50 51 D I A M O N D L I G H T S O U R C E A N N U A L R E V I E W 2 0 2 0 / 2 1 D I A M O N D L I G H T S O U R C E A N N U A L R E V I E W 2 0 2 0 / 2 1 Structures and Surfaces Group Beamlines I05 and I09 Gainingmagnetic insights froma non-magnetic probe Related publication: SunkoV., Mazzola F., Kitamura S., Khim S., Kushwaha P., Clark O. J.,Watson M. D., Marković I., Biswas D., Pourovskii L., Kim T. K., Lee T. L., Thakur P. K., Rosner H., Georges A., Moessner R., Oka T., Mackenzie A. P. & King P. D. C. Probing spin correlations using angle-resolved photoemission in a coupledmetallic/Mott insulator system. Sci. Adv. 6 , eaaz0611 (2020). DOI: 10.1126/sciadv.aaz0611 Publication keywords: PdCrO2; Delafossite; Spin correlations; Angle-resolved photoemission A n international group of researchers wanted to study the electronic properties of an unusual coupled system. It has one layer that supports very mobile carriers, and one that supports Mott insulating and magnetically-ordered states. They performed initial studies using angle-resolved photoemission spectroscopy (ARPES) on beamline I05 at Diamond Light Source, observing some unusual spectral signatures. Theoretical calculations suggested that correlations and interlayer interactions had an unusual role in their generation. To understand the origin of these unusual spectral signatures, the team used Diamond’s Surface and Interface Structural Analysis beamline (I09) to performARPES measurements in the soft X-ray regime. The combined nature of the study, with closely integrated work on I09 and I05, applying photoemissionmeasurements in different regimes, was crucial to the success of this work. By combining theory with the results from I09 and I05, the team were able to show that an intertwining of the spin and charge response in the system dominates the photoemission response. ARPES is usually a non-magnetic probe, but this work demonstrated that in certain circumstances it becomes sensitive to spin-correlations in solids. Scientists could use the same approach to study materials that are incompatible with other, more conventional probes of spin- spin correlation functions. This potentially opens up new systems to experimental study, and an improved understanding of their magnetic properties would be important for real-world applications such as 2D spintronics. PdCrO 2 is a layered triangular lattice material, which can be thought of as an alternating stack of Pd and CrO 2 layers 1 . The electronic properties of the two layers are strikingly different: the Pd layer is highly metallic, while the CrO 2 layer is strongly correlated and magnetically-ordered. Coupling between them can be expectedtoyieldexoticphysics,whichisthemainfocusofthiswork.Theproperties ofthemetallicPd layerarebestunderstoodbyreferringtothenon-magneticsister compound PdCoO 2 , which has been extensively studied due to its remarkably high conductivity. Its electronic structure features a single broad conduction band derived from Pd states, forming a two-dimensional hexagonal Fermi surface (Fig. 1a,b). The CoO 2 layers in PdCoO 2 are rather benign. In contrast, the Cr ions in PdCrO 2 carry a localised spin of S = 3/2 and order into a 120° antiferromagnetic structure at 37.5 K 2 . The low-energy electronic structure is still dominated by the Pd-derived states: consistent with previous findings 3,4 , our high resolution ARPES measurements taken at I05 reveal a “main band” very similar to the conduction band inPdCoO 2 .Butadditionalweakspectralweightappears inPdCrO 2 ascopiesof themain band, offset by the antiferromagnetic ordering vector (Fig. 1c,d). The observation of localised 3/2 spins on the Cr sites suggests that the CrO 2 layer is Mott insulating. This hypothesis has been supported by dynamical mean- field theory calculations, which predicted that the Cr-derived states form a lower Hubbard band 1 to 2 eV below the Fermi level (E F ). To experimentally verify this picture,wehaveusedsoftX-rayARPESatI09to investigatetheatomicallyresolved electronic structure, tuning the probing photon energy into resonance with the Cr L 2,3 absorption edge. Comparing on- to off-resonant spectra reveals a marked enhancement of spectral weight of a very weakly dispersing and broad feature centred at approximately 2 eV below E F (Fig. 2a-c). The integrated weight of this feature follows the absorption spectrum (Fig. 2d), thus establishing its Cr-derived origin and providing strong evidence that this is the spectroscopic signal of a lower Hubbard band of a Mott insulating state. PdCrO 2 can therefore be considered as an unusual combination of an atomic layer-by-layer superlattice of a nearly free electronmetal and aMott insulator. Given the antiferromagnetic order of the latter, the observation of replicas of the metallic main band shown in Fig. 1c-d might seem unremarkable: when electrons feel an additional periodic potential the band structure is reconstructed. This standard picture, however, cannot explain the experimental observations of PdCrO 2 . The spectral weight of the replicas observable by ARPES should fall off rapidlyawayfromthenewzoneboundaries.Experimentally,however,thereplicas are clearly observed all the way from the magnetic zone boundary to the E F (Fig. 1c); over the same energy range, the simple“band folding”model predicts a 100- fold decrease in spectral weight (Fig. 3a, dashed line). In contrast, the measured intensity of the reconstructed weight (IRW) changes by less than a factor of 2 (Fig. 3a, symbols). Wehavediscoveredthattheanswertotheabovepuzzlelies inMott insulator– free electron coupling. Rather than treating the CrO 2 layer as a passive source of a periodic potential, it is necessary to take into account its dynamical degrees of freedom. Once this is done formally, it becomes apparent that PdCrO 2 can be described by the well-known Kondo Hamiltonian 5 , but with the Kondo coupling being an interlayer effect. The key insights it provides come from using it to calculate the photoemission spectral functions. While photoemission from the Pd layer is not significantly altered by this coupling, an entirely new route for photoemission from the Cr layer becomes available. For finite interlayer coupling, a hole created in theMott layer can rapidlymove to the itinerant layer where it can propagate. This results in the spectral function for the removal of electrons from theMott layer becoming a convolution of the itinerant electron spectrumwith the spin correlation function of the Mott layer. In this way, the spin response of the Mott layer and the charge response of the itinerant layer become intertwined. In the case of antiferromagnetically ordered PdCrO 2 , the resulting prediction is that Cr spectral weight follows the dispersion of the nearly free electron Pd band, but translated by the wave vector of the AF order, with no significant binding energy dependence of its intensity (Fig. 3a, full line). The intertwined spin-charge model therefore agrees with the experiment, but it is also making a remarkable and falsifiableprediction:thebackfoldedspectralweight,despiteappearingasasharp band-like feature, is actually a property of the Cr removal spectral function rather than the Pd one. The key diagnostic for the validity of the intertwined spin-charge model is, therefore, to establish the underlying atomic origin of the reconstructed spectral weight. To do this, we again employed soft X-ray ARPES at I09. Quantitative analysis of measurements over a broad photon energy range shows (i) that the photon energy dependence of the IRW closely traces that of the Cr-derived lower Hubbard band (Fig. 3b) and (ii) that its ratio to the Pd-derivedmain band intensity tracks the Cr 3d:Pd 4d ionic cross-section ratio (Fig. 3c). These observations all point to a dominant Cr character of the backfolded spectral weight. To provide an independent confirmation, we again made use of resonant measurements, finding that the reconstructed weight is markedly enhanced when the photon energy is tuned to the Cr L 3 -edge resonance (Fig. 3d-e), thus proving its Cr-derived nature. Although the initial motivation for this work was understanding the physics of the spectroscopic signatures in PdCrO 2 , its implications are much broader. First of all, it establishes PdCrO 2 as a benchmark system to study the properties of the Kondo Hamiltonian with experimentally-constrained parameters. Furthermore, it opens a new route to investigate static and dynamical spin susceptibilities using ARPES, including systems that are not accessible to more traditional magnetic probes. The ability to identify the orbital content of the various features of the electronic structure, made possible by the soft X-ray ARPES experiments at I09, was critical to this discovery. References: 1. Shannon R. D. et al. Chemistry of NobleMetal Oxides. I. Syntheses and Properties of ABO2 Delafossite Compounds. Inorg. Chem. 10 , 713–718 (1971). DOI: 10.1021/ic50098a011 2. Takatsu H. et al. Magnetic structure of the conductive triangular-lattice antiferromagnet PdCrO 2. Phys. Rev. B - Condens. Matter Mater. Phys. 89 , 104408 (2014). DOI: 10.1103/PhysRevB.89.104408 3. Sobota J. A. et al. Electronic structure of themetallic antiferromagnet PdCrO2measured by angle-resolved photoemission spectroscopy. Phys. Rev. B - Condens. Matter Mater. Phys. 88 , 125109 (2013). DOI: 10.1103/ PhysRevB.88.125109 4. Noh H. J. et al. Direct Observation of Localized Spin Antiferromagnetic Transition in PdCrO2 by Angle-Resolved Photoemission Spectroscopy. Sci. Rep. 4 , 3680 (2014). DOI: 10.1038/srep03680 5. Löhneysen H.V. et al. Fermi-liquid instabilities at magnetic quantum phase transitions. Rev. Mod. Phys. 79 , 1015–1075 (2007). DOI: 10.1103/ RevModPhys.79.1015 Funding acknowledgement: We acknowledge support from the European Research Council (grant nos. ERC-714193-QUESTDO and ERC-319286-QMAC), the Royal Society, the LeverhulmeTrust (grant nos. RL-2016-006 and PLP-2015-144R), theMax- Planck Society, the Simons Foundation, and the International Max-Planck Partnership for Measurement and Observation at the QuantumLimit.V.S. and O.J.C. acknowledge EPSRC for PhD studentship support through grant numbers EP/L015110/1 and EP/K503162/1. I.M. acknowledges PhD studentship support from the IMPRS for the Chemistry and Physics of QuantumMaterials. We thank Diamond Light Source for access to beamlines I09 (proposal no. SI19479) and I05 (proposal no. SI17699).The work at theMax Planck Institute for the Physics of Complex Systems was supported in part by the Deutsche Forschungsgemeinschaft under grants SFB 1143 (project-id 247310070) and the cluster of excellence ct.qmat (EXC 2147, project-id39085490). Corresponding authors: DrVeronika Sunko, Max Planck Institute for Chemical Physics of Solids,
[email protected] ; Prof. Phil King, School of Physics and Astronomy, University of St Andrews,
[email protected] Figure 1: Low-energy electronic structure of Pd-based delafossites measured using ARPES at I05. (a) Dispersion and (b) Fermi surface of PdCoO 2 ; (c) dispersion and (d) Fermi surface of PdCrO 2 . Note the additional weak spectral weight in (c,d) which appears as a copy of the main underlying band, similar to in PdCoO 2 , but shifted by the antiferromagnetic wavevector of the CrO 2 layer. E-E F [eV] -0.6 -0.4 -0.2 0 0.1 1 I RW / I RW (-0.7eV) 60eV, s - pol. 110eV, p - pol. Band folding Cr spectral function a b d e c -1 0 1 k x [Å -1 ] -1 0 1 k y [Å -1 ] -1 0 1 k x [Å -1 ] h ν = 578eV h ν = 581.7eV h ν [eV] h ν [eV] 1 0 I / I (110eV) 0.2 0.0 Ratio 350 250 150 350 250 150 I LHB Reconstructed weight ( I RW ) Measured I RW : I MB Calc. cross-section (Cr3d:Pd4d) x 0.023 Figure 3: Cr-character of the reconstructed weight. (a) Analysis of the apparent main-band replica shows its spectral weight is nearly constant vs. binding energy, inconsistent with typical pictures for band folding, but consistent with our theoretical model for an intertwined spin-charge response arising due to coupling between the layered sub-systems. Consistent with this picture, our measurements indicate this feature has dominant Cr character; (b) Its spectral weight follows that of the Hubbard band; (c) The cross-section variation with photon energy matches that of a Cr-derived state; (d) It is clearly visible only on-resonance, and barely resolved in Fermi surfaces measured off-resonance. -4 -3 -2 -1 0 k y [Å -1 ] I [arb. u.] I / I (575eV) XAS [arb. u.] 1 k y [Å -1 ] -1 0 1 -1 0 Min Max E-E F [eV] a b d c 600 590 580 570 Photon energy [eV] I LHB h ν = 578 eV 578 eV h ν = 581.7 eV 581.7 eV 5 3 1 XAS I LHB I MB Figure 2: Resonant photoemission of PdCrO 2 using soft X-ray ARPES at I09. Valence band spectra measured using photon energies (a) Just below and (b) On-resonance with the Cr L 3 absorption edge; (c) Comparison of the integrated spectra; (d) The spectral weight of the non- dispersive states at ~2 eV binding energy tracks the X-ray absorption across the Cr L 2,3 edge, indicating their Cr-derived character. In contrast, the steep band shows no spectral weight enhancement across this absorption edge, pointing to its dominant Pd-derived character.