Charge ordering in Ir dimers in the ground state of Ba$_5$AlIr$_2$O$_{11}$
Vamshi M. Katukuri, Xingye Lu, D. E. McNally, Marcus Dantz, Vladimir N. Strocov, M. Moretti Sala, M. H. Upton, J. Terzic, G. Cao, Oleg V. Yazyev, Thorsten Schmitt
It has been well established experimentally that the interplay of electronic correlations and spin-orbit interactions in Ir$^{4+}$ and Ir$^{5+}$ oxides results in insulating J$_{\rm eff}$=1/2 and J$_{\rm eff}$=0 ground states, respectively. However, in compounds where the structural dimerization of iridum ions is favourable, the direct Ir $d$--$d$ hybridisation can be significant and takes a key role. Here, we investigate the effects of direct Ir $d$--$d$ hybridisation in comparison with electronic correlations and spin-orbit coupling in Ba$_5$AlIr$_2$O$_{11}$, a compound with Ir dimers. Using a combination of $ab$ $initio$ many-body wave function quantum chemistry calculations and resonant inelastic X-ray scattering (RIXS) experiments, we elucidate the electronic structure of Ba$_5$AlIr$_2$O$_{11}$. We find excellent agreement between the calculated and the measured spin-orbit excitations. Contrary to the expectations, the analysis of the many-body wave function shows that the two Ir (Ir$^{4+}$ and Ir$^{5+}$) ions in the Ir$_2$O$_9$ dimer unit in this compound preserve their local J$_{\rm eff}$ character close to 1/2 and 0, respectively. The local point group symmetry at each of the Ir sites assumes an important role, significantly limiting the direct $d$--$d$ hybridisation. Our results emphasize that minute details in the local crystal field (CF) environment can lead to dramatic differences in electronic states in iridates and 5$d$ oxides in general.
The electronic states of many Mott insulators, including iridates, are often conceptualized in terms of localized atomic states such as the famous "$J_\text{eff}=1/2$ state". Although, orbital hybridization can strongly modify such states and dramatically change the electronic properties of materials, probing this process is highly challenging. In this work, we directly detect and quantify the formation of dimer orbitals in an iridate material Ba$_5$AlIr$_2$O$_{11}$ using resonant inelastic x-ray scattering (RIXS). Sharp peaks corresponding to the excitations of dimer orbitals are observed and…
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…
The effect of the charge ordering on the spin-Peierls (SP) state has been examined by using a Peierls-Hubbard model at quarter-filling with dimerization, on-site and nearest-neighbor repulsive interactions. By taking account of the presence of dimerization, a bond distortion is calculated variationally with the renormalization group method based on bosonization. When the charge ordering appears at V=V_c with increasing the nearest-neighbor interaction (V), the distortion exhibits a maximum due to competition between the dimerization and the charge ordering. It is shown that the second-order ph…
We study the interplay of spin, orbital and lattice degrees of freedom in a one-dimensional Kugel-Khomskii model coupled to phonons. In the vicinity of the dimer point we analyze the excitation spectrum, mapping the spin and orbital degrees of freedom to bond operators. In particular we study the renormalization of the phonon propagator due to coupling to the orbital and magnetic excitations. Considering both, ferro- and antiferro-orbital ordering we will show that the appearance of orbiton shake-up processes in the phonon spectrum is sensitive to the type of Jahn-Teller distortion. The releva…
We study a phase transition in a 3D lattice gauge theory, a "coarse-grained" version of a classical dimer model. Duality arguments indicate that the dimer lattice theory should be dual to a XY model coupled to a gauge field with geometric frustration. The transition between a Coulomb phase with dipolar correlations and a long range ordered columnar phase is understood in terms of a Higgs mechanism. Monte Carlo simulations of the dual model indicate a continuous transition with exponents close but apparently different from those of the 3d XY model. The continuous nature of the transition is con…
We use exact diagonalization combined with mean-field theory to investigate the phase diagram of the spin-orbital model for cubic vanadates. The spin-orbit coupling competes with Hund's exchange and triggers a novel phase, with the ordering of $t_{2g}$ orbital magnetic moments stabilized by the tilting of VO$_6$ octahedra. It explains qualitatively spin canting and reduction of magnetization observed in YVO$_3$. At finite temperature an orbital Peierls instability in the $C$-type antiferromagnetic phase induces modulation of magnetic exchange constants even in absence of lattice distortions. T…
Recently, a Verwey-type transition in the mixed-valence alkali sesquioxide Cs$_4$O$_6$ was deduced from the charge ordering of molecular peroxide O$_2^{2-}$ and superoxide O$_2^-$ anions accompanied by the structural transformation and a dramatic change in electronic conductivity [Adler et al, Sci. Adv 4, eaap7581 (2018)]. Here, we report that in the sister compound Rb$_4$O$_6$ a similar Verwey-type charge ordering transition is strongly linked to O$_2^-$ orbital and spin dynamics. On cooling, a powder neutron diffraction experiment reveals a charge ordering and a cubic-to-tetragonal transitio…
The weakly interacting S=1/2 dimers system Sr3Cr2O8 has been investigated by powder neutron diffraction and inelastic neutron scattering. Our data reveal a structural phase transition below room temperature corresponding to an antiferro-orbital ordering with nearly 90 degrees arrangement of the occupied 3z^2-r^2 d-orbital. This configuration leads to a drastic reduction of the inter-dimer exchange energies with respect to the high temperature orbital-disorder state, as shown by a spin-dimer analysis of the super-superexchange interactions performed using the Extended Huckel Tight Binding metho…
We study S=1/2 Heisenberg model on the honeycomb lattice with first and second neighbor antiferromagnetic exchange (J_{1}-J_{2} model), employing exact diagonalization in both S_z=0 basis and nearest neighbor singlet valence bond (NNVB) basis. We find that for 0.2<J_2/J_1<0.3, NNVB basis gives a proper description of the ground state in comparison with the exact results. By analyzing the dimer-dimer as well as plaquette-plaquette correlations and also defining appropriate structure factors, we investigate possible symmetry breaking states as the candidate for the ground state in the frustrated…
We study the spin-pseudospin Hamiltonian of the Ising Model in Transverse Field (IMTF) for pseudospins, coupled to the XY-spins on a triangular lattice. This model appears from analyses of the quarter-filled ladder compound $NaV_2O_5$, and pseudospins represent its charge degrees of freedom. In the molecular-field approximation we find that the model possesses two phases: charge-disordered without spin gap; and a low-temperature phase containing both the anti-ferroelectric (zigzag) charge order and spin dimerization (spin gap). The phase transition is of the second kind, and the calculated phy…
The low and high-temperature phases of V$_4$O$_7$ have been studied by \textit{ab initio} calculations. At high temperature, all V atoms are electronically equivalent and the material is metallic. Charge and orbital ordering, associated with the distortions in the V pseudo-rutile chains, occur below the metal-insulator transition. Orbital ordering in the low-temperature phase, different in V$^{3+}$ and V$^{4+}$ chains, allows to explain the distortion pattern in the insulating phase of V$_4$O$_7$. The in-chain magnetic couplings in the low-temperature phase turn out to be antiferromagnetic, bu…
We theoretically investigate the effects of charge order and spin frustration on the spin ordering in TMTTF salts. Using first-principles band calculations, we find that a diagonal inter-chain transfer integral $t_{q1}$, which causes spin frustration between the inter-chain dimers in the dimer-Mott insulating state, strongly depends on the choice of anion. Within the numerical Lanczos exact diagonalization method, we show that the ferroelectric charge order changes the role of $t_{q1}$ from the spin frustration to the enhancement of the two-dimensionality in spin sector. The results indicate t…
Using x-ray absorption spectroscopy at the Ru-$L_{2,3}$ edge we reveal that the Ru$^{4+}$ ions remain in the $S$=1 spin state across the rare 4d-orbital ordering transition and spin-gap formation. We find using local spin density approximation + Hubbard U (LSDA+U) band structure calculations that the crystal fields in the low temperature phase are not strong enough to stabilize the $S$=0 state. Instead, we identify a distinct orbital ordering with a significant anisotropy of the antiferromagnetic exchange couplings. We conclude that La$_{4}$Ru$_{2}$O$_{10}$ appears to be a novel material in wh…
We study the charge ordering (CO) in the one-dimensional (1D) extended Hubbard model at quarter filling where the nearest-neighbor Coulomb repulsion and dimerization in the hopping parameters are included. Using the cluster mean-field approximation to take into account the effect of quantum fluctuations, we determine the CO phase boundary of the model in the parameter space at T=0 K. We thus find that the dimerization suppresses the stability of the CO phase strongly, and in consequence, the realistic parameter values for quasi-1D organic materials such as (TMTTF)$_2$PF$_6$ are outside the reg…
Magnetoresistance measurements have been carried out along the highly conducting a axis in the FISDW phase of hydrogened and deuterated (TMTSF)$_2$ClO$_4$ for various cooling rates through the anion ordering temperature. With increasing the cooling rate, a) the high field phase boundary $β_{\rm {HI}}$, observed at 27 T in hydrogened samples for slowly cooled, is shifted towards a lower field, b) the last semimetallic SDW phase below $β_{\rm {HI}}$ is suppressed, and c) the FISDW insulating phase above $β_{\rm {HI}}$ is enhanced in both salts. The cooling rate dependence of the FISDW transition…
Using a combination of Density Functional Theory, mean-field analysis and exact diagonalization calculations we reveal the emergence of a dimerized charge ordered state in TMTTF$_2$-PF$_6$ organic crystal. The interplay between charge and spin order leads to a rich phase diagram. Coexistence of charge ordering with a structural dimerization results in a ferroelectric phase, which has been observed experimentally. The tendency to the dimerization is magnetically driven revealing TMTTF$_2$-PF$_6$ as a multiferroic material.
Quasi-one-dimensional antiferromagnetic (AF) quantum spin systems show a wide range of interesting phenomena such as the spin-Peierls transition and disorder driven long range ordering. While there is no magnetic long range order in strictly one-dimensional systems, in real systems some amount of interchain coupling is always present and AF long range order may appear below a Neel ordering temperature T_N. We study the effect of bond randomness on Neel ordering in weakly coupled random AF S=1/2 chains both with and without dimerization (or spin-Peierls order). We use the real space renormaliza…
Long range antiferromagnetic (AFM) ordering of Ni spins in Ni2NbBO6 has been studied with single crystal from spin susceptibility measurement and comparedwith the ab initio calculation results consistently. Below TN = 23.5 K, the S = 1 spins align along the a direction for edge-shared NiO6 octahedra which form crystallographic armchair chains along the b direction. The isothermal magnetization M(H) below TN shows spin-flop transition for magnetic field above 36 kOe along the a axis,which indicates the spin anisotropy is along the a direction. The electronic and magnetic structures of Ni2NbBO6 …
We show that the proposed zig--zag charge--ordering model for alpha'--NaV2O5 is incompatible with a single transition that induces both charge--ordering and spin gap. We introduce a two--band model for alpha'--NaV2O5 within which the simultaneous charge--spin order transition is driven principally by electron-phonon interactions. The spin gap is due to the formation of local dimers, thus explaining the weak magnetic effect on this transition.
Recent state-of-the-art crystallographic investigations of transition metal spinel compounds have revealed that the d- orbital charge carriers undergo ordering transitions with the formation of local "molecular bonding" units such as dimers in MgTi2O4, octomers in CuIr2S4, and heptamers in AlV2O4. Herein, we provide a unifying scheme involving one- dimensional orbital wave ordering applicable to all of these spinels. The relative phase of the orbitals in the chains is shown to be crucial to the formation of different local units, and thus both the amplitude and phase of the orbital wave play i…
Inelastic neutron scattering measurements on the molecular dimer-Mott insulator $κ$-(BEDT-TTF)$_{2}$Cu[N(CN)$_{2}$]Cl reveal a phonon anomaly in a wide temperature range. Starting from $T_{\rm ins}\sim50$-$60$ K where the charge gap opens, the low-lying optical phonon modes become overdamped upon cooling towards the antiferromagnetic ordering temperature $T_\mathrm{N} = 27$ K, where also a ferroelectric ordering at $T_{\rm FE} \approx T_{\rm N}$ occurs. Conversely, the phonon damping becomes small again when spins and charges are ordered below $T_\mathrm{N}$, while no change of the lattice sym…
We perform a general study of spin ordering on the pyrochlore lattice with a 3:1 proportionality of two spin polarizations. Equivalently, this describes valence bond solid conformations of a quantum dimer model on the diamond lattice. We determine the set of likely low temperature ordered phases, on the assumption that the ordering is weak, i.e the system is close to a ``U(1)'' quantum spin liquid in which the 3:1 proportionality is maintained but the spins are strongly fluctuating. The nature of the 9 ordered states we find is determined by a ``projective symmetry'' analysis. All the phases e…
We extend Quantum Dimer Model (QDM) introduced by Rokhsar and Kivelson in such a way that the model includes resonance processes on larger loops. The strategy is to first construct a pseudo spin Hamiltonian which is defined not by the S =1/2 but by the S=1 representation and then establish the correspondence between the pseudo-spin-1 configurations and those of dimers. The standard QDM keeps only the lowest resonance processes for pairs of parallel dimers and its validity in describing the realistic spin systems is not obvious. Our extended QDM (EQDM) improves this point and contains a novel r…
We theoretically investigate the competition between charge-ordered state and Mott insulating state at finite temperatures in quarter-filled quasi-one-dimensional electron systems, by studying dimerized extended Hubbard chains with interchain Coulomb interactions. In order to take into account one-dimensional fluctuations properly, we apply the bosonization method to an effective model obtained by the interchain mean-field approximation. The results show that lattice dimerization, especially in the critical region, and frustration in the interchain Coulomb interactions reduce the charge-orderi…
We explore several classes of quadrupolar ordering in a system of antiferromagnetically coupled quantum spin-1 dimers, which are stacked in the triangular lattice geometry forming a bilayer. Low-energy properties of this model is described by an $\mathcal{S}=1$ hard-core bosonic degrees of freedom defined on each dimer-bond, where the singlet and triplet states of the dimerized spins are interpreted as the vacuum and the occupancy of boson, respectively. The number of bosons per dimer and the magnetic and density fluctuations of bosons are controlled by the inter-dimer Heisenberg interactions.…
Several spin systems with low dimensionality develop a spin-dimer phase within a molecular orbital below TS, competing with long-range antiferromagnetic order. Very often, preferential orbital occupancy and ordering are the actual driving force for dimerization, as in the so-called orbitally-driven spin-Peierls compounds (MgTi2O4, CuIr2S4, La4Ru2O10, NaTiSi2O6, etc.). Through a microscopic analysis of the thermal conductivity k (T) in La4Ru2O10, we show that the orbital occupancy fluctuates rapidly above TS, resulting in an orbital-liquid state. The strong orbital-lattice coupling introduces d…
We study the spin ordering within the 3-leg ladders present in the oxyborate Fe(3)O(2)BO(3) consisting of localized classical spins interacting with conduction electrons (one electron per rung). We also consider the competition with antiferromagnetic superexchange interactions to determine the magnetic phase diagram. Beside a ferromagnetic phase we find (i) a phase with ferromagnetic rungs ordered antiferromagnetically (ii) a zig-zag canted spin ordering along the legs. We also determine the induced charge ordering within the different phases and the interplay with lattice instability. Our mod…
The magnetization measurements have been performed on the doped spin gap system TlCu_{1-x}Mg_xCl_3 with x <= 0.025. The parent compound TlCuCl_3 is a three-dimensional coupled spin dimer system with the excitation gap Delta/k_B = 7.7 K. The impurity-induced antiferromagnetic ordering was clearly observed. The easy axis lies in the (0,1,0) plane. It was found that the transition temperature increases with increasing Mg^{2+} concentration x, while the spin-flop transition field is almost independent of x. The magnetization curve suggests that the impurity-induced antiferromagnetic ordering coexi…
When an electronic system has strong correlations and a large spin-orbit interaction, it often exhibits a plethora of mutually competing quantum phases. How a particular quantum ground state is selected out of several possibilities is a very interesting question. However, equally fascinating is how such a quantum entangled state breaks up due to perturbation. This important question has relevance in very diverse fields of science from strongly correlated electron physics to quantum information. Here we report that a quantum entangled dimerized state or valence bond crystal (VBC) phase of Li2Ru…
Motivated by the co-existing charge and spin order found in strongly correlated ladder systems, we study an effective pseudospin model on a coupled two-leg ladder. A bosonisation analysis yields a rich phase diagram showing Wigner/Peierls charge order and Neel/dimer spin order. In a broad parameter regime, the orbital antiferromagnetic phase is found to be stable. An intermediate gapless phase of finite width is found to lie in between two charge-ordered gapped phases. Our work is potentially relevant for a unified description of a class of strongly correlated, quarter-filled ladder systems.
Quantum entanglement of XY-type spin dimers in Shastry-Sutherland lattice
Oak Ridge National Laboratory（橡树岭国家实验室）；University of Arizona（亚利桑那大学）；Kennesaw State University（肯尼索州立大学）；Louisiana State University（路易斯安那州立大学）；University of Tennessee, Knoxville（田纳西大学）
How particular bonds form in quantum materials has been a long-standing puzzle. Two key concepts dealing with charge degrees of freedom are dimerization (forming metal-metal bonds) and charge ordering (CO). Since the 1930s, these two concepts have been frequently invoked to explain numerous exciting quantum materials, typically insulators. Here we report dimerization and CO within the dimers coexisting in metallic NaRu$_2$O$_4$. By combining high-resolution x-ray diffraction studies and theoretical calculations, we demonstrate that this unique phenomenon occurs through a new type of bonding, w…
Field-induced magnetic order has been investigated in detail in the interacting spin 3/2 dimer system Cs_3Cr_2Br_9. Elastic and inelastic neutron scattering measurements were performed up to H = 6 T, well above the critical field H_c1 = 1.5 T. The ordering displays incommensurabilities and a large hysteresis before a commensurate structure is reached. This structure is fully determined. Surprisingly, the lowest excitation branch never closes. Above H_c1, the gap increases slowly with field. An analysis in terms of projected pseudo-spin is given.
Magnetization measurements were performed to investigate the critical behavior of the field-induced magnetic ordering in gapped spin system TlCuCl$_3$. The critical density of the magnons was obtained as a function of temperature and the magnon-magnon interaction constant was evaluated. The experimental phase boundary for $T < 5$ K agrees almost perfectly with the magnon BEC theory based on the Hartree-Fock approximation with realistic dispersion relations. The phase boundary can be described by the power law $[H_{N}(T)-H_{c}] propto T^{phi}$. With decreasing fitting temperature range, the cri…
Magnetic phase transitions under hydrostatic pressures in spin gap systems TlCu$_{0.988}$Mg$_{0.012}$Cl$_3$ and KCu$_{0.973}$Mg$_{0.027}$Cl$_3$ were investigated by magnetization measurements. The present doped systems exhibit impurity-induced magnetic orderings. With increasing pressure, ordering temperature $T_{\rm N}$ increases. With a further increase in pressure, the present systems undergo phase transitions to uniform antiferromagnetic phases due to the closing of the triplet gap in the intact dimers. The crossover from the impurity-induced ordered phase to the uniform antiferromagnetic …
We report on the charge-ordered structure of LiRh2O4 arising below the metal-insulator transition at 170 K. Structural studies using synchrotron X-rays have revealed that the charge-ordered states of Rh3+ and Rh4+ with dimerization are realized in the low-temperature phase below 170 K. Although the low-temperature ground state resembles that of CuIr2S4, a charge ordering pattern satisfying the Anderson condition is realized in LiRh2O4. Based on structural information such as the short-range order of dimers appearing above the transition temperature and the weakening of the correlation between …
The classical cubic-lattice dimer model undergoes an unconventional transition between a columnar crystal and a dimer liquid, in the same universality class as the deconfined quantum critical point in spin-1/2 antiferromagnets but with very different microscopic physics and microscopic symmetries. Using Monte Carlo simulations, we show that this transition has an emergent SO(5) symmetry relating quantities characterizing the two adjacent phases. While the low-temperature phase has a conventional order parameter, the defining property of the Coulomb liquid on the high-temperature side is deconf…
Specific heat measurements have been performed in the coupled dimer system TlCuCl$_3$, which has a singlet ground state with the excitation gap $Δ\simeq 7.5$K. The cusplike anomaly indicative of the 3D magnetic ordering was clearly observed in magnetic fields higher than the critical field $H_c$ corresponding to the gap $Δ$. The phase boundary determined by the present specific heat measurements coincides with that determined by previous magnetization measurements. The phase boundary can be described by the power law $[ H_{\rm c}(T)-H_{\rm g} ] \propto T^ϕ$ with $ϕ=2.1(1)$. This result support…
Sr$_{3}$Cr$_{2}$O$_{8}$ consist of a lattice of spin-1/2 Cr$^{5+}$ ions, which form hexagonal bilayers and which are paired into dimers by the dominant antiferromagnetic intrabilayer coupling. The dimers are coupled three-dimensionally by frustrated interdimer interactions. A structural distortion from hexagonal to monoclinic leads to orbital order and lifts the frustration giving rise to spatially anisotropic exchange interactions. We have grown large single crystals of Sr$_{3}$Cr$_{2}$O$_{8}$ and have performed DC susceptibility, high field magnetisation and inelastic neutron scattering meas…
Magnetization measurements under a hydrostatic pressure of P = 1.4 GPa were performed on the coupled spin dimer system TlCuCl_3, which exhibits a pressure-induced quantum phase transition from a gapped singlet state to an antiferromagnetic state at P_c = 0.042 GPa. Antiferromagnetic ordering with ordered moments parallel to the ac plane was observed at T_N = 16.7 K at 1.4 GPa. The spin reorientation phase transition was observed at T_R ~ 9.2 K for zero magnetic field, at which the ordered moments start to incline towards the b axis. With increasing external field parallel to th b axis, a secon…
We have synthesized and studied a new iridate, Ba13Ir6O30, with unusual Ir oxidation states: 2/3 Ir6+(5d3) ions and 1/3 Ir5+(5d4) ions. Its crystal structure features dimers of face-sharing IrO6 octahedra, and IrO6 monomers, that are linked via long, zigzag Ir-O-Ba-O-Ir pathways. Nevertheless, Ba13Ir6O30 exhibits two transitions at TN1 = 4.7 K and TN2 = 1.6 K. This magnetic order is accompanied by a huge Sommerfeld coefficient 200 mJ/mole K below TN2, signaling a coexisting frustrated/disordered state persisting down to at least 0.05 K. This iridate hosts unusually large Jeff=3/2 degrees of fr…
We report quadruple configuration interaction calculations within the extended Pariser$-$Parr$-$Pople Hamiltonian on the excited states of aggregates of polyenes, crystalline acenes, and covalently linked dimers of acene molecules. We determine the precise energy orderings and analyze the cluster wave functions in order to arrive at a comprehensive physical understanding of singlet fission in these diverse families of materials. Our computational approach allows us to retain a very large number of basis states and thereby obtain the correct relative energy orderings of one electron$-$one hole …
We investigate theoretically charge ordered states on the anisotropic triangular lattice characteristic of the theta-(BEDT-TTF)_2 X materials. Using exact diagonalization studies, we establish that the charge order (CO) pattern corresponds to a ``horizontal'' stripe structure, with ...1100... CO along the two directions with larger electron hopping (p-directions), and ...1010... CO along the third direction (c-direction). The CO is accompanied by co-operative bond dimerizations along all three directions in the highest spin state. In the lowest spin state bonds along the p-directions are tetra…
By means of density-functional simulations for half-doped manganites, such as pseudocubic Pr0.5Ca0.5MnO3 and bilayer PrCa2Mn2O7, we discuss the occurrence of ferroelectricity and we explore its crucial relation to the crystal structure and to peculiar charge/spin/orbital ordering effects. In pseudocubic Pr0.5Ca0.5MnO3, ferroelectricity is induced in the Zener polaron type structure, where Mn ions are dimerized. In marked contrast, in bilayer PrCa2Mn2O7, it is the displacements of apical oxygens bonded to either Mn3+ or Mn4+ ions that play a key role in the rising of ferroelectricity. Important…
We study a one-dimensional extended Hubbard model with longer-range Coulomb interactions at quarter-filling in the strong coupling limit. We find two different charge-ordered ground states as the strength of the longer range interactions is varied. At lower energies, these charge ordered states drive two different spin-ordered ground states. A variety of response functions computed here bear a remarkable resemblance to recent experimental observations for organic TMTSF systems, and so we propose that these systems are proximate to a quantum critical point (QCP) associated with T=0 charge order…
The charge degrees of freedom in several different organic charge transfer salts display slow or glassy dynamics. In order to gain insight into this behaviour, we obtain the low energy theory for an extended dimer Hubbard model, taking into account the occupations of sites on neighbouring dimers. We take a classical limit of the resulting effective model of coupled spins and dimers and study it using classical Monte Carlo simulations. We find that frustration induced by intra- and inter-dimer interactions leads to glassiness in the charge degress of freedom in the absence of ordering of the sp…
Specific heat and magnetization measurements of the compound [Cu2(apyhist)2Cl2](ClO4)2, where apyhist = (4-imidazolyl)ethylene-2-amino-1-ethylpyridine), were used to identify a magnetic-field-induced long-range antiferromagnetic ordered phase at low temperatures (T < 0.36 K) and magnetic fields (1.6 T < H < 5.3 T). This system consists of a Schiff base copper(II) complex, containing chloro-bridges between adjacent copper ions in a dinuclear arrangement, with an antiferromagnetic intradimer interaction |Jintra|/kB = 3.65 K linked by an antiferromagnetic coupling |Jinter|z/kB = 2.7 K. The magnet…
We study the effect of spin-Peierls instability on the phase-diagram of a frustrated antiferromagnetic spin-1/2 ladder, with weak transverse and diagonal rung coupling. Our analysis focuses on a one-dimensional version of the model (i.e. a single two-leg ladder) where we consider two forms of spin-Peierls (SP) instabilities on the legs: columnar dimers (CD) and staggered dimers (SD). We particularly examine the regime of parameters (corresponding to an intermediate XXZ anisotropy) where the SP and rung coupling terms are equally relevant. In both the CD and SD cases we find that the effective …
The ground state of $λ$-(BEDT-TTF)$_2$GaCl$_4$, which has the same structure as the organic superconductor $λ$-(BETS)$_2$GaCl$_4$, was investigated by magnetic susceptibility and $^{13}$C NMR measurements. The temperature dependence of the magnetic susceptibility revealed an antiferromagnetic (AF) correlation with $J/k_{\rm B} \simeq$ 98 K. NMR spectrum splitting and the divergence of $1/T_1$ were observed at approximately 13 K, which is associated with the AF transition. We found that the AF structure is commensurate according to discrete NMR peak splitting, suggesting that the ground state o…
KCuCl$_3$ is a three-dimensional coupled spin-dimer system and has a singlet ground state with an excitation gap $Δ/k_{\rm B}=31$ K. High-field magnetization measurements for KCuCl$_3$ have been performed in static magnetic fields of up to 30 T and in pulsed magnetic fields of up to 60 T. The entire magnetization curve including the saturation region was obtained at $T=1.3$ K. From the analysis of the magnetization curve, it was found that the exchange parameters determined from the dispersion relations of the magnetic excitations should be reduced, which suggests the importance of the renorma…
We present a $^2$D NMR investigation of the gapped spin-1/2 compound $Cu_2 (C_5 H_{12} N_2)_2 Cl_4$. Our measurements reveal the presence of a magnetic field induced transverse staggered magnetization (TSM) which persists well below and above the field-induced 3D long-range magnetically ordered (FIMO) phase. The symmetry of this TSM is different from that of the TSM induced by the order parameter of the FIMO phase. Its origin, field dependence and symmetry can be explained by an intra-dimer Dzyaloshinskii-Moriya interaction, as shown by DMRG calculations on a spin-1/2 ladder. This leads us to …
We study field-induced magnetic order in cubic lattices of dimers with antiferromagnetic Heisenberg interactions. The thermal critical exponents at the quantum phase transition from a spin liquid to a magnetically ordered phase are determined from Stochastic Series Expansion Quantum Monte Carlo simulations. These exponents are independent of the interdimer coupling ratios, and converge to the value obtained by considering the transition as a Bose-Einstein condensation of magnons, alpha_(BEC) = 1.5. The scaling results are of direct relevance to the spin-dimer systems TlCuCl_3 and KCuCl_3, and …
The charge ordering phenomena in quasi two-dimensional 1/4-filled organic compounds (ET)_2X (ET=BEDT-TTF) are investigated theoretically for the $θ$ and $α$-type structures, based on the Hartree approximation for the extended Hubbard models with both on-site and intersite Coulomb interactions. It is found that charge ordered states of stripe-type are stabilized for the relevant values of Coulomb energies, while the spatial pattern of the stripes sensitively depends on the anisotropy of the models. By comparing the results of calculations with the experimental facts, where the effects of quantu…
K$_3$Cu$_3$AlO$_2$(SO$_4$)$_4$ is a highly one-dimensional spin-1/2 inequilateral diamond-chain antiferromagnet. Spinon continuum and spin-singlet dimer excitations are observed in the inelastic neutron scattering spectra, which is in excellent agreement with a theoretical prediction: a dimer-monomer composite structure, where the dimer is caused by strong antiferromagnetic (AFM) coupling and the monomer forms an almost isolated quantum AFM chain controlling low-energy excitations. Moreover, muon spin rotation/relaxation spectroscopy shows no long-range ordering down to 90~mK, which is roughly…
The layered perovskite compound NaV_2O_5 exhibits charge ordering (CO) and spin gap formation which is driven by inter- site Coulomb forces and exchange dimerisation. Experimentally it was found that the CO transition is rapidly reduced by doping. Charge ordering in NaV_2O_5 has a quasi 1D character due to inter- ladder frustration in the Trellis lattice. Based on an extended pseudospin (T=1) approach for hole doped NaV_2O_5 ladders we construct an Ising like model that explains qualitatively the destruction of the CO phase as function of hole doping δand show how the CO parameter depends on δ…
We study the iron dimer by using an accurate ansatz for quantum chemical calculations based on a simple variational wave function, defined by a single geminal expanded in molecular orbitals and combined with a real space correlation factor. By means of this approach we predict that, contrary to previous expectations, the neutral ground state is $^7 Δ$ while the ground state of the anion is $^8 Σ_g^-$, hence explaining in a simple way a long standing controversy in the interpretation of the experiments. Moreover, we characterize consistently the states seen in the photoemission spectroscopy by …
Interesting emergent behavior in quantum materials arises when the interaction of electrons with the lattice leads to partial localization and ordering of charge at low temperatures. The triangular lattice of some transition metal dichalcogenides additionally presents an interesting case, where spin order is frustrated, leading to an additional complex interplay of interactions involving spin, charge and lattice degrees of freedom. Here we present a study of local symmetry breaking of the lattice structure in the layered dichalcogenide material 1T-TaS$_{2}$ using x-ray pair-distribution functi…
