Conflicting interpretations of experimental data preclude the understanding of the quantum magnetic state of spin-orbit coupled d$^2$ double perovskites. Whether the ground state is a Janh-Teller-distorted order of quadrupoles or the hitherto elusive
octupolar order remains debated. We resolve this uncertainty through direct calculations of all-rank inter-site exchange interactions and inelastic neutron scattering (INS) cross-section for the d$^2$ double perovskite series Ba$_2M$OsO$_6$ ($M$= Ca, Mg, Zn). Using advanced many-body first principles methods we show that the ground state is formed by ferro-ordered octupoles coupled within the ground-stated $E_g$ doublet. Computed ordering temperature of the single second-order phase-transition and gapped excitation spectra are fully consistent with observations. Minuscule distortions of the parent cubic structure are shown to qualitatively modify the structure of magnetic excitations.
In this work we study the complex entanglement between spin interactions, electron correlation and Janh-Teller structural instabilities in the 5d$^1$ $J_{eff}=frac{3}{2}$ spin-orbit coupled double perovskite $rm Ba_2NaOsO_6$ using first principles ap
proaches. By combining non-collinear magnetic calculations with multipolar pseudospin Hamiltonian analysis and many-body techniques we elucidate the origin of the observed quadrupolar canted antifferomagnetic. We show that the non-collinear magnetic order originates from Jahn-Teller distortions due to the cooperation of Heisenberg exchange, quadrupolar spin-spin terms and both dipolar and multipolar Dzyaloshinskii-Moriya interactions. We find a strong competition between ferromagnetic and antiferromagnetic canted and collinear quadrupolar magnetic phases: the transition from one magnetic order to another can be controlled by the strength of the electronic correlation ($U$) and by the degree of Jahn-Teller distortions.
The nature of order in low-temperature phases of some materials is not directly seen by experiment. Such hidden orders (HO) may inspire decades of research to identify the mechanism underlying those exotic states of matter. In insulators, HO phases o
riginate in degenerate many-electron states on localized f or d shells that may harbor high-rank multipole moments. Coupled by inter-site exchange, those moments form a vast space of competing order parameters. Here, we show how the ground state order and magnetic excitations of a prototypical HO system, neptunium dioxide NpO$_2$, can be fully described by a low-energy Hamiltonian derived by a many-body ab initio force-theorem method. Superexchange interactions between the lowest crystal-field quadruplet of Np$^{4+}$ ions induce a primary non-collinear order of time-odd rank-5 (triakontadipolar) moments with a secondary quadrupole order preserving the cubic symmetry of NpO$_2$. Our study also reveals an unconventional multipolar exchange-striction mechanism behind the anomalous volume contraction of the NpO$_2$ HO phase.
We discuss the role of dynamical many-electron effects in the physics of iron and iron-rich solid alloys under applied pressure on the basis of recent ab initio studies employing the dynamical mean-field theory (DMFT). Electronic correlations in iron
in the moderate pressure range up to 60 GPa are discussed in the first section. DMFT-based methods predict an enhancement of electronic correlations at the pressure-induced transition from body-centered cubic (bcc) alpha-Fe to hexagonal close-packed (hcp) epsilon-Fe. In particular, the electronic effective mass, scattering rate and electron-electron contribution to the electrical resistivity undergo a step-wise increase at the transition point. One also finds a significant many-body correction to the epsilon-Fe equation of state, thus clarifying the origin of discrepancies between previous DFT studies and experiment. An electronic topological transition is predicted to be induced in epsilon-Fe by many-electron effects; its experimental signatures are analyzed. Next section focuses on the geophysically relevant pressure-temperature regime of the Earths inner core (EIC) corresponding to the extreme pressure of 360 GPa combined with temperatures up to 6000 K. The three iron allotropes (bcc, hcp and face-centered-cubic) previously proposed as possible stable phases at such conditions are found to exhibit qualitatively different many-electron effects as evidenced by a strongly non-Fermi-liquid metallic state of bcc-Fe and an almost perfect Fermi liquid in the case of hcp-Fe. A recent active discussion on the electronic state and transport properties of hcp-Fe at the EIC conditions is reviewed in details. We also discuss the impact of a Ni admixture, which is expected to be present in the core matter. We conclude by outlining some limitation of the present DMFT-based framework and perspective directions for further development.
The origin of non-collinear magnetic order in UO$_{2}$ is studied by an ab initio dynamical-mean-field-theory framework in conjunction with a linear-response approach for evaluating inter-site superexchange interactions between U 5$f^{2}$ shells. The
calculated quadrupole-quadruple superexchange interactions are found to unambiguously resolve the frustration of face-centered-cubic U sublattice toward stabilization of the experimentally observed non-collinear 3k-magnetic order. Therefore, the exotic 3k antiferromagnetic order in UO$_{2}$ can be accounted for by a purely electronic exchange mechanism acting in the undistorted cubic lattice structure. The quadrupolar short-range order above magnetic ordering temperature $T_N$ is found to qualitatively differ from the long-range order below $T_N$.
We show that the heavy-fermion compound CeCu2Si2 undergoes a transition between two regimes dominated by different crystal-field states. At low pressure P and low temperature T the Ce 4f electron resides in the atomic crystal-field ground state, whil
e at high P or T the electron occupancy and spectral weight is transferred to an excited crystal-field level that hybridizes more strongly with itinerant states. These findings result from first-principles dynamical-mean-field-theory calculations. We predict experimental signatures of this orbital transition in X-ray spectroscopy. The corresponding fluctuations may be responsible for the second high-pressure superconducting dome observed in this and similar materials.
We demonstrate that a theoretical framework fully incorporating intra-atomic correlations and multiplet structure of the localized 4f states is required in order to capture the essential physics of rare-earth semiconductors and semimetals. We focus i
n particular on the rare-earth semimetal erbium arsenide (ErAs), for which effective one-electron approaches fail to provide a consistent picture of both high and low-energy electronic states. We treat the many-body states of the Er 4f shell within an atomic approximation in the framework of dynamical mean-field theory. Our results for the magnetic-field dependence of the 4f local moment, the influence of multiplets on the photoemission spectrum, and the exchange splitting of the Fermi surface pockets as measured from Shubnikov-de Haas oscillations, are found to be in good agreement with experimental results.
