2g states are also allowed, leading to the feature at around 528.4 eV. As the temperature increases this lower energy feature gains gradually spectral weight at the expense of the higher energy feature. From the Co-L_2,3 XAS, it was estimated that at 650 K, 50% of the Co ions are in the HS state and 50% in the LS [35].

In determining the spin-state configurations for GdBaCo₂O_5.5 at 78 K, we assume that its Co³⁺_pyr ions are in the HS state like in Sr₂CoO₃Cl and we start by investigating the LS scenario for the Co³⁺_oct ions as proposed in several studies [12, 13, 16]. To this end we sum the Sr₂CoO₃Cl spectrum (blue) and the LaCoO₃ at 20 K (black). The result is displayed in figure 1(c) (magenta). One can clearly observe that this is very different from the GdBaCo₂O_5.5 spectrum in figure 1(a). The LS Co³⁺_oct scenario can thus be safely ruled out. Next, we take the LaCoO₃ at 650 K (red) as ansatz for the Co³⁺_oct part. The sum is shown in figures 1(b) and (a) (green). Surprisingly, this sum reproduces the GdBaCo₂O_5.5 spectrum at 78 K very well. This strongly suggests that GdBaCo₂O_5.5 in the low-temperature phase has 50% of its Co³⁺_oct ions in the LS state and 50% in the HS. All of its Co³⁺_pyr ions are HS. Remarkable is also the very modest temperature dependence in the GdBaCo₂O_5.5 spectra, i.e. very much unlike the LaCoO₃ case, suggesting that only a small part of the Co_oct ions participate in a spin-state transition across the MIT.

More support for the above results can be found from Co-L_2,3 spectroscopy. Figure 2(a) depicts the isotropic Co-L_2,3 XAS spectrum of GdBaCo₂O_5.5 at 78 K. The Co 2p core-hole spin–orbit coupling splits the spectrum roughly into two parts, namely the L₃ (at 780.5 eV) and L₂ (at 795 eV) white line regions. The strong absorption at 5 eV above the Co-L_2,3 white lines is due to the Ba-M_4,5 signal (shaded area) as shown by the BaFeO₃ spectrum in figure 2(b). We now use this BaFeO₃ spectrum to remove the Ba-M_4,5 signal from the GdBaCo₂O_5.5 Co-L_2,3 spectra. The result is given in figure 3(a), which displays the net Co-L_2,3 spectra of GdBaCo₂O_5.5 taken at 78, 285 and 400 K. The set is at first sight similar to those reported earlier [23, 24], but it is in fact essentially different in detail. Firstly, our spectra do not show a shoulder at 3 eV below the main peak at the Co-L₃ edge, which would represent a significant amount of Co²⁺ in the sample. This indicates that our spectra are free from Co²⁺ impurity signal [30]. Secondly, our set includes the very important low-temperature (78 K) spectrum.

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To analyse the Co-L_2,3 spectra, we have performed theoretical simulations based on the multiplet cluster method [34, 35] using the XTLS 8.3 code [36], taking into account the real local environment of the Co³⁺ ions in GdBaCo₂O_5.5, which we assume to be the same as in TbBaCo₂O_5.5 [18]. The simulations for the octahedral HS (orange), octahedral LS (black) and pyramidal HS (light blue) Co³⁺ clusters are shown in figure 3(e). We first make a sum of these contributions in a 1:1:2 ratio and we also add a standard edge jump (dashed curve) to take into account transitions to continuum states¹². Figure 3(b) clearly shows that this sum agrees excellently with the experimental 78 K spectrum. This confirms our O-K XAS finding, namely that the low-temperature phase of GdBaCo₂O_5.5 consists of 50% LS–50% HS Co_oct.¹³ To double check, we also make a sum in a 0:2:2 ratio to mimic the commonly accepted scenario for the low-temperature phase in which all Co_oct are believed to be in the LS state. Figure 3(c) reveals unambiguously significant discrepancies from the experiment as marked by ellipses. We can therefore safely reject this scenario.

Figure 3(a) shows also that there is only a very small temperature dependence in the Co-L_2,3 spectra of GdBaCo₂O_5.5, in strong contrast to, for example, LaCoO₃ [35]. This observation indicates again a very modest and only partial spin-state transition of the Co_oct ions in GdBaCo₂O_5.5 across the MIT, fully in agreement with the findings of the O-K XAS study above. Our data therefore also rule out the commonly accepted scenario of a sharp and massive LS–HS transition across T_MI. For completeness, we have investigated what the spectral lineshape of an all HS Co_oct high-temperature phase could look like, and we can see from figure 3(d) that the 2:0:2 sum strongly disagrees with the experimental 400 K spectrum.

Recent diffraction data showed that in going from high to low temperature, the MIT is accompanied by a structural transition towards a distorted structure with two inequivalent Co³⁺_oct sites, one with the average Co–O bond length of 1.928 Å, called Co³⁺_oct1, and the other with 1.978 Å, called Co³⁺_oct2 [18, 22]. This transition was interpreted as the effect of an orbital [17, 23] or a spin-state order transition [22]. Our results showing a 50:50 mixture of LS/HS Co³⁺_oct ions provide direct evidence that these low temperature distortion and superstructure are caused by LS/HS spin-state ordering of the Co³⁺ ions at the octahedral sublattice. Also a direct link can then be made between the differences in Co–O bond lengths with differences in the spin state [35]. In LaCoO₃, for example, the bond length is 1.925, 1.949 and 1.962 Å at 5, 650 and 1000 K, respectively [39]. The Co³⁺_oct1 ion in GdBaCo₂O_5.5 has a bond length close to LaCoO₃ at 5 K, i.e. LS. The Co³⁺_oct2 ion has a bond length even larger than LaCoO₃ at 1000 K, i.e. HS, again fully consistent with the above finding.

We now investigate the effect of the spin-state configurations on the band width and band gap of GdBaCo₂O_5.5. Figure 4 shows the valence band PES at temperatures below and above T_MI. Surprisingly, and in contradiction with a previous report¹⁴, the valence band PES of GdBaCo₂O_5.5 reveals that the spectral weight at the Fermi level is negligible at 78 K (black) and 285 K (blue), and still very weak at 400 K (red), so that we have to conclude that actually the material is an insulator or semiconductor even above T_MI. What we found is that the band gap is indeed reduced when the temperature is increased: the top of the valence band (figure 4, left panel) moves up by about 60 meV in going from 285 to 400 K, while the bottom of the conduction band (figure 4, right panel) shifts downwards by 70 meV from 285 to 400 K. So, in total, the band gap is reduced by about 130 meV across T_MI. Using ρ∝e^E_g/k_BT_MI with k_BT_MI ∼ 30 meV, this gap narrowing accounts well for the observed reduction of resistivity by two orders of magnitude at T_MI [5, 9, 11, 14, 16]. From figure 4 one can see that there is no pronounced LS peak at 0.8 eV as found in the spectrum (magenta) of LaCoO₃ at 65 K, where the Co³⁺ ions are basically in the LS state [35]. However, we see that the weak feature at 0.6 eV in GdBaCo₂O_5.5 corresponding to 50% LS Co³⁺_oct ions loses spectral weight with increasing temperature.

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The following picture now emerges from our electronic structure measurements concerning the MIT in this system. In the low temperature phase, the superstructure associated with the 50% LS–50% HS spin-state ordering of Co³⁺_oct ions stabilizes the insulating state of the GdBaCo₂O_5.5 system. On increasing the temperature across T_MI, part of the LS Co³⁺_oct ions undergo a transition to the HS state, thereby breaking down the superstructure as is shown by x-ray diffraction [17]. This loss of order causes a reduction of the band gap. In converting an HS–LS neighbouring pair into an antiferromagnetic HS–HS pair by a rise in temperature, one can transfer an e_g electron both ways instead of only from HS to LS, thereby increasing the amount of charge fluctuations. However, the band gap does not vanish since the hopping of an extra hole or electron is energetically quite difficult in such an antiferromagnetic situation. Reversely, the observation that the changes in widths of the valence (PES) and conduction (O-K XAS) bands are very modest reaffirms that the IS state scenario does not become active, since otherwise the presence of IS Co³⁺_oct ions would allow for free propagation of an extra hole or electron in a ferromagnetically aligned e_g band.

To summarize, we have utilized O-K and Co-L_2,3 XAS spectroscopy to reveal that the low-temperature insulating phase of GdBaCo₂O_5.5 is characterized by a LS–HS spin-state ordering in the Co³⁺_oct sublattice. We found a very modest spin-state transition in the Co³⁺_oct with increasing temperature across the insulator–metal transition. Our photoemission experiments show that the band gap is reduced but does not close, in quantitative agreement with the change in resistivity. The MIT should be modelled in terms of a spin-state order–disorder transition with a modest gain in band width.

The research at Köln was supported by the Deutsche Forschungsgemeinschaft through SFB 608. The work at Minsk was supported in part by INTAS grant no. 01-0278 and by SNSF in the framework of the SCOPES programme, grant no. 7BYPJ65732. HW is supported by the NSF of China (grant no. 11274070) and the WHMFC (grant no. WHMFCKF2011008). YYC was supported by the EU through the Marie Curie (FP7) ITN SOPRANO project.

Here we describe the procedure for data analysis and the model calculation of the XAS spectra.

A.1. Oxygen K-edge data analysis (figure 1)

A.2. Cobalt L-edge data analysis and model calculation (figures 2 and 3)

The total electron yield was divided by I₀ (the intensity of the incoming beam). Then a (constant) pre-edge background was subtracted. As normalization we divided each background-subtracted spectrum by the average of its spectral intensity in the energy range 807–815 eV.

The energy of each GdBaCo₂O_5.5 spectrum was calibrated using a (simultaneously recorded) reference CoO spectrum identifying the first peak of CoO to be at 778.1 eV [40]. For each temperature we averaged the E∥ab and E∥c spectra with a weighting ratio 2:1 in order to obtain the isotropic spectrum. In order to subtract the Ba M-edge signal we measured a polycrystalline BaFeO₃ spectrum. This BaFeO₃ spectrum has a background with a slope; the pre-edge background was fitted using a linear function (for the fit we considered the first 40 points) and we subtracted this linear background from the spectrum. Then the BaFeO₃ spectrum was subtracted from the GdBaCo₂O_5.5 spectra—the scaling factor and energy position of the BaFeO₃ spectrum were adjusted such that the irregularities in the difference spectrum were minimized.

A theoretical calculation of the x-ray absorption spectra was performed with the program XTLS 8.3 [42]. The following parameters have been used (HF refers to Hartree–Fock calculations for a single Co ion):

• Slater integrals were reduced to 80% of the HF values¹⁵.
• For the 3d spin–orbit coupling HF values were used.
• Electron–electron Coulomb repulsion: U_3d3d = 5.5 eV, U_3d2p = 7.0 eV [41, 43].
• Charge transfer energy (from the oxygen ligand to Co 3d): Δ = + 2.0 eV [43].
• Energy splitting of ligand orbitals due to ligand–ligand hybridization: 2T_pp = + 1.0 eV [41].
• Hybridization parameters of Co d-electrons and oxygen ligand p-electrons were estimated according to the distance to the power of 7/2 law by Harrison [44], starting from V_pdσ = −1.7 eV for a Co–O distance of 1.925 Å [43].
• The ionic crystal field was taken into account by a purely octahedral splitting parameter 10Dq.
• For the final state we used the same values of the hybridization parameters and reduced the ionic crystal field parameter 10Dq by 30% with respect to the initial state value.

• (i)  
  Octahedral sites HS.
• (ii)  
  Octahedral sites LS.
• (iii)  
  Pyramidal sites HS.

XAS spectra are calculated using the finite imaginary constant iΓ in the denominator of Green's function with Γ = 0.1 eV (much larger than the step size of 0.02 eV). In order to take into account experimental resolution and lifetime effects, we applied additional line broadening to the spectra: (i) a Gaussian broadening with 0.45 eV FWHM, and (ii) an energy-dependent Lorentzian broadening.

An edge jump was added to the results of the calculation. The edge jump I_edge(E) is modelled by the formula

$$\begin{eqnarray*} &&\fl I_{{\rm edge}}(E)=0.0164 \left[\pi/2+ {\arctan}\left(1.5\left(\frac{E}{\rm eV}-783.2\right)\right)\right] \\ &&+0.0134 \left[\pi/2+{\arctan}\left(1.5\left(\frac{E}{\rm eV}-795.0\right)\right)\right]. \end{eqnarray*}$$

The results of the model calculation are compared with the experimental data in figure 3 of the main text. The sum of oct-HS, oct-LS and pyr-HS contributions with the 1:1:2 spectral weight agrees best with the experimental data and supports our conclusion about the presence of a LS–HS spin-state ordering in the Co³⁺_oct sublattice of GdBaCo₂O_5.5.

A.3. PES data analysis (figure 4)