Dynamical Mean-field Theory Approach Research Articles

Signatures of Hund metal and finite-frequency nesting in Sr2RuO4 revealed by electronic Raman scattering

We investigate the electronic Raman scattering of Sr2RuO4 using a material-realistic dynamical mean-field theory approach. We identify the low-energy Fermi liquid behavior and point out that the enhanced Raman response at higher energies is a fingerprint of Hund metals. These signatures originate in the two-stage coherence of Hund metals and associated quasiparticle “unrenormalization.” In agreement with recent experimental observations, we find the B1g and B2g responses differ, but our calculations suggest a novel interpretation of this dichotomy. The B1g response is dominated by the xy orbital and the B2g response receives contributions from all orbitals and is strongly affected by previously unnoticed finite-frequency interband nesting. We calculate the vertex-corrections to Raman response and show that their effect is nonvanishing but small. Published by the American Physical Society 2024

Heteronuclear Magnetisms with Ultracold Spinor Bosonic Gases in Optical Lattices

Motivated by recent realizations of spin-1 NaRb mixtures in the experiments [Phys. Rev. Lett. 114, 255301 (2015); Phys. Rev. Lett. 128, 223201 (2022)], we investigate heteronuclear magnetism in the Mott-insulating regime. Different from the identical mixtures where the boson statistics only admits even parity states from angular momentum composition, for heteronuclear atoms in principle all angular momentum states are allowed, which can give rise to new magnetic phases. While various magnetic phases can be developed over these degenerate spaces, the concrete symmetry breaking phases depend on not only the degree of degeneracy but also the competitions from many-body interactions. We unveil these rich phases using the bosonic dynamical mean-field theory approach. These phases are characterized by various orders, including spontaneous magnetization order, spin magnitude order, singlet pairing order, and nematic order, which may coexist specially in the regime with odd parity. Finally we address the possible parameter regimes for observing these spin-ordered Mott phases.

Electronic correlations and intrinsic magnetism of interstitial quasi-atomic states in Li8Au electride.

We investigate the electronic sub-system of a recently designed Li8Au superconducting electride to reveal its many-body correlated nature and magnetic properties. Using maximally localized Wannier functions (MLWFs) to describe the interstitial anion electron (IAE) states, it was found that these states are partially occupied with a population of 1.5e- and have negligible hybridization with the almost completely filled p-Au states. The averaged interaction screened Hubbard parameter U for quasi-atomic IAE states evaluated by the constrained random-phase approximation (CRPA) method is 2 eV, comparable to the width of the electride band suggesting moderate electronic correlations. Using dynamical mean field theory (DMFT) approach we found that IAEs in Li8Au electride behave as magnetic centers and possess their own well localised magnetic moments of 0.5μB per quasi-atomic IAE. The obtained results deepen the understanding of the significance of many-body effects in the IAE subsystem of electronic states and reveal the mechanism for the formation of intrinsic magnetic moments on IAEs, which behave like ferromagnetic quasi-atoms in the Li8Au electride. Overall, the observed correlation effects in Li8Au emphasize their importance in materials with excess electrons confined in cavities.

Multiorbital Nature of Doped Sr_{2}IrO_{4}.

The low-energy j_{eff}=1/2 band of Sr_{2}IrO_{4} bears stark resemblances with the x^{2}-y^{2} band of La_{2}CuO_{4}, and yet no superconductivity has been found so far by doping Sr_{2}IrO_{4}. Behind such a behavior could be inherent failures of the j_{eff}=1/2 picture, in particular when electrons or holes are introduced in the IrO_{2} planes. In view of this, here we reanalyze the j_{eff}=1/2 scenario. By using the local-density approximation plus dynamical mean-field theory approach, we show that the form of the effective j_{eff}=1/2 state is surprisingly stable upon doping. This supports the j_{eff}=1/2 picture. We show that, nevertheless, Sr_{2}IrO_{4} remains in essence a multiorbital system: The hybridization with the j_{eff}=3/2 orbitals sizably reduces the Mott gap by enhancing orbital degeneracy, and part of the holes go into the j_{eff}=3/2 channels. These effects cannot be reproduced by a simple effective screened Coulomb repulsion. In the optical conductivity spectra, multiorbital processes involving the j_{eff}=3/2 states contribute both to the Drude peak and to relatively low-energy features.

Exchange interactions in iron and nickel: DFT+DMFT study in paramagnetic phase

We analyze possible ways to calculate magnetic exchange interactions within the density functional theory plus dynamical mean-field theory (DFT+DMFT) approach in the paramagnetic phase. Using the susceptibilities obtained within the ladder DMFT approach together with the random phase approximation result for the Heisenberg model, we obtain bilinear exchange interactions. We show that the earlier obtained result of Stepanov et al. [Phys. Rev. Lett. 121, 037204 (2018); Phys. Rev. B 105, 155151 (2022)] corresponds to considering individual magnetic moments in each orbital in the leading-order approximation in the non-local correlations. We consider a more general approach and apply it to evaluate the effective magnetic parameters of iron and nickel. We show that the analysis, based on the inverse orbital-summed susceptibilities, yields reasonable results for both, weak and strong magnets. For iron we find, in the low-temperature limit, the exchange interaction $J_0\simeq 0.20$ eV, while for nickel we obtain $J_0\simeq 1.2$ eV. The considered method also allows one to describe the spin-wave dispersion at temperatures $T\sim T_C$, which is in agreement with the experimental data.

Commensurate and spiral magnetic order in the doped two-dimensional Hubbard model: Dynamical mean-field theory analysis

We develop a dynamical mean-field theory approach for the spiral magnetic order, changing to a local coordinate frame with preferable spin alignment along the $z$-axis, which can be considered with the impurity solvers treating the spin diagonal local Green's function. We furthermore solve the Bethe-Salpeter equations for nonuniform dynamic magnetic susceptibilities in the local coordinate frame. We apply this approach to describe the evolution of magnetic order with doping in the $t-t'$ Hubbard model with $t'=0.15$, which is appropriate for the description of the doped La$_2$CuO$_4$ high-temperature superconductor. We find that with doping the antiferromagnetic order changes to the $(Q,\pi)$ incommensurate one, and then to the paramagnetic phase. The spectral weight at the Fermi level is suppressed near half filling and continuously increases with doping. The dispersion of holes in the antiferromagnetic phase shows qualitative agreement with the results of the $t$-$J$ model consideration. In the incommensurate phase we find two branches of hole dispersions, one of which crosses the Fermi level. The resulting Fermi surface forms hole pockets. We also consider the dispersion of the magnetic excitations, obtained from the non-local dynamic magnetic susceptibilities. The transverse spin excitations are gapless, fulfilling the Goldstone theorem; in contrast to the mean-field approach the obtained magnetic state is found to be stable. The longitudinal excitations are characterized by a small gap, showing the rigidity of the spin excitations. For realistic hopping and interaction parameters we reproduce the experimentally measured spin-wave dispersion of La$_2$CuO$_4$.

Spin density wave, charge density wave, and bond disproportionation wave instabilities in hole-doped infinite-layer RNiO2

Using \emph{ab initio} band structure methods and DFT+dynamical mean-field theory approach we explore the possible formation of spin and charge stripes in the Ni-O plane of hole-doped infinite-layer nickelates, $R$NiO$_2$. Our results reveal a remarkable instability of the $C$-type $(110)$ spin state with undistorted lattice towards the formation of the spin-density, charge- and bond-disproportionation stripe phases accompanied by in-plane``breathing''-like distortions of the crystal structure. Our work gives a comprehensive picture of competing charge and spin stripe states, with possible frustration of different stripe patterns upon doping. It suggests that the spin and charge stripe state likely arises from strong magnetic correlations (with concomitant lattice distortions), which play a key role for understanding the anomalous properties of hole-doped layered nickelates.

Kondo entanglement in the quasi-two-dimensional heavy fermion compound CeSb2

In the heavy fermion system, development of the Kondo coherence usually occurs as a crossover behavior. However, accurate definition of the onset temperature for complete formation of the heavy quasiparticles is to some extent controversial. Here, the electronic structure of the quasi-two-dimensional Kondo lattice ${\mathrm{CeSb}}_{2}$ has been studied by high resolution angle-resolved photoemission spectroscopy (ARPES) and dynamical mean-field theory approach combined with density functional theory. A heavy quasiparticle band, which originates from the hybridization between $f$ electrons and conduction electrons, has been observed directly. Moreover, temperature-dependent electronic structure study reveals a transition from high-temperature local spins to low-temperature itinerant electrons in ${\mathrm{CeSb}}_{2}$ and the onset temperature of the hybridized c-f spectral weight revealed by laser-ARPES is consistent with the crossover temperature from transport and magnetic measurements. Our findings are essential for a microscopic understanding of different energy scales in the heavy fermion system and demonstrate the probability of laser-ARPES in studying the bulk 4f-electron properties of Ce-based compounds.

Electronic structure of rare-earth mononitrides: quasiatomic excitations and semiconducting bands

The electronic structure of the rare-earth mononitrides LnN (where Ln = rare-earth), which are promising materials for future spintronics applications, is difficult to resolve experimentally due to a strong influence of defects on their transport and optical properties. At the same time, LnN are challenging for theory, since wide semiconducting 2p and 5d bands need to be described simultaneously with strongly correlated 4f states. Here, we calculate the many-body spectral functions and optical gaps of a series of LnN (with Ln = Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er) by a density-functional + dynamical mean-field theory (DFT + DMFT) approach treating the correlated Ln 4f shells within the quasi-atomic Hubbard-I approximation. The on-site Coulomb interaction in the 4f shell is evaluated by a constrained DFT + Hubbard-I approach. Furthermore, to improve the treatment of semiconducting bands in DFT + DMFT, we employ the modified Becke–Johnson semilocal exchange potential. Focusing on the paramagnetic high-temperature phase, we find that all investigated LnN are pd semiconductors with gap values ranging from 1.02 to 2.14 eV along the series. The pd band gap is direct for light Ln = La…Sm and becomes indirect for heavy rare-earths. Despite a pronounced evolution of the Ln 4f states along the series, empty 4f states are invariably found above the bottom of the 5d conduction band. The calculated spectra agree well with those available from x-ray photoemission, x-ray emission and x-ray absorption measurements.

Unified Green's function approach for spectral and thermodynamic properties from algorithmic inversion of dynamical potentials

Dynamical potentials appear in many advanced electronic-structure methods, including self-energies from many-body perturbation theory, dynamical mean-field theory, electronic-transport formulations, and many embedding approaches. Here, we propose a novel treatment for the frequency dependence, introducing an algorithmic inversion method that can be applied to dynamical potentials expanded as sum over poles. This approach allows for an exact solution of Dyson-like equations at all frequencies via a mapping to a matrix diagonalization, and provides simultaneously frequency-dependent (spectral) and frequency-integrated (thermodynamic) properties of the Dyson-inverted propagators. The transformation to a sum over poles is performed introducing $n$-th order generalized Lorentzians as an improved basis set to represent the spectral function of a propagator, and using analytic expressions to recover the sum-over-poles form. Numerical results for the homogeneous electron gas at the $G_0W_0$ level are provided to argue for the accuracy and efficiency of such unified approach.

Combining semilocal exchange with dynamical mean-field theory: Electronic structure and optical response of rare-earth sesquioxides

In rare-earth semiconductors, wide ligand $p$ and rare-earth 5$d$ bands coexist with localized, partially filled 4$f$ shells. A simultaneous description for both extended and localized states represents a significant challenge for first-principles theories. Here, we combine an {\it ab initio} dynamical mean-field theory approach to strong local correlations with a perturbative application of the semi-local modified Becke-Johnson exchange potential to correct the semiconducting gap. We apply this method to calculate the electronic structure and optical response of the light rare-earth sesquioxides RE$_2$O$_3$ (RE= La, Ce, Pr and Nd). Our calculations correctly capture a non-trivial evolution of the optical gap in RE$_2$O$_3$ due to a progressive lowering of the 4$f$ states along the series and their multiplet structure. 2$p$ $-$ 4$f$ hybridization is found to induce a substantial upward shift for the occupied 4$f$ states occurring within the $p-d$ gap, thus reducing the magnitude of the optical gap. We show that a characteristic plateau observed in the optical conductivity in the Pr and Nd sequioxides right above their absorption edge is a fingerprint of 4$f$ states located within the $p-d$ gap.

Calculating dynamical mean-field theory forces in ab initio ultrasoft pseudopotential formalism

In this paper, we show how to calculate analytical atomic forces within self-consistent density functional theory + dynamical mean-field theory (DFT+DMFT) approach in the case when ultra-soft or norm-conserving pseudopotentials are used. We show how to treat the non-local projection terms arising within the pseudopotential formalism and circumvent the problem of non-orthogonality of the Kohn-Sham eigenvectors. Our approach is, in principle, independent of the DMFT solver employed, and here was tested with the Hubbard I solver. We benchmark our formalism by comparing against the forces calculated in Ce$_{2}$O$_{3}$ and PrO$_2$ by numerical differentiation of the total free energy, as well as by comparing the energy profiles against the numerically integrated analytical forces.

Electronic structure and magnetic properties of the effective spin Jeff=12 two-dimensional triangular lattice K3Yb(VO4)2

We report the structural, magnetic, specific heat, and electronic structure studies of the material ${\mathrm{K}}_{3}\mathrm{Yb}{({\mathrm{VO}}_{4})}_{2}$, which has two-dimensional triangular layers constituted by rare-earth magnetic ${\mathrm{Yb}}^{3+}$ ions. Magnetic susceptibility data show the absence of magnetic long-range order down to $0.5\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. No bifurcation is observed between zero-field-cooled and field-cooled magnetic susceptibility data, ruling out the possibility of spin-glassiness down to $0.5\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. From the fit to magnetic susceptibility data with Curie-Weiss law in the low-temperature region, the observed Curie-Weiss temperature $(\ensuremath{\theta}{}_{\mathrm{CW}})$ is about $\ensuremath{-}1\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, implying an antiferromagnetic coupling between the ${\mathrm{Yb}}^{3+}$ ions. Magnetic field-dependent specific heat fits well with two-level Schottky behavior. The analysis of magnetization and specific heat data confirms that the ${\mathrm{Yb}}^{3+}$ ion hosts the effective spin ${J}_{\mathrm{eff}}=1/2$ state. To provide a microscopic understanding of the ground state nature of the titled material, we carried out state-of-the-art first-principles calculations based on density functional theory $+$ Hubbard U and density functional theory $+$ dynamical mean-field theory approaches. Our calculations reveal that the system belongs to the novel class of spin-orbit driven Mott Hubbard insulators and possesses large in-plane magnetocrystalline anisotropy.

Magnetic superexchange couplings in Sr2IrO4

We investigate the magnetic couplings in ${\mathrm{Sr}}_{2}{\mathrm{IrO}}_{4}$ in the Mott-insulating picture, combining density-functional theory, dynamical mean-field theory, and many-body perturbation theory. We first determine the form of the ${j}_{\mathrm{eff}}=1/2$ pseudospin via the local-density-approximation $+$ dynamical mean-field theory approach. Next we study the magnetic interactions in the strong-to-intermediate coupling regime. To this end, we calculate the superexchange pseudospin tensors ${\mathrm{\ensuremath{\Gamma}}}_{1}, {\mathrm{\ensuremath{\Gamma}}}_{2}$, and ${\mathrm{\ensuremath{\Gamma}}}_{3}$ up to fourth order and analyze their dependence on the screened Coulomb interaction integrals $U$ and $J$. We show that, due to term cancellations, the experimental nearest-neighbor coupling ${\mathrm{\ensuremath{\Gamma}}}_{1}$ is reasonably well reproduced for a whole range of realistic $(U,J)$ values. We show that increasing the Hund's rule coupling $J$ (within the window of realistic values) can lead to large fourth-order contributions, which could explain the ferromagnetic next-nearest-neighbor coupling ${\mathrm{\ensuremath{\Gamma}}}_{2}$ extracted from the spin-wave dispersion. This regime is characterized by a sizable ring exchange $K$. For $(U,J)$ values that yield a Mott insulator with a half-filled ${j}_{\mathrm{eff}}=1/2$ state, however, fourth-order terms remain minor even if the gap is small. For no realistic parameters, we find a sizable next-next-nearest-neighbor coupling ${\mathrm{\ensuremath{\Gamma}}}_{3}\ensuremath{\sim}|{\mathrm{\ensuremath{\Gamma}}}_{2}|$. Possible implications are discussed.

Effect of lattice strain on the electronic structure and magnetic correlations in infinite-layer (Nd,Sr)NiO2

We report a theoretical study of the effect of electron-electron interactions and Sr doping on the electronic structure of infinite-layer (Nd,Sr)NiO2 using the DFT+dynamical mean-field theory approach (DFT+DMFT). Here, we explore the effect of lattice strain that experience (Nd,Sr)NiO2 films upon growing on the SrTiO3 substrate on the electronic properties, magnetic correlations, and exchange couplings of (Nd,Sr)NiO2. For both strained and unstrained Sr-doped NdNiO2 our results reveal the crucial importance of orbital-dependent correlation effects in the Ni 3d shell. Upon doping with Sr, it undergoes a Lifshitz transition which is accompanied by a reconstruction of magnetic correlations. For Sr x < 0.2 (Nd,Sr)NiO2 adopts the Néel (111) antiferromagnetic (AFM) order, while for x > 0.3 the C-type (110) AFM sets in the unstrained (Nd,Sr)NiO2, with a highly frustrated region at x ≃ 0.2, all within DFT+DMFT at T = 290 K. Our results for the Néel AFM at Sr x = 0 suggest that AFM NdNiO2 appears at the verge of a Mott-Hubbard transition, providing a plausible explanation for the experimentally observed weakly insulating behavior of NdNiO2 for Sr x < 0.1. We observe that the Lifshitz transition makes a change of the band structure character from electron- to hole-like with Sr x, in agreement with recent experiments. We conclude that the in-plane strain adjusts a bandwidth of the Ni x2−y2 band, i.e., controls the effect of electron correlations in the Ni x2−y2 orbitals. It leads to a suppression of the static C-type (110) ordering in (Nd,Sr)NiO2 for Sr x > 0.3. Our results for the electronic structure and magnetic correlations of (Nd,Sr)NiO2 reveal an anomalous sensitivity upon a change of the crystal structure parameters.

Correlated electronic structure and optical response of rare-earth based semiconductors

The coexistence of Mott localized $f$ states with wide conduction and valence bands in $f$-electron semiconductors results, quite generically, in a complex optical response with the nature of the absorption edge difficult to resolve both experimentally and theoretically. Here, we combine a dynamical mean-field theory approach to localized $4f$ shells with an improved description of band gaps by a semilocal exchange-correlation potential to calculate the optical properties of the light rare-earth fluorosulfides $Ln\mathrm{SF}$ ($Ln=\mathrm{Pr}$, Nd, Sm, Gd) from first principles. In agreement with experiment, we find the absorption edge in SmSF to stem from $\mathrm{S}\text{\ensuremath{-}}3p$ to $\mathrm{Sm}\text{\ensuremath{-}}4f$ transitions, while the Gd compound behaves as an ordinary $p\text{\ensuremath{-}}d$ gap semiconductor. In the unexplored PrSF and NdSF systems we predict a rather unique occurrence of strongly hybridized $4f\text{\ensuremath{-}}5d$ states at the bottom of the conduction band. The nature of the absorption edge results in a characteristic anisotropy of the optical conductivity in each system, which may be used as a fingerprint of the relative energetic positions of different states.

Photo-emission signatures of coherence breakdown in Kondo alloys: dynamical mean-field theory approach

We study the Kondo alloy model on a square lattice using dynamical mean-field theory for Kondo substitution and disorder effects, together with static mean-field approximations. We computed and analyzed photoemission properties as a function of electronic filling n c , Kondo impurity concentration x, and strength of Kondo temperature T K. We provide a complete description of the angle resolved photoemission spectroscopy (ARPES) signals expected in the paramagnetic (PM) Kondo phases. By analyzing the Fermi surface (FS), we observe the Lifshitz-like transition predicted previously for strong T K at x = n c and we discuss the evolution of the dispersion from the dense coherent to the dilute Kondo regimes. At smaller T K, we find that this transition marking the breakdown of coherence at x = n c becomes a crossover. However, we identify another transition at a smaller concentration x ⋆ where the effective mass continuously vanishes. x ⋆ separates the one-branch and the two-branches ARPES dispersions characterizing respectively dilute and dense Kondo PM regimes. The x − T K phase diagrams are also described, suggesting that the transition at x ⋆ might be experimentally observable since magnetically ordered phases are stabilized at much lower T K. FS reconstructions in antiferromagnetic and ferromagnetic phases are also discussed.

Ab Initio Full Cell GW+DMFT for Correlated Materials

Quantitative prediction of electronic properties in correlated materials requires simulations without empirical truncations and parameters. We present a method to achieve this goal through a new ab initio formulation of dynamical mean-field theory (DMFT). Instead of using small impurities defined in a low-energy subspace, which require complicated downfolded interactions which are often approximated, we describe a full cell $GW$+DMFT approach, where the impurities comprise all atoms in a unit cell or supercell of the crystal. Our formulation results in large impurity problems, which we treat here with efficient quantum chemistry impurity solvers that work on the real-frequency axis, combined with a one-shot $G_0W_0$ treatment of long-range interactions. We apply our full cell approach to bulk Si, two antiferromagnetic correlated insulators NiO and $\alpha$-Fe$_2$O$_3$, and the paramagnetic correlated metal SrMoO$_3$, with impurities containing up to 10 atoms and 124 orbitals. We find that spectral properties, magnetic moments, and two-particle spin correlation functions are obtained in good agreement with experiments. In addition, in the metal oxide insulators, the balanced treatment of correlations involving all orbitals in the cell leads to new insights into the orbital character around the insulating gap.

DMFTwDFT: An open-source code combining Dynamical Mean Field Theory with various density functional theory packages

Dynamical Mean Field Theory (DMFT) is a successful method to compute the electronic structure of strongly correlated materials, especially when it is combined with density functional theory (DFT). Here, we present an open-source computational package (and a library) combining DMFT with various DFT codes interfaced through the Wannier90 package. The correlated subspace is expanded as a linear combination of Wannier functions introduced in the DMFT approach as local orbitals. In particular, we provide a library mode for computing the DMFT density matrix. This library can be linked and then internally called from any DFT package, assuming that a set of localized orbitals can be generated in the correlated subspace. The existence of this library allows developers of other DFT codes to interface with our package and achieve the charge-self-consistency within DFT+DMFT loops. To test and check our implementation, we computed the density of states and the band structure of well-known solid-state correlated materials, namely LaNiO3, SrVO3, and NiO. The obtained results are compared to those obtained from other DFT+DMFT implementations. Program summaryProgram title: DMFTwDFTCPC Library link to program files:https://doi.org/10.17632/y27fngtkdw.1Licensing provisions: GNU General Public License 3Programming language: Python2/3, C++, and FORTRANExternal routines: MPI, FFTW, BLAS, LAPACK, Numpy, Scipy, mpi4py, Glib, gsl, weave, PyProcar, and PyChemiaSubprograms used: Wannier90 (v3.0), Siesta (v4.1-b4), VASP (v5.4.4), Quantum Espresso (v6.5), CTQMCNature of problem: Need for a simple, efficient, higher-level, and open-source package to study strongly correlated materials interfacing to various DFT codes regardless of basis sets used in DFT.Solution method: We present an open-source Python code which can be easily interfaced with Wannier90 and different DFT packages and perform a full charge-self-consistent DFT+DMFT calculation using a modern continuous-time quantum Monte Carlo (CTQMC) impurity solver.

Extended Falicov–Kimball model: Hartree–Fock vs DMFT approach

In this work, we study the extended Falicov–Kimball model at half-filling within the Hartree–Fock approach (HFA) (for various crystal lattices) and compare the results obtained with the rigorous ones derived within the dynamical mean field theory (DMFT). The model describes a system, where electrons with spin-↓ are itinerant (with hopping amplitude t), whereas those with spin-↑ are localized. The particles interact via on-site U and intersite V density–density Coulomb interactions. We show that the HFA description of the ground state properties of the model is equivalent to the exact DMFT solution and provides a qualitatively correct picture also for a range of small temperatures. It does capture the discontinuous transition between ordered phases at U = 2V for small temperatures as well as correct features of the continuous order–disorder transition. However, the HFA predicts that the discontinuous boundary ends at the isolated-critical point (of the liquid-gas type) and it does not merge with the continuous boundary. This approach cannot also describe properly a change of order of the continuous transition for large V as well as various metal–insulator transitions found within the DMFT.