With octahedrally coordinated $t_{\rm 2g}$ orbitals which are active at filling $n=2$, the $\rm Sr_2CrO_4$ compound exhibits rich interplay of spin-orbital physics with tetragonal distortion induced crystal field tuning by external agent such as pressure. Considering both reversed and restored crystal field regimes, collective spin-orbital excitations are investigated in the antiferromagnetic state using the generalized self consistent + fluctuations approach including spin-orbit coupling (SOC). A transition is found from staggered to entangled orbital order at critical SOC value in the realistic regime. Behavior of the calculated energy scales of collective excitations with crystal field is in striking similarity to that of the transition temperatures with pressure as obtained from susceptibility and resistivity anomalies in high-pressure studies.
Excitonic magnetism involving superpositions of singlet and triplet states is expected to arise for two holes in strongly correlated and spin-orbit coupled $t_{2g}$ orbitals. However, uncontested material examples for its realization are rare. Applying the Variational Cluster Approach to the square lattice, we find conventional spin antiferromagnetism combined with orbital order at weak and excitonic order at strong spin-orbit coupling. We address the specific example of Ca$_2$RuO$_4$ using ab-initio modeling and conclude it to realize excitonic magnetism despite its pronounced orbital polariz…
The combination of Rashba spin-orbit coupling and electron correlations can induce unusual phenomena in the metallic interface between SrTiO$_3$ and LaAlO$_3$. We consider effects of Rashba spin-orbit coupling at this interface in the context of the recent observation of anisotropic magnetism. Firstly, we show how Rashba spin-orbit coupling in a system near a band-edge can account for the observed magnetic anisotropy. Secondly, we investigate the coupling between in-plane magnetic-moment anisotropy and nematicity in the form of an orbital imbalance between d$_{xz}$ / d$_{yz}$ orbitals. We esti…
The magnetic and electronic properties of Ba$_4$Ru$_3$O$_{10}$ were investigated by the ab-initio and model calculations. It is shown that nonmagnetic ground state of the one-third Ru$^{4+}$ ions is not due to the correlation effects. It is rather caused by the charge disproportionation between crystallographically different Ru and the molecular orbital formation in the Ru's trimer.
Orbital magnetization is known empirically to play an important role in several magnetic phenomena, such as permanent magnetism and ferromagnetic superconductivity. Within the recently developed ''modern theory of orbital magnetization'', theoretical insight has been gained into the nature of this often neglected contribution to magnetism, but is based on an underlying mean-field approximation. From this theory, a few treatments have emerged which also take into account correlations beyond the mean-field approximation. Here, we apply the scheme developed in a previous work [Phys. Rev. B ${\bf …
Quasi one-dimensional magnetism driven by unusual orbital ordering in CuSb2O6
基本上所有未掺杂的铜氧化物都表现出准平面的四重Cu-O配位，负责磁活性反键3d-（x^2-y^2）-like态。在这里，我们提出了一个电子结构的CuSb 2 O 6的研究，显示，相反，一个半满的3d-（3z^2-r^2）轨道。这种迄今为止未观察到的基态起源于格形内和格形外轨道的竞争，其中强烈的库仑排斥驱动了令人惊讶的和独特的轨道排序。这反过来又引起了意想不到的准一维磁行为。我们的结果提供了一个一致的解释最近的衍射和中子衍射测量。
The local magnetism induced by vacancies in the presence of the spin-orbital interaction is investigated based on the half-filled Kane-Mele-Hubbard model on the honeycomb lattice. Using the self-consistent mean-field theory, we find that the spin-orbital coupling will enhance the localization of the spin moments near a single vacancy. We further study the magnetic structures along the zigzag edges formed by a chain of vacancies. We find that the spin-orbital coupling tends to suppress the counter-polarized ferrimagnetic order on the upper and lower edges, because of the open of the spin-orbita…
For the past decades, the low-temperature phase of Ca$_3$Ru$_2$O$_7$ below the 48K first-order phase transition remains a puzzle with controversial suggestions involving metallic ferroelectric, orbital or magnetic ordering. Through analysis of experimental lattice structure, density functional theory calculation, and effective model analysis, we propose that the 48K phase transition is a bond formation transition promoted by the magnetism mediated orbital re-polarization. Most interestingly, this transition is accompanied by a switch of \textit{two} metallic ferroelectric orders from a $xy+y$ …
The electronic and magnetic properties of Ba$_5$AlIr$_2$O$_{11}$ containing Ir-Ir dimers are investigated using the GGA and GGA+SOC calculations. We found that strong suppression of the magnetic moment in this compound recently found in [J. Terzic {\it et al.}, Phys. Rev. B {\bf 91}, 235147 (2015)] is not due to charge-ordering, but is related to the joint effect of the spin-orbit interaction and strong covalency, resulting in the formation of metal-metal bonds. They conspire and act against the intra-atomic Hund's rule exchange interaction to reduce total magnetic moment of the dimer. We argu…
We have used a combination of resonant magnetic x-ray scattering (RMXS) and x-ray absorption spectroscopy (XAS) to investigate the properties of the doped spin-orbital Mott insulator Sr2Ir(1-x)Rh(x)O4 (0.07 < x < 0.70). We show that Sr2Ir(1-x)Rh(x)O4 represents a unique model system for the study of dilute magnetism in the presence of strong spin-orbit coupling, and provide evidence of a doping-induced change in magnetic structure and a suppression of magnetic order at x_c ~ 0.17. We demonstrate that Rh-doping introduces Rh3+/Ir5+ ions which effectively hole-dope this material. We propose that…
Magnons, as the most elementary excitations of magnetic materials, have recently emerged as a prominent tool in electrical and thermal manipulation and transport of spin, and magnonics as a field is considered as one of the pillars of modern spintronics. On the other hand, orbitronics, which exploits the orbital degree of freedom of electrons rather than their spin, emerges as a powerful platform in efficient design of currents and redistribution of angular momentum in structurally complex materials. Here, we uncover a way to bridge the worlds of magnonics and electronic orbital magnetism, whi…
We have studied Ir spin and orbital magnetic moments in the double perovskites La$_{2-x}$Sr$_x$CoIrO$_6$ by x-ray magnetic circular dichroism. In La$_2$CoIrO$_6$, Ir$^{4+}$ couples antiferromagnetically to the weak ferromagnetic moment of the canted Co$^{2+}$ sublattice and shows an unusually large negative total magnetic moment (-0.38\,$μ_{\text B}$/f.u.) combined with strong spin-orbit interaction. In contrast, in Sr$_2$CoIrO$_6$, Ir$^{5+}$ has a paramagnetic moment with almost no orbital contribution. A simple kinetic-energy-driven mechanism including spin-orbit coupling explains why Ir is …
The magnetic structure of Ca$_2$MnReO$_6$ double perovskite is investigated by neutron powder diffraction and bulk magnetization, showing dominant non-collinear Mn magnetic moments [$4.35(7)$ $μ_B$] that are orthogonally aligned with the small Re moments [$0.22(4)$ $μ_B$]. $Ab$-initio electronic structure calculations show that the strong spin-orbit coupling for Re $5d$ electrons combined with a relatively modest on-site Coulomb repulsion ($U_{eff}^{Re} \gtrsim 0.6$ eV) is sufficient to render this material insulating. This is a rare example of spin-orbit assisted Mott insulator outside the re…
We investigate the evolution of magnetic properties as a function of hydrogen doping in iron based superconductor LaFeAsO$_{1-x}$H$_x$ using the dynamical mean-field theory combined with the density-functional theory. We find that two independent consequences of the doping, the increase of the electron occupation and the structural modification, have the opposite effects on the strength of electron correlation and magnetism, resulting in the minimum of the calculated magnetic moment around the intermediate doping level as a function of $x$. Our result provides a natural explanation for the puz…
We derive the effective heat current density operator for the strong-coupling regime of Mott insulators. Similarly to the case of the electric current density, the leading contribution to this effective operator is proportional to the local scalar spin chirality $\hatχ_{jkl}= \mathbf{S}_l\cdot\left(\mathbf{S}_j\times \mathbf{S}_k\right)$. This common form of the effective heat and electric current density operators leads to a novel cross response in Mott insulators. A heat current induces a distribution of orbital magnetic moments in systems containing loops of an odd number of hopping terms. …
Strongly interacting phonons and orbital excitations are observed in the same energy range for CuSb$_2$O$_6$, unlocking a so-far unexplored type of electron-phonon interaction. An orbital wave at $\sim 550$ cm$^{-1}$ softens on warming and strongly interferes with a phonon at $\sim 500$ cm$^{-1}$, giving rise to a merged excitation of mixed character. An electronic continuum grows on warming to the orbital ordering temperature $T_{OO}$=400 K, generating an important phonon decay channel. This direct and simultaneous observation of orbital and vibrational excitations reveals details of their co…
We study magnetism on the fcc lattice with tetragonal distortions, with general exotic directional magnetic interactions allowed by symmetry. We consider two models, corresponding to a uniform tetragonal distortion, or a two-sublattice model with a tetragonal screw axis. We establish their low temperature phase diagrams in the semi-classical limit using classical optimization and consideration of fluctuations both analytically and by Monte Carlo simulation. Both order by disorder and exchange anisotropy mechanisms favor a $\langle 110\rangle$ easy axis for magnetization. We also show that spin…
The strain tuned magnetism of YTiO$_3$ film grown on the LaAlO$_3$ ($110$) substrate is studied by the method of the first principles, and compared with that of the ($001$)-oriented one. The obtained magnetism is totally different, which is ferromagnetic for the film on the ($110$) substrate but A-type antiferromagnetic on the ($001$) one. This orientation-dependent magnetism is attributed to the subtle orbital ordering of YTiO$_3$ film. The $d_{xz}$/$d_{yz}$-type orbital ordering is predominant for the ($001$) one, but for the ($110$) case, the $d_{xy}$ orbital is mostly occupied plus a few c…
We study the interplay between spin-orbit coupling (SOC) and Coulomb repulsion in a Hubbard model on a decorated honeycomb lattice which leads to a plethora of phases. While a quantum spin hall insulator is stable at weak Coulomb repulsion and moderate SOC, a semimetallic phase emerges at large SOC in a broad range of Coulomb repulsion. This semimetallic phase has topological properties not observed in conventional metals such as a finite, non-quantized spin Hall conductivity. At large Coulomb repulsion and negligible spin-orbit coupling, electronic correlations stabilize a resonance valence b…
The orbital effect on the anomalous magnetism and evolution of low La-doping single crystals, La$_x$Y$_{1-x}$VO$_{3}$ (x = 0, 0.1, and 0.2), has been investigated by applying the X-ray diffraction, specific heat, magnetization and Raman scattering techniques. The larger nearest-neighbor (NN) exchange interaction along c-axis stabilizes the fluctuant G-type orbital ordering (G-OO) which favors the exotic C-type antiferromagnetic order (C-AF). It is found that the NN exchange interaction in ab plane is anisotropy relating to the in plane magnetic anisotropy, which becomes smaller in high La-dope…
Carnegie Mellon University（卡内基梅隆大学）；Harvard-Smithsonian Center for Astrophysics（哈佛-史密森天体物理中心）；Harvard University（哈佛大学）；Delft University of Technology（代尔夫特理工大学）
Using density functional calculations, we demonstrate that the spin-orbit coupling (SOC) of the Ir4+ ion plays an essential role in determining the antiferromagnetism of the hexagonal spin-chain system Sr3MIrO6 (M = Ni, Co) by tuning the crystal-field level sequence and altering the Ir-M inter-orbital interactions. The SOC splits the e'_{g} doublet of the octahedral Ir4+ ion (t_{2g}^5) in a trigonal crystal field, and the single t_{2g} hole resides on the e'_{g} upper branch and gives rise to the antiferromagnetic superexchange. In absence of the SOC, however, the single t_{2g} hole would occu…
Motivated by the recent angle-resolved photoemission spectroscopy (ARPES) on FeSe and iron pnictide families of iron-based superconductors, we have studied the orbital nematic order and its interplay with antiferromagnetism within the two-orbital Hubbard model. We used random phase approximation (RPA) to calculate the dependence of the orbital and magnetic susceptibilities on the strength of interactions and electron density (doping). To account for strong electron correlations not captured by RPA, we further employed non-perturbative variational cluster approximation (VCA) capable of capturin…
Study of the combined effects of strong electronic correlations with spin-orbit coupling (SOC) represents a central issue in quantum materials research. Predicting emergent properties represents a huge theoretical problem since the presence of SOC implies that the spin is not a good quantum number. Existing theories propose the emergence of a multitude of exotic quantum phases, distinguishable by either local point symmetry breaking or local spin expectation values, even in materials with simple cubic crystal structure such as Ba$_2$NaOsO$_6$. Experimental tests of such theories by local probe…
Single-crystal x-ray diffraction studies with synchrotron radiation on the honeycomb iridate $α$-Li$_{2}$IrO$_{3}$ reveal a pressure-induced structural phase transition with symmetry lowering from monoclinic to triclinic at a critical pressure of $P_{c}$ = 3.8 GPa. According to the evolution of the lattice parameters with pressure, the transition mainly affects the $ab$ plane and thereby the Ir hexagon network, leading to the formation of Ir--Ir dimers. These observations are independently predicted and corroborated by our \textit{ab initio} density functional theory calculations where we find…
We employ a combination of density functional theory and dynamical mean-field theory to investigate the electronic structure of the recently synthesized insulator BaCrO$_3$. Our calculations show that Hund's coupling is responsible for strong correlation effects, which are however not sufficient to turn the system insulating. A finite Jahn-Teller distortion lifting the orbital degeneracy is necessary to stabilize an insulating state with orbital ordering and consequent magnetic ordering.
Quantum magnets with spin $J=2$, which arise in spin-orbit coupled Mott insulators, can potentially display multipolar orders. We carry out an exact diagonalization study of a simple octahedral crystal field Hamiltonian for two electrons, incorporating spin-orbit coupling (SOC) and interactions, finding that either explicitly including the $e_g$ orbitals, or going beyond the rotationally invariant Coulomb interaction within the $t_{2g}$ sector, causes a degeneracy breaking of the $J\!=\!2$ level degeneracy. This can lead to a low-lying non-Kramers doublet carrying quadrupolar and octupolar mom…
We discuss the thermodynamic and magnetic properties of a competing high-spin/low-spin two-orbital two-electron model on a square-lattice possibly relevant to the nickelates such as Ba$_2$NiO$_2$(AgSe)$_2$ (BNOAS). We focus on parameter regimes where a high-spin ($S=1$) and a low-spin ($S=0$) state are energetically close to each other and discuss various exchange processes in such a system. The model we study is a variant of, but different from the Kondo-necklace model proposed for the system by Jin et al (H. S. Jin, W. E. Pickett and K. W. Lee, Phys. Rev. Research 2, 033197 (2020)). Although…
Intensive studies of the interplay between spin-orbit coupling (SOC) and electronic correlations in transition metal compounds have recently been undertaken. In particular, $j_{\rm eff}$ = 1/2 bands on a honeycomb lattice provide a pathway to realize Kitaev's exactly solvable spin model. However, since current wisdom requires strong atomic SOC to make $j_{\rm eff}=1/2$ bands, studies have been limited to iridium oxides. Contrary to this expectation, we demonstrate how Kitaev interactions arise in 4$d$-orbital honeycomb $α$-RuCl$_3$, despite having significantly weaker SOC than the iridium oxid…
Based on density functional calculations, we report on the orbital order and microscopic magnetic model of FeNCN, a prototype compound for orbital-only models. Despite having a similar energy scale, the spin and orbital degrees of freedom in FeNCN are only weakly coupled. The ground-state configuration features the doubly occupied d_{3z^2-r^2} (a1g) orbital and four singly-occupied d orbitals resulting in the spin S=2 on the Fe+2 atoms, whereas alternative (Eg') configurations are about 75 meV/f.u. higher in energy. Calculated exchange couplings and band gap are in good agreement with the avai…
We explore the relative strengths of spin orbit coupling and crystal field splitting in the Ir5+ compounds Ba2-xSrxYIrO6. In the case of strong spin orbit coupling and regular Ir5+ octahedra, one expects a nonmagnetic J = 0 state; in the case of distorted octahedra where crystal field effects dominate, the t2g manifold splits into a magnetic ground state. We report the results of continuously transitioning from the cubic Ba2YIrO6 double perovskite with ideal octahedra to the monoclinic Sr2YIrO6 double perovskite with distorted octahedra. We see no emergence of an enhanced Ir5+ magnetic moment …
We present a microscopic theory that shows the importance of spin-orbit coupling in perovskite compounds with heavy ions. In BiFeO3 (BFO) the spin-orbit coupling at the bismuth ion sites results in a special kind of magnetic anisotropy that is linear in the applied E-field. This interaction can convert the cycloid ground state into a homogeneous antiferromagnet, with a weak ferromagnetic moment whose orientation can be controlled by the E-field direction. Remarkably, the E-field control of magnetism occurs without poling the ferroelectric moment, providing a pathway for reduced energy dissipat…
An intriguing idea of spin-orbit Mott insulator has been proposed to explain magnetic insulating behavior in various iridates. This scenario relies on the strength of the spin-orbit coupling being comparable to electronic correlations, and it is not a priori obvious whether this picture is valid for all iridates. In particular, Sr3Ir2O7 exhibits a small charge gap and magnetic moment compared to Sr2IrO4, questioning the validity of such hypothesis. To understand the microscopic mechanism for magnetism in Sr3Ir2O7, we construct a tight binding model taking into account the full t2g- orbitals, t…
The electronic structure and magnetism of Sr$_2$CeIrO$_6$, an Ir-based double perovskite system has been investigated using first-principles calculations. We found that a strong spin-orbit coupling dictate the electronic and magnetic properties of this system. A small value of $U$ along with SOC could open up a gap at the Fermi level, offering the possibility of novel J$_{eff}$ = 1/2 Mott quantum state. Our calculations reveal that the magnetic ground state is antiferromagnetic in agreement with the magnetization data and provide the value of spin and orbital moment for this system which is in…
I study the electronic structure and magnetism of postperovskite CaIrO$_3$ using first-principles calculations. The density functional calculations within the local density approximation without the combined effect of spin-orbit coupling and on-site Coulomb repulsion show the system to be metallic, which is in disagreement with the recent experimental evidences that show CaIrO$_3$ to be an antiferromagnetic Mott insulator in the $J_\textrm{eff}$ = 1/2 state. However, when spin-orbit coupling is taken into account, the Ir $t_{2g}$ bands split into fully filled $J_\textrm{eff}$ = 3/2 bands and h…
We have carried out a detailed first-principles study of a d$^{4.5}$ quaternary iridate Ba$_3$YIr$_2$O$_9$ both in its 6H-perovskite-type ambient pressure (AP) phase and also for the high pressure (HP) cubic phase. Our analysis reveals that the AP phase belongs to the intermediate spin-orbit coupling (SOC) regime. This is further supported by the identification of the spin moment as the primary order parameter (POP) obtained from a magnetic multipolar analysis. The large $t_{2g}$ band width renormalizes the strength of SOC and the Ir intersite exchange interaction dominates resulting in long r…
We study the orbitally frustrated singlet-triplet models that emerge in the context of spin-orbit coupled Mott insulators with $t_{2g}^4$ electronic configuration. In these compounds, low-energy magnetic degrees of freedom can be cast in terms of three-flavor "triplon" operators describing the transitions between spin-orbit entangled $J=0$ ionic ground state and excited $J=1$ levels. In contrast to a conventional, flavor-isotropic O(3) singlet-triplet models, spin-orbit entangled triplon interactions are flavor-and-bond selective and thus highly frustrated. In a honeycomb lattice, we find clos…
We performed spin-polarized density functional calculations of lanthanide-series (Ln) iron oxypnictides LnFeAsO (Ln=La, Ce, Pr, Nd, Sm, and Gd) with constrained Fe magnetic moments, finding that in-plane dxy and out-of-plane dyz orbital characters are preferred for small Fe magnetic moments. Comparison of LnFeAsO compounds shows that the antiferromagnetism (AFM) from the Fe dxy orbital is itinerantly driven by orbital-dependent Fermi-surface nesting while AFM from the Fe dyz orbital is driven by superexchange mechanism. The Fe magnetic moments of the two orbital characters show different coupl…
To understand the rich electronic phase diagram in FeSe under pressure that vividly demonstrates the strong interplay between the nematicity, magnetism and superconductivity, we analyze the electronic states by including the higher-order many-body effects called the vertex correction (VC). We predict the pressure-induced emergence of xy-orbital hole-pocket based on the first-principles analysis. Due to this pressure-induced Lifshitz transition, the spin fluctuations on the xy orbital are enhanced, whereas those on xz,yz orbitals are gradually reduced. For this reason, nonmagnetic orbital order…
Recently synthesised Ba4NbMn3O12 belong to cluster magnets - systems with tightly bound groups of magnetism ions, in this case Mn3 trimers. Often such magnetic clusters can be described by molecular orbitals (MO), however strong electron correlations may invalidate this description. To understand the electronic and magnetic state of Ba4NbMn3O12 we carried out ab initio calculations and show that this system is better described not in MO picture, but as a system with electrons localized on the Mn ions, with strong intra-cluster and weaker inter-cluster exchange. The calculated spin of the Mn3 t…
