Antiferromagnetic Spin Chain Research Articles

Gapless chiral spin liquid in a kagome Heisenberg model

Motivated by recent experiments on the Heisenberg S=1/2 quantum spin liquid candidate material kapellasite, we classify all possible chiral (time-reversal symmetry breaking) spin liquids with fermionic spinons on the kagome lattice. We obtain the phase diagram for the physically relevant extended Heisenberg model, comparing the energies of a wide range of microscopic variational wave functions. We propose that, at low temperature, kapellasite exhibits a gapless chiral spin liquid phase with spinon Fermi surfaces. This two-dimensional state inherits many properties of the nearby one-dimensional phase of decoupled anti-ferromagnetic spin chains, but also shows some remarkable differences. We discuss the spin structure factors and other physical properties.

Low dimensionalization of magnetic ordering inSr2VO4by hydride ion substitution

Substitution of an oxygen anion with a hydrogen anion induced the low dimensionalization of magnetic ordering in a transition metal oxide $\mathrm{S}{\mathrm{r}}_{2}\mathrm{V}{\mathrm{O}}_{4}$. Upon increasing $x$ up to $\ensuremath{\sim}1$ in $\mathrm{S}{\mathrm{r}}_{2}\mathrm{V}{\mathrm{O}}_{4\ensuremath{-}x}{\mathrm{H}}_{x}$, the hydride ions were ordered linearly, and the magnetic susceptibility was simultaneously suppressed. It was found that this suppression was attributed to the formation of a quasi-one-dimensional antiferromagnetic spin chain, maintaining that each of the vanadium cations is two-dimensionally bridged by hydride and oxide ions. Density functional theory calculations demonstrate that the quasi-one-dimensional property is caused by much enhanced anisotropic exchange couplings $({J}_{1}/{J}_{2}\ensuremath{\sim}6)$ originating from the absence of $\ensuremath{\pi}$ bonding between $\mathrm{H}\phantom{\rule{0.28em}{0ex}}1s$ and $\mathrm{V}\phantom{\rule{0.28em}{0ex}}3d$ orbitals. Utilizing a hydride ion that has an ionic radius similar to an oxygen anion and only one energetically available orbital of $1s$ is a different approach to realization of magnetic low dimensionalization in $3d$ early transition metal oxides.

Suppression of the impurity-induced local magnetism by the opening of a spin pseudogap in Ni-dopedSr2CuO3

The $S=1/2$ antiferromagnetic Heisenberg spin chain compound ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}$ doped with $1%$ and $2%$ of Ni impurities has been studied by means of $^{63}\mathrm{Cu}$ nuclear magnetic resonance. A strong decrease of the spin-lattice relaxation rate ${T}_{1}^{\ensuremath{-}1}$ at low temperatures points toward a spin gap, while a stretching exponent $\ensuremath{\lambda}<1$ and a frequency dependence of ${T}_{1}^{\ensuremath{-}1}$ indicate that this spin gap varies spatially and should rather be characterized as a spin pseudogap. The magnitude of the spin pseudogap scales with doping level. Our results therefore evidence the finite-size character of this phenomenon. Moreover, an unusual narrowing of the low-temperature NMR lines reveals the suppression of the impurity-induced staggered paramagnetic response with increasing doping level.

A study of the magnetic properties of a quasi-one-dimensional magnet β-TeVO4 in the frame of the J1–J2 model

Magnetic properties of single crystal β-TeVO4 with a zigzag chain of magnetic centers (V4+ ions, S = 1/2) are analyzed in the framework of the J1–J2 model. The best agreement with experimental data is obtained for the J1–J2 model with parameters J1/kB = −38.33 K and J2/kB = 29.48 K (gb = 2.07, ga,c = 1.99). In contrast to the previously used model (a uniform antiferromagnetic spin chain system with J1/kB = 21.4 K (gb = 2.28, ga,c = 2.18)), this improved result allows one to consider the object under study as a zigzag chain system with a dominant ferromagnetic exchange between the nearest neighbors and an antiferromagnetic interaction between the next-nearest neighbors.

Phonon-Modulated Magnetic Interactions and Spin Tomonaga-Luttinger Liquid in the p-Orbital Antiferromagnet CsO2.

The magnetic response of antiferromagnetic CsO2, coming from the p-orbital S=1/2 spins of anionic O2(-) molecules, is followed by 133Cs nuclear magnetic resonance across the structural phase transition occurring at T(s1)=61 K on cooling. Above T(s1), where spins form a square magnetic lattice, we observe a huge, nonmonotonic temperature dependence of the exchange coupling originating from thermal librations of O2(-) molecules. Below T(s1), where antiferromagnetic spin chains are formed as a result of p-orbital ordering, we observe a spin Tomonaga-Luttinger-liquid behavior of spin dynamics. These two interesting phenomena, which provide rare simple manifestations of the coupling between spin, lattice, and orbital degrees of freedom, establish CsO2 as a model system for molecular solids.

Many-body localization transition in random quantum spin chains with long-range interactions

While there are well-established methods to study delocalization transitions of single particles in random systems, it remains a challenging problem how to characterize many-body delocalization transitions. Here, we use a generalized real-space renormalization group technique to study the anisotropic Heisenberg model with long-range interactions, decaying with a power α, which are generated by placing spins at random positions along the chain. This method permits a large-scale finite-size scaling analysis. We examine the full distribution function of the excitation energy gap from the ground state and observe a crossover with decreasing α. At the full distribution coincides with a critical function. Thereby, we find strong evidence for the existence of a many-body localization transition in disordered antiferromagnetic spin chains with long-range interactions.

Magnetization plateaus in the antiferromagnetic Ising chain with single-ion anisotropy and quenched disorder

We have studied the presence of plateaus on the low-temperature magnetization of an antiferromagnetic spin-1 chain, as an external uniform magnetic field is varied. A crystal-field interaction is present in the model and the exchange constants follow a random quenched (Bernoulli or Gaussian) distribution. Using a transfer-matrix technique we calculate the largest Lyapunov exponent and, from it, the magnetization at low temperatures as a function of the magnetic field, for different values of the crystal field and the width of the distributions. For the Bernoulli distribution, the number of plateaus increases, with respect to the uniform case [Litaiff etal., Solid State Commun. 147, 494 (2008)] and their presence can be linked to different ground states, when the magnetic field is varied. For the Gaussian distributions, the uniform scenario is maintained, for small widths, but the plateaus structure disappears as the width increases.

Electron Spin Resonance in Quasi-One-Dimensional Quantum Antiferromagnets: Relevance of Weak Interchain Interactions

We discuss universal features on the electron spin resonance (ESR) of a temperature-induced Tomonaga-Luttinger liquid phase in a wide class of weakly coupled $S=1/2$ antiferromagnetic spin chains such as spin ladders, spin tubes and three-dimensionally coupled spin chains. We show that the ESR linewidth of various coupled chains increases with lowering temperature while the linewidth of a single spin chain is typically proportional to temperature. This broadening with lowering temperature is attributed to anisotropic interchain interactions and has been indeed observed in several kinds of three-dimensional (3D) magnets of weakly coupled spin chains above the 3D ordering temperature. We demonstrate that our theory can account for anomalous behaviors of the linewidths in an $S=1/2$ four-leg spin tube compound Cu$_2$Cl$_4 \cdot $H$_8$C$_4$SO$_2$ (abbreviated to Sul-Cu$_2$Cl$_4$) and a three-dimensionally coupled $S=1/2$ spin chain compound CuCl$_2\cdot 2$NC$_5$H$_5$.

Spin dynamics of the anisotropic spin-1 antiferromagnetic chain at finite magnetic fields

We present results of a study of the antiferromagnetic spin-1 chain, subject to the simultaneous presence of single-ion anisotropy and external magnetic fields. Using quantum Monte-Carlo based on the stochastic series expansion method we first uncover a rich quantum phase diagram comprising N\'eel, Haldane, Luttinger liquid, and large anisotropy phases. Second, we scan across this phase diagram over a wide range of parameters, evaluating the transverse dynamic structure factor, which we show to exhibit sharp massive modes, as well as multi particle continua. For vanishing anisotropy and fields, comparison with existing results from other analytic and numerical approaches shows convincing consistency.

Experimental realization of long-distance entanglement between spins in antiferromagnetic quantum spin chains

Quantum communication relies on the ability to entangle quantum states. Experiments now show that this is possible in a bulk material, with unpaired spins at the ends of antiferromagnetic spin chains entangled over long distances.

Optimizing quantum state transfer in multi-excitation spin chains via information flux

The transfer of quantum states between distant nodes is one of the most fundamental tasks in quantum-information processing. Recent studies show that the antiferromagnetic spin chain initially prepared in a multi-excitation state can provide suitable pathways for quantum state transfer. In this paper, we investigate the quality of state transfer through a uniformly coupled antiferromagnetic spin chain where the initial state of the channel varies with the number of spin excitations. Firstly, by analyzing the dynamics of observables for the output qubit using the information-flux approach, the explicit relation about how the average fidelity of state transfer depends on the initial state of the spin channel is obtained. The results show that the average fidelity of state transfer through a multi-excitation spin channel only relates to the parity of the number of spin excitations in the channel. Then we compare the maximum average fidelity of state transfer through the odd-excitation with those through the even-excitation spin channels, and provide a simple criterion to optimize the quality of state transfer by choosing appropriate channels from the odd-excitation and the even-excitation channels. Compared with the previous studies which initialize the chains into the ground state of the ferromagnetic medium or the Nel state, the maximum average fidelity of state transfer is evidently enhanced by using the optimized channel. Moreover, we analyze the entanglement distribution through the channel having different number of spin excitations via the information-flux approach. It is found that the quality of entanglement distribution not only relates to the number of initial spin excitations present in the channel, but also depends on the initial ordering of these excited spins. The numerical results suggest that the amount of distributed entanglement and duration of distribution in the channel where all spins are down or up are larger than those in other excited channels. Based on these results, we can choose appropriate quantum channels for state transfer and entanglement distribution in practice.

Frustration and multicriticality in the antiferromagnetic spin-1 chain

We study the spin $S=1$ Heisenberg chain, with nearest neighbor, next nearest neighbor ($\alpha$) and biquadratic ($\beta$) interactions using a combination of the density matrix renormalization group (DMRG), an analytic variational matrix product state wavefunction, and non-Abelian bosonization. We study the effect of frustration ($\alpha>0$) on the Haldane phase with $-1\leq \beta < 1$ which reveals a rich phase diagram. For $-1<\beta<\beta^\ast$, we establish the existence of a spontaneously dimerized phase for large $\alpha>\alpha_c$, separated from the Haldane phase by the critical line $\alpha_c(\beta)$ of second-order phase transitions connected to the Takhtajan--Babudjian integrable point $\alpha_c(\beta=-1)=0$. In the opposite regime, $\beta>\beta^\ast$, the transition from the Haldane phase becomes first-order into the next nearest neighbor (NNN) AKLT phase. Based on field theoretical arguments and DMRG calculations, we conjecture that these two regimes are separated by a multicritical point ($\beta^\ast, \alpha^\ast$) of a different universality class, described by the $SU(2)_4$ Wess--Zumino--Witten critical theory. From the DMRG calculations we estimate this multicritical point to lie in the range $-0.2<\beta^\ast<-0.15$ and $0.47<\alpha^\ast < 0.53$. We find that the dimerized and NNN-AKLT phases are separated by a line of first-order phase transitions that terminates at the multicritical point. Inside the Haldane phase, we show the existence of two incommensurate crossovers: the Lifshitz transition and the disorder transition of the first kind, marking incommensurate correlations in momentum and real space, respectively. We show these crossover lines stretch across the entire $(\beta,\alpha)$ phase diagram, merging into a single incommensurate-to-commensurate transition line for negative $\beta\lesssim \beta^\ast$ outside the Haldane phase.

Magnetocaloric effect in the spin-1/2 chain with competing interactions

We study the magnetocaloric effect for the integrable antiferromagnetic Heisenberg spin chain with competing interactions. We computed the Grüneisen parameter, which is closely related to the magnetocaloric effect, for the quantum spin chain in the thermodynamic limit. This is obtained by means of the solution of a set of non-linear integral equations, which describes the thermodynamics of the model. We also provide results for the entropy S and the isentropes in the (H, T) plane.

Magnetization and phase transition induced by circularly polarized laser in quantum magnets

We theoretically predict a nonequilibrium phase transition in quantum spin systems induced by a laser, which provides a purely quantum-mechanical way of coherently controlling magnetization. Namely, when a circularly polarized laser is applied to a spin system, the magnetic component of a laser is shown to induce a magnetization normal to the plane of polarization, leading to an ultrafast phase transition. We first demonstrate this phenomenon numerically for an $S=1$ antiferromagnetic Heisenberg spin chain, where a new state emerges with magnetization perpendicular to the polarization plane of the laser in place of the topologically ordered Haldane state. We then elucidate its physical mechanism by mapping the system to an effective static model. The theory also indicates that the phenomenon should occur in general quantum spin systems with a magnetic anisotropy. The required laser frequency is in the terahertz range, with the required intensity being within a prospective experimental feasibility.

Experimental confirmation of spin gap in antiferromagnetic alternating spin-32chain substancesRCrGeO5(R=YorSm154) by inelastic neutron scattering experiments

A spin-singlet ground state with a spin gap has been discovered in antiferromagnetic spin chain substances when the spin value is 1/2, 1, or 2. To find spin-gap (singlet-triplet) excitations in spin-$\frac{3}{2}$ chain substances, we performed inelastic neutron scattering and magnetization measurements on $R\mathrm{CrGeO}{}_{5}$ ($R=\text{Y}$ or Sm) powders. As expected, we observed spin-gap excitations and the dispersion relation of the lowest magnetic excitations. We proved that the spin system of $\mathrm{Cr}{}^{3+}$ was an antiferromagnetic alternating spin-$\frac{3}{2}$ chain. We describe the influence of frustration between nearest-neighbor and next-nearest-neighbor exchange interactions in the chain.

Sign structure and ground-state properties for aspin−St−Jchain

The antiferromagnetic Heisenberg spin chain of odd spin $S$ is in the Haldane phase with several defining physical properties, such as thermodynamical ground-state degeneracy, symmetry-protected edge states, and nonzero string order parameter. If nonzero hole concentration $\ensuremath{\delta}$ and hole hopping energy $t$ are considered, the spin chain is replaced by a $\text{spin}\ensuremath{-}S$ $t\ensuremath{-}J$ chain. The motivation of this paper is to generalize the discussions of the Haldane phase to the doped spin chain. The first result of this paper is that, for the model considered here, the ${\mathbb{Z}}_{2}$ sign structure in the usual Ising basis can be totally removed by two consecutive unitary transformations consisting of a spatially local one and a nonlocal one. Direct from the sign structure, the second result of this paper is that the Marshall theorem and the Lieb-Mattis theorem for pure spin systems are generalized to the $t\ensuremath{-}J$ chain for arbitrary $S$ and $\ensuremath{\delta}$. A corollary of the theorem provides us with the ground-state degeneracy in the thermodynamic limit. The third result of this paper is about the phase diagram. We show that the defining properties of the Haldane phase survive in the small $t/J$ limit. The large $t/J$ phase supports a gapped spin sector with similar properties (ground-state degeneracy, edge state, and string order parameter) of the Haldane chain, although the charge sector is gapless.

EffectiveS=12description of theS=1chain with strong easy-plane anisotropy

We present a study of the one-dimensional S=1 antiferromagnetic spin chain with large easy plane anisotropy, with special emphasis on field-induced quantum phase transitions. Temperature and magnetic field dependence of magnetization, specific heat, and thermal conductivity is presented using a combination of numerical methods. In addition, the original S=1 model is mapped into the low-energy effective S=1/2 XXZ Heisenberg chain, a model which is exactly solvable using the Bethe ansatz technique. The effectiveness of the mapping is explored, and we show that all considered quantities are in qualitative, and in some cases quantitative, agreement. The thermal conductivity of the considered S=1 model is found to be strongly influenced by the underlying effective description. Furthermore, we elucidate the low-lying electron spin resonance spectrum, based on a semi--analytical Bethe ansatz calculation of the effective S=1/2 model.

Variational cluster approximation to the thermodynamics of quantum spin systems

We derive a variational cluster approximation for Heisenberg spin systems at finite temperature based on the ideas of the self-energy functional theory by Potthoff for fermionic and bosonic systems with local interactions. Partitioning the real system into a set of clusters, we find an analytical expression for the auxiliary free energy, depending on a set of variational parameters defined on the cluster, whose stationary points provide approximate solutions from which the thermodynamics of spin models can be obtained. We explicitly describe the technical details of how to evaluate the free energy for finite clusters and remark on specific problems and possible limitations of the method. To test the approximation we apply it to the antiferromagnetic spin chain and compare the results for varying cluster sizes and choices of variational parameters with the exact Bethe ansatz solution.

Spin gap in the single spin-12chain cuprateSr1.9Ca0.1CuO3

We report $^{63}$Cu nuclear magnetic resonance and muon spin rotation measurements on the S=1/2 antiferromagnetic Heisenberg spin chain compound Sr$_{1.9}$Ca$_{0.1}$CuO$_3$. An exponentially decreasing spin-lattice relaxation rate 1/T$_1$ indicates the opening of a spin gap. This behavior is very similar to what has been observed for the cognate zigzag spin chain compound Sr$_{0.9}$Ca$_{0.1}$CuO$_2$, and confirms that the occurrence of a spin gap upon Ca doping is independent of the interchain exchange coupling $J'$. Our results therefore generally prove the appearance of a spin gap in an antiferromagnetic Heisenberg spin chain induced by a local bond disorder of the intrachain exchange coupling $J$. A low temperature upturn of 1/T$_1$ evidences growing magnetic correlations. However, zero field muon spin rotation measurements down to 1.5 K confirm the absence of magnetic order in this compound which is most likely suppressed by the opening of the spin gap.

Crystal structure, physical properties, and electronic and magnetic structure of the spin S = 5/2 zigzag chain compound Bi2Fe(SeO3)2OCl3.

We report the synthesis and characterization of the new bismuth iron selenite oxochloride Bi2Fe(SeO3)2OCl3. The main feature of its crystal structure is the presence of a reasonably isolated set of spin S = 5/2 zigzag chains of corner-sharing FeO6 octahedra decorated with BiO4Cl3, BiO3Cl3, and SeO3 groups. When the temperature is lowered, the magnetization passes through a broad maximum at Tmax ≈ 130 K, which indicates the formation of a magnetic short-range correlation regime. The same behavior is demonstrated by the integral electron spin resonance intensity. The absorption is characterized by the isotropic effective factor g ≈ 2 typical for high-spin Fe(3+) ions. The broadening of ESR absorption lines at low temperatures with the critical exponent β = 7/4 is consistent with the divergence of the temperature-dependent correlation length expected for the quasi-one-dimensional antiferromagnetic spin chain upon approaching the long-range ordering transition from above. At TN = 13 K, Bi2Fe(SeO3)2OCl3 exhibits a transition into an antiferromagnetically ordered state, evidenced in the magnetization, specific heat, and Mössbauer spectra. At T < TN, the (57)Fe Mössbauer spectra reveal a low saturated value of the hyperfine field Hhf ≈ 44 T, which indicates a quantum spin reduction of spin-only magnetic moment ΔS/S ≈ 20%. The determination of exchange interaction parameters using first-principles calculations validates the quasi-one-dimensional nature of magnetism in this compound.