Orbital Fluctuations Research Articles

Multiplet effects in orbital and spin ordering phenomena: A hybridization-expansion quantum impurity solver study

We use an efficient general hybridization-expansion continuous-time quantum Monte Carlo impurity solver (Krylov approach) to study orbital and spin ordering phenomena in strongly correlated systems within the local-density approximation plus dynamical mean-field theory approach. This allows us to include often-neglected interaction terms, to study models with large basis sets, to consider crystals with low-symmetry distortions, and to reach the very low experimental temperatures. We use this solver to study ordering phenomena in a selection of exemplary low-symmetry transition-metal oxides. For the rare-earth manganites, we show that including spin-flip and pair-hopping terms does not affect the Kugel-Khomskii orbital-order melting transition. For LaMnO${}_{3}$, we find that the commonly used two-band model with classical ${t}_{2g}$ spin gives a good description of the ${e}_{g}$ electrons when compared with the full five-orbital Hubbard model. Surprisingly not only the occupied orbital but also the ${e}_{g}$ spectral matrix is well reproduced. For the ${d}^{1}$ perovskites CaVO${}_{3}$ and YTiO${}_{3}$ we show that spin-flip and pair-hopping terms only weakly affect orbital fluctuations. Moreover, for the Mott insulator YTiO${}_{3}$ we can study the ferromagnetic polarization to very low temperatures, finding a transition temperature in remarkably good agreement with experiments.

Sudden reversal in the pressure dependence of Tc in the iron-based superconductor KFe2As2

The pairing mechanism in iron-based superconductors is the subject of ongoing debate. Proximity to an antiferromagnetic phase suggests that pairing is mediated by spin fluctuations, but orbital fluctuations have also been invoked. The former typically favour a pairing state of extended s-wave symmetry with a gap that changes sign between electron and hole Fermi surfaces (s+-), while the latter yield a standard s-wave state without sign change (s++). Here we show that applying pressure to KFe2As2 induces a change of pairing state. The critical temperature Tc decreases with pressure initially, and then suddenly increases, above a critical pressure Pc. The constancy of the Hall coefficient through Pc rules out a change in the Fermi surface. There is compelling evidence that the pairing state below Pc is d-wave, from bulk measurements at ambient pressure. Above Pc, the high sensitivity to disorder argues for a particular kind of s+- state. The change from d-wave to s-wave is likely to proceed via an unusual s + id state that breaks time-reversal symmetry. The proximity of two distinct pairing states found here experimentally is natural given the near degeneracy of d-wave and s+- states found theoretically. These findings make a compelling case for spin-fluctuation-mediated superconductivity in this key iron-arsenide material.

Possible high-pressure orbital quantum criticality and an emergent resistive phase in PbRuO3

The orbital ordering transition in the metallic perovskite PbRuO${}_{3}$ is suppressed from 90 K at ambient pressure towards zero temperature at 50 kbar, where non-Fermi liquid resistivity with a temperature exponent $n$ $=$ 1.6 is observed. This evidences a possible quantum critical point brought about by orbital fluctuations, rather than spin fluctuations as observed in Sr${}_{3}$Ru${}_{2}$O${}_{7}$ and heavy fermion conductors. An anomalous increase of resistivity is observed at pressures above \ensuremath{\sim}100 kbar, and a transition to a more resistive, possibly semiconducting, phase is observed at 300 kbar and ambient temperature.

Orbital-spin-coupled fluctuations in spinel vanadate MnV2O4

The elastic properties of a spinel vanadate MnV${}_{2}$O${}_{4}$ that has an orbital degree of freedom in the triply degenerate ${t}_{2g}$ orbital at V${}^{3+}$(${d}^{2}$) sites are investigated by ultrasonic pulse-echo measurement. Considerable softening of the shear elastic constant $({C}_{11}\ensuremath{-}{C}_{12})/2$ is observed as the temperature approaches the first-order transition from the high-temperature orbital-disordered cubic phase to the low-temperature orbital-ordered tetragonal phase. The softening is attributed to fluctuations between ${d}_{yz}$ and ${d}_{zx}$. Moreover, the elastic anomaly is found to be sensitive to the external magnetic field, revealing a coupling between spin and orbital fluctuations. The elastic anomaly is well reproduced theoretically based on Landau theory and elucidates a characteristic precursor phenomenon in MnV${}_{2}$O${}_{4}$.

Exotic spin orders driven by orbital fluctuations in the Kugel-Khomskii model

We study zero temperature phase diagram of the three-dimensional Kugel-Khomskii model on a cubic lattice using the cluster mean field theory and different perturbative expansions in the orbital sector. The phase diagram is rich, goes beyond the single-site mean field theory due to spin-orbital entanglement. In addition to the antiferromagnetic (AF) and ferromagnetic (FM) phases, one finds also a plaquette valence-bond phase with singlets ordered either on horizontal or vertical bonds. More importantly, for increasing Hund's exchange we identify three phases with exotic magnetic order stabilized by orbital fluctuations in between the AF and FM order: (i) an AF phase with two mutually orthogonal antiferromagnets on two sublattices in each $ab$ plane and AF order along the c axis (ortho-$G$-type phase), (ii) a canted-$A$-type AF phase with a non-trivial canting angle between nearest neighbor FM layers along the c axis, and (iii) a striped-AF phase with anisotropic AF order in the $ab$ planes. We elucidate the mechanism responsible for each of the above phases by deriving effective spin models which involve second and third neighbor Heisenberg interactions as well as four-site spin interactions going beyond Heisenberg physics, and explain how the entangled nearest neighbor spin-orbital superexchange generates spin interactions between more distant spins.

Spin-Fluctuation-Driven Orbital Nematic Order in Ru-Oxides: Self-Consistent Vertex Correction Analysis for Two-Orbital Model

To reveal the origin of the "nematic electronic fluid phase" in Sr$_3$Ru$_2$O$_7$, we apply the self-consistent vertex correction analysis to the ($d_{xz},d_{yz}$)-orbital Hubbard model. It is found that the Aslamazov-Larkin type vertex correction causes the strong coupling between spin and orbital fluctuations, which corresponds to the Kugel-Khomskii spin-orbital coupling in the local picture. Due to this mechanism, orbital nematic order with $C_2$ symmetry is induced by the magnetic quantum criticality in multiorbital systems, while this mechanism is ignored in the random-phase-approximation. The present study naturally explains the intimate relation between the magnetic quantum criticality and the nematic state in Sr$_3$Ru$_2$O$_7$ and Fe-based superconductors.

Superconductivity and electronic state of annealed single-crystals of FeSe1−xTex (0.6 ≦x≦1) studied by specific heat

We have investigated the superconductivity and electronic state in FeSe1−xTex (0.6 ≦ x ≦ 1) from the specific heat measurements, using annealed single-crystals of good quality. First, it has been found that annealed single-crystals of x = 0.6–0.9 exhibit bulk superconductivity with a clear specific-heat jump at the superconducting (SC) transition temperature, Tc. Both 2Δ0/kBTc [Δ0: the SC gap at 0 K] and Δ C/(γn-γ0)Tc [Δ C: the specific-heat jump at Tc, γn: the electronic specific-heat coefficient in the normal state, γ0: the residual electronic specific-heat coefficient at 0 K in the SC state] are largest at x = 0.7 and are 4.29 and 2.38, respectively, indicating that the superconductivity is strong-coupling. Secondly, it has been found that the γn value is much larger than that estimated from the band calculation and increases with increasing x and suddenly decreases above x = 0.9 due to the antiferromagnetic ordering around x = 1. The large value of γn is guessed to be due to the enhancement of the effective mass related to spin fluctuation and/or orbital fluctuation. Finally, it has been found that there remains a finite value of the electronic specific-heat coefficient at 0 K even in the SC state at x = 0.8–0.9. This suggests that a phase separation into SC and normal-state regions takes place at x = 0.8–0.9. Otherwise, there might remain a normal-state pocket at the Fermi surface even in the SC state.

Direct evidence of non-Zhang-Rice Cu3+centers in La2Li0.5Cu0.5O4

A well-isolated Zhang-Rice (ZR) singlet as a ground state of the Cu${}^{3+}$ center in hole-doped cuprates is a leading paradigm in modern theories of high-temperature superconductivity. However, a dramatic temperature evolution of the ${}^{6,7}$Li NMR signal in La${}_{2}$Li${}_{0.5}$Cu${}_{0.5}$O${}_{4}$, a system with a regular lattice of well-isolated Cu${}^{3+}$ centers, reveals significant magnetic fluctuations and suggests a quasidegeneracy to be a generic property of their ground state at variance with the simple ZR model. We argue for a competition of the ZR state with nearby states formed by a ``doped'' hole occupying purely oxygen nonbonding ${a}_{2g}(\ensuremath{\pi})$ and ${e}_{u}(\ensuremath{\pi})$ orbitals rather than a conventional ${b}_{1g}({d}_{{x}^{2}\ensuremath{-}{y}^{2}})$ Cu 3$d$-O 2$p$ hybrid. The temperature variation of the ${}^{6,7}$Li NMR line shape and spin-lattice relaxation rate point to a gradual slowing down of some magnetic order parameter's fluctuations without distinct signatures of a phase transition down to $T=2$ K. This behavior agrees with a stripelike ferrodistortive fluctuating $Ammm$ order in a two-dimensional structure of the (CuLi)O${}_{2}$ planes accompanied by unconventional oxygen orbital antiferromagnetic fluctuations.

Non-Fermi liquid due to orbital fluctuations in iron pnictide superconductors

We study the influence of quantum fluctuations on the electron self energy in the normal state of iron-pnictide superconductors using a five orbital tight binding model with generalized Hubbard on-site interactions. Within a one-loop treatment, we find that an overdamped collective mode develops at low frequency in channels associated with quasi-1D $d_{xz}$ and $d_{yz}$ bands. When the critical point for the $C_4$ symmetry broken phase (structural phase transition) is approached, the overdamped collective modes soften, and acquire increased spectral weight, resulting in non-Fermi liquid behavior at the Fermi surface characterized by the frequency dependence of the imaginary part of electron self energy of the form $\omega^\lambda$, $0<\lambda<1$. We argue that this non-Fermi liquid behavior is responsible for the recently observed zero-bias enhancement in the tunneling signal in quantum point contact spectroscopy. A key experimental test of this proposal is the absence of the non-Fermi liquid behaviour in the hole-doped materials. Our result suggests that quantum criticality plays an important role in understanding the normal state properties of iron-pnictide superconductors.

Fractional power-law behavior and its origin in iron-chalcogenide and ruthenate superconductors: Insights from first-principles calculations

We perform realistic first-principles calculations of iron chalcogenides and ruthenate-based materials to identify experimental signatures of Hund's-coupling-induced correlations in these systems. We find that FeTe and K${}_{x}$Fe${}_{2\ensuremath{-}y}$Se${}_{2}$ display unusual orbital-dependent fractional power-law behavior in their quasiparticle self-energy and optical conductivity, a phenomenon first identified in SrRuO${}_{3}$. Strong incoherence in the paramagnetic state of these materials results in electronic states hidden to angle-resolved photoemission spectroscopy which reemerge at low temperatures. We identify the effective low-energy Hamiltonian describing these systems and show that these anomalies are not controlled by the proximity to a quantum critical point but result from coexistence of fast quantum mechanical orbital fluctuations and slow spin fluctuations.

Pressure-Induced Heavy Fermion Superconductivity in the Nonmagnetic Quadrupolar SystemPrTi2Al20

We report the discovery of a pressure-induced heavy fermion superconductivity in a nonmagnetic orbital ordering state in the cubic compound PrTi(2)Al(20). In particular, we found that the transition temperature and the effective mass associated with the superconductivity are dramatically enhanced as the system approaches the putative quantum critical point of the orbital order. Our experiment indicates that the strong orbital fluctuations may provide a nonmagnetic glue for Cooper pairing.

Exploring spin-orbital models with dipolar fermions in zigzag optical lattices

Ultracold dipolar spinor fermions in zig-zag--type optical lattices can mimic spin-orbital models relevant in solid-state systems, as transition-metal oxides with partially filled $d$ levels, with the interesting advantage of reviving the quantum nature of orbital fluctuations. We discuss two different physical systems in which these models may be simulated, showing that the interplay between lattice geometry and spin-orbital quantum dynamics produces a wealth of novel quantum phases.

Self-consistent Vertex Correction Analysis for Iron-based Superconductors: Mechanism of Coulomb Interaction-Driven Orbital Fluctuations

We study the mechanism of orbital or spin fluctuations due to multiorbital Coulomb interaction in iron-based superconductors, going beyond the random-phase approximation. For this purpose, we develop a self-consistent vertex correction (VC) method, and find that multiple orbital fluctuations in addition to spin fluctuations are mutually emphasized by the "multimode interference effect" described by the VC. Then, both antiferro-orbital and ferro-orbital (=nematic) fluctuations simultaneously develop for J/U~0.1, both of which contribute to the s-wave superconductivity. Especially, the ferro-orbital fluctuations give the orthorhombic structure transition as well as the softening of shear modulus C(66).

Probing orbital fluctuations inRVO3(R=Y, Gd, or Ce) by ellipsometry

We study optical excitations across the Mott gap in the multiorbital Mott-Hubbard insulators $R$VO${}_{3}$. The multipeak structure observed in the optical conductivity can be described consistently in terms of the different $3{d}^{3}$ multiplets or upper Hubbard bands. The spectral weight is very sensitive to nearest-neighbor spin-spin and orbital-orbital correlations and thus shows a pronounced dependence on both temperature and polarization. Comparison with theoretical predictions based on either rigid orbital order or strong orbital fluctuations clearly rules out that orbital fluctuations are strong in $R$VO${}_{3}$. Both the line shape and the temperature dependence give clear evidence for the importance of excitonic effects.

Spin density wave and superconductivity in CaFe1−xCoxAsF studied by nuclear magnetic resonance

We performed nuclear magnetic resonance (NMR) measurements to investigate the evolution of spin-density-wave (SDW) and superconducting (SC) states upon electron doping in CaFe_{1-x}Co_{x}AsF, which exhibits an intermediate phase diagram between those of LaFeAsO_{1-x}F_x and Ba(Fe_{1-x}Co_x)_2As_2. We found that homogeneous coexistence of the incommensurate SDW and SC states occurs only in a narrow doping region around the crossover regime, which supports S_{+-}-wave symmetry. However, only the structural phase transition survives upon further doping, which agrees with predictions from orbital fluctuation theory. The transitional features upon electron doping imply that both spin and orbital fluctuations are involved in the superconducting mechanism.

Filamentary superconductivity across the phase diagram of Ba(Fe,Co)2As2

We show magnetotransport results on Ba(Fe${}_{1\ensuremath{-}x}$Co${}_{x}$)${}_{2}$As${}_{2}$ ($0.0\ensuremath{\leqslant}x\ensuremath{\leqslant}0.13$) single crystals. We identify the low-temperature resistance step at 23 K in the parent compound with the onset of filamentary superconductivity (FLSC), which is suppressed by an applied magnetic field in a similar manner to the suppression of bulk superconductivity (SC) in doped samples. FLSC is found to persist across the phase diagram until the long-range antiferromagnetic order is completely suppressed. A significant suppression of FLSC occurs for $0.02&lt;x&lt;0.04$, the doping concentration where bulk SC emerges. Based on these results and the recent report of an electronic anisotropy maximum for 0.02 $\ensuremath{\leqslant}x\ensuremath{\leqslant}$ 0.04 [Chu et al., Science 329, 824 (2010)], we speculate that, besides spin fluctuations, orbital fluctuations may also play an important role in the emergence of SC in iron-based superconductors.

IMPACT OF THE ORDER PARAMETER SYMMETRIES ON THE VORTEX CORE STRUCTURE IN IRON-BASED SUPERCONDUCTORS

Effects of the order parameter symmetries on the cutoff parameter ξh (determining the magnetic field distribution) in the mixed state are investigated in the framework of quasiclassical Eilenberger theory for isotropic s±, s++ and anisotropic dx2-y2-wave superconducting pairings. These symmetries are proposed for the pairing state of the Fe -pnictides. In s± pairing symmetry, the gap function has opposite sign at the electron and hole pockets of the Fermi surface, it is connected with interband antiferromagnetic spin fluctuations. In s++ pairing symmetry, the gap function has the same sign at the Fermi surface, it is mediated by moderate electron–phonon interaction due to Fe -ion oscillation and the critical orbital fluctuation. The dx2-y2 pairing symmetry can rise from intraband antiferromagnetic spin fluctuation in strongly hole overdoped iron pnictide KFe 2 As 2 and ternary chalcogenides. The s± pairing symmetry results in different effects of intraband (Γ0) and interband (Γπ) impurity scattering on ξh. It is found that ξh/ξc2 value decreases with Γ0 leading to the values much less than those predicted by the analytical Ginzburg–Landau (AGL) theory for high Γ0. At very high Γ0, the interband scattering suppresses ξh/ξc2 considerably below one in the whole field range making it flat for both s± and s++ pairing symmetries. Scaling of the cutoff parameter with the electromagnetic coherence length shows the importance of the nonlocal effects in mixed state. The small values of ξh/ξc2 were observed in μSR measurements of Co -doped BaFe 2 As 2. If Γ0 and Γπ are small and equal than the ξh/ξc2(B/Bc2) dependence for s± symmetry behaves like that of the AGL model and shows a minimum with value much more than that obtained for s++ superconductors. With high Γπ, the ξh/ξc2(B/Bc2) dependence resides above the AGL curve for s± pairing symmetry, as observed in SANS measurements of stoichiometrical LiFeAs compound. In d-wave superconductors, ξh/ξc2 always increases with Γ similar to the s± symmetry case with Γ0 = Γπ.

Erratum: Orbital fluctuations and orbital order below the Jahn-Teller transition in Sr3Cr2O8[Phys. Rev. B83, 201102(R) (2011)

Erratum: Orbital fluctuations and orbital order below the Jahn-Teller transition in Sr<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow /><mml:mn>3</mml:mn></mml:msub></mml:math>Cr<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow /><mml:mn>2</mml:mn></mml:msub></mml:math>O<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow /><mml:mn>8</mml:mn></mml:msub></mml:math>[Phys. Rev. B<b>83</b>, 201102(R) (2011)

Electronic reconstruction through the structural and magnetic transitions in detwinned NaFeAs

We use angle-resolved photoemission spectroscopy to study twinned and detwinned iron pnictide compound NaFeAs. Distinct signatures of electronic reconstruction are observed to occur at the structural (TS) and magnetic (TSDW) transitions. At TS, C4 rotational symmetry is broken in the form of an anisotropic shift in the orthogonal dxz and dyz bands. The magnitude of this orbital anisotropy rapidly develops to near completion upon approaching TSDW, at which temperature band folding occurs via the antiferromagnetic ordering wave vector. Interestingly, the anisotropic band shift onsetting at TS develops in such a way as to enhance the nesting conditions in the C2 symmetric state, and hence is intimately correlated with the long-range collinear antiferromagnetic (AFM) order. Furthermore, similar behaviors of the electronic reconstruction in NaFeAs and Ba(Fe1−xCox)2As2 suggest that this rapid development of large orbital anisotropy between TS and TSDW is likely a general feature of the electronic nematic phase in the iron pnictides, and the associated orbital fluctuations may play an important role in determining the ground state properties.

Infrared phonons and specific heat in the gapped quantum magnet Ba3Cr2O8

We report on the phonon spectrum of the spin-gapped quantum magnet Ba${}_{3}$Cr${}_{2}$O${}_{8}$ determined by infrared spectroscopy, and on specific heat measurements across the Jahn-Teller transition in magnetic fields up to 9 T. Phonon modes split below the Jahn-Teller transition, which occurs at ${T}_{\text{JT}}=70$ K as detected by specific-heat measurements. The field-dependent specific heat data is analyzed in terms of the contributions from lattice, magnetic and orbital degrees of freedom. In contrast to the isostructural compound Sr${}_{3}$Cr${}_{2}$O${}_{8}$, our analysis does not indicate the existence of orbital fluctuations below the Jahn-Teller transition in Ba${}_{3}$Cr${}_{2}$O${}_{8}$.