Eel Order Research Articles

Determination of the magnetic order and the crystal symmetry in the multiferroic ground state of Ba2CoGe2O7

Detailed structural investigation of Ba${}_{2}$CoGe${}_{2}$O${}_{7}$ was performed in its low-temperature multiferroic state combining neutron diffraction with magnetization measurements and the optical study of lattice vibrations on single crystals. The crystal structure above (10.4 K) and the crystal and magnetic structures below (2.2 K) the antiferromagnetic transition temperature of ${T}_{N}$ $=$ 6.7 K were determined using neutron diffraction. The tetragonal space group (SG) $P$-42${}_{1}m$, corresponding to the average structure at room temperature, was found to also describe the structure at low temperatures well. Neutron diffraction data and infrared phonon mode analysis imply no structural phase transition down to 2.2 K. Orthorhombic polar SG Cmm2 is proposed as a true crystal structure. Below ${T}_{N}$, the spins of the Co${}^{2+}$ ions form a square-lattice N\'eel order within the ($a$,$b$) plane, while their alignment is ferromagnetic along the $c$ axis. The magnitude of the ordered moment, fully lying within the ($a$,$b$) plane, is found to be 2.9(1) ${\ensuremath{\mu}}_{B}$/Co${}^{2+}$ and the easy axis of the sublattice magnetizations corresponds to the [110] direction. A noncollinear spin structure due to small canting is allowed.

Advantages of Mass-Imbalanced Ultracold Fermionic Mixtures for Approaching Quantum Magnetism in Optical Lattices

We study magnetic phases of two-component mixtures of ultracold fermions with repulsive interactions in optical lattices in the presence of hopping imbalance. Our analysis is based on dynamical mean-field theory (DMFT) and its real-space generalization at finite temperature. We study the temperature dependence of the transition into the ordered state as a function of the interaction strength and the imbalance parameter in two and three spatial dimensions. We show that below the critical temperature for Néel order mass-imbalanced mixtures also exhibit a charge-density wave, which provides a directly observable signature of the ordered state. For the trapped system, we compare our results obtained by real-space DMFT to a local-density approximation. We calculate the entropy for a wide range of parameters and identify regions, in which mass-imbalanced mixtures could have clear advantages over balanced ones for the purpose of obtaining and detecting quantum magnetism.

Entanglement scaling in two-dimensional gapless systems

We numerically determine subleading scaling terms in the ground-state entanglement entropy of several two-dimensional (2D) gapless systems, including a Heisenberg model with N\'eel order, a free Dirac fermion in the {\pi}-flux phase, and the nearest-neighbor resonating-valence-bond wavefunction. For these models, we show that the entanglement entropy between cylindrical regions of length x and L - x, extending around a torus of length L, depends upon the dimensionless ratio x/L. This can be well-approximated on finite-size lattices by a function ln(sin({\pi}x/L)), akin to the familiar chord-length dependence in one dimension. We provide evidence, however, that the precise form of this bulk-dependent contribution is a more general function in the 2D thermodynamic limit.

Heat transport of the quasi-one-dimensional Ising-like antiferromagnet BaCo2V2O8in longitudinal and transverse fields

The very-low-temperature thermal conductivity (\kappa) is studied for BaCo_2V_2O_8, a quasi-one-dimensional Ising-like antiferromagnet exhibiting an unusual magnetic-field-induced order-to-disorder transition. The nearly isotropic transport in the longitudinal field indicates that the magnetic excitations scatter phonons rather than conduct heat. The field dependence of \kappa shows a sudden drop at \sim 4 T, where the system unndergoes the transition from the N\'eel order to the incommensurate state. Another dip at lower field of \sim 3 T indicates an unknown magnetic transition, which is likely due to the spin-flop transition. Moreover, the \kappa(H) in the transverse field shows a very deep valley-like feature, which moves slightly to higher field and becomes sharper upon lowering the temperature. This indicates a magnetic transition induced by the transverse field, which however is not predicted by the present theories for this low-dimensional spin system.

Lattice Model for theSU(N)Néel to Valence-Bond Solid Quantum Phase Transition at LargeN

We generalize the SU(N=2) S=1/2 square-lattice quantum magnet with nearest-neighbor antiferromagnetic coupling (J(1)) and next-nearest-neighbor ferromagnetic coupling (J(2)) to arbitrary N. For all N>4, the ground state has valence-bond-solid order for J(2)=0 and Néel order for J(2)/J(1)≫1, allowing us access to the transition between these types of states for large N. Using quantum Monte Carlo simulations, we show that both order parameters vanish at a single quantum-critical point, whose universal exponents for large enough N (here up to N=12) approach the values obtained in a 1/N expansion of the noncompact CP(N-1) field theory. These results lend strong support to the deconfined quantum-criticality theory of the Néel-valence-bond-solid transition.

Spin-12J1-J2Heisenberg antiferromagnet on a square lattice: A plaquette renormalized tensor network study

We apply the plaquette renormalization scheme of tensor network states [Phys. Rev. E 83, 056703 (2011)] to study the spin-1/2 frustrated Heisenberg ${J}_{1}$-${J}_{2}$ model on an $L\ifmmode\times\else\texttimes\fi{}L$ square lattice with $L$ $=$ 8, 16, and 32. By treating tensor elements as variational parameters, we obtain the ground states for different ${J}_{2}/{J}_{1}$ values, and investigate staggered magnetizations, nearest-neighbor spin-spin correlations, and plaquette order parameters. In addition to the well-known N\'eel order and collinear order at low and high ${J}_{2}/{J}_{1}$, we observe a plaquettelike order at ${J}_{2}/{J}_{1}\ensuremath{\approx}0.5$. A continuous transition between the N\'eel order and the plaquettelike order near ${J}_{2}^{{c}_{1}}\ensuremath{\approx}0.40{J}_{1}$ is observed. The collinear order emerges at ${J}_{2}^{{c}_{2}}\ensuremath{\approx}0.62{J}_{1}$ through a first-order phase transition.

Ab initioStudies on the Interplay between Spin-Orbit Interaction and Coulomb Correlation inSr2IrO4andBa2IrO4

Ab initio analyses of A(2)IrO(4) (A=Sr,Ba) are presented. Effective Hubbard-type models for Ir 5d t(2g) manifolds downfolded from the global band structure are solved based on the dynamical mean-field theory. The results for A=Sr and Ba correctly reproduce paramagnetic metals undergoing continuous transitions to insulators below the Néel temperature T(N). These compounds are classified not into Mott insulators but into Slater insulators. However, the insulating gap opens by a synergy of the Néel order and significant band renormalization, which is also manifested by a 2D bad metallic behavior in the paramagnetic phase near the quantum criticality.

Pair-density-wave superconducting order in two-leg ladders

We show using bosonization methods that extended Hubbard-Heisenberg models on two types of two leg ladders (without flux and with flux $\pi$ per plaquette) have commensurate pair-density wave (PDW) phases. In the case of the conventional (flux-less) ladder the PDW arises when certain filling fractions for which commensurability conditions are met. For the flux $\pi$ ladder the PDW phase is generally present. The PDW phase is characterized by a finite spin gap and a superconducting order parameter with a finite (commensurate in this case) wave vector and power-law superconducting correlations. In this phase the uniform superconducting order parameter, the $2k_F$ charge-density-wave (CDW) order parameter and the spin-density- wave N\'eel order parameter exhibit short range (exponentially decaying) correlations. We discuss in detail the case in which the bonding band of the ladder is half filled for which the PDW phase appears even at weak coupling. The PDW phase is shown to be dual to a uniform superconducting (SC) phase with quasi long range order. By making use of bosonization and the renormalization group we determine the phase diagram of the spin-gapped regime and study the quantum phase transition. The phase boundary between PDW and the uniform SC ordered phases is found to be in the Ising universality class. We generalize the analysis to the case of other commensurate fillings of the bonding band, where we find higher order commensurate PDW states for which we determine the form of the effective bosonized field theory and discuss the phase diagram. We compare our results with recent findings in the Kondo-Heisenberg chain. We show that the formation of PDW order in the ladder embodies the notion of intertwined orders.

Quantum phase transitions in a strongly entangled spin-orbital chain: A field-theoretical approach

Motivated by recent experiments on quasi-one-dimensional vanadium oxides, we study quantum phase transitions in a one-dimensional spin-orbital model describing a Haldane chain and a classical Ising chain locally coupled by the relativistic spin-orbit interaction. By employing a field-theoretical approach, we analyze the topology of the ground-state phase diagram and identify the nature of the phase transitions. In the strong coupling limit, a long-range N\'eel order of entangled spin and orbital angular momenta appears in the ground state. We find that, depending on the relative scales of the spin and orbital gaps, the linear chain follows two distinct routes to reach the N\'eel state. First, when the orbital exchange is the dominating energy scale, a two-stage ordering takes place in which the magnetic transition is followed by melting of the orbital Ising order; both transitions belong to the two-dimensional Ising universality class. In the opposite limit, the low-energy orbital modes undergo a continuous reordering transition which represents a line of Gaussian critical points. On this line the orbital degrees of freedom form a Tomonaga--Luttinger liquid. We argue that the emergence of the Gaussian criticality results from merging of the two Ising transitions in the strong hybridization region where the characteristic spin and orbital energy scales become comparable. Finally, we show that, due to the spin-orbit coupling, an external magnetic field acting on the spins can induce an orbital Ising transition.

Quantum paramagnetic ground states on the honeycomb lattice and field-induced Néel order

Motivated by recent experiments on Bi$_3$Mn$_4$O$_{12}$(NO$_3$), and a broader interest arising from numerical work on the honeycomb lattice Hubbard model, we have studied the effect of a magnetic field on honeycomb lattice spin models with quantum paramagnetic ground states. For a model with frustrating second-neighbor exchange, $J_2$, we use a Lindemann-like criterion within spin wave theory to show that N\'eel order melts beyond a critical $J_2$. The critical $J_2$ increases with a magnetic field, implying the existence of a field-induced paramagnet-N\'eel transition over a range of $J_2$. We also study bilayer model using a spin-$S$ generalization of bond operator mean field theory. We show that there is a N\'eel-dimer transition for various spin values with increasing bilayer coupling, and that the resulting interlayer dimer state undergoes a field induced transition into a state with transverse N\'eel order. Finally, we study a spin-3/2 model which interpolates between the Heisenberg model and the Affleck-Kennedy-Lieb-Tasaki (AKLT) parent Hamiltonian. Using exact diagonalization, we compute the fidelity susceptibility to locate the Neel-AKLT quantum critical point, obtain the spin gap of the AKLT parent Hamiltonian, and argue that AKLT state also undergoes field-induced Neel ordering.

Multi-component quantum gases in spin-dependent hexagonal lattices

Periodicity is one of the most fundamental structural characteristics of systems occurring in nature. The properties of these systems depend strongly on the symmetry of the underlying periodic structure. In solid state materials - for example - the static and transport properties as well as the magnetic and electronic characteristics are crucially influenced by the crystal symmetry. In this context, hexagonal structures play an extremely important role and lead to novel physics like that of carbon nanotubes or graphene. Here we report on the first realization of ultracold atoms in a spin-dependent optical lattice with hexagonal symmetry. We show how combined effects of the lattice and interactions between atoms lead to a forced antiferromagnetic N\'eel order when two spin-components localize at different lattice sites. We also demonstrate that the coexistence of two components - one Mott-insulating and the other one superfluid - leads to the formation of a forced supersolid. Our observations are consistent with theoretical predictions using Gutzwiller mean-field theory.

Functional renormalization group for the anisotropic triangular antiferromagnet

We present a functional renormalization group scheme that allows us to calculate frustrated magnetic systems of arbitrary lattice geometry beyond $O(200)$ sites from first principles. We study the magnetic susceptibility of the antiferromagnetic (AFM) spin-$1/2$ Heisenberg model ground state on the spatially anisotropic triangular lattice, where ${J}^{\ensuremath{'}}$ denotes the coupling strength of the intrachain bonds along one lattice direction and $J$ the coupling strength of the interchain bonds. We identify three distinct phases of the Heisenberg model. Increasing $\ensuremath{\xi}={J}^{\ensuremath{'}}/J$ from the effective square lattice $\ensuremath{\xi}=0$, we find an AFM N\'eel order to spiral order transition at ${\ensuremath{\xi}}_{c1}~0.6--0.7$, with an indication that it is of second order. In addition, above the isotropic point at ${\ensuremath{\xi}}_{c2}~1.1$, we find a first-order transition to a magnetically disordered phase with collinear AFM stripe fluctuations.

Schwinger boson mean field theories of spin liquid states on a honeycomb lattice: Projective symmetry group analysis and critical field theory

Motivated by the recent numerical evidence[1] of a short-range resonating valence bond state in the honeycomb lattice Hubbard model, we consider Schwinger boson mean field theories of possible spin liquid states on honeycomb lattice. From general stability considerations the possible spin liquids will have gapped spinons coupled to Z$_2$ gauge field. We apply the projective symmetry group(PSG) method to classify possible Z$_2$ spin liquid states within this formalism on honeycomb lattice. It is found that there are only two relevant Z$_2$ states, differed by the value of gauge flux, zero or $\pi$, in the elementary hexagon. The zero-flux state is a promising candidate for the observed spin liquid and continuous phase transition into commensurate N\'eel order. We also derive the critical field theory for this transition, which is the well-studied O(4) invariant theory[2-4], and has an irrelevant coupling between Higgs and boson fields with cubic power of spatial derivatives as required by lattice symmetry. This is in sharp contrast to the conventional theory[5], where such transition generically leads to non-colinear incommensurate magnetic order. In this scenario the Z$_2$ spin liquid could be close to a tricritical point. Soft boson modes will exist at seven different wave vectors. This will show up as low frequency dynamical spin susceptibility peaks not only at the $\Gamma$ point (the N\'eel order wave vector) but also at Brillouin zone edge center $M$ points and twelve other points. Some simple properties of the $\pi$-flux state are studies as well. Symmetry allowed further neighbor mean field ansatz are derived in Appendix which can be used in future theoretical works along this direction.

Magnetic excitations in ferropnictide materials controlled by a quantum critical point into hidden order

The two-orbital ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model that describes a square lattice of frustrated spin-1 iron atoms is analyzed within the linear spin-wave approximation and by exact diagonalization over a $4\ifmmode\times\else\texttimes\fi{}4$ cluster. A quantum critical point (QCP) is identified that separates hidden magnetic order at weak Hund's rule coupling from a commensurate spin-density wave (cSDW) at strong Hund's rule coupling. Although the moment for cSDW order is small at the QCP, the critical linear spin-wave spectrum shows strong low-energy excitations centered at the wave numbers that correspond to cSDW order. These disperse anisotropically. A fit to the magnetic excitation spectrum of ferropnictide materials obtained recently by inelastic neutron-scattering measurements notably accounts for the absence of softening at the wave number that corresponds to N\'eel order.

Spiral order by disorder and lattice nematic order in a frustrated Heisenberg antiferromagnet on the honeycomb lattice

Motivated by recent experiments on Bi$_3$Mn$_4$O$_{12}$(NO$_3$), we study a frustrated $J_1$-$J_2$ Heisenberg model on the two dimensional (2D) honeycomb lattice. The classical $J_1$-$J_2$ Heisenberg model on the two dimensional (2D) honeycomb lattice has N\'eel order for $J_2 < J_1/6$. For $J_2 > J_1/6$, it exhibits a one-parameter family of degenerate incommensurate spin spiral ground states where the spiral wave vector can point in any direction. Spin wave fluctuations at leading order lift this accidental degeneracy in favor of specific wave vectors, leading to spiral order by disorder. For spin $S=1/2$, quantum fluctuations are, however, likely to be strong enough to melt the spiral order parameter over a wide range of $J_2/J_1$. Over a part of this range, we argue that the resulting state is a valence bond solid (VBS) with staggered dimer order - this VBS is a nematic which breaks lattice rotational symmetry. Our arguments are supported by comparing the spin wave energy with the energy of the dimer solid obtained using a bond operator formalism. Turning to the effect of thermal fluctuations on the spiral ordered state, any nonzero temperature destroys the magnetic order, but the discrete rotational symmetry of the lattice remains broken resulting in a thermal analogue of the nematic VBS. We present arguments, supported by classical Monte Carlo simulations, that this nematic transforms into the high temperature symmetric paramagnet via a thermal phase transition which is in the universality class of the classical 3-state Potts (clock) model in 2D. We discuss the possible relevance of our results for honeycomb magnets, such as Bi$_3$M$_4$O$_{12}$(NO$_3$) (with M=Mn,V,Cr), and bilayer triangular lattice magnets.

Interplay of strongly correlated electrons and localized Ising moments in one dimension

We study ground-state properties of a one-dimensional quarter-filled strongly correlated electronic chain coupled to an antiferromagnetic Ising chain by the density-matrix renormalization-group method. We focus on the case where large Coulomb interactions localize the charges on every other site. Both the electronic spins and the Ising moments interact antiferromagnetically within each chain. Since the number of electrons is half as that of Ising moments, the two intrachain N\'eel orders are incompatible and compete with each other. When the Ising chain is ordered (gapped), the electrons are magnetically frustrated, which is reflected in the nearly degenerate energy levels with different magnetization. The resultant magnetoelectric effect is elucidated as a suppression of a charge gap by the magnetic field.

Magnetic structure of an imbalanced Fermi gas in an optical lattice

We analyze the repulsive fermionic Hubbard model on square and cubic lattices with spin imbalance and in the presence of a parabolic confinement. We analyze the magnetic structure as a function of the repulsive interaction strength and polarization. In the first part of the article, we perform unrestricted Hartree-Fock calculations for the two-dimensional (2D) case and find that above a critical interaction strength ${U}_{c}$ the system turns ferromagnetic at the edge of the trap, which is in agreement with the ferromagnetic Stoner instability of a homogeneous system away from half-filling. For $U&lt;{U}_{c}$, we find a canted antiferromagnetic structure in the Mott region in the center and a partially polarized compressible edge. The antiferromagnetic order in the Mott plateau is perpendicular to the direction of the imbalance. In this regime, the same qualitative behavior is expected for 2D and three-dimensional (3D) systems. In the second part of the article, we give a general discussion of magnetic structures above ${U}_{c}$. We argue that spin conservation leads to nontrivial textures, both in the ferromagnetic polarization at the edge and for the N\'eel order in the Mott plateau. We discuss differences in magnetic structures for 2D and 3D cases.

Honeycomb antiferromagnet with a triply degenerate dimer ground state

We present an antiferromagnetic quantum spin-1/2 model on honeycomb lattice. It has two parts, one of which is the usual nearest-neighbor Heisenberg model. The other part is a certain multiple spin interaction term, introduced by us, which is exactly solvable for the ground state. Without the Heisenberg part, the model has an exact threefold degenerate dimer ground state. This exact ground state is also noted to exist for the general spin-S case. For the spin-1/2 case, we further carry out the triplon analysis in the ground state, to study the competition between the Heisenberg and the multiple spin interactions. This approximate calculation exhibits a continuous quantum phase transition from the dimer order to N\'eel order.

Quantum phase transition in the four-spin exchange antiferromagnet

We study the $S=1/2$ Heisenberg antiferromagnet on a square lattice with nearest-neighbor and plaquette four-spin exchanges [introduced by A. W. Sandvik, Phys. Rev. Lett. 98, 227202 (2007).] This model undergoes a quantum phase transition from a spontaneously dimerized phase to N\'eel order at a critical coupling. We show that as the critical point is approached from the dimerized side, the system exhibits strong fluctuations in the dimer background, reflected in the presence of a low-energy singlet mode, with a simultaneous rise in the triplet quasiparticle density. We find that both singlet and triplet modes of high density condense at the transition, signaling restoration of lattice symmetry. In our approach, which goes beyond mean-field theory in terms of the triplet excitations, the transition appears sharp; however since our method breaks down near the critical point, we argue that we cannot make a definite conclusion regarding the order of the transition.

Antiferromagnetic order of repulsively interacting fermions on optical lattices

The N\'eel state in fermionic mixtures of two pseudospin species in an optical lattice is analyzed at low temperatures. Experimentally it remains a challenge to demonstrate antiferromagnetic correlations in ultracold fermionic quantum gases. We find that, while in balanced systems the N\'eel order parameter can point in any spatial direction, in imbalanced mixtures antiferromagnetism is strictly perpendicular to the quantization axis (i.e., the $z$ axis). Since, experimentally, one always has to assume some minimal imbalance this should have important consequences for ongoing experiments.