The misfit layered Bi2A2Co2O8 (A = Ca, Sr, Ba) compounds experience an insulator to metal transition as A’s ionic radius increases. This feature is contradictory to the conventional wisdom that larger lattice constant favors insulating rather than metallic state, and is also difficult to be reconciled using the Anderson weak localization theory. In this paper, we show from the first-principles calculation that an insulator-metal transition takes place from a nonmagnetic low-spin state of Co3+ ions to a hexagonally arranged intermediate-spin low-spin mixed-state in CoO2 plane when ionic radius increases from Ca to Ba. The predicted low-spin state of Bi2Ca2Co2O8 and Bi2Sr2Co2O8 and intermediate-spin low-spin mixed-state of Bi2Ba2Co2O8 are consistent not only with their measured transport properties, but also with the magnetic-field suppressed specific-heat peak observed at the transition temperature. In agreement with experiments, strong electronic correlation is required to stabilize the low-spin insulator and intermediate-spin low-spin metal.
Describing the microscopic behavior of strongly correlated electronic systems in transition-metal oxides with geometrically frustrated lattice structures is a fundamental challenge1,2. Strong correlations coexist with magnetic frustration, orbital degeneracy, and charge-ordering effects often lead to novel physical phenomena3,4. For examples, unconventional superconductivity was discovered in water-intercalated NaxCoO25 and dome-shape relationship, similar to high temperature superconductor oxides, between transition temperature and doping is observed near x ≈ 0.306. Also, large thermoelectric power was unveiled in Na0.5CoO27. The Seebeck coefficient was strongly suppressed under magnetic field indicating the important role of spin-fluctuation8,9. All these properties originate from the archetype structure of hexagonal CoO2 layers which includes all the necessary ingredients for correlated electronic systems.
Inspired by the novel property of hexagonal CoO2 layers, recent studies have been extended to the so-called misfit layered Bi-A-Co-O compounds (A = Ca, Sr, Ba)10. Similar to Na0.5CoO2, a large thermoelectric power of over 100 μV/K was observed in Bi2A2Co2O8 (A = Ca, Sr, Ba)11,12 and Ca3Co4O913. Thus, the excellent thermoelectric property seems to be a common feature of hexagonal CoO2 layers. What is unique about misfit layered Bi2A2Co2O8 is an interesting insulator-metal (I-M) transition when either temperature or A’s ionic radius (r) increases14,15,16. Bi2Ca2Co2O8(BCCO) (rCa = 0.99 Å)17 and Bi2Sr2Co2O8 (BSCO)(rSr = 1.13 Å)17 with smaller r are insulators at low temperature and make a transition into metallic states at high temperature. The transition temperature TC is around 140 K for Bi2Ca2Co2O8 and 60 K for Bi2Sr2Co2O8. Bi2Ba2Co2O8(BBCO) (rBa = 1.35 Å)17 with large r is different. It remains a metal and shows no insulator-metal transition as temperature varies16. Since high temperature means larger lattice constants of crystal structures, one is tempted to conclude that misfit layered Bi2A2Co2O8 is likely to take a metallic state at larger lattice constant while stays in an insulator state at smaller lattice constant.
To understand the nature of this insulator-metal transition, specific-heat data was very helpful. A sharp peak was observed to coincide with the transition temperature in Bi2−xPbxSr2Co2Oz14. The insulator-metal transition is, thus, of the second order. Most strikingly, the magnitude of specific-heat peak strongly depends on external magnetic field and is suppressed when magnetic field is large (B = 13.2 T)14. The field-dependence of I-M transition is also confirmed by the zero-field-μ+-spin-rotation spectra where a magnetic anomaly is found at the transition temperature of BSCO18. Further implication involving spin-degree of freedom is the sizeable negative magnetoresistance observed in insulating Bi2Ca2Co2O8 and Bi2Sr2Co2O8 and positive magnetoresistance in metallic Bi2Ba2Co2O816. In addition, the magnetic susceptibility of Bi2Ba1.8Co2.2O8 shows a typical Curie-law behavior near zero temperature and bump-like structure reminiscent to a nonmagnetic to magnetic transition at finite temperature15. However, the presence of Co3O4 clusters makes it difficult to identify the exact magnetic state involved in pure misfit layered compounds19. More recently, angle-resolved-photoemission spectra (ARPES) have been carried out for the electronic structure of Bi2Ba2Co2O820,21,22. A hexagonal Fermi surface indicated that CoO2 layers are responsible for the metallic property20,21. Therefore, regarding the misfit layered Bi2A2Co2O8 compounds, important issues to be addressed are the natures of electronic states below and above the insulator-metal transition temperature.
The crystal structures of misfit layered Bi2A2Co2O8 are characterized by the so-called “composite structure” in which a CoO2 block and a rock-salt block composed of four layers of the types AO-BiO-BiO-AO interleave with each other10. The CoO2 block consists of a two-dimensional triangular lattice of Co ions, octahedrally coordinated with O ions above and below the Co plane. The formal valence of Co ions deduced from the chemical composition Bi2A2Co2O8 is 3+, leaving 6 electrons in Co-3d orbitals. In the edge sharing hexagonal CoO2 layer, the trigonal distortion of CoO2 octahedra reduces the Oh local point group to a d3 subgroup, further splitting the t2g orbitals into an a1g singlet and an doublet23.
The previous local density approximation (LDA) study concentrated on the nonmagnetic state of Bi2A2Co2O816. The Bi-p derived conduction bands and Co-d(t2g) derived valence bands overlap with each other and result in a metallic ground state. The metallic state explains the transport property of Bi2Ba2Co2O8 well, but is in contradiction with those of insulating Bi2Ca2Co2O8 and Bi2Sr2Co2O8. To reconcile the apparent discrepancy, Anderson weak localization mechanism was invoked and impurity-induced localization was attributed as a cause. If the Anderson weak localization mechanism is the sole cause for the insulator nature, one expects the negative magnetoresistance phenomena for all Bi2A2Co2O8 compounds. This is, however, not the case16. Also the suppression of the specific-heat peak and Seebeck coefficient under strong magnetic field cannot be understood since LDA calculation does not consider spin degrees of freedom. In fact, if Anderson weak localization mechanism was effective, carriers in Bi2Ba2Co2O8 would be the most vulnerable to localize since larger lattice constant implies narrower electronic bands. Important factors missing in previous theoretical calculation are strong electronic correlation and spin fluctuation. They are revealed by both the ARPES spectra20,22 and large thermoelectric power9. To manifest such effects, the Coulomb on-site repulsion on Co-d orbitals is an indispensable component. In fact, the on-site Coulomb repulsion modifies the above picture in two fundamental ways. Firstly, the Hubbard U pulls the occupied Co-d(t2g) orbitals downwards with respect to the unoccupied Bi-p and Co-d(eg) orbitals, thus a metal-insulator transition takes place eventually when U is large enough. This makes a correlation induced insulator possible20,22. Secondly, Hubbard U tends to forbid the double occupancy of Co-d orbitals, paving the way for magnetic moment formation.
In the prototype spin-state transition compound LaCoO324, Co-d orbitals are decomposed into a t2g triplet (xy, yz, zx) and eg doublet (x2 − y2, 3z2 − r2) separated by a crystal-field-splitting 10Dq25,26. Depending on the competition between Hund’s rule coupling JH and crystal-field-splitting energy 10Dq, low-spin (LS: , S = 0), intermediate-spin (IS: , S = 1), and high-spin (HS: , S = 2) states are all possible candidates25,26,27,28. In particular, 10Dq can easily be tuned either by ionic radius or temperature since it is inversely proportional to the fifth power of lattice constant. Previous studies showed that LaCoO3 experiences two physical transitions as temperature increases24. The first one takes place at 90 K and brings LaCoO3 from a nonmagnetic low-spin insulator to a paramagnetic insulator. The second one at 500 K eventually brings the compound into a paramagnetic metal. The high temperature phases are all connected with either IS state or HS state27,28.
Above analysis suggests that electronic structure and spin-state strongly depend on the exact A’s ionic radius and Coulomb repulsion U on Co-d orbitals. The insulator-metal transition in Bi2A2Co2O8 may have the same origin as that of the well-known spin-state transition in LaCoO325,26. To seek for the most probable ground states of Bi2A2Co2O8 as a function of ionic radius, a comprehensive numerical calculation has been carried out in this paper within the local-spin density approximation plus U scheme (LSDA + U). In particular, the relative stabilities are sought for in (U, r) parameter space among different spin-states of fully relaxed crystal structures. Consistent with experimental observations, our study shows that only LS state and hexagonally arranged IS-LS mixed-state are the most probable candidates for ground states in the phase diagram. These two states offer consistent description of the physical properties of Bi2A2Co2O8 both below and above the transition temperature and the insulator-metal transition separating Bi2Ca2Co2O8, Bi2Sr2Co2O8, and Bi2Ba2Co2O8 compounds.
Relaxed P-1 crystal structure of Bi2A2Co2O8
An initial 28-atom unit cell of (Bi2A2O4)2(CoO2)4 is adopted to best describe the measured superstructure, in which the rectangular lattice of rock salt block (, b = 2d) and hexagonal lattice of CoO2 block (d) form a commensurate periodic structure shown in Fig. 1. This structure is first optimized using local-density approximation (LDA) for the lattice parameters and atomic positions assuming the LS state of Co3+ ions. Then the crystal energy is further optimized by reducing crystal symmetry. P-1 crystal group is finally obtained and its optimized lattice parameters are listed in Table 1 together with those of measured ones14,15,29 listed in Table 2. The overall agreement is reasonable and discrepancy mainly results from the extra oxygens in the non-stoichiometric samples.
Two types of competing ground states for Bi2A2Co2O8
The LDA electronic band structures of Bi2A2Co2O8 reproduced the metallic property obtained in previous study due to the overlap between Bi-p derived conduction bands and Co-d(t2g) derived valence bands. Although the result agrees with the metallic property of Bi2Ba2Co2O8, it disagrees with the insulator properties of Bi2Ca2Co2O8 and Bi2Sr2Co2O8. However, the band-overlap can be removed once Hubbard U increases to a critical value, and a correlation induced metal-insulator transition becomes possible20,22. The critical UC is 5.80, 6.55, 6.25 eV for A = Ca, Sr, and Ba, respectively. The non-monotonic behavior of UC is caused by the complex structural change as a function of A’s ionic radius. Since Hubbard U is intra-ionic in nature and only depends weakly on structural details, it is impossible to choose one value of U to fit the transport properties of all three Bi2A2Co2O8 compounds. Furthermore, LS state of Bi2A2Co2O8 does not include spin degree of freedom, so magnetic-field suppressed spin-fluctuation phenomena cannot be understood. This suggests that strong Hubbard U induced IS or HS state of Co ions must be a possibility.
As shown in Fig. 2, (Bi2A2O4)2(CoO2)4 unit cell contains four Co ions. Two of the Co ions (Co-3, Co-4) of CoO6 octahedra sit between the A and O atoms of AO rock-salt layers and their positions are equivalent. Other two (Co-1, Co-2) sit between the interstitial regions of rock-salt layers and are different. To find out the most probable spin structures of CoO2 block, we compare the energies of different spin-states of Co ions and spin structures with different combinations of LS, IS, and HS states in the unit cell. Our systematic study shows that uniform LS state is consistently lower in energy (0.416 eV at U = 8.0 eV) than the uniform IS state, IS state is much lower in energy (1.119 eV at U = 8.0 eV) than the uniform HS state. Thus, for uniform spin structures, LS state is the best candidate for the ground state of Bi2A2Co2O8. It remains to find out the other relevant magnetic structure. To this end, we first consider one, two, and three IS (HS) Co3+ ions in the background of LS Co3+ ions.
For single IS- or HS-Co3+ ions embedded in the background of LS-Co3+ ions in the unit cell, we have six inequivalent spin-structures. Table 3 shows the typical energies calculated at U = 8 eV. It is found that the energies of single IS-Co3+ cases are always lower than those of single HS-Co3+ cases, thus we focus on IS-state only below for more complex magnetic structures. In fact, single IS-Co3+-ion embedded in the background of LS-Co3+ ions can have even lower energy than that of the uniform LS state when U is larger while the opposite is true when U is smaller. To check whether single IS-Co3+-ion embedded in the background of LS-Co3+ ions is the most favored magnetic state, we have also considered double and triple IS-Co3+-ions embedded in LS-Co3+ ions and their energies are listed in Tables 4, 5 and 6. From Table 4 for parallel-spin and Table 5 for anitiparallel-spin configurations, double IS-Co3+-ions at Co-1 and Co-2 positions with parallel spins yields the lowest energy among the classes, but the energy is higher by 161.1 meV than that of single IS-Co3+-ion at Co-1. Also, triple IS-Co3+-ions case is higher in energy by 463.6 meV than that of single IS-Co3+-ion at Co-1. Thus, we conclude that single IS-Co3+-ion at Co-1 position has the lowest energy for one unit-cell configuration.
To restore the hexagonal symmetry of the Fermi surface observed experimentally, we double the unit cell along a-axis. Because the single IS Co-1 and Co-2 configurations are very close in energy (≈2.8 meV at U = 8.0 eV), we interchange the spin states of Co-1 and Co-2 ions of the second unit cell. In this way, we arrived at the hexagonally arranged IS-LS mixed-state whose energy is further lowered by 52 meV (at U = 8.0 eV) per unit cell. We shall show that this state possesses all the essential properties of metallic state observed either in the high temperature phase of Bi2Ca2Co2O8 and Bi2Sr2Co2O8 or Bi2Ba2Co2O8 at full temperature range.
Insulator-metal phase diagram of Bi2A2Co2O8
Although the hexagonally arranged IS-LS mixed-state is the most favored state in energy among the magnetic structures investigated, the relative stability between this state and uniform LS state depends on both the Hubbard U and A’s ionic radius. To quantitatively analyze the insulator-metal transition in Bi2A2Co2O8, we have numerically computed the phase diagram of these two electronic states in Fig. 3 using the same double-cell. The critical UC separating the insulator (LS state) and metal (hexagonally arranged IS-LS mixed-state) is 8.16, 7,62, and 6.90 eV for Bi2Ca2Co2O8, Bi2Sr2Co2O8, and Bi2Ba2Co2O8, respectively. The monotonic decreasing value of UC is directly related to the increased lattice constant, thus reduced crystal-field-splitting energy. The weakened crystal-field-splitting makes the IS-LS mixed-state possible. To conform to the experimentally observed transport properties of Bi2A2Co2O8 compounds, strong electronic correlation (6.90 eV < U < 7.62 eV) is required.
The Hubbard U and Hund’s exchange coupling JH are usually extracted from fitting the core-electron satellite spectra of transition-metal oxides to a cluster model, and the values vary depending on the crystal structures and the valence of Co-ions. The values, 5 eV < U < 8 eV, JH = 1 eV, recommended by Singh23 were widely cited for cobalt based perovskite. Korotin et al.30 obtained similar values (U = 7.8 eV, JH = 0.92 eV) in discussing the IS state associated with the high temperature magnetic structure of LaCoO3. However, Solovyev, Hamada, and Terakura31 showed that effective Hubbard U of Co-d-orbitals depends on how to differentiate the localized orbitals from extended orbitals. They suggested U = 9.5eV if treating all d-orbitals as localized or a significantly smaller 2 eV for Co-d(t2g) orbitals if treating d(t2g) orbitals as localized while letting d(eg) orbitals extended. Thus, the value of Hubbard U is rather scattered, and this is the reason why we treat the Hubbard U as a parameter to derive the insulator-metal phase diagram. Our required Hubbard U (6.90 eV < U < 7.62 eV) is, however, within the accepted range.
Electronic structures and atom-resolved partial densities of states
To check the transport properties of Bi2A2Co2O8 compounds, the electronic band structures and atom-resolved partial densities of states (DOS) are calculated at U = 7.5 eV. They are presented in Fig. 4 for the LS state insulators of Bi2Ca2Co2O8 and Bi2Sr2Co2O8, and the IS-LS mixed-state metal of Bi2Ba2Co2O8, respectively. Left panel plots the band structures computed along the high symmetrical points X( 00), Γ(000), Y(00), L(0), Γ(000) in the irreducible Brillouin zone, and right panel plots the total as well as Co and Bi atom-resolved partial densities of states. It is seen that Bi2Ca2Co2O8 and Bi2Sr2Co2O8 are indirect band-gap insulators, and the band-gaps are 0.416 eV and 0.236 eV, respectively. The valence bands derive from CoO2 layers with Co-d(t2g) character while conduction bands mainly come from BiO rock-salt layer. Bi2Ba2Co2O8 is a typical spin-polarized semi-metal due to the overlap between the spin-degenerated conduction bands derived from BiO layer and up-spin valence band from the d(eg) orbitals of CoO2 layer. The charge carriers involve both electrons and holes and exact charge carrier type depends on the stoichiometry of the compound.
The band characters mentioned above can be seen clearly from the corresponding atom-resolved densities of states shown in the right panel. While the valence bands originate from CoO2 layers and conduction bands originate from BiO layers for both the correlation-induced LS state insulator and hexagonally arranged IS-LS mixed-state metal, the orbital characters of valence bands show a notable difference for these two electronic states. For LS state insulator, all Co-spins are almost the same and local symmetry is high around Co ions. Co-d orbitals are splitted into a d(t2g) triplet and d(eg) doublet separated by about 3.5 eV. d(t2g) triplet are fully occupied and the nonmagnetic valence band is of Co-d(t2g) character. However, for IS-LS mixed-state metal, the presence of two types of Co-spins reduces the local symmetries both around LS and IS Co ions. In particular, Jahn-Teller distortion of IS CoO6 octahedra induces a bond elongation of 9% along a-axis which is significant enough to pull one of up-spin eg orbitals down below the Fermi energy while push one of the down-spin t2g orbitals high above the Fermi energy. This forms an IS-state of Co ions and valence band is of Co-d(eg) character. The magnetic moment of IS Co ions can be calculated from the Co-resolved partial DOS. This yields a value of 1.90 μB which is consistent with that of IS Co ions. For the detailed information on the spin states and valence states of Co-ions, the density matrices of Co-d orbitals are included in Supplementary Information. The diagonalized density matrices clearly show that all Co-ions of Bi2Ca2Co2O8 and Bi2Sr2Co2O8 are indeed in LS state while quarter of Co-ions of Bi2Ba2Co2O8 are in IS state. The valence states of Co-ions are somewhat less than Co3+ because of strong covalence bonding with oxygen atoms. We speculate that the Co4+-ions observed in the experiment16 are most probably due to the extra oxygen atoms presented in nonstoichiometric samples.
Now we are in position to discuss the various experimental phenomena with the above two electronic states. (1) LS state insulator and IS-LS mixed-state metal agree perfectly well with the insulating properties of Bi2Ca2Co2O8 and Bi2Sr2Co2O8 and the metallic property of Bi2Ba2Co2O8. If one associates the LS state insulator (stable at small A’s ionic radius) with low-temperature phase and IS-LS mixed-state metal (stable at large A’s ionic radius) with high-temperature phase as customarily done in spin-state transition phenomena30, the insulator-metal phase transition of Bi2Ca2Co2O8 and Bi2Sr2Co2O8 at finite temperatures can be also qualitatively understood with these two states. (2) The magnetic nature of the IS-LS mixed-state suggests that spin fluctuation is involved in the insulator-metal phase transition of Bi2Sr2Co2O8, thus the specific-heat peak caused by spin-fluctuation should be suppressed by external magnetic field as was observed in experiment14. (3) Since the ground states of stoichiometric Bi2A2Co2O8 (A = Ca, Sr) are nonmagnetic insulators, the electron and hole concentrations at low temperature are very diluted. The scattering probability is low and phase coherence is maintained. Thus Anderson weak localization mechanism works and back-scattering is dominant32. Applying external magnetic field destroys the back-scattering and results in a negative magnetoresistance33. For metallic Bi2Ba2Co2O8, finite carrier density is present at Fermi energy and scattering is strong. Electric conductivity is of diffusive type and positive magnetoresistance prevails. The linear B-dependent magnetoresistance may be related to the layered semi-metal property of Bi2Ba2Co2O834. (4) Our LSDA + U band structure predicts a spin-polarized semi-metal for Bi2Ba2Co2O8, thus the transport and magnetoresistance phenomena can be qualitatively understood. But the LSDA + U band structures did not take the charge and spin fluctuations into account, direct comparison with the ARPES spectra is not feasible. To better describe the renormalized quasiparticle spectra, the dynamical mean-field theory for a supercell with 8 Co-ions (40 d-orbitals) has to be implemented which is a challenging issue. In addition, our study suggests that sizeable Hubbard U is required to stabilize both the insulator property of LS state and metallic property of IS-LS mixed-state. The strong electronic correlation is a prerequisite in explaining the ARPES spectra20,22 and thermoelectric properties of Bi2A2Co2O8 compounds11,12.
In summary, we propose in this paper that the LS state insulator and IS-LS mixed-state metal are the two electronic states involved in the insulator-metal transition observed in Bi2A2Co2O8 compounds. The physical properties of the two states offer satisfactory explanations not only to the magnetic-field suppressed specific-heat peak associated with the insulator-metal transition, but also to the distinct magnetoresistance features observed in Bi2Ca2Co2O8 and Bi2Sr2Co2O8, and Bi2Ba2Co2O8. Although the conclusion is mainly drawn based on Bi2A2Co2O8 series of compounds, it is of interest to explore whether similar phenomena appear in other hexagonally structured CoO2 compounds.
The parameter setting for density functional theory
To search for the relevant electronic states, the calculations were performed by using a plane wave pseudopotential approach to the density-functional theory (DFT) as implemented in the Vienna ab initio Simulation Package (VASP 5.3.5)35,36. We use the Ceperley-Alder (CA) functional as the exchange-correlation potential37. The projector augmented wave (PAW) potentials explicitly include 10 valence electrons for Ca (Sr, Ba) (3s23p64s2), 17 for Co (3s23p63d74s2), 5 for Bi (6s26p3) and 6 for O (2s22p4). The default PAW spheres sizes are supplied by VASP program. The rotationally invariant LSDA + U approach introduced by Liechtenstein et al.38 was adopted for Co 3d orbitals. The wave functions are expanded using a plane-waves basis with an energy cutoff of 600 eV. 8 × 8 × 2 and 4 × 8 × 2 Monkhorst-Pack k-point meshes are used for (Bi2A2O4)2(CoO2)4 unit cell (28 atoms) and double-cell, respectively39. The total energy and density of states were calculated using the linear tetrahedron method with Bloch corrections40. Each self-consistent electronic calculation is converged to 10−5 eV and the tolerance force is set to 0.01 eV/Å for ionic relaxation. As was usually done for later transition-metal element Co, the Hund’s rule coupling JH was fixed at 1 eV31 while on-site Hubbard U is allowed to vary between 5 to 8 eV according to Singh23. To obtain the self-consistent electronic structures and total-energies, we first set up an initial spin configuration of Co-ions according to the specific spin-states. The orbital and spin electron occupations are then allowed to relax and are iterated until full convergence. The converged spin-states of Co-ions are then determined by the integrated magnetic moments. In this way, we are able to map the phase diagram of misfit layered Bi2A2Co2O8 compounds with different U and A’s ionic radius.
How to cite this article: Huang, X. and Zhang, W. How does the spin-state of Co ions affect the insulator-metal transition in Bi2A2Co2O8 (A=Ca, Sr, Ba)? Sci. Rep. 6, 38212; doi: 10.1038/srep38212 (2016).
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This work was supported in part by the NNSFC under Grant No. 11474148. Part of the numerical calculations were carried out in the High Performance Computing Center (HPCC) of Nanjing University.