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Orbital molecules in electronic materials
J. Paul Attfield
Citation: APL Materials 3, 041510 (2015); doi: 10.1063/1.4913736 View online: http://dx.doi.org/10.1063/14913736
View Table of Contents: http://scitation.aip.org/content/aip/joumal/aplmater/3/4?ver=pdfcov Published by the AIP Publishing
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Orbital molecules in electronic materials
J. Paul Attfield3
Centre for Science at Extreme Conditions and School of Chemistry, University of Edinburgh, West Mains Road, Edinburgh EH9 3JZ, United Kingdom
(Received 22 December 2014; accepted 17 February 2015; published online 24 February 2015)
Orbital molecules are made up of coupled orbital states on several metal ions within an orbitally ordered (and sometimes also charge-ordered) solid such as a transition metal oxide. Spin-singlet dimers are known in many materials, but recent discoveries of more exotic species such as 18-electron heptamers in AlV2O4 and magnetic 3-atom trimerons in magnetite (Fe3O4) have shown that orbital molecules constitute a general new class of quantum electronic states in solids. © 2015 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. [http://dx.doi.org/10.1063/L4913736]
Transition metal oxides and related materials such as chalcogenides and pnictides have been at the heart of electronic materials research since the ground-breaking discoveries of high-temperature superconductivity in copper oxides in the 1980's, and of colossal magnetoresistance (CMR) and associated phenomena in manganite perovskites from the mid-1990's.1-3 The electronic states in such materials result from coupling between three degrees of freedom.
• Charge—referring to potentially mobile d-electrons, often the extra electron or hole in mixed valence materials, e.g., doping Sr2+ for La3+ in La1-xSrxMnO3 introduces Mn4+ states equivalent to eg holes.
• Orbital—crystal fields split the d-orbital energies. In the most common, octahedral configuration, d-orbitals are split into t2g and eg symmetry sets. Degenerate states arising from unequal fillings of these sets undergo Jahn-Teller distortions that are often cooperative in highly connected oxide lattices, resulting in spatial order of the occupied and unoccupied orbitals—an orbital order.
• Spin—many dn configurations have a net spin S. These couple ferro- or antiferro-magnetically to produce magnetically ordered states.
Many complex and often competing ground states result from different couplings of charge, orbital, and spin degrees of freedom. A notable example is in semivalent manganite perovskites such as La0 5Ca0 5MnO3 where long range order of charges, orbitals, and spins was discovered at low temperatures through X-ray and neutron diffraction studies. Coupling such orders to the lattice can also lead to centre-of-symmetry breaking distortions that couple electrical and magnetic polarisations, generating multiferroic materials, e.g., BiFeO3.4 Transitions between low temperature charge, orbital, or spin ordered states and high temperature disordered or dynamic phases are often observed. Local clusters of these degrees of freedom and their dynamics are important, for example, nematic charge stripes evidenced in cuprates (related to the "orbital molecules" in this paper) may be important to theories of superconductivity.5
Spintronics and orbitronics have emerged from studies of spin and orbital physics. Coupling of spin and charge transport gives rise to spintronic materials and devices, and oxide spintronics has become a major scientific and technological field over the last 15 years. Exciting possibilities for analogous "orbitronics" based on orbital angular-momentum currents have been proposed more recently. Spin-orbit coupling is predicted to develop an intrinsic orbital angular-momentum current even in non-magnetic doped Si under the influence of an electric field.6 However, the effects can
aEmail: j.p.attfield@ed.ac.uk
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be much larger in transition metal compounds with unpaired spins; a recent paper has predicted giant orbital Hall effects in the metallic oxides Sr2MO4 (M = Ru, Rh, and Mo).7 In a related context that may also be important to future orbitronics, spontaneous circular orbital currents have been predicted in Mott insulators such as transition metal oxides associated with geometric frustration and charge order,8 and the orbital current was recently observed in CuO.9
Understanding and manipulating orbital states in transition metal compounds is of fundamental importance as well as having potential future applicability in orbitronics. Cooperatively ordered orbital states like that of La05Cac.5MnO3 are generally well understood, but studies over the last decade have shown that directly bonded clusters of orbitally ordered atoms are formed in some materials. A particularly striking and unexpected recent discovery was that the ground state of magnetite (Fe3O4) is a self-organised crystal of such clusters, as will be described below, and this gave rise to the recognition of the general class of "orbital molecule" quantum states and their potential importance to the chemistry, physics, and ultimately applications, of electronic oxides.
Localised ground states like that of La0 5Cao.5MnO3 can be described in terms of atomic charge, orbital, and spin states in transition metal (M) oxides such as perovskites where M-M separations are too great for direct electronic interactions to be significant. However, when M-M separations are relatively short, as a result of edge or face-sharing by MO6 octahedra, then weak bonding interactions between M ions having localised t2g orbital orders can give rise to more complex quantum states. The simplest examples are spin singlet dimers, but more complex clusters involving up to 7 atoms are reported, as will be described below. Orbital molecules are usually formed below an orbital ordering transition marked by a structural change and a metal (or semiconductor) to insulator anomaly in conductivity. This class of quantum electronic states has not been given a consistent name in the scientific literature, so we use the term "orbital molecule" (which does not have other uses), as these molecule-like objects are created by orbital order at the metal sites.10 Orbital molecules amplify the anisotropy associated with orbital order and thus may be useful to future orbitronics if transport of robust orbital molecules can be demonstrated.
Evidence for the formation of orbital molecules comes primarily from structural studies showing that M-M distances within small clusters of ions are shortened below an orbital ordering transition. Goodenough's estimates for the critical interatomic distances below which bonds may be formed for given transition metals provide a useful empirical guide for orbital molecule formation.11 Most orbital molecules are singlet species so the opening of a spin gap at the orbital order transition is observed. Spectroscopic techniques such as NMR can also evidence orbital molecule formation. Recent electronic structure treatments have shown that the localised states can be described by quasi-molecular bonding orbitals, while other electrons in the system remain decoupled and may participate in magnetic orders.12 Examples of structurally characterised orbital molecule formation are shown below.
The simplest type of orbital molecule is where spin-paired M-M dimers (spin singlets) are formed between two t2g orbitals each containing one electron. The two neighbouring magnetic ions form a quantum superposition of spin-paired states so that the local magnetic moment is zero. There are many examples of spin singlet dimer formation in transition metal oxide structures containing edge- or face-sharing octahedra. Well-known cases are based on 3d1 cations such as Ti3+ or V4+.
VO2 has a regular rutile type structure and is metallic at high temperatures, but undergoes a metal-insulator transition at 340 K below which the structure is distorted.13,14 V-V spacings within chains of edge-sharing VO6 octahedra are equal above the transition, but alternation of long (3.1 A) and short (2.7 A) V-V distances is observed in the insulating phase. The short bonds evidence the formation of dimers. This transition exemplifies a Peierls distortion, where the wavevector of the distortion opens a gap at the Fermi level of the one-dimensional high temperature state. However, a recent study has shown that the dimerization transition is observed in VO2 films down to a thickness of three VO6 octahedra,15 where the band picture of the chains is no longer meaningful. This demonstrates that dimer formation results from local interactions through strong electron-electron correlation, essentially V-V covalent bonding. NbO2 displays a similar metal-insulator and dimerization transition at 1080 K,16 the high temperature in comparison to VO2 reflects the greater stability of orbital molecule dimers made from more spatially extended 4d1 states. The Magneli phase V4O7 has a more complex ground state with dimers formed between some pairs of V4+ and V3+
FIG. 1. Self-organisation of dimer orbital molecules in spinels. (a) Polyhedral view of the chiral low-temperature MgTi2O4 structure, where each helix such as that highlighted in yellow consists of alternating short (orbital dimer) and long Ti3+-Ti3+ distances. Reprinted with permission from Schmidt et al., Phys. Rev. Lett. 92, 056402 (2004). Copyright 2004 by American Physical Society. (b) Low-temperature structure of CuIr2S4 showing Ir3+/Ir4+ charge order on the B sites as red/blue octahedra, and Ir4+-Ir4+ spin-dimer orbital molecules as light-blue bonds. Reprinted with permission from Radaelli et al., Nature 416, 155 (2002). Copyright 2002 by Nature.
ions below the 250 K metal-insulator transition.17 A similar situation with spin-singlet V4+-V4+ and V3+-V3+ dimers confined in the two chains of a double-chain ribbon is observed in the hollandite K2
V8O16.18
Many Ti3+ oxides form spin singlet dimers. Magneli phases TinO2n-1 present some famous examples. Ti3O5 is charge ordered with Ti3+-Ti3+ dimers, and undimerised Ti4+ sites at room temperature.19 A transition to the high temperature paramagnetic and metallic non-dimerized state occurs at 450 K.20 (Ti3+)2 dimers are also reported below a 150 K insulator-to-metal transition in Ti4O7.21 Dimer formation has been established in more complex structures such as the pyroxene NaTiSi2O6 below a 210 K orbital ordering transition.22 A remarkable self-organisation of (Ti3+)2 dimers is observed below the 260 K metal-insulator transition of the spinel MgTi2O4.23 The short dimerized bonds alternate with long bonds to form helices so that the electron ordered state is chiral (with space group P41212 or P43212), as shown in Fig. 1(a).
Spin singlet dimer formation is also possible for low spin d5 cations which have a t2g5 configuration. An important example is the spinel CuIr2S4 which undergoes a metal insulator transition accompanied by Ir3+/Ir4+ charge ordering at 340 K.24 The two charge states form 8-membered rings as shown in Fig. 1(b). No dimerisation of the Ir3+ (t2g6) states is observed, but the Ir4+ (t2g5) ion forms spin-dimers evidenced by short Ir-Ir bonds. This complex emergent order has attracted much subsequent attention; a new incommensurate phase with short-range charge order is induced by X-irradiation below 50 K, and the electronic structures of both phases have recently been studied by resonant x-ray spectroscopy.25
Li2RuO3 provides a complex example of spin singlet dimerization between Ru4+ ions with the t2g4 configuration. Dimer formation is observed below 540 K and an electronic mechanism involving both a direct t2g-t2g overlap and an indirect coupling through n-interactions with oxygen orbitals has been proposed.26 A recent study of local structure using x-ray pair distribution function (PDF) analysis has revealed that Ru4+-Ru4+ dimers are present up to at least 920 K, far above the long range dimerization transition.27 This demonstrates that the dimers in Li2RuO3, and perhaps orbital molecules in other materials, can exist in a disordered orbital molecule glass or liquid state within the high temperature average structure far above the orbital ordering transition temperature. A similar observation has been made for the spinel LiRh2O4, where short Rh-Rh distances are observed up to 350 K in the PDF, far above the 170 K metal-insulator and long range dimerization transition.28 However, a PDF study of CuIr2S4 reported that the Ir-Ir dimers disappear in both the average and local structure above the metal-insulator transition.29
Face-sharing of octahedra allows direct overlap between all three t2g orbitals on transition metal ions, so dimers with bond orders up to three (having six paired electrons) may be formed. Six-electron (Ru5+)2 spin singlet dimers are observed in the 6H hexagonal perovskite Ba3CaRu2O9,30
FIG. 2. Trimeric spin singlet orbital molecules in the low temperature structure of BaVioOi5. The left image shows a projection of V sites within the unit cell. Sites V2B, V3, and V3B form the V39+ orbital molecules, and V1 and V2 do not participate in trimers and are spin ordered at low temperatures. Participation of 3dxy, 3dxz, and 3dyz orbitals in the V39+ trimer is shown to the right. Reprinted with permission from Takubo et al., Phys. Rev. B 86, 085141 (2012). Copyright 2012 by American Physical Society.
while Ba3NaRu2O9 has an unusual long range charge order of (Ru5+)2 and (Ru6+)2 dimers below a metal-insulator transition at 210 K.31 Non-conservation of magnetic neutron scattering during dimer formation confirms that these species are spin singlets rather than antiferromagnetically coupled pairs of spins.
There are many reported examples of dimeric orbital molecules, as outlined above. However, reported examples of larger orbital molecules are much rarer. A few examples of orbital trimers are known, and both triangular and linear geometries have been reported.
Triangular (V3+)3 orbital molecules are observed in some layered AxVO2 phases and in BaV10O15. These are electron-precise species as V3+ has the t2g2 configuration so each V-V bond is formed by a pair of electrons, and the overall orbital molecule is a 6-electron spin singlet species. The presence of (V3+)3 trimers in LiVO2 is widely discussed and is consistent with 51V NMR measurements,32 although not yet confirmed by crystallography. However, long range order of the trimers is reported in Na0.5VO2.33 BaV10O15 undergoes a structural and semiconductor-insulator transition at 130 K and structural34 and resonant X-ray scattering35 studies show that triangular V39+ spin singlet trimers are formed (Fig. 2). Isolated V2+ and V3+ sites are also present and their spins order at a separate 46 K N6el transition.
Linear units of three face-sharing RuO6 octahedra are present in Ba4Ru3O12. Below a semiconductor-semiconductor transition and N6el transition at 105 K, the (Ru4+)3 trimers form a 12-electron orbital molecule in which each d-electron of the central Ru4+ ion is spin-paired with an electron from the terminal ions, leaving an unpaired electron on each terminal Ru4+. The terminal spins have a long range antiferromagnetic order.36
A linked network of linear trimeric orbital molecules (termed "trimerons") has recently been discovered within the low temperature structure of magnetite, Fe3O4. This is at the heart of the solution to the long running Verwey problem as briefly described below.
Magnetite (Fe3O4) is a ferrimagnetic inverse spinel; there are twice as many B-site Fe3+ 3d5 S = 5/2 up-spins as there are down-spins at the A sites, as shown in Fig. 3. Rapid hopping of an "extra" down-spin electron between B sites leads to the charge distribution Fe3+(Fe2 5+)2O4 and results in minority-spin-polarised electronic conductivity so that magnetite is an important spintronic material. In 1939, Verwey reported a sharp first-order transition in magnetite at around 125 K.37 He invented the concept of a charge ordering transition to account for these ideas, but convincing experimental evidence for Fe2+/Fe3+ order in the low temperature phase was difficult to obtain and the problem soon became a contentious issue.38,39 Partial structure refinements from powder diffraction data40-42 and resonant X-ray studies43-45 led to a variety of proposed charge-ordered models, some including bond-dimerized orbital molecules.46-48 The Verwey structure was recently solved using a high energy microcrystal x-ray diffraction method.49 Fe2+/Fe3+ charge ordering and Fe2+ orbital ordering was evidenced, showing that Verwey's hypothesis was correct to a useful first approximation. However, additional structural distortions in which B site Fe-Fe distances within linear Fe-Fe-Fe units are anomalously shortened showed that the "extra" down-spin electrons are
2+ 3+ r, -Í
Fe Fe B-sites
/^Strong Antiferromagnetic Superexchange
A-sites
FIG. 3. (a) Schematic representation of the 3d-electron arrangement in one formula unit of Fe3O4. The "extra" minority spin electrons are delocalised between B sites in the cubic ambient temperature form, but are localised in the Verwey phase below 125 K. (b) Minority spin electron distribution and associated atomic displacements (purple arrows) within a trimeron. Orbital order at the central Fe2+ site (blue) localises the minority spin electron in one of the t2g orbitals and elongates the four Fe-O bonds perpendicular to the local Jahn-Teller axis. Weak bonding interactions transfer minority spin density into coplanar t2g orbitals at two neighbouring B sites and shorten the Fe-Fe distances. The minority spin electron density is approximated by the ellipsoid shown. (c) Trimeron distribution in the low temperature magnetite structure, following the experimentally observed distortions, with first approximation Fe2+/Fe3+ states shown as blue/yellow spheres and trimeron ellipsoids as in (b).
not fully localised as Fe2+ states, but are instead spread over three sites resulting in highly structured three-site polarons termed "trimerons" (Fig. 3(b)). Trimerons share corners according to simple connectivity rules, leading to a complex self-organised network (Fig. 3(c)). Electronic structure calculations using the experimental low temperature coordinates show that the minority spin extra electrons occupy a narrow band just below the Fermi energy.10 The real space density distribution of these states confirms the trimeron description.
Anomalous properties such as a smaller-than-predicted transition entropy and a positive conductivity-temperature slope up to a maximum at ~400 K have been cited for many years as evidence for the persistence of low temperature Verwey correlations in the cubic phase above the transition. Now that trimerons are identified as the dominant ordered species in the Verwey phase, glassy or liquid-like correlations of these orbital molecules are expected in the cubic phase above the Verwey transition, in keeping with the observed persistence of dimers in Li2RuO3 noted above.
Orbital molecules consisting of more than three metal ions are not well-characterized except for one spectacular example of a 7-atom molecule. AlV2O4 has a high temperature charge ordering transition at ~700 K. The structure, determined from room temperature synchrotron X-ray data, retains a relatively high (rhombohedral) lattice symmetry but the supercell contains remarkable heptameric orbital molecules as shown in Fig. 4.50 The charge distribution is (Al3+)4[V3+(V717+)]O4. The heptamer has a total of 18 d-electrons in the 9 bonding orbitals shown in Fig. 4(b), and has a spin-singlet state in agreement with an observed spin gap in the magnetic susceptibility data. These heptamers represent the most complex orbital molecules reported to date, and suggest that at least 4-6 atom species should also be possible.
Orbital molecules represent new quantum electronic states that go beyond the standard singleion charge/orbital/spin degrees of freedom description for transition metal oxides and related materials. In some cases such as Ba3NaRu2O9 and Ba4Ru3O12, the dimer or trimer units are naturally present in the structure, although symmetry-breaking electronic transitions such as the charge ordering in Ba3NaRu2O9 may still take place. However, many of the above observations show that
FIG. 4. The V-V network in AlV2O4 showing in red the short bonds that define the V717+ orbital molecules. Schematic bonding orbitals in one heptamer are shown to the right. Reprinted with permission from Horibe et al., Phys. Rev. Lett. 96, 086406 (2006). Copyright 2006 by American Physical Society.
orbital molecules are formed through breaking of translational symmetry in lattices of extended M-M connections at the orbital ordering transition, often also associated with charge ordering and a metal-insulator change. These transitions arise from Peierls or other electronic instabilities in many cases, but electron-electron correlation effects may also be important. Most reported orbital molecules are dimers, but triatomic species have been reported in Fe3O4 and BaVi0Oi5, and a remarkable 7-atom molecule is observed in AlV2O4. From an electron counting viewpoint, small orbital molecules such as dimers and V39+ triangles are electron-precise with one pair of t2g electrons per M-M bond, but the more extended, mixed-valent, Fe38+ trimerons in magnetite and V717+ heptamers in AlV2O4 are formally multicentre bonded. The latter situation is reminiscent of electron bonding schemes in other molecular clusters such as boranes (boron hydrides) and transition metal carbonyl clusters. Most discovered orbital molecules are non-magnetic spin singlets, but the discovery of trimerons with effective-spin 1/2 in Fe3O4 shows that orbital molecules can carry spin and orbital angular momenta.
Orbital molecule order coupled to charge and orbital orders in insulators can lead to low symmetry structures with associated physical properties such as ferroelectricity and multiferroism. Orbital molecule self-organisation leads to acentric symmetries in the ferroelectric (and hence mul-tiferroic) Verwey phase of Fe3O4, and in the chiral molecule ordered phase of MgTi2O4. Orbital molecule formation at metal-insulator transitions is closely connected to electronic instabilities such as nesting or Peierls distortions from one-dimensional bands. Recent PDF studies of materials such as Li2RuO3 demonstrate that orbital molecules can persist in a disordered glassy or liquid state within the high temperature average structure to far above the orbital ordering transition temperature. Hence, orbital molecules may be relevant quasiparticles in metallic spinel phases with implications for Cooper pairing in superconducting LiTi2O4 (cf. stripe-pairing mechanisms in copper oxides),51 and may lead to effective mass enhancement in the unusual heavy fermion metal LiV2O4.52 The strong orbital anisotropy associated with orbital molecule formation should enhance spin-orbit and orbit-lattice couplings and hence orbital currents, and may ultimately be exploited in future orbitronic technologies based on the creation and manipulation of orbital molecules in transition metal oxides.
Taken together, these reports demonstrate that orbital molecules may be identified as a class of quantum electronic states formed through orbital order in structures where direct metal-metal interactions are significant. Structures such as that of the Verwey phase of magnetite demonstrate that complex electronic orders can emerge from the self-organisation of orbital molecules in solids, analogous to the formation of complex molecules from atoms in conventional matter.
The author acknowledges collaboration with co-authors of J.P.A. papers cited below, and financial support from EPSRC and ERC.
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