The peculiar correlation effects on the triangular lattice are studied by means of the rotationally invariant slave boson method in a cellular cluster approach. Hence nonlocal correlations are included in a short-range regime. Their impact for the single-band Hubbard model is studied at half filling, i.e., on the Mott transition, and with doping. Using the realistic band structure of Na$_x$CoO$_2$, we may also shed light on the cobaltate physics for $x$$\ge$1/3, with the in-plane transition from antiferromagnetic tendencies towards the onset of ferromagnetism for a finite Hubbard $U$.
We study the interplay between correlation, itinerant ferromagnetism and local moment formation on the electron doped triangular lattice of sodium cobaltates Na$_x$CoO$_2$. We find that strong correlation renormalizes the Stoner criterion and stabilizes the paramagnetic state for $x<x_c\simeq0.67$. For $x>x_c$, ferromagnetic (FM) order emerges. The enhanced Na dopant potential fluctuations play a crucial role in the sodium rich phases and lead to an inhomogeneous FM state, exhibiting nonmagnetic Co$^{3+}$ patches, antiferromagnetic (AF) correlated regions, and FM clusters with AF domains. Hole…
Puzzling properties of sodium cobaltates Na${}_x$CoO${}_2$ become an issue of numerous recent theoretical and experimental investigations because of very high thermopower and intricate phase diagram of this material. Experiments indicated Na${}_{2/3}$CoO${}_2$ to have a kagome-like cobalt sublattice, which implies additional complexity of this strongly correlated system. In the present work we have employed the ab-initio GGA+U modeling method to investigate spin states of Na${}_{2/3}$CoO${}_2$, using an exact crystal cell established in the experiment. Stability of sodium imprint for concentra…
Temperature-driven sodium-ion dynamical-to-static crossover in the zig-zag ordered phase of Na$_{0.5}$CoO$_2$
Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院人工结构与量子控制教育部重点实验室）；School of Physical Science and Technology, Lanzhou University（兰州大学物理科学与技术学院）；International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院物质科学量子创新中心）；Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所北京凝聚态物理国家实验室）
The triangular lattice compound TlYbS$_2$ was prepared as large single crystals via a molten flux growth technique using sodium chloride. Anisotropic magnetic susceptibility measurements down to 0.4 K indicate a complete absence of long-range magnetic order. Despite this lack of long-range order, short-range antiferromagnetic interactions are evidenced through broad transitions, suggesting frustrated behavior. Variable magnetic field measurements reveal metamagnetic behavior at temperatures less than 2 K. Complex low temperature field-tunable magnetic behavior, in addition to no observable lon…
In this study, we synthesized single crystals of Na$_{x}$CoO$_{2}$ with $x\sim0.8$ using the optical floating zone technique. A thorough electrochemical treatment of the samples permitted us to control the de-intercalation of Na to obtain single crystal samples of stable Na ordered phases with $x=0.5-0.8$. Comparisons of the bulk magnetic properties with those observed in the Na ordered powder samples confirmed the high quality of these single crystal phases. The ab plane resistivity was measured for the Na ordered samples and it was quite reproducible for different sample batches. The data we…
The sodium cobaltate system Na$_{x}$CoO$_2$ is a prominent representant of strongly correlated materials with promising thermoelectric response. In a combined theoretical and experimental study we show that by doping the Co site of the compound at $x$=0.7 with iron, a further increase of the Seebeck coefficient is achieved. The Fe defects give rise to effective hole doping in the high-thermopower region of larger sodium content $x$. Originally filled hole pockets in the angular-resolved spectral function of the Fe-free material shift to low energy when introducing Fe, leading to a multi-sheet …
We have grown single crystals of Na$_x$Ca$_y$CoO$_2$ and determined their superstructures as a function of composition using neutron and x-ray diffraction. Inclusion of Ca$^{2+}$ stabilises a single superstructure across a wide range of temperatures and concentrations. The superstructure in the Na$^+$ layers is based on arrays of divacancy clusters with Ca$^{2+}$ ions occupying the central site, and it has an ideal concentration Na$_{4/7}$Ca$_{1/7}$CoO$_2$. Previous measurements of the thermoelectric properties on this system are discussed in light of this superstructure. Na$_{4/7}$Ca$_{1/7}$C…
Engineered $Na_{0.75}CoO_2$ is considered a prime candidate to achieve high-efficiency thermoelectric systems to regenerate electricity from waste heat. In this work, three elements with outmost electronic configurations, (1) an open d shell (Ni), (2) a closed d shell (Zn), and (3) a half filled f shell (Eu) with maximum unpaired electrons, were selected to outline the dopants' effects on electronic and crystallographic structures of $Na_{0.75}CoO_2$. Systematic $ab$ $initio$ density functional calculations with $DMOL^3$ package showed that the Ni and Zn were more stable when substituting Co w…
Using large-scale dynamical cluster quantum Monte Carlo simulations, we explore the unconventional superconductivity in the hole-doped Hubbard model on the triangular lattice. Due to the interplay of electronic correlations, geometric frustration, and Fermi surface topology, we find a doubly degenerate singlet pairing state at an interaction strength close to the bare bandwidth. Such an unconventional superconducting state is mediated by antiferromagnetic spin fluctuations along the $Γ$-$K$ direction, where the Fermi surface is nested. An exact decomposition of the irreducible particle-particl…
We unambiguously demonstrate, based on high-energy x-ray diffraction data and LDA calculations, that sodium-density stripes are formed in Na0.75CoO2 at low temperatures and rule out the previously proposed Na-ordering models. The LDA calculations prove, that the sodium-density stripes lead to a sizeable dip in the density of the Co-states at the Fermi level, pointing to band structure effects as a driving force for the stripe formation. This indicates that the sodium ordering is connected to stripe-like charge correlations within the CoO2 layers, leading to an astonishing similarity between th…
We present a combination of thermodynamic and dynamic experimental signatures of a disorder driven dynamic cooperative paramagnet in a 50% site diluted triangular lattice spin-1/2 system, Y$_2$CuTiO$_6$. Magnetic ordering and spin freezing are absent down to 50 mK, far below the Curie Weiss scale of ~-134 K. We observe scaling collapses of the magnetic field- and temperature-dependent magnetic heat capacity and magnetisation data, respectively, in conformity with expectations from the random singlet physics. Our experiments establish the suppression of any freezing scale, if at all present, by…
Recently the unusual metallic state with a substantially non-uniform distribution of a charge and mag\-ne\-tic density in CoO$_2$ planes was found experimentally in the Na$_x$CoO$_2$ compound with $x>0.6$. We have investigated an origin of such electron disproportionation in the lamellar sodium cobaltates by calculating the ion states as a function of a strength of the electron correlations in the $d$(Co)-shells within the GGA+U approximation for the system with a realistic crystal structure. It was found that the nonuniformity of spin and charge densities are induced by an ordering of the sod…
The electronic state in layered cobalt oxides with hexagonal structure is examined. We find that the electronic structure reflects the nature of the Kagomé lattice hidden in the CoO_2 layer which consists of stacked triangular lattices of oxygen ions and of cobalt ions. A fundamental model for the electron system is proposed and the mechanism of the unique transport and magnetic properties of the cobalt oxides are discussed in the light of the model.
We investigate the electronic states of the CoO_2 plane in the layered cobalt oxides Na_{0.5}CoO_{2} using the realistic 11 band d-p model on a two-dimensional triangular lattice. Effects of the Coulomb interaction on a Co site: the intra- and inter-orbital direct terms U and U', the exchange coupling J and the pair-transfer J', are treated within the Hartree-Fock approximation. It is found that the metallic antiferromagnetism takes place below T_{c1} and, in addition, the orbital order accompanied by the small charge order takes place below T_{c2} (< T_{c1}) where the system becomes insulator…
We report the first 17-O NMR studies of a triangular-lattice superconductor Na{1/3}CoO{2}-[4/3]H{2}O and the host material Na{x}CoO{2} (x=0.35 and 0.72). Knight shift measurements reveal that p-d hybridization induces sizable spin polarization in the O triangular-lattice layers. Water-intercalation makes CoO{2} planes homogeneous, and enhances low frequency spin fluctuations near T{c}=4.5 K at some finite wave-vectors different from both the ferromagnetic and ``120 degree'' modes.
Exchange bias (EB) refers to a shift of the hysteresis loop along the field axis in materials consisting of ferromagnetic (FM) and antiferromagnetic (AFM) layers, generally after a cooling procedure in high magnetic field. This effect is highly desirable for technological applications ranging from spintronics to magnetic recording. Achieving giant EB effect near room temperature in a small cooling field is thus an on-going technologically relevant challenge for the materials science community. In this work, we present the experimental realization of such a fundamental goal by demonstrating the…
The metal-insulator transition of the quarter-filled Hubbard model on triangular lattice is studied at the mean field level. We find a quasi-one dimensional metallic state with a collinear magnetic order competes closely with an insulating state with a non-coplanar magnetic order for both signs of the hopping integral $t$. In the strong correlation regime($U/|t|\gg1$), it is found that the metal-insulator transition of the system occurs in a two-step manner. The quasi-one dimensional metallic state with collinear magnetic order is found to be stable in an intermediate temperature region betwee…
Single crystals of sodium cobaltates Na$_{x}$CoO$_{2}$ with $x \approx 0.8$ were grown by the floating zone technique. Using electrochemical Na de-intercalation method we reduced the sodium content in the as-grown crystals down to pure phase with 22 K Néel temperature and $x \approx 0.77$. The $^{59}$Co NMR study in the paramagnetic state of the $T_{N}=22$ K phase permitted us to evidence that at least 6 Co sites are differentiated. They could be separated by their magnetic behaviour into three types: a single site with cobalt close to non-magnetic Co$^{3+}$, two sites with the most magnetic c…
A 59Co NMR study of CoO2, the x=0 end member of AxCoO2 (A = Na, Li...) cobaltates, reveals a metallic ground state, though with clear signs of strong electron correlations: low-energy spin fluctuations develop at wave vectors q different from 0 and a crossover to a Fermi-liquid regime occurs below a characteristic temperature T*~7 K. Despite some uncertainty over the exact cobalt oxidation state n this material, the results show that electronic correlations are revealed as x is reduced below 0.3. The data are consistent with NaxCoO2 being close to the Mott transition in the x -> 0 limit.
Synchrotron X-ray diffraction investigations of two single crystals of Na_xCoO_2 from different batches with composition x = 0.525-0.530 reveal homogeneous incommensurate sodium ordering with propagation vector (0.53 0.53 0) at room-temperature. The incommensurate (qq0) superstructure exists between 220 K and 430 K. The value of q varies between q = 0.514 and 0.529, showing a broad plateau at the latter value between 260 K and 360 K. On cooling, unusual reversible phase segregation into two volume fractions is observed. Below 220 K, one volume fraction shows the well-known commensurate orthorh…
We probed the local electronic properties of the mixed-valent Co(+4-x) triangular-lattice in Na{x}CoO{2}-yH{2}O by 59-Co NMR. We observed two distinct types of Co sites for x>=1/2, but the valence seems averaged out for x~1/3. Local spin fluctuations exhibit qualitatively the same trend down to ~100 K regardless of the carrier-concentration x, and hence the nature of the electronic ground state. A canonical Fermi-liquid behavior emerges below ~100 K only for x~1/3.
We report the finding of time-reversal-symmetry-breaking $d_{x^2-y^2}+ id_{xy}$ superconducting ground state in the slave-boson mean-field theory for the t-J model on triangular lattice. For $t/J=-5$ ($t/J=-9$) pairing exists for $x < 13%$ ($x<8%$) upon electron doping, and $x <56%$ ($x<13%$) upon hole doping. These results are potentially relevant to doped Mott insulators Na$_x$CoO$_2$.yH$_2$O and Na$_{1-x}$TiO$_2$.
The nature of electronic states due to strong correlation and geometric frustration on the triangular lattice is investigated in connection to the unconventional insulating state of Na$_x$CoO$_2$ at $x=0.5$. We study an extended Hubbard model using a spatially unrestricted Gutzwiller approximation. We find a new class of charge and spin ordered states at $x=1/3$ and $x=0.5$ where antiferromagnetic (AF) frustration is alleviated via weak charge inhomogeneity. At $x=0.5$, we show that the $\sqrt{3}a\times2a$ off-plane Na dopant order induces weak $\sqrt{3}a\times1a$ charge order in the Co layer.…
The determination by powder neutron diffraction of the ambient temperature crystal structures of compounds in the NaxCoO2 family, for 0.3 < x <= 1.0, is reported. The structures consist of triangular CoO2 layers with Na ions distributed in intervening charge reservoir layers. The shapes of the CoO6 octahedra that make up the CoO2 layers are found to be critically dependent on the electron count and on the distribution of the Na ions in the intervening layers, where two types of Na sites are available. Correlation of the shapes of cobalt-oxygen octahedra, the Na ion positions, and the electroni…
We systematically study Raman spectroscopy of cleaved Na$_x$CoO$_2$ single crystals with 0.37 $\leq$ x $\leq$ 0.80. The Raman shift of A$_{1g}$ mode is found to be linearly dependent on Na content, while the Raman shift of E$_{1g}$ mode has an abnormal shift to high frequency around x = 0.5. The abnormal shift is ascribed to the occurrence of Na rearrangement in O1 structure. Temperature dependent Raman spectrum for x = 0.56 sample shows that Na rearrangement transition from O1 structure to H1 structure occurs around 240 K. Electronic transport and susceptibility for the sample with $x=0.56$ s…
We show that geometric frustration and strong correlation in the triangular lattice Hubbard model lead a rich and novel phase structure of $\sqrt{3}\times\sqrt{3}$ spin-charge textured electronic states over a wide region of electron doping $0\le x \le 0.40$. In addition to the 120$^\circ$ Néel ordered insulator at half-filling, we found a novel spin-charge ordered insulator at $x=1/3$ with collinear antiferromagnetic (AF) order on the underlying unfrustrated honeycomb lattice. Separating the two insulating phases is a Lifshitz transition between a noncollinear AF ordered metal and one with co…
Within the t-J model we study several experimentally accessible properties of the 2D-triangular lattice system Na$_x$CoO$_2$, using a numerically exact canonical ensemble study of 12 to 18 site triangular toroidal clusters as well as the icosahedron. Focusing on the doping regime of $x\sim0.7$, we study the temperature dependent chemical potential, specific heat, magnetic susceptibility and the dynamic Hall coefficient $R_H(T,ω)$ as well as the magnetic field dependent thermopower. We find a crossover between two phases near $x \sim 0.75$ in susceptibility and field suppression of the thermopo…
We have synthesized and characterized different stable phases of sodium cobaltates Na$_{x}$CoO$_{2}$ with sodium content $0.65<x<0.80$. We demonstrate that $^{23}$Na NMR allows to determine the difference in the susceptibility of the phases and reveals the presence of Na order in each phase. $^{59}$Co NMR experiments give clear evidence that Co charge disproportionation is a dominant feature of Na cobaltates. Only a small fraction ($\approx$ 25%) of cobalts are in a non-magnetic Co$^{3+}$ charge state whereas electrons delocalize on the other cobalts. The magnetic and charge properties of the …
Motivated by the recent discovery of superconductivity in two dimensional CoO$_2$ layers, we present some possibly useful results of the RVB mean field theory applied to the triangular lattice. Away from half filling, the order parameter is found to be complex, and yields a fully gapped quasiparticle spectrum. The sign of the hopping plays a crucial role in the analysis, and we find that superconductivity is as fragile for one sign as it is robust for the other. Na$_x$CoO$_2\cdot y$H$_2$O is argued to belong to the robust case, by comparing the LDA Fermi surface with an effective tight binding…
NiGa$_2$S$_4$ is a triangular lattice S=1 system with strong two-dimensionality of the lattice, actively discussed as a candidate to host spin-nematic order brought about by strong quadrupole coupling. Using Raman scattering spectroscopy we identify a phonon of E$_g$ symmetry which can modulate magnetic exchange $J_1$ and produce quadrupole coupling. Additionally, our Raman scattering results demonstrate a loss of local inversion symmetry on cooling, which we associate with sulfur vacancies. This will lead to disordered Dzyaloshinskii-Moriya interactions, which can prevent long range magnetic …
We show that finite angular momentum pairing chiral superconductors on the triangular lattice have point zeroes in the complex gap function. A topological quantum phase transition takes place through a nodal superconducting state at a specific carrier density $x_c$ where the normal state Fermi surface crosses the isolated zeros. For spin singlet pairing, we show that the second nearest neighbor $d+id$-wave pairing can be the dominant pairing channel. The gapless critical state at $x_c\simeq0.25$ has six Dirac points and is topologically nontrivial with a $T^3$ spin relaxation rate below $T_c$.…
Stimulated by the recent finding of Na$_{0.35}$CoO$_2$.1.3H$_2$O superconductor, we investigate superconducting instabilities on a 2D triangular lattice in the repulsive Hubbard model. Using the third-order perturbation expansion with respect to the on-site repulsion $U$, we evaluate the linearized Dyson-Gor'kov equation. We find that an $f$-wave spin-triplet pairing is the most stable in a wide range of the next nearest neighbor hopping integral $t'$ and an electron number density $n$. The introduction of $t'$ is crucial to adjust the van Hove singularities to the neighborhood of the Fermi su…
We present a finite temperature ($T$) study of the t-J model on the two-dimensional triangular lattice for the negative hopping $t$, as relevant for the electron-doped Na$_x$CoO$_2$ (NCO). To understand several aspects of this system, we study the $T$-dependent chemical potential, specific heat, magnetic susceptibility, and the dynamic Hall-coefficient across the entire doping range. We show systematically, how this simplest model for strongly correlated electrons describes a crossover as function of doping ($x$) from a Pauli-like weakly spin-correlated metal close to the band-limit (density $…
We synthesized a quasi-two-dimensional distorted triangular lattice antiferromagnet Ca$_3$CoNb$_2$O$_9$, in which the effective spin of Co$^{2+}$ is 1/2 at low temperatures, whose magnetic properties were studied by dc susceptibility and magnetization techniques. The x-ray diffraction confirms the quality of our powder samples. The large Weiss constant $θ_{CW}\sim$ $-55$ K and the low Neel temperature($T_N\sim$ 1.45 K) give a frustration factor $f$ ($=\midθ_{CW}/T_N \mid$) $\approx$ 38, suggesting that Ca$_3$CoNb$_2$O$_9$ resides in strong frustration regime. Slightly below $T_N$, deviation be…
The CoO$_{2}$ layers in sodium-cobaltates Na$_{x}$CoO$_{2}$ may be viewed as a spin $S=1/2$ triangular-lattice doped with charge carriers. The underlying physics of the cobaltates is very similar to that of the high $T_{c}$ cuprates. We will present unequivocal $^{59}$Co NMR evidence that below $T_{CO}\sim51 K$, the insulating ground state of the itinerant antiferromagnet Na$_{0.5}$CoO$_{2}$ ($T_{N}\sim 86 K$) is induced by charge ordering.
The nonstoichiometric NaxCoO2 system exhibits extraordinary physical properties that correlate with temperature and Na concentration in its layered lattice without evident long-range structure modification when conventional crystallographic techniques are applied. For instance, Na0.7CoO2, a thermodynamically stable phase, shows large thermoelectric power; water-intercalated Na0.33CoO2.1.3H2O is a newly discovered superconductor with Tc ~ 4K, and Na0.5CoO2 exhibits an unexpected charge ordering transition at around Tco ~ 55 K. Recent studies suggest that the transport and magnetic properties in…
A linear spin-wave approach, a variational method and exact diagonlization are used to investigate the magnetic long-range order (LRO) of the spin-1/2 Heisenberg antiferromagnet on a two-dimensional 1/7-depleted triangular (maple leaf) lattice consisting of triangles and hexagons only. This lattice has z=5 nearest neighbors and its coordination number z is therefore between those of the triangular (z=6) and the kagome (z=4) lattices. Calculating spin-spin correlations, sublattice magnetization, spin stiffness, spin-wave velocity and spin gap we find that the classical 6-sublattice LRO is stron…
We study the spin dynamics of t-J model on triangular lattice in the Slave-Boson-RPA scheme in light of the newly discovered superconductor Na$_{x}$CoO$_{2}$. We find resonant peak in the dynamic spin susceptibility in the $d+id^{^{\prime}}$-wave superconducting state for both hole and electron doping in large doping range. We find the geometrical frustration inherent of the triangular lattice provide us a unique opportunity to discriminate the SO(5) and RPA-like intepretation of the origin of the resonant peak.
The electronic state in a CoO_2 plane of the layered cobalt oxides Na_{x}CoO_2 is investigated by using the 11 band d-p model on a two-dimensional triangular lattice, where the tight-binding parameters are determined so as to fit the LDA band structure. Effects of the Coulomb interaction at a Co site: the intra- and inter-orbital direct terms U and U', the exchange coupling J and the pair-transfer J', are treated within the Hartree-Fock approximation. We also consider the effect of the Na order at x=0.5, where Na ions form one dimensional chains, by taking into account of an effective one-dime…
Emergent Gauge Flux and Spin Ordering in Magnetized Triangular Spin Liquids: Applications to Hofstadter-Hubbard Model
International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料中心）；Beijing Key Laboratory of Quantum Devices, Peking University（北京大学北京量子器件重点实验室）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）
Motivated by the absence of cooperative Jahn-Teller effect in LiNiO2 and BaVS3, two layered oxides with triangular planes, we study the SU(4) symmetric spin-orbital model on the triangular lattice. Upon reducing the next-nearest neighbour coupling, we show that the system undergoes a quantum phase transition to a liquid phase. A variational approach to this liquid phase shows that simple types of long-range correlations are suppressed, suggesting that it is stable against lattice distortions.
By performing experiment and model studies on a triangular-lattice dipolar magnet KBaGd(BO$_3$)$_2$ (KBGB), we find the highly frustrated magnet with a planar anisotropy hosts a strongly fluctuating dipolar spin liquid (DSL), which originates from the intriguing interplay between dipolar and Heisenberg interactions. The DSL constitutes an extended regime in the field-temperature phase diagram, which gets lowered in temperature as field increases and eventually ends with an unconventional quantum critical point (QCP) at $B_c\simeq 0.75$~T. Based on dipolar Heisenberg model calculations, we iden…
To investigate the possibility of charge order and superconductivity in a doped two-dimensional triangular lattice, we study the extended Hubbard model with variational Monte Carlo method. At n=2/3, a commensurate filling for a triangular lattice, it is shown that the nearest-neighbor Coulomb interaction V induces honeycomb-type charge order and antiferromagnetic spin order at U>10t. We also discuss the possibility of superconductivity induced by charge fluctuation and the relation to the superconductivity in Na_{0.35}CoO_{2}1.3H_{2}O and theta-type organic condoctors.
We propose that unconventional superconductivity in hydrated sodium cobaltate $Na_xCoO_2$ results from an interplay of electronic correlations and electron-phonon interactions. On the basis of the $t-V$ model plus phonons we found evidences for a) unconventional superconductivity, b) realistic values of $T_c$ and c) the dome shape existing near $x \sim 0.35$. This picture is obtained for $V$ close to the critical Coulomb repulsion $V_c$ which separates the uniform Fermi liquid from $\sqrt{3} \times \sqrt{3}$ CDW ordered phase.
The influence of electrostatic interactions on the ordering of sodium ions in Na$_x$CoO$_2$ is studied theoretically through Monte-Carlo simulations. For large $x$ small di- or tri-vacancy clusters are stable with respect to isolated Na vacancies. At commensurate fillings these small clusters order in triangular superstructures. These results agree with recent electron diffraction data at $x=1/2$ and 3/4. We have performed neutron Laüe diffraction experiments at higher $x$, which confirm the predictions of this simple model. The consequences on the properties of the electronic charges in the C…
We investigate the Hubbard model on the anisotropic triangular lattice as a suggested effective description of the Mott phase in various triangular organic compounds. Employing the variational cluster approximation and the ladder dual-fermion approach as complementary methods to adequately treat the zero-temperature and the finite-temperature domains, we obtain a consistent picture of the phase diagram as a function of anisotropy and interaction strength. The metal-insulator transition substantially depends on the anisotropy, and so does the nature of magnetism and the emergence of a nonmagnet…
Basic mechanisms controlling orbital order and orbital fluctuations in transition metal oxides are discussed. The lattice driven classical orbital picture, e.g. like in manganites LaMnO$_3$, is contrasted to the quantum behavior of orbitals in frustrated superexchange models as realised in pseudocubic titanites ATiO$_3$ and vanadates AVO$_3$. In YVO$_3$, the lattice and superexchange effects strongly compete -- this explains the extreme sensitivity of magnetic states to temperature and doping. Lifting the $t_{2g}$ orbital degeneracy by a relativistic spin-orbital coupling is considered on exam…
We uncover four new spin-charge ordered ground states in the strong coupling limit of the Kondo lattice model on triangular geometry. Two of the states at one-third electronic filling ($n=1/3$) consist of decorated ferromagnetic chains coupled antiferromagnetically with the neighboring chains. The third magnetic ground state is noncollinear, consisting of antiferromagnetic chains separated by a pair of canted ferromagnetic chains. An even more unusual magnetic ground state, a variant of the $120^{\circ}$ Yafet-Kittel phase, is discovered at $n=2/3$. These magnetic orders are stabilized by open…
Based on the ladder dual-fermion approach, we present a comprehensive study of the phases of the isotropic Hubbard model on the triangular lattice. We find a rich phase diagram containing most of the phases that have already been experimentally observed in systems where the interplay between geometric frustration and electronic correlations is important: paramagnetic metal, paramagnetic insulator, Mott-insulator with $120^{\circ}$ antiferromagnetic and a non-magnetic insulating state, i.e. possibly a spin liquid state. This establishes that the Hubbard model on frustrated lattices can serve as…
We obtain the electronic states and structures of two-dimensional cobalt oxides, Na$_{x}$CoO$_{2}$ (x=0, 0.35, 0.5 and 0.75) by utilizing the full-potential linear muffin-tin orbitals (FP-LMTO) methods, from which some essential electronic interaction parameters are estimated: the bare on-site Coulomb interaction of cobalt U$_{dd}$=7.5 eV renormalizes to 5 eV for x=0.35, the $pd$ hybridizations t$_{pdσ}$ and t$_{pdπ}$ are -1.40 and 0.70 eV, respectively. The density of states at E$_{F}$ decreases from 6-7 states/eV in the local density approximation (LDA) to about 1.0 states/eV in the LDA+U sc…
We investigate the excitation spectrum of strongly correlated sodium cobaltate within a realistic many-body description beyond dynamical mean-field theory (DMFT). At lower doping around $x$=0.3, rather close to Mott-critical half-filling, the single-particle spectral function of Na$_x$CoO$_2$ displays an upper Hubbard band which is captured within DMFT. Momentum-dependent self-energy effects beyond DMFT become dominant at higher doping. Around a doping level of $x\sim 0.67$, the incoherent excitations give way to finite-energy spin-polaron excitations in close agreement with optics experiments…
Neutron diffraction studies have been carried out in the temperature(T) range between 10 K and 130 K on a single crystal of YBaCo4O7, which has the stacking of kagome and triangular lattices of CoO4 tetrahedra along the c-axis. Structural transitions have been found at two temperatures Tc1~70 K and Tc2~105 K. With decreasing T, magnetic order appears along with the transition at Tc2, but it does not grow to an ideal long-range order even at the lowest T studied (~10 K). Two groups of magnetic diffuse reflections, which originate from the Co-moments of the kagome and triangular lattices, are ob…
Ag2MnO2 is studied as a possible candidate compound for an antiferromagnetic XY spin model on a triangular lattice. In spite of the large Curie-Weiss temperature of -430 K found in magnetic susceptibi-lity, Mn3+ spins with S = 2 do not undergo a conventional long-range order down to 2 K probably owing to the geometrical frustration and two dimensionality in the system. Instead, a unique phase transition is found at 80 K, where specific heat exhibits a clear sign of a second-order phase transition, while magnetic susceptibility changes smoothly without a distinct anomaly. We think that this tra…
The electronic structure of Na$_x$CoO$_2$ revealed by recent photoemission experiments shows important deviations from band theory predictions. The six small Fermi surface pockets predicted by LDA calculations have not been observed as the associated $e_g^\prime$ band fails to cross the Fermi level for a wide range of sodium doping concentration $x$. In addition, significant bandwidth renormalizations of the $t_{2g}$ complex have been observed. We show that these discrepancies are due to strong electronic correlations by studying the multi-orbital Hubbard model in the Hartree-Fock and strong-c…
The temporal magnetic correlations of the triangular lattice antiferromagnet NiGa$_2$S$_4$ are examined through thirteen decades ($10^{-13}-1$~sec) using ultra-high-resolution inelastic neutron scattering, muon spin relaxation, AC and nonlinear susceptibility measurements. Unlike the short-ranged {\it spatial} correlations, the temperature dependence of the {\it temporal} correlations show distinct anomalies. The spin fluctuation rate decreases precipitously upon cooling towards $T^{\ast}=8.5$~K, but fluctuations on the microsecond time scale then persist in an anomalous dynamical regime for 4…
Motivated by experiments on the layered compounds $κ$-(BEDT-TTF)$_2$X, Cs$_2$CuCl$_4$, and very recently Na$_x$CoO$_2 \cdot y$H$_2$O, we present a weak-coupling functional renormalization-group analysis of the Hubbard model on the anisotropic triangular lattice. As the model interpolates between the nearest-neighbor square lattice and decoupled chains via the isotropic triangular lattice, it permits the study of competition between antiferromagnetic and BCS Cooper instabilities. We begin by reproducing known results for decoupled chains, and for the square lattice with only nearest-neighbor ho…
α-SrCr2O4 has a triangular planar lattice of d3 Cr3+ made from edge sharing CrO6 octahedra; the plane shows a very small orthorhombic distortion from hexagonal symmetry. With a Weiss temperature of -596 K and a three-dimensional magnetic ordering temperature of 43 K, the magnetic system is quasi two-dimensional and frustrated. Neutron powder diffraction shows that the ordered state is an incommensurate helical magnet, with an in-plane propagation vector of k = (0,0.3217(8),0). Temperature dependent synchrotron powder diffraction characterization of the structure shows an increase in the inter-…
Band structure of metallic sodium cobaltate Na$_x$CoO$_2$ ($x$=0.33, 0.48, 0.61 0.72) has been investigated by local density approximation+Hubbard $U$ (LDA+$U$) method and within Gutzwiller approximation for the Co-$t_{2g}$ manifold. Correlation effects being taken into account results in suppression of the $e'_g$ hole pockets at the Fermi surface in agreement with recent angle-resolved photo-emission spectroscopy (ARPES) experiments. In the Gutzwiller approximation the bilayer splitting is significantly reduced due to the correlation effects. The formation of high spin (HS) state in Co $d$-sh…
We propose a minimal model resolving a puzzle of enigmatic correlations observed in sodium-rich Na$_x$CoO$_2$ where one expects a simple, free motion of the dilute $S=1/2$ holes doped into a band insulator NaCoO$_2$. The model also predicts singlet superconductivity at experimentally observed compositions. The model is based on a key property of cobalt oxides -- the spin-state quasidegeneracy of CoO$_6$ octahedral complex -- leading to an unusual physics of, {\it e.g.}, LaCoO$_3$. We show that correlated hopping between $t_{2g}$ and $e_g$ states leads to the spin-polaron physics at $x\sim 1$, …
We study the $S = 1$ triangular lattice Ising antiferromagnet by Monte Carlo simulations. Frustrations between a major antiferromagnetic third-neighbor interaction $J_3$ and a minor ferromagnetic nearest-neighbor interaction $J_1$ cause incommensurate short-range orders at intermediate temperatures. At low temperatures (below $T/J_3 \lesssim 0.2$ for $J_1/J_3 = -1/3$), the system exhibits fourfold periodic ordered state. In the short-range order phase, the system shows a glassy two-step relaxation. We demonstrate that the features of the short-range order are attributed to the cooperation betw…
