Photoemission and Dynamical Mean Field Theory Study of Electronic Correlation in a $t_{2g}^{5}$ Metal of SrRhO$_{3}$ Thin Film

TL;DR

This study investigates the electronic correlation and magnetic properties of SrRhO₃ thin films using photoemission spectroscopy and advanced theoretical calculations, revealing discrepancies between experimental observations and theoretical predictions regarding metallicity and magnetic behavior.

Contribution

The paper combines experimental and theoretical approaches to clarify the electronic structure and correlation effects in SrRhO₃ thin films, highlighting the limited role of spin-orbit coupling.

Findings

Experimental DOS at Fermi level is very small and persists up to room temperature.

Theoretical calculations indicate metallic behavior and stronger correlations in thin films.

Spin-orbit coupling has a moderate effect and is not crucial for electronic correlation.

Abstract

Perovskite rhodates are characterized by intermediate strengths of both electronic correlation as well as spin-orbit coupling (SOC) and usually behave as moderately correlated metals. A recent publication (Phys. Rev. B 95, 245121(2017)) on epitaxial SrRhO$_3$ thin films unexpectedly reported a bad-metallic behavior and suggested the occurrence of antiferromagnetism below 100 K. We studied this SrRhO$_3$ thin film by hard x-ray photoemission spectroscopy and found a very small density of states (DOS) at Fermi level, which is consistent with the reported bad-metallic behavior. However, this negligible DOS persists up to room temperature, which contradicts with the explanation of antiferromagnetic transition at around 100 K. We also employed electronic structure calculations within the framework of density functional theory and dynamical mean-field theory. In contrast to the experimental results, our calculations indicate metallic behavior of both bulk SrRhO$_3$ and the SrRhO$_3$ thin film. The thin film exhibits stronger correlation effects than the bulk, but the correlation effects are not sufficient to drive a transition to an insulating state. The calculated uniform magnetic susceptibility is substantially larger in the thin film than that in the bulk. The role of SOC was also investigated and only a moderate modulation of the electronic structure was observed. Hence SOC is not expected to play an important role for electronic correlation in SrRhO$_3$.

Full text

I Introduction

4$d$ transition metal compounds are characterized by the moderate strengths of both electronic correlation and spin-orbit coupling (SOC) compared to their strongly correlated 3$d$ and strongly spin-orbit-coupled 5$d$ counterparts. Nevertheless, 4$d$ systems do exhibit interesting physical properties as well. Notable examples are found especially in the perovskite ruthenate family: unconventional superconductivity in Sr2RuO4 [1_maeno1994superconductivity, 2_mackenzie2003superconductivity], ferromagnetism (FM) in SrRuO3 [3_kanbayasi1976magnetic], and current-induced insulator-metal transition in Ca2RuO4 [4_nakamura2013electric, 5_sow2017current], etc. Magnetism plays an important role in many 4$d$ systems. Spin-triplet superconductivity in Sr2RuO4 was argued to be related to ferromagnetic spin fluctuations [1_maeno1994superconductivity, 2_mackenzie2003superconductivity]. FM is realized in SrRuO3 [3_kanbayasi1976magnetic] while CaRuO3 [6_cao1997thermal] and Sr3Ru2O7 [7_cao1997observation, 8_ikeda2000ground] are presumably close to FM. On the other hand, Ca2RuO4 is a special case that exhibits an antiferromagnetic (AFM) insulating ground state and insulator-metal transition [9_nakatsuji1997ca2ruo4, 10_carlo2012new]. However, generally magnetic ordering is rarely observed in other perovskite 4$d$ oxides [11_oka2015intrinsic, 12_wadati2014photoemission].

Since Rh is the neighbour of Ru in the 4$d$ transition metal series, Rh-based perovskite oxides, such as SrRhO3 [13_yamaura2001enhanced, 14_singh2003prospects, 15_yamaura2003electronic, 16_nichols2017electronic], Sr2RhO4 [17_perry2006sr2rho4, 18_haverkort2008strong, 19_liu2008coulomb, 20_martins2011reduced] and Sr3Rh2O7 [21_yamaura2002crystal], have also attracted considerable research attention. In the bulk state, these rhodates are usually correlated metals without magnetic ordering. Among them, SrRhO3 has the most simple crystal structure. As first reported by Yamaura et al. [13_yamaura2001enhanced], bulk SrRhO3 has a GdFeO3-type distorted perovskite structure with space group Pnma. Metallic transport behavior was observed down to 1.8 K [13_yamaura2001enhanced] and covalent doping of Ca at the Sr-site does not have significant influence on the metallic state of SrRhO3 [14_singh2003prospects]. Nevertheless, there are several reports that strongly indicate the instability towards magnetic ordering in SrRhO3. An enhanced paramagnetic susceptibility [13_yamaura2001enhanced] and related theoretical investigations [15_yamaura2003electronic] indicate that SrRhO3 is near a quantum critical point with significant ferromagnetic quantum fluctuation.

Recently, epitaxial SrRhO3 thin films were successfully synthesized and their transport and magnetic properties were reported by Nichols et al. [16_nichols2017electronic]. No FM was observed in the SrRhO3 thin films but subtle anomalies appeared at around 100 K in magnetization and magnetoresistance, which indicates the possibility of a magnetic transition. Based on density functional theory (DFT) +$U$ calculations, Ref. [16_nichols2017electronic] suggested that a C-type AFM structure is energetically favorable. One remarkable result from Ref. [16_nichols2017electronic] is that the resistivity of SrRhO3 is very weakly dependent on temperature at high temperature and exhibits an upturn upon cooling below 100 K, showing a weakly insulating behavior. Although this behavior is probably related to some AFM order, there is no direct experimental confirmation about this point so far.

In the present work, we studied SrRhO3 epitaxial thin film by hard x-ray photoemission spectra (HAXPES) to characterize its electronic structure and the correlation effects, as was earlier done for other perovskite transition metal oxides in Refs. [22_takizawa2005manifestation, 23_sekiyama2004mutual, 24_takizawa2009coherent, 12_wadati2014photoemission]. Instead of a coherent peak, a negligible density of states (DOS) near Fermi level ($E_{F}$) was observed. This is the case for the results both at room temperature and at 80 K, which precludes the interpretation of the resistivity upturn upon cooling for temperature around 100 K in terms of the gap opening induced by AFM order. Realistic dynamic mean field theory (DMFT) calculations were conducted to investigate the electronic correlation and instability towards magnetic ordering in the SrRhO3 thin film. Since SOC can also play a significant role to influence the electronic structure of 4$d$ perovskite oxides such as Sr2RuO4 [18_haverkort2008strong, 25_kim2018spin] and Sr2RhO4 [18_haverkort2008strong, 19_liu2008coulomb, 20_martins2011reduced], the possible effects of SOC are investigated and discussed as well.

II Methods

A 9 nm-thick epitaxial SrRhO3 thin film was grown on a SrTiO3(001) single crystalline substrate by pulsed laser deposition. The details of the fabrication methods and basic characterization of the sample were previously reported in Ref. [16_nichols2017electronic].

HAXPES of the SrRhO3 thin film was measured at BL47XU of SPring-8. The incidence angle of linearly polarized ($\pi$-polarization) 7.94 keV hard x-ray was set at 1o and photoemission spectra were collected by a Scienta R-4000 electron energy analyzer with an energy resolution of around 250 meV. Surface-sensitive soft x-ray photoemission spectra (SXPES) were measured by a PHI 5000 VersaProbe system (ULVAC-PHI Inc.) with perpendicular incidence of Al $K\alpha$ radiation (1468.7 eV). The energy resolution of the SXPES measurement was around 450 meV. The position of $E_{F}$ and the energy resolution of both photoemission measurements were determined by measuring and fitting the spectra of a Au reference sample, which was in electrical contact with the SrRhO3 thin film. For temperature dependent HAXPES measurement, a He-flow cryostat was employed to cool the sample down to 80 K.

X-ray linear dichroism (XLD) and resonant magnetic x-ray diffraction (RMXD) measurements of the SrRhO3 thin film at the Rh $L$ edge were carried out at beamline 4-ID-D of Advanced Photon Source. For the room temperature XLD measurement, linearly polarized x-rays with electric field component E perpendicular and parallel to the sample surface were utilized to measure the x-ray absorption spectra (XAS). The incidence angle of the x-rays was set at around 3o and the XAS signal was collected by partial fluorescence yield mode. RXMD measurement was conducted at 30 K by cooling the sample with an ARS He Displex cryocooler.

For the DFT calculation, we used the Wien2k package [26_blaha2001wien2k] and local density approximation (LDA) was employed for the calculation of the exchange correlation potential. For the DFT+DMFT calculation, we used the TRIQS framework [27_aichhorn2016triqs, 28_parcollet2015triqs, 29_seth2016triqs, 30_gull2011continuous] and treated $t_{2g}$ orbitals by using a rotationally invariant Kanamori Hamiltonian with parameters $U=2.3$ eV and $J=0.4$ eV, which has been used to precisely describe the neighbouring ruthenates [31_mravlje2011coherence, 32_dang2015electronic]. To compute the magnetic susceptibility by DFT+DMFT, we applied a magnetic field of 5 meV (around 86 T) and allowed symmetry breaking of spin up and down. For crystal structure optimization of the SrRhO3 thin film, we assumed the in-plane symmetry and lattice constants of the SrTiO3 substrate and relaxed the internal positions of atoms in the unit cell by using DFT [16_nichols2017electronic].

III Photoemission Results

Fig.1 shows the core level HAXPES and SXPES results of the SrRhO3 thin film. HAXPES is quite bulk-sensitive and the detection depth is beyond the thickness of the film since the photoemission signal of Ti in the substrate can be observed. On the other hand, SXPES is very surface sensitive, whose typical detection depth is around 1 to 2 nm [33_seah1979quantitative]. It can be noticed in Fig.1 that surface components (-532 eV O 1$s$ peak in Fig.1(a); -135.7 eV/-133.9 eV Sr 3$d$ peaks in Fig.1(b); C 1$s$ contamination signal at -285.5 eV in Fig.1(c); left shoulders of Sr 3$p$ in Fig.1(c) and left shoulders of Rh 3$d$ in Fig.1(d)) have different binding energies compared to the bulk components (-528.9 eV O 1$s$ peak in Fig.1(a); -133.9 eV/-132.1 eV Sr 3$d$ peaks in Fig.1(b); main peaks of Sr 3$p$ at -278.2 eV/-267.9 eV in Fig.1(c) and main peaks of Rh 3$d$ at -313.3 eV/-308.5 eV in Fig.1(d)). The surface components have little influence on the HAXPES results. The binding energies of peaks in the Rh 3$d$ spectra are also consistent with previous reports of Rh4+ oxides [34_le2011electronic].

The valence band HAXPES and SXPES results are displayed in Fig.2(a). Due to the different photoionization cross section of $p$ and $d$ levels for hard and soft x-rays [35_trzhaskovskaya2001photoelectron], HAXPES is more sensitive to $p$ levels and SXPES is more sensitive to $d$ levels. By comparing the HAXPES and SXPES results, it can be concluded that the features in the energy range from $-10$ eV to $-3$ eV are dominated by O 2$p$ emission and the features above $-3$ eV mainly come from Rh 4$d$ emission. Fig.2(b) shows the valence band spectra in an expanded region near $E_{F}$. Surprisingly, the coherent peak is totally absent for both HAXPES and SXPES. The difference between HAXPES and SXPES at $E_{F}$ is mainly due to the different energy resolution of HAXPES and SXPES. By comparing with the corresponding spectra of the Au reference sample, it is clear that both HAXPES and SXPES have negligible intensity at $E_{F}$. It should be noted that the SrTiO3 substrate could also contribute to the HAXPES valence band spectra due to the large detection depth of HAXPES. However, since SrTiO3 is an insulator with $d^{0}$ configuration, it has nearly no contribution to the intensity above $-3$ eV [36_haruyama1996angle].

In Ref. [16_nichols2017electronic], the possibility of magnetic ordering in the SrRhO3 thin film with a transition temperature of around 100 K was proposed. To investigate the temperature dependence of the electronic structure in the SrRhO3 thin film, we also conducted HAXPES measurement at 80 K. However, nearly no temperature dependence was observed, as shown in Fig.2(b). Since the SrTiO3 substrate has a structural phase transition near this temperature [37_ohama1984temperature], the reported anomalies in transport properties [16_nichols2017electronic] may be related to the change of substrate strain rather than a real magnetic transition. Consequently, the valence band structure of the SrRhO3 thin film does not show a significant temperature dependence.

IV DFT and DFT+DMFT Results

The photoemission results above suggest negligibly small DOS near $E_{F}$ in the SrRhO3 thin film, in contrast to bulk SrRhO3 that exhibits metallic behavior [13_yamaura2001enhanced]. In order to understand this phenomenon, we now turn to the DFT(+DMFT) calculations, performed for both the bulk and the thin film.

The total DOS obtained by DFT+DMFT is shown in Fig.3(a,b). One can notice that DFT+DMFT calculations predict metallic behavior for both the bulk and the thin film. Only moderate effects of electronic correlation with renormalization of $Z\approx 0.5$ are observed ($Z=(1-\frac{\partial Re\Sigma(\omega)}{\partial\omega})^{-1}|_{\omega\rightarrow 0}$), as obtained by the self-energy results shown in Fig.4. The thin film is slightly more correlated with smaller values of $Z$, but no major difference between the thin film and the bulk is observed, in contrast to the experimental results.

According to the orbitally resolved DFT+DMFT DOS in Fig.3(c,d), due to the larger bandwidth of the $xy$ orbital than that of the $xz/yz$ orbitals, the occupancy of the $xy$ orbital (1.50) is smaller than that of the $xz/yz$ orbitals (1.58) in the thin film, which is consistent with the Rh $L_{2}$ edge XLD results. As depicted in Fig.3(e-g), XLD is defined as the difference of XAS measured by using incident x-rays with $E//a$ and $E//c$, where $a$ and $c$ are the in-plane [100] and the out-of-plane [001] directions, respectively. Since the XAS intensity at the Rh $L$ edge is proportional to the number of 4$d$ holes, a positive XLD signal indicates a preferred occupation of out-of-plane 4$d$ orbitals and less occupation of in-plane 4$d$ orbitals. Note that the sign change in the $L_{3}$ edge XLD spectrum could often be observed in other systems as well, while the spectrum at the $L_{2}$ edge can usually reflect the orbital occupation more unambiguously [38_pesquera2012surface]. These experimental and calculation results are consistent with the biaxial compressive strain from the SrTiO3 substrate [16_nichols2017electronic].

On the other hand, in contrast to the strong orbital anisotropy of spectral weight in between the $xy$ and the $xz/yz$ orbitals, the orbital dependence of quasiparticle renormalization is not as strong as that in Sr2RuO4 [31_mravlje2011coherence, 39_tamai2018high], which is consistent with the claim in Ref. [40_yamaura2004ferromagnetic] that correlation effects are weaker in SrRhO3 than in perovskite ruthenates. The electronic correlation changes the effective energy level of the $xz$, $yz$, and $xy$ orbitals. In the DFT calculation, the center energy of the $xy$ orbital is 618 meV higher than that of the $xz/yz$ orbitals in the SrRhO3 thin film. In the DFT+DMFT self-energy of the thin film (Fig.4(b)), the $xz/yz$ orbitals are shifted up with respect to the $xy$ level for 212 meV, as shown by the difference of the real part of self-energy at zero energy. As a result, the effective energy level of $xy$ with respect to that of $xz/yz$ is reduced from 618 meV to 404 meV by electronic correlation in DFT+DMFT calculations. Since the Van-hove peaks of the $xz/yz$ orbitals in DFT are close to $E_{F}$ within 30 meV (Fig.3(a,b)), the correlation-induced shift-up of the $xz/yz$ orbitals gives rise to the reduction of the DOS at $E_{F}$ in DFT+DMFT, as shown in Fig.5(a). Both the bulk and the thin film show a similar trend that the total DOS at $E_{F}$ is reduced by correlation, which is qualitatively consistent with the small electronic component of the experimental specific heat of SrRhO3 [13_yamaura2001enhanced]. It is noteworthy that the $xz/yz$ orbitals have a larger DOS at $E_{F}$ than the $xy$ orbital in the thin film. Meanwhile, the result that $Z\approx 0.5$ for all orbitals implies that electronic correlation is not so sensitive to the value of the DOS at small energies, which is different from Hund’s metals such as ruthenates and iron-based superconductors [31_mravlje2011coherence, 41_georges2013strong].

We also calculated the uniform magnetic susceptibility of both the bulk and the thin film, as shown in Fig.5(b). In contrast to the self-energy, the calculated magnetic susceptibility does show a substantially different behavior in the thin film. The magnetic susceptibility of the thin film is 6 to 7 times larger and exhibits a stronger temperature dependence than that of the bulk case, in contrast to the nearly temperature independent total DOS in the bulk and the thin film (Fig.5(a)). The difference in the calculated magnetic susceptibility for the bulk and the thin film can be understood as follows. First, the larger total DOS at $E_{F}$ in the thin film with respect to that in the bulk (Fig.3(b)) gives rise to a larger magnetic susceptibility. Second, the stronger electronic correlation of the $xz/yz$ orbitals in the thin film compared to that in the bulk (Fig.4(a-d)) gives rise to a larger magnetic instability in the thin film. Third, the sharper slope in the DOS of the $xz/yz$ orbitals in the thin film compared to that in the bulk (Fig.3(c,d)) gives rise to a stronger temperature dependence of the magnetic susceptibility in the thin film. These results are inherited from the tetragonal symmetry of the lattice of the thin film, which gives rise to the presence of the Van-hove singularity of the $xz/yz$ orbitals near Fermi level.

In our photoemission results, it is clearly shown that there is a negligible temperature dependence of the DOS between 80 K and 300 K. The present DFT+DMFT results with similar renormalization for both the bulk and thin film suggest that if there is a real transition of the electronic structure, it will not be a simple metal-insulator transition with a Mott gap. The larger magnetic susceptibility in the thin film compared to that in the bulk implies that the SrRhO3 thin film has a much stronger intrinsic instability towards magnetically ordered phases. This magnetic instability is mainly induced by the anisotropy of the crystal environment, such as crystal field symmetry and bandwidth anisotropy. However, whether this larger magnetic susceptibility is a side effect (or indicator) of some actual electronic instability that in turn is responsible for the experimentally observed neglibible DOS at $E_{F}$ is an open question.

Earlier DFT calculations reported the occurrence of an AFM state in SrRhO3 thin films [16_nichols2017electronic]. We investigated the possibility of magnetic ordering by DFT+$U$ calculation and found that we need $U>5$ eV for the stabilization of the C-type AFM state, which is too large for the 4$d$ shell [42_deng2016transport, 43_fang2004orbital]. We also conducted RXMD experiments at the Rh $L$ edges to attest the existence of AFM ordering peaks. Due to the restricted $Q$ range that the Rh $L$ edge x-ray (around 3 keV) can reach, $Q$ vectors of (0 0 0.5) (A-type), (0.5 0.5 1) (C-type) and (0.5 0.5 0.5) (G-type) were investigated at 30 K but no observable diffraction appeared within the detection limit.

V About Negligible DOS at $E_{F}$ in SrRhO3 Thin Film: SOC, Ordering and Beyond

In principle, a possible origin of the small value of measured DOS at $E_{F}$ and the absence of a coherent peak could be SOC, which can play an important role in $t_{2g}^{5}$ iridates [44_kim2008novel, 45_moon2008dimensionality]. If SOC were strong enough to split the $J$eff$=1/2$ and $J$eff$=3/2$ states significantly, one could expect that an insulating behavior would be promoted by the half-filled $J$eff$=1/2$ band. We are unable to run the DFT+DMFT calculation in the presence of SOC because of the fermionic sign problem in the quantum impurity solver [29_seth2016triqs, 30_gull2011continuous]. But to get a first impression of the possible role of SOC, we calculated the hybridization functions, which determine the behavior of the DMFT calculation in the presence of SOC. The results shown in Fig.6(a,b) imply that SOC moderately affects the electronic structure of SrRhO3. As also shown by DFT results with and without SOC in Fig.6(c,d), in the thin film, due to the SOC-induced band splitting around $E_{F}$ (along $\Gamma$ to X line), SOC reduces the hybridization function of the $xy$ orbital for a small energy scale of 1 to 2 eV (Fig.6(b)). Provided the fact that quasiparticle residue $Z\approx 0.5$ and a small orbital dependence of the Fermi velocity, we suggest that SOC can not trigger the metal-insulator transition but might give rise to a strong magnetic instability in the SrRhO3 thin film. For bulk SrRhO3, the effect of SOC is even smaller due to the lower lattice symmetry, as shown in Fig.6(a). Note that even in SrIrO3, the 5$d$ counterpart of SrRhO3, SOC is still not strong enough to trigger an insulating behavior [45_moon2008dimensionality]. Moreover, we can get similar conclusion by analyzing the branching ratio (BR) of XAS results shown in Fig.3(e,f). The BR between the white-line intensities of Rh $L_{3}$ and $L_{2}$ edges is related to the ground-state expectation value of the angular part of SOC [46_van1988local]. A large deviation from the statistical BR=2 indicates the presence of strong SOC effects. The experimental BR at the Rh $L_{3,2}$ edges is close to the statistical value of 2 (estimated as around 2.3 from Fig.3(e,f)), indicating weak SOC effects in the SrRhO3 thin film. This is in contrast to the Ir 5$d$ cases where large deviations (BR$>4$) from the statistical value, thus large SOC, have been observed [47_laguna2010orbital, 48_clancy2012spin, 49_kim2018controlling].

There is also the possibility of more complicated magnetic or charge ordering, such as helical magnetic ordering or spin/charge density waves, which could be responsible for the absence of coherent peak in the SrRhO3 thin film. Another possible mechanism could be formation of polarons induced by electron-phonon interaction. These possibilities should be considered and investigated in future to further clarify the electronic structure of SrRhO3 thin films.

VI Conclusions

In summary, we experimentally and theoretically investigated the effects of electronic correlation in SrRhO3. The photoemission results indicate a negligible DOS at $E_{F}$ in the SrRhO3 thin film with little temperature dependence. We considered SrRhO3 within band-structure calculation taking into account the electronic correlation with a DFT+DMFT approach. In our calculation the small DOS at $E_{F}$ could not be reproduced, rather a moderately correlated metallic behavior was observed. Our attempts to detect the AFM magnetic diffraction by experiment and to stabilize magnetically ordered states in the calculations both failed. But the calculation did reveal an interesting behavior in the magnetic susceptibility that is substantially larger for the thin film. This result is mainly induced by the difference of crystal anisotropy between the bulk and the thin film. Further investigations are welcome to identify the possible magnetic ordering and clarify the effects of SOC in SrRhO3. Moreover, 5$d$ transition metal oxides, such as SrIrO3 or Sr2IrO4, have strong SOC effects on the electronic correlation [50_zhang2013effective]. We are also looking forward to comparative theoretical studies on them.

VII Acknowledgements

This work was supported by Grant-in-Aid for JSPS fellows (No. 17F17327). The HAXPES experiments at SPring-8 were performed under the approval of the Japan Synchrotron Radiation Research Institute (Proposal No. 2018B1449). This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. The work at ORNL was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. M. K. acknowledges support from Grant No. NSF DMR-1733071, and grateful to CPHT computer support team. We are thankful to the support and advices provided by A. Georges, V. R. Cooper, S. F. Yuk, and A. Rastogi. And we also acknowledge the support provided by K. Ikeda, S. Sakuragi and H. Kinoshita, as well as enlightening discussion about this work with J. W. Kim and H. Zhou during our beamtime in Advanced Photon Source.