arXiv subjects

A. A. Katanin

Publications and source records attributed to A. A. Katanin.

At least 37 records · Page 2Linked to original sources

arXiv2023

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.

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arXiv2023

Commensurate and incommensurate 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 $(Q,π)$ 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$_4$.

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arXiv2023

Ferromagnetic instability in itinerant fcc lattice electron systems with higher order van Hove singularities: Functional renormalization group study

We investigate the possibility of ferromagnetic ordering in the non-degenerate Hubbard model on the face-centered cubic lattice within the functional renormalization group technique using temperature as a scale parameter. We assume the relations between nearest, next-nearest, and next-next-nearest hopping parameters providing higher order (giant) van Hove singularity of the density of states. The ferromagnetic instability formation with lowering temperature is described consistently in the one-loop approximation for a one-particle irreducible vertex of two-particle electron interaction. The chemical potential versus temperature phase diagrams are calculated. We find ferromagnetic order only for sufficiently strong divergence of the density of states and fillings in the vicinity of van Hove singularity. The obtained Curie temperature is more than an order of magnitude smaller than the results of the random-phase approximation. The main origin of the suppression of ferromagnetism is the screening of interaction in the particle-particle channel. We also do not find the pronounced tendency towards incommensurate order when the Fermi level is moved away from a van Hove singularity, such that the first order quantum phase transitions from the ferro- to paramagnetic phase are obtained.

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arXiv2023

Transition from Pauli paramagnetism to Curie-Weiss behaviour in vanadium

We study electron correlations and their impact on magnetic properties of bcc vanadium by a combination of density functional and dynamical mean-field theory. The calculated uniform magnetic susceptibility {in bcc structure} is of Pauli type at low temperatures, while it obeys the Curie-Weiss law at higher temperatures. Thus, we qualitatively reproduce the experimental temperature dependence of magnetic susceptibility without introducing the martensitic phase transition. Our results for local spin-spin correlation function and local susceptibility reveal that the Curie-Weiss behavior appears due to partial formation of local magnetic moments, which originate from $t_{2g}$ states and occur due to local spin correlations caused by Hund's rule coupling. At the same time, the fermionic quasiparticles remain well-defined, while the formation of local moments is accompanied by a deviation from the Fermi-liquid behavior. In particular, the self-energy of the $t_{2g}$ states shows the non-analytic frequency dependence, which is a characteristic of the spin-freezing behavior, while the quasiparticle damping changes approximately linearly with temperature in the intermediate temperature range $200$--$700$~K. By analyzing the momentum dependence of static magnetic susceptibility, we find incommensurate magnetic correlations, which may provide a mechanism for unconventional superconductivity at low temperatures.

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arXiv2022

The effect of local magnetic moments on spectral properties and resistivity near the interaction- and doping induced Mott transitions

We study the effect of the formation and screening of local magnetic moments on the temperature- and interaction dependencies of spectral functions and resistivity in the vicinity of the metal-insulator transition. We use the dynamical mean-field theory for the strongly correlated Hubbard model and associate the peculiarities of the above mentioned properties with those found for the local charge $χ_c$ and spin $χ_s$ susceptibilities. We show that at half filling the maximum of resistivity at a certain temperature $T^*$ corresponds to the appearance of central quasiparticle peak of the spectral function and entering the metallic regime with well defined fermionic quasiparticles. At the same time, the temperature of the crossover to the regime with screening of local magnetic moments, determined by the minimum of double occupation, is smaller than the temperature scale $T^*$ and coincides at half filling with the boundary $T_{β=1}(U)$ corresponding to the exponent of resistivity $β\equiv d\ln ρ/d\ln T=1$. Away from half filling we find weak increase of the temperature of the beginning and completion of the screening (i.e. Kondo temperature) of local magnetic moments, while the unscreened local magnetic moments exist only up to few percents of doping. In the low temperature regime $T<T_{β=1}$ simultaneous presence of itinerant and localized degrees of freedom yields almost linear temperature dependence of scattering rate and resistivity.

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arXiv2022

Charge and spin correlations in insulating and incoherent metal states of twisted bilayer graphene

We study electronic, charge, and magnetic properties of twisted bilayer graphene with fillings $2\leq n\leq 6$ per moire unit cell within the recently introduced formulation of extended dynamical mean-field theory (E-DMFT) for two-sublattice systems. We use previously obtained hopping parameters between the states, described by Wannier functions, centered at the lattice spots of AB and BA stacking, and the long-range Coulomb interaction, obtained within cRPA analysis. We show that account of spin exchange between AB and BA nearest neighbour spots is crucial to introduce charge and spin correlations between these spots. Account of this exchange yields preferable concentration of electrons in the same valley, with the tendency of parallel spin alignment of electrons in AB and BA spots, in agreement with earlier results of the strong coupling analysis, suggested SU(2)$\times$SU(2) emergent spin-valley symmetry. The local spectral functions show almost gapped state at the fillings $n=2,4,6$, and incoherent metal state for the other fillings. We find that in both cases the local states of electrons have rather long lifetime. At the same time, the non-local charge- and spin susceptibilities, obtained within the ladder approximation, are peaked at incommensurate wave vectors, which implies that the above discussed ordering tendencies are characterised by an incommensurate pattern.

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arXiv2022

Coulomb correlations and magnetic properties of L1$_0$ FeCo: a DFT+DMFT study

We consider electronic correlation effects and their impact on magnetic properties of tetragonally distorted chemically ordered FeCo alloys (L1$_0$ structure) being a promising candidate for rare-earth-free permanent magnets. We employ a state-of-the-art method combining density functional and dynamical mean-field theory. According to our results, the predicted Curie temperature reduces with increase of lattice parameters ratio $c/a$ and reaches nearly 850 K at ${c/a=1.22}$. For all considered $c/a$ from 1 to $\sqrt{2}$, we find well-localized magnetic moments on Fe sites, which are formed due to strong correlations originating from Hund's coupling. At the same time, magnetism of Co sites is more itinerant with a much less lifetime of local magnetic moments. However, these short-lived local moments are also formed due to Hund's exchange. Electronic states at Fe sites are characterized by a non-quasiparticle form of self-energies, while the ones for Co sites are found to have a Fermi-liquid-like shape with quasiparticle mass enhancement factor ${m^*/m\sim 1.4}$, corresponding to moderately correlated metal. The strong electron correlations on Fe sites leading to Hund's metal behaviour can be explained by peculiarities of the density of states, which has pronounced peaks near the Fermi level, while weaker many-body effects on Co sites can be caused by stronger deviation from half-filling of their $3d$ states. The obtained momentum dependence of magnetic susceptibility suggests that the ferromagnetic ordering is the most favourable one except for the near vicinity of the fcc structure and the magnetic exchange is expected to be of RKKY type.

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arXiv2022

Local magnetic moment formation and Kondo screening in the half filled two dimensional single band Hubbard model

We study formation of local magnetic moments in strongly correlated Hubbard model within dynamical mean field theory and associate peculiarities of temperature dependence of local charge $χ_c$ and spin $χ_s$ susceptibilities with different stages of local moment formation. Local maximum of temperature dependence of the charge susceptibility $χ_c$ is associated with beginning of local magnetic moments formation, while the minimum of the susceptibility $χ_c$ and double occupation, as well as low temperature boundary of the plateau of effective local magnetic moment $μ_{\rm eff}^2=Tχ_s$ temperature dependence are connected with full formation of local moments. We also obtain interaction dependence of the Kondo temperature $T_K$, which is compared to the fingerprint criterion of Phys. Rev. Lett. 126, 056403 (2021). Near the Mott transition the two criteria coincide, while further away from Mott transition the fingerprint criterion somewhat overestimates Kondo temperature. The relation of the observed features to the behavior of eigenvectors/eigenvalues of fermionic frequency-resolved charge susceptibility and divergences of irreducible vertices is discussed.

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arXiv2021

Generalized dynamical mean-field theory of two-subalttice systems with non-local interactions and its application to study charge and spin correlations in graphene

We investigate magnetic and charge correlations in graphene by using the formulation of extended dynamical mean-field theory (E-DMFT) for two-sublattice systems. First, we map the average non-local interaction onto the effective static interaction between different sublattices, which is treated together with the local interaction within an effective "two-orbital" local model. The remaining part of the non-local interaction is considered by introducing an effective retarded interaction within the E-DMFT approach. The non-local susceptibilities in charge and spin channel are further evaluated in the ladder approximation. We verify the applicability of the proposed method to describe the effect of uniformly screened long-range Coulomb potential $\propto 1/r$, as well as screened realistic long-range electron interaction [T. O. Wehling et al., Phys. Rev. Lett. 106, 236805 (2011)] in graphene. We show that the developed approach describes a competition of semimetal, spin density wave (SDW), and charge-density-wave (CDW) correlations. The obtained phase diagram is in a good agreement with recent results of functional renormalization group (fRG) for finite large graphene nanoflakes and scaling analysis of quantum Monte Carlo data on finite clusters. Similarly to the previously obtained results within the fRG approach, the realistic screening of Coulomb interaction by $σ$ bands causes moderate (strong) enhancement of critical long-range interaction strength, needed for the SDW (CDW) instability, compared to the results for the uniformly screened Coulomb potential.

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arXiv2021

Magnetic, charge, and transport properties of graphene nanoflakes

We investigate magnetic, charge and transport properties of hexagonal graphene nanoflakes (GNFs) connected to two metallic leads by using the functional renormalization group (fRG) method. The interplay between the on-site and long-range interactions leads to a competition of semimetal (SM), spin density wave (SDW), and charge-density-wave (CDW) phases. The ground-state phase diagrams are presented for the GNF systems with screened realistic long-range electron interaction [T. O. Wehling, et. al., Phys. Rev. Lett. 106, 236805 (2011)], as well as uniformly screened long-range Coulomb potential $\propto 1/r$. We demonstrate that the realistic screening of Coulomb interaction by $σ$ bands causes moderate (strong) enhancement of critical long-range interaction strength, needed for the SDW (CDW) instability, compared to the results for the uniformly screened Coulomb potential. This enhancement gives rise to a wide region of stability of the SM phase for realistic interaction, such that freely suspended GNFs are far from both SM-SDW and SM-CDW phase-transition boundaries and correspond to the SM phase. Close relation between the linear conductance and the magnetic or charge states of the systems is discussed. A comparison of the results with those of other studies on GNFs systems and infinite graphene sheet is presented.

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arXiv2021

Itinerant magnetism of chromium under pressure: a DFT+DMFT study

We consider electronic and magnetic properties of chromium, a well-known itinerant antiferromagnet, by a combination of density functional theory (DFT) and dynamical mean-field theory (DMFT). We find that electronic correlation effects in chromium, in contrast to its neighbours in the periodic table, are weak, leading to the quasiparticle mass enhancement factor ${m^*/m \approx 1.2}$. Our results for local spin-spin correlation functions and distribution of weigths of atomic configurations indicate that the local magnetic moments are not formed. Similarly to previous results of DFT at ambient pressure, the non-uniform magnetic susceptibility as a function of momentum possesses close to the wave vector ${{\mathbf Q}_{\rm H}=(0,0,2π/a)}$ ($a$ is the lattice constant) sharp maxima, corresponding to Kohn anomalies. We find that these maxima are preserved by the interaction and are not destroyed by pressure. Our calculations qualitatively capture a decrease of the Néel temperature with pressure and a breakdown of itinerant antiferomagnetism at pressure of $\sim$9 GPa in agreement with experimental data, although the Néel temperature is significantly overestimated because of the mean-field nature of DMFT.

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arXiv2021

Extracting Kondo temperature of strongly-correlated systems from the inverse local magnetic susceptibility

The temperature scales of screening of local magnetic and orbital moments are important characteristics of strongly correlated substances. In a recent paper X. Deng et al. using dynamic mean-field theory (DMFT) have identified temperature scales of the onset of screening in orbital and spin channels in some correlated metals from the deviation of temperature dependence of local susceptibility from the Curie law. We argue that the scales obtained this way are in fact much larger, than the corresponding Kondo temperatures, and, therefore, do not characterize the screening process. By reanalyzing the results of this paper we find the characteristic (Kondo) temperatures for screening in the spin channel $T_K\approx 100$ K for V$_2$O$_3$ and $T_K\approx 350$ K for Sr$_2$RuO$_4$, which are almost an order of magnitude smaller than those for the onset of the screening estimated in the paper ($1000$ K and $2300$ K, respectively); for V$_2$O$_3$ the obtained temperature scale $T_K$ is therefore comparable to the temperature of completion of the screening, $T^{\rm comp}\sim 25$ K, which shows that the screening in this material can be described in terms of a single temperature scale.

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arXiv2021

The non-analytic momentum dependence of spin susceptibility of Heisenberg magnets in paramagnetic phase and its effect on critical exponents

We study momentum dependence of static magnetic susceptibility $χ(q)$ in paramagnetic phase of Heisenberg magnets and its relation to critical behavior within nonlinear sigma model (NLSM) at arbitrary dimension $2 5/2$. Using NLSM, we obtain the contribution of the"anomalous" term $ξ^{-2}f(qξ)$ to the critical exponent $ν$, comparing it to the contribution of the non-analytical dependence, originating from the critical exponent $η$ (the obtained critical exponents $ν$ and $η$ agree with previous studies). In the range $3\leq d<4$ we find that the former contribution dominates, and fully determines $1/N$ correction to the critical exponent $ν$ in the limit $d\rightarrow 4.$

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arXiv2020

Electronic correlations, spectral and magnetic properties of ZrZn$_2$

We present results of a theoretical study of a prototypical weak ferromagnet ZrZn$_2$. We use the density-functional theory (DFT)+dynamical mean-field theory (DMFT) method to study the electronic and local magnetic properties. The obtained DFT+DMFT electronic self-energies are Fermi-liquid like, indicating a small effective mass enhancement of the Zr $4d$ states $m^*/m\sim 1.1 - 1.3$ accompanied by partly formed local moments within the electronic states of $t_{2g}$ symmetry. The effect of electronic interaction is shown to be essential for determining the correct topology of some of the Fermi surface sheets. To study in detail the pressure dependence of the Curie temperature $T_{\rm C}$ and corresponding pressure-induced quantum phase transition, we consider an effective single-band model, constructed using the Zr $4d$ contribution to the total density of states. The model is studied within static and dynamic mean-field theory, as well as spin-fermion approach. We show that the spin-fermion approach yields the temperature dependence of susceptibility at ambient pressure and the pressure dependence $T_{\rm C}(p)$, including the first-order quantum phase transition at $p\approx 1.7$~GPa, comparable well with the experimental data.

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arXiv2020

Electronic correlation effects and local magnetic moments in L1$_0$ phase of FeNi

We study the electronic and magnetic properties of L1$_0$ phase of FeNi, a perspective rare-earth-free permanent magnet, by using a combination of density functional and dynamical mean-field theory. Although L1$_0$ FeNi has a slightly tetragonally distorted fcc lattice, we find that magnetic properties of its constituent Fe atoms resemble those in pure bcc Fe. In particular, our results indicate the presence of well-localized magnetic moments on Fe sites, which are formed due to Hund's exchange. At the same time, magnetism of Ni sites is much more itinerant. Similarly to pure bcc Fe, the self-energy of Fe $3d$ states is found to show the non-Fermi-liquid behavior. This can be explained by peculiarities of density of Fe $3d$ states, which has pronounced peaks near the Fermi level. Our study of local spin correlation function and momentum dependence of particle-hole bubble suggests that the magnetic exchange in this substance is expected to be of RKKY-type, with iron states providing local-moment contribution, and the states corresponding to nickel sites (including virtual hopping to iron sites) providing itinerant contribution.

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arXiv2019

Quantum criticality in the two-dimensional periodic Anderson model

We study the phase diagram and quantum critical region of one of the fundamental models for electronic correlations: the periodic Anderson model. Employing the recently developed dynamical vertex approximation, we find a phase transition between a zero-temperature antiferromagnetic insulator and a Kondo insulator. In the quantum critical region, we determine a critical exponent $γ\!=\!2$ for the antiferromagnetic susceptibility. At higher temperatures, we have free spins with $γ\!=\!1$ instead, whereas at lower temperatures, there is an even stronger increase and suppression of the susceptibility below and above the quantum critical point, respectively.

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arXiv2019

The (extended) dynamical mean field theory combined with the two-particle irreducible functional renormalization-group approach as a tool to study strongly-correlated systems

We propose new approach for treatment of local and non-local interactions in correlated electronic systems, which uses self-energy and the two-particle irreducible vertices, obtained from (extended) dynamical mean-field theory, as an input of two-particle irreducible functional renormalization-group (2PI-fRG) approach. Using 2PI-fRG approach allows us to treat both, local and non-local interactions. In case of purely local interaction the corresponding equations have similar (although not identical) structure to the earlier developed DMF$^2$RG approach. In a simplest truncation, neglecting scale-dependence of the two-particle irreducible vertices, we reproduce the results for the two-particle vertices/susceptibilities in the ladder approximation of the dual boson or D$Γ$A approach; in more sophisticated truncations the method allows us to consider non-local corrections to the self-energy, as well as the interplay of charge- and spin correlations. treatment of vertex renormalizations. The proposed scheme is tested on the two-dimensional standard and extended $U$-$V$ half-filled Hubbard models. For the standard Hubbard model we obtain non-local self-energy, which is in agreement with numerical studies; for the extended Hubbard model we obtain the boundary of charge instability, which agrees well with the results of the dual boson (DB) approach. We also find that the effect of spin correlations on electron interaction in the charge channel, not considered previously in the DB approach, only slightly reduces critical next-nearest-neighbor interaction of charge instability of the extended Hubbard model at the considered finite small temperature, yielding better agreement with dynamic cluster approximation. The considered method is rather general and can be applied to study various phenomena in strongly-correlated electronic systems.

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arXiv2019

Local magnetic moments and electronic transport in closed loop quantum dot systems: a case of quadruple quantum dot ring at and away from equilibrium

We apply the non-equilibrium functional renormalization group approach treating flow of the electronic self-energies, to describe local magnetic moments formation and electronic transport in a quadruple quantum dot (QQD) ring, coupled to leads, with moderate Coulomb interaction on the quantum dots. We find that at zero temperature depending on parameters of the QQD system the regimes with zero, one, or two almost local magnetic moments in the ring can be realized, and the results of the considered approach in equilibrium agree qualitatively with those of more sophisticated fRG approach treating also flow of the vertices. It is shown that the almost formed local magnetic moments, which exist in the equilibrium, remain stable in a wide range of bias voltages near equilibrium. The destruction of the local magnetic moments with increasing bias voltage is realized in one or two stages, depending on the parameters of the system; for two-stage process the intermediate phase possesses fractional magnetic moment. We present zero-temperature results for current-voltage dependences and differential conductances of the system, which exhibit sharp features at the transition points between different magnetic states. The occurrence of interaction induced negative differential conductance phenomenon is demonstrated and discussed. For one local moment in the ring and finite hopping between the opposite quantum dots, connected to the leads, we find suppression of the conductance for one of the spin projections in infinitesimally small magnetic field, which occurs due to destructive interference of different electron propagation paths and can be used in spintronic devices.

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