Emergent excitation at the magnetic metal-insulator transition in the pyrochlore osmate Cd2Os2O7

The rich physics manifested by 5d oxides falls outside the Mott-Hubbard paradigm used to successfully explain the electronic and magnetic properties of 3d oxides. Much consideration has been given to the extent to which strong spin-orbit coupling (SOC), in the limit of increased bandwidth and reduced electron correlation, drives the formation of novel electronic states, as manifested through the existence of metal-insulator transitions (MITs). SOC is believed to play a dominant role in 5d5 systems such as iridates (Ir4+), undergoing MITs which may or may not be intimately connected to magnetic order, with pyrochlore and perovksite systems being examples of the former and latter, respectively. However, the role of SOC for other 5d configurations is less clear. For example, 5d3 (e.g Os5+) systems are expected to have an orbital singlet and consequently a reduced effect of SOC in the groundstate. The pyrochlore osmate Cd2Os2O7 nonetheless exhibits a MIT intimately entwined with magnetic order with phenomena similar to pyrochlore iridates. Here we report the first resonant inelastic X-ray scattering (RIXS) measurements on an osmium compound, allowing us to determine the salient electronic and magnetic energy scales controlling the MIT in Cd2Os2O7, which we benchmark against detailed quantum chemistry calculations. In particular, we reveal the emergence at the MIT of a magnetic excitation corresponding to a superposition of multiple spin-flip processes from an Ising-like all-in/all-out magnetic groundstate. We discuss our results with respect to the role of SOC in magnetically mediated MITs in 5d systems

The diverse physics of transition metal oxides has stimulated interest for decades. Particular focus has resided on 3d oxides where the strong electron correlations dominate, with a dramatic manifestation being the occurrence of the Mott MIT. 1,2 Contrastingly in 5d oxides the relativistic SOC is increased to such an extent that competition occurs with the on-site electron correlations, as well as further interactions such as the crystalline electric field (CEF), local multiplet physics and bandwidth. The consequence of these often finely balanced interactions in 5d oxides is the emergence of new physics, such as a SOC dominated Mott-like insulating state, initially observed in perovskite iridates, 3,4 and Weyl semi-metal, non-trivial topological insulators and magnetic MITs in pyrochlore iridates. 2,5 We focus here on the pyrochlore osmate Cd 2 Os 2 O 7 where the concomitant magnetic ordering and MIT cannot be reconciled with the Mott-Hubbard paradigm. 6,7,8,9,10 Instead the behavior was initially considered to be the first manifestation of a Slater transition where the onset of magnetic order creates the insulating phase by introducing a periodic potential that localizes the conduction electrons. 11 More recently, however, the mechanism of the MIT has been argued to be a Lifshitz transition normally associated with metal-metal transitions and generally not explicitly requiring magnetic order. 6,7 Phenomenologically the behavior of Cd 2 Os 2 O 7 is analogous to iridate pyrochlores: they both undergo temeperature dependent continuous MITs suggested to be associated with all-in/all-out (AIAO) magnetic ground states where all spins either point in or out of the center of the tetrahedron. 12,13,14 One consequence of the AIAO ground state is that since the ordering breaks time-reversal symmetry but maintains the cubic symmetry of the lattice such systems can host Weyl semi-metal behavior. 5 In this investigation we are able to access the magnetic Os sublattice with neutrons and confirm the AIAO magnetic structure, thereby going beyond the strong but indirect evidence presented for AIAO ordering of the Ir sublatttice in the pyrochlore iridates. Although there exists apparent similarities between osmate and iridate pyrochlores they contain distinct electronic occupancies of 5d 5 in the iridates and 5d 3 in osmates. Consequently SOC has been considered to play an explicit role in the behavior of iridates while in the osmates the influence of SOC is less clear and often considered implicitly. By probing the electronic and magnetic ground and excited states in Cd 2 Os 2 O 7 we are able to disintangle the degree to which SOC determines the manifested behavior and in doing so consider both the similarities and distinctions between 5d 3 and 5d 5 based systems.
In order to access the exotic physics in Cd 2 Os 2 O 7 , and 5d systems in general, it is crucial to explicate the electronic ground state and subsequent excited states that emerge. These derive from the competing interactions acting on the 5d ion and consequently the relevant microscopic interactions, and their energy hierarchy, need to be determined. By performing momentum and temperature dependent osmium L-edge RIXS we directly probe the 5d electrons and uncover the salient features of the electronic ground state and magnetic excitations. These measurements extend the RIXS technique to 5d materials beyond iridates, 15,16,17,18,19,20 and in doing so provide access to previously inaccesible spin excitations.
To guide our Os RIXS measurements and gain fundamental insights we make contact with detailed theory. In Cd 2 Os 2 O 7 we find electronic excitations that are markedly different from iridates thereby revealing a divergent role of SOC between these systems, particularly in the degree that SOC plays in the creation of the electronic ground state. However, when considering interactions that derive from more than one Os ion we find an elevated role of SOC in Cd 2 Os 2 O 7 and similar behavior to pyrochlore iridates as, for example, manifested by the magnetic ground state that points towards related mechanisms driving the MITs in both systems. Moreover, our RIXS measurements reveal an excitation characteristic of magnon energies. By considering the relevant energy scales and interactions uncovered allows a comprehensive description of this excitation as a magnetic excitation that emerges in Cd 2 Os 2 O 7 due to the cooperation of the large SOC, single ion-anisotropy and Dzyaloshinskii-Moria (DM) interactions that combine to form a superposition of spin states.

Results
RIXS measurements at the osmium L 3 -edge within the magnetic insulating phase of Cd 2 Os 2 O 7 . We first discuss fixed incident energy RIXS measurements, the spectrum is shown in Fig. 1a. Two pronounced features are evident, labeled "E B " and "E C ", each significantly broader than the experimental energy resolution and located at E B =0.92 (6) eV and E C =4.5(1) eV. In addition, a small, sharp resolutionlimited feature "E A " is observed at E A =0. 16(1) eV. (E A is more apparent in Fig. 2). Much can be learned by probing the intensity dependence of the inelastic spectra at different fixed incident energies, as shown in Fig. 1b. These measurements reveal features E A and E B have their maximum resonant intensity at the same incident energy, 10.8755 (5) keV, whereas E C shows a maximum intensity at a higher incident energy of 10.879(1) keV. The different incident energy dependence is a consequence of the excitations accessing different core-hole (2p-5d) transitions during L-edge RIXS due to the splitting of the osmium 5d manifold, nominally into t 2g and e g sub-manifolds. 17,18 The scattering involving excitations within the t 2g manifold will occur at a lower energy than scattering involving e g levels, with the energy difference corresponding to the t 2g and e g splitting. This allows us to assign features E A and E B to intra-t 2g processes and E C as involving an e g process.
To further interpret the underlying processes leading to the measured RIXS spectra we benchmark our results against recent many-body quantum chemistry calculations. 21 Those calculations predicted Os d-d multiplet excitations in Cd 2 Os 2 O 7 starting around 1.5 eV, which is consistent with the measured energy for E B and moreover corresponded to an intra-t 2g process. This intra-t 2g (t 2g 3 à t 2g 3 ) excitation at E B corresponds to a spin flip of one of the three electrons in the 5d 3 valance band at the osmium site changing the total local spin from high-spin S=3/2 to low-spin S=1/2, shown in Fig. 1c manifold in the form of a "spin-orbit" exciton, 15,16,17,18,19 for example in the pyrochlore iridates the measured t 2g splitting is of order 0.4 eV. 23 The absence of a SOC driven exciton in the RIXS spectra of Cd 2 Os 2 O 7 , with instead the presence of E B , indicates that SOC does not strongly split the t 2g manifold, i.e.
the SOC driven J eff =1/2 electronic ground state is not realized in this 5d 3 osmate.
The higher energy excitation E C involves transitions that access the e g level, as shown in Fig. 1b.
Calculations predicted inter t 2g -e g excitations (t 2g 3 à t 2g 2 e g 1 ) at 5 eV, 16  intuitively, is not at odds with the expectations of observable effects of the large SOC that is intrinsic to 5d systems. 6,10 For example, as we discuss further, the role of SOC comes to the fore when either considering excited magnetic and electronic states or when going beyond the single ion ground state.

Momentum and temperature dependence of excitation E A with RIXS.
Having characterized the electronic ground state from RIXS excitations at 1 eV and above we now focus on feature E A at 160 meV.
This energy does not correspond to any expected "d-d" energy scale for the d 3 electronic configuration in a nearly cubic CEF, see e.g. Ref. 24. Moreover, E A is distinct from the d-d excitations E B and E C in being much sharper in energy. Figure 2a-c shows the intensity of E A follows an order parameter-like behavior with temperature, with E A appearing at the magnetic MIT, and remains at the same energy of 160 meV.
We followed the momentum dependence, main panel of Fig. 2d, and conclude E A is a non-dispersive excitation, within the 130 meV experimental resolution. While the intensity of E A appears to show some variation within the Brillouin zone, this is, at least in part, an artifact of the observed variation of the elastic line as the crystal is necessarily measured in slightly different physical orientations altering the xray beam attenuation.
The origin and behavior of mode E A is puzzling for a variety of reasons. Interpretation of this feature in terms of a conventional magnetic excitation initially appears problematic given the small magnetic structure and furthermore allowed the ordered moment to be found of 0.59 (8) with unitary vectors ! ∈ 111 and !" ∈ 110 were obtained for given 4-site and 8-site clusters that encompass the full AIAO magnetic ground state with a fixed parameter set reported in Ref. 16, that includes d=1.7 meV, D=-6.8 meV and J=6.4 meV. The ED calculations take into account explicitly the quantum nature of the spin states and the interactions between them. The results are shown in Fig. 3c. The calculated energy shows excellent agreement with experiment. We note that the intensities calculated are the density of states (DOS) and therefore are not directly proportional to the RIXS cross-section, which is non-trivial to calculate.
In the classical limit, equation 1, the possible spin-flip excitations for a S=3/2 system of ΔS z =1,2,3 have distinct energies. Conversely the spectra for the ΔS z excitations from ED calculations are mixed and rather similar with an overlapping single peaked excitation. The only distinction between the different ΔS z processes from ED calculations is a slight variation in energy and an overall intensityscaling factor in their DOS, as shown by the red, green and blue regions in Fig. 3c The strong agreement between the observed magnetic excitation energy and that predicted from ED calculations based on the inclusion of the J, d and D interactions predicted in Ref. 16, with essentially no free parameters, indicates that this model robustly describes the essential physics of the system.
Interestingly the ED calculations predict the strongest DOS contribution to be from the ΔS z =3 process.
Such an excitation is forbidden by RIXS spin-only selection rules that limits the possible measurable excitations to ΔS z =1 and 2. 25 The ΔS z =3 process, however, becomes experimentally allowed in Cd 2 Os 2 O 7 in the intermediate RIXS process due to the creation of a 5d 4 state (2p 6 5d 3 à2p 5 5d 4 ). In this intermediate state S is no longer a good quantum number, nevertheless, the experimental RIXS cross section will be expected to be dominated by the single-magnon followed by the two-magnon processes.
Further experimental support for the magnetic origin of excitation E A is found when recalling the RIXS incident energy dependence (Fig. 1b). The incident energy spectra showed both E A and E B had the same incident energy resonance dependence indicating they both involve solely intra-t 2g excitations.
Additionally, we observed E A is non-dispersive (Fig. 2d). This is indeed expected in a system that is predominantly of Ising type since the AIAO structure is a lowest energy, rather than degenerate, ground state, and will suppress the propagation of a flipped spin that alters the magnetic ordering.

Discussion
The Os L-edge RIXS and neutron measurements have provided direct access to the 5d electrons, competing inter and intra-ion interactions and AIAO magnetic ground state and subsequent excitations in measurements. This non-degenerate ground state is selected in the frustrated pyrochlore structure due to the appreciable single-ion anisotropy in the system. A similar mechanism is expected to exist in pyrochlore iridates, although the AIAO ordering has not been directly measured on the Ir sublattice.
Nevertheless the AIAO magnetic ordering has been the focus of considerable interest in pyrochlore iridates due to the potential for exotic phenomena including Weyl semi-metal and topological insulating behavior. 2,5,12,13,14 Analogous behavior can be mapped over to pyrochlore osmates with AIAO ordering.
In terms of the observed MITs in pyrochlore iridates the AIAO ordering is predicted to play a direct role, with the existence of either concurrent or proximate magnetic ordering. 5 Considering the phenomenologically similar behavior between the pyrochlore iridates and the pyrochlore osmate Cd 2 Os 2 O 7 suggests an analogous underlying mechanism for the magnetic MITs. Our results indicate neither of the divergent electronic ground states adopted within the 5d 3 osmate and 5d 5 iridate pyrochlore systems of orbital singlet with quenched SOC and SOC enhanced J eff =1/2, respectively, play a dominant role with regards to creating the MITs. Instead the underlying mechanism appears directly related to the enhanced SOC in both systems that produces the strong single-ion anisotropy and subsequent AIAO magnetic ordering.
Considering the emergence of the magnetic excitation at E A =160 meV in the RIXS measurements of Cd 2 Os 2 O 7 provides further evidence for the enhanced role of SOC in 5d 3 systems. The existence of this excitation from the AIAO ground state was shown to be a direct consequence of the strong DM exchange interaction and single-ion axial anisotropy that couple with the comparable energy of the magnetic exchange interaction; with the concomitant behavior necessary to create the observed magnetic excitation.
The coupling of these interactions on the Ising-like AIAO ground state results in a magnetic excitation that corresponds to a superposition of multiple spin-flip process that obeys the Hamiltonian described in equation 2, which includes comparable DM, single-ion axial anisotropy and magnetic exchange interactions.
Collectively the Os L-edge RIXS measurements on Cd 2 Os 2 O 7 , coupled with neutron diffraction, have provided a unique and direct probe of the 5d electrons responsible for the concurrent magnetic order and MIT in both the metallic and insulating regimes. The results revealed the electronic ground state, showing a mechanism of strong CEF (10Dq≈4.5 eV), moderate Hunds coupling (J H ≈0.3eV) and quenched SOC that does not split the t 2g manifold but enhances the anisotropic magnetic couplings to create an AIAO magnetic ground state. This reveals a non-trivial and variable role of effective SOC in 5d 3 based systems compared to 5d 5    and allows a categorization of the excitations as intra-t 2g or t 2g -e g . (c) Schematic of the initial and final RIXS process. The initial electronic ground state prior to exciting an electron is indicated by the red spins in the limit of cubic CEF splitting of the 5d manifold. The final RIXS states for E B (intra-t 2g ) and E C (t 2ge g ) are indicated by the blue and green spins, respectively. All measurements were performed at 60 K. The Brillouin zone in the (HKK) plane is shown (grey) and the directions measured (red).