Frustrated Spin Chain Research Articles

Detecting quantum phase transitions in a frustrated spin chain via transfer learning of a quantum classifier algorithm

Detecting quantum phase transitions in a frustrated spin chain via transfer learning of a quantum classifier algorithm

The thermally assisted magnetization and dielectric relaxation in spin frustrated Ca3Co2O6

The incompatibility between the antiferromagnetic exchange interaction and the triangular lattice makes Ca3Co2O6 become a frustrated system. It leads to the existence of disordered magnetic structure in the frustrated spin chains. At low temperature, the disordered spins are frozen. In this study, the Ca3Co2O6 was prepared and its low temperature dynamic behaviors were characterized. The spin freezing peak and the decay of magnetization with time well confirm the thermally assisted magnetization. Since that the flip of the spins can result in the conservation of the total angular momentum and the conserved angular momentum can make the adjacent lattice feel a transfer torque. In response to variation of magnetization, the dielectric permittivity of Ca3Co2O6 also presents relaxation feature. For the isothermal dielectric permittivity, it not only depends greatly on the sweep rates of magnetic field but also decays with time. This detectable variation of the dielectric property in Ca3Co2O6 suggests that the thermally assisted dielectric relaxation is an alternative method for characterizing the dynamic behaviors of the frustrated system.

A metamagnetoelectric view of the linarite PbCuSO[formula omitted](OH)2 cuprate spin chain

The cross responses of the magnetic and electric properties of linarite PbCuSO4(OH)2 to the conjugated electric and magnetic fields are investigated. The theoretical laboratory is built on a frustrated spin chain model of the crystal. A critical phase of metatransitions is strongly highlighted below TN. The sharp magnetic and electric anomalies are attributed to spin-flops. Moreover, the metamagnetic and metaelectric transitions fitting exactly at the same points as the same phenomenon in the magnetoelectric design appear as a signature of the metamagnetoelectric effect. These findings suggest that linarite could be classified as a metamagnetoelectric multiferroic, with promising applications.

Emergent O(4) symmetry at an one-dimensional deconfined quantum tricritical point

We show an O(4) symmetry emerges at a deconfined quantum tricritical point of a valence bond solid (VBS) and two ferromagnetic phases in an S = 1/2 frustrated spin chain by combining analytical analysis and numerical calculations with the time evolution of infinite matrix product states. With this symmetry, the valence-bond solid and the three magnetic order parameters form an O(4) pseudovector in the infrared limit, and can continuously rotate into each other. We numerically determine the location of the quantum tricritical point and study the scaling of the correlation functions of the O(4) vector components and associated conserved currents. The critical behaviors of these correlation functions are all in accord with field theoretical results. The emergent O(4) symmetry at the tricritical point is justified by the integer value of the scaling dimension of the emergent Noether conserved currents. Our findings not only give direct evidence of such a high emergent symmetry at an one-dimensional VBS to magnetic transition but also shed light on exploring emergent symmetries in higher dimensions.

Excitation and transport of bound magnon clusters in frustrated ferromagnetic chain

We investigate magnetic excitations and spin transport properties of a frustrated spin chain with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor exchange couplings in a magnetic field by density-matrix renormalization group methods. In the field-induced quadrupole and octupole regimes, the low-energy excitation is governed by two-and three-magnon bound states, respectively, so that bound magnon clusters would contribute to the spin transport. We show that spin current correlations decrease when the system goes from the quadrupole regime into the octupole regime. This indicates that the spin transport is suppressed in the octupole regime, although bound three-magnon clusters carry a larger amount of angular momentum than bound two-magnon clusters.

Fate of local order in topologically frustrated spin chains

It has been recently shown that the presence of topological frustration, induced by periodic boundary conditions in an antiferromagnetic $XY$ chain made of an odd number of spins, prevents the realization of a perfectly staggered local order. Starting from this result and exploiting a recently introduced approach that enables the direct calculation of the expectation value of any operator with support over a finite range of lattice sites, in this work, we investigate the possible fates of local orders. We show that, regardless of the variety of possible situations, they can be all arranged in two different cases. A system admits a finite local order only if the ground state is degenerate, with at least two elements whose momenta differ, in the thermodynamic limit, by $\ensuremath{\pi}$, and this order breaks translational symmetry. In all other cases, any local order decays to zero, algebraically (or faster) in the chain length. Moreover, we show that, in some cases, which of the two possibilities is realized, may depend on the sequence of chain lengths with which the thermodynamic limit is reached. These results are established both analytically and by exact diagonalization and illustrated through examples.

Control of a polar order via magnetic field in a vector-chiral magnet

Vector-chiral (VC) antiferromagnetism is a spiral-like ordering of spins which may allow ferroelectricity to occur due to loss of space inversion symmetry. In this paper we report direct experimental observation of ferroelectricity in the VC phase of $\beta$-TeVO$_4$, a frustrated spin chain system with pronounced magnetic anisotropy and a rich phase diagram. Saturation polarization is proportional to neutron scattering intensities that correspond to the VC magnetic reflection. This implies that inverse Dzyaloshinskii-Moriya mechanism is responsible for driving electric polarization. Linear magnetoelectric coupling is absent, however an unprecedented dependence of electric coercive field on applied magnetic field reveals a novel way of manipulating multiferroic information.

Ground-state properties of a quantum frustrated spin chain with side spins and arbitrary spin s

The properties of the spin-s frustrated antiferromagnetic Heisenberg chain with side spins are studied by means of the coupled cluster method and the numerical exact diagonalization method. The results of the two methods both manifest that the ground state quantum phase diagram of the model consists of the Néel phase and the canted phase characterized by two pitch angles, irrespective of the value of the spin quantum number s. Although the phenomenon of quantum melting of magnetic long-range order is absent in the model, quantum fluctuation exerts an important influence on the property of the model. In addition to the reduction of magnetization, the nature of the phase transition from the Néel state to the canted state transforms from a classical second-order transition to a quantum first-order transition at any finite value of s. It is observed that the ways one of the two pitch angles evolves with frustration in quantum and classical cases, are qualitatively different in the large frustration parameter region. The location of the critical point and the physical quantities, including the ground state energy per spin and the magnetic order parameter, move toward their classical values in the form of power series in s.

Probing the interplay between lattice dynamics and short-range magnetic correlations in CuGeO3 with femtosecond RIXS

Investigations of magnetically ordered phases on the femtosecond timescale have provided significant insights into the influence of charge and lattice degrees of freedom on the magnetic sub-system. However, short-range magnetic correlations occurring in the absence of long-range order, for example in spin-frustrated systems, are inaccessible to many ultrafast techniques. Here, we show how time-resolved resonant inelastic X-ray scattering (trRIXS) is capable of probing such short-ranged magnetic dynamics in a charge-transfer insulator through the detection of a Zhang–Rice singlet exciton. Utilizing trRIXS measurements at the O K-edge, and in combination with model calculations, we probe the short-range spin correlations in the frustrated spin chain material CuGeO3 following photo-excitation, revealing a strong coupling between the local lattice and spin sub-systems.

Effect of Spin Fluctuations on Magnetic Properties of Frustrated Spin Chains

Using functional integral method, we investigate the magnetic properties of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${J_1} - {J_2}$</tex-math></inline-formula> frustrated spin chain in the presence of a longitudinal magnetic field and a single-ion anisotropy at the vicinity of zero temperature and at finite temperatures for both cases <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${J_1} &gt; 0$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${J_1} &lt; 0$</tex-math></inline-formula> . We focus on the range of the frustrated parameter where the ground state is still ferromagnetic or antiferromagnetic. From that, we discuss the significant effect of the thermal and quantum fluctuations due to the frustration and find critical values of the frustrated parameter. Thus, we see a drastic effect due to the fluctuations at the critical points, which can cause a breakdown of a given approach. We also compared the obtained results to the experimental data from Cu[ampy]Br <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and found an agreement between the calculated susceptibility and the experimental susceptibility, except that an antiferromagnetic phase transition is found only in the calculated susceptibility.

Haldane and dimer phases in a frustrated spin chain: an exact groundstate and associated topological phase transition

A Heisenberg spin-s chain with alternating ferromagnetic (FM) () and antiferromagnetic () nearest-neighbor (NN) interactions, exhibits the dimer and spin-2s Haldane phases in the limits and respectively. These two phases are understood to be topologically equivalent. Induction of the frustration through the next NN FM interaction () produces a very rich quantum phase diagram. With frustration, the whole phase diagram is divided into a FM and a nonmagnetic (NM) phase. For s = 1/2, the full NM phase is seen to be of Haldane–dimer type, but for s > 1/2, a spiral phase comes between the FM and the Haldane–dimer phases. The study of a suitably defined string-order parameter and spin-gap at the phase boundary indicates that the Haldane–dimer and spiral phases have different topological characters. We also find that, along the line in the NM phase, an NN dimer state is the exact groundstate, provided where κ ⩽ s + h for applied magnetic field h. Without magnetic field, the position of JC is on the FM–NM phase boundary when s = 1/2, but for s > 1/2, the location of JC is on the phase separation line between the Haldane–dimer and spiral phases.

Thermal density matrix renormalization group for highly frustrated quantum spin chains: A user perspective

Thermal DMRG is investigated with emphasis of employability in molecular magnetism studies. To this end magnetic observables at finite temperature are evaluated for two one-dimensional quantum spin systems: a Heisenberg chain with nearest-neighbor antiferromagnetic interaction and a frustrated sawtooth (delta) chain. It is found that thermal DMRG indeed accurately approximates magnetic observables for the chain as well as for the sawtooth chain, but in the latter case only for sufficiently high temperatures. We speculate that the reason is due to the peculiar structure of the low-energy spectrum of the sawtooth chain induced by frustration.

Coexistence of valence-bond formation and topological order in the Frustrated Ferromagnetic $J_1$-$J_2$ Chain

Frustrated one-dimensional (1D) magnets are known as ideal playgrounds for new exotic quantum phenomena to emerge. We consider an elementary frustrated 1D system: the spin-\frac{1}{2}12 ferromagnetic (J_1J1) Heisenberg chain with next-nearest-neighbor antiferromagnetic (J_2J2) interactions. On the basis of density-matrix renormalization group calculations we show the existence of a finite spin gap at J_2/|J_1|&gt;1/4J2/|J1|&gt;1/4 and we find the ground state in this region to be a valence bond solid (VBS) with spin-singlet dimerization between third-neighbor sites. The VBS is the consequence of spontaneous symmetry breaking through order by disorder. Quite interestingly, this VBS state has a Affleck-Kennedy-Lieb-Tasaki-type topological order. This is the first example of a frustrated spin chain in which quantum fluctuations induce gapped topological order.

Thermodynamics of metamagnetoelectric effect in multiferroics

Abstract Magnetoelectric coupling in multiferroics gives rise to various properties such as metamagnetoelectric effect since external fields act. In this study, a general thermodynamic framework is developed to investigate metamagnetoelectric effects in multiferroic materials. The model used is a quasi-two dimensional frustrated spin chain controlled by a static electric field in y-direction and magnetic field in z-direction. The effects of metamagnetoelectric transitions on entropy, heat capacity and on the linear magnetoelectric coupling factor are assessed using Fermi-Dirac statistics of quantum gases and the Landau theory. The entropy behavior is shown to be similar to that of the magnetic susceptibility. In fact, while the magnetic susceptibility characterizes the variations of magnetization and accordingly emphasizes the ferroic transition points of this order, the intrinsic physics of these transition points highlights a muddle occurring due to a rearrangement of magnetic moments in the system, and this is accurately described in terms of entropy. The transition effects due to this rearrangement described in terms of entropy at the corresponding critical points show different loop to that of the heat capacity. The opposite loop showed by the heat capacity compared to the entropy is its weakening at the exact transition point in spite of its strengthening during the transition process. It is also recorded only a few ranges of the electric field which allows the effect provided. The temperature dependence of the magnetoelectric coupling highlights how it is continuously weakened by the increase of temperature, leading to a second order transition from the metamagnetoelectric state.

Rigorous decoupling between edge states in frustrated spin chains and ladders

We investigate the occurrence of exact zero modes in one-dimensional quantum magnets of finite length that possess edge states. Building on conclusions first reached in the context of the spin-1/2 XY chain in a field, then for the spin-1 $J_1-J_2$ Heisenberg model, we show that the development of incommensurate correlations in the bulk invariably leads to oscillations in the sign of the coupling between edge states, hence to exact zero energy modes at the crossing points where the coupling between the edge states rigorously vanishes. This is true regardless of the origin of the frustration (e.g. next-nearest neighbor coupling or biquadratic coupling for the spin-1 chain), of the value of the bulk spin (we report on spin-1/2, spin-1 and spin-2 examples), and of the value of the edge-state emergent spin (spin-1/2 or spin-1).

Spin-specific heat determination of the ratio of competing first- and second-neighbor exchange interactions in frustrated spin- 12 chains

The magnetic susceptibility $\chi(T)$ of spin-1/2 chains is widely used to quantify exchange interactions, even though $\chi(T)$ is similar for different combinations of ferromagnetic $J_1$ between first neighbors and antiferromagnetic $J_2$ between second neighbors. We point out that the spin specific heat $C(T)$ directly determines the ratio $\alpha = J_2/|J_1|$ of competing interactions. The $J_1-J_2$ model is used to fit the isothermal magnetization $M(T,H)$ and $C(T,H)$ of spin-1/2 Cu(II) chains in LiCuSbO$_4$. By fixing $\alpha$, $C(T)$ resolves the offsetting $J_1$, $\alpha$ combinations obtained from $M(T,H)$ in cuprates with frustrated spin chains.

Competing interactions in artificial spin chains

The low-energy magnetic configurations of artificial frustrated spin chains are investigated using magnetic force microscopy and micromagnetic simulations. Contrary to most studies on two-dimensional artificial spin systems where frustration arises from the lattice geometry, here magnetic frustration originates from competing interactions between neighboring spins. By tuning continuously the strength and sign of these interactions, we show that different magnetic phases can be stabilized. Comparison between our experimental findings and predictions from the one-dimensional Anisotropic Next-Nearest-Neighbor Ising (ANNNI) model reveals that artificial frustrated spin chains have a richer phase diagram than initially expected. Besides the observation of several magnetic orders and the potential extension of this work to highly-degenerated artificial spin chains, our results suggest that the micromagnetic nature of the individual magnetic elements allows observation of metastable spin configurations.

Crossover from an incommensurate singlet spiral state with a vanishingly small spin gap to a valence-bond solid state in dimerized frustrated ferromagnetic spin chains

Motivated by the magnetic properties of the spin-chain compounds LiCuSbO$_4$$\equiv$LiSbCuO$_4$ and Rb$_2$Cu$_2$Mo$_3$O$_{12}$, we study the ground state of the Heisenberg chain with dimerized nearest-neighbor ferromagnetic (FM)($J_1, J_1^\prime<0$) and next-nearest-neighbor antiferromagnetic ($J_2>0$) couplings. Using the density-matrix renormalization group technique and spin-wave theory we find a first-order transition between a fully-polarized FM and an incommensurate spiral state at $2\alpha=\beta/(1+\beta)$, where $\alpha$ is the frustration ratio $J_2/|J_1|$ and $\beta$ the degree of dimerization $J_1^\prime/J_1$.In the singlet spiral state the spin-gap is vanishingly small in the vicinity of the FM transition, corresponding to a situation of LiCuSbO$_4$. For larger $\alpha$, corresponding to Rb$_2$Cu$_2$Mo$_3$O$_{12}$, and smaller $\beta$ there is a crossover from this frustration induced incommensurate state to an Affleck-Lieb-Kennedy-Tasaki-type valence bond solid state with substantial spin-gaps.

Angular dependence of electron spin resonance for detecting the quadrupolar liquid state of frustrated spin chains

Spin nematic phase is a phase of frustrated quantum magnets with a quadrupolar order of electron spins. Since the spin nematic order is usually masked in experimentally accessible quantities, it is important to develop a methodology for detecting the spin nematic order experimentally. In this paper we propose a convenient method for detecting quasi-long-range spin nematic correlations of a quadrupolar Tomonaga-Luttinger liquid state of $S=1/2$ frustrated ferromagnetic spin chain compounds, using electron spin resonance (ESR). We focus on linewidth of a so-called paramagnetic resonance peak in ESR absorption spectrum. We show that a characteristic angular dependence of the linewidth on the direction of magnetic field arises in the spin nematic phase. Measurments of the angular dependence give a signature of the quadrupolar Tomonaga-Luttinger liquid state. In our method we change only the direction of the magnetic field, keeping the magnitude of the magnetic field and the temperature. Therefore, our method is advantageous for investigating the one-dimensional quadrupolar liquid phase that usually occupies only a narrow region of the phase diagram.

Frustrated Antiferromagnetic Spin Chains of Edge-Sharing Tetrahedra in Volcanic Minerals K3Cu3(Fe0.82Al0.18)O2(SO4)4 and K4Cu4O2(SO4)4MeCl

The calculation of the sign and strength of magnetic interactions in two noncentrosymmetric minerals (klyuchevskite, K3Cu3(Fe0.82Al0.18)O2(SO4)4 and piipite, K4Cu4O2(SO4)4Cu0.5Cl) has been performed based on the structural data. As seen from the calculation results, both minerals comprise quasi-one-dimensional frustrated antiferromagnets. They contain frustrated spin chains from edge-sharing Cu4 tetrahedra with strong antiferromagnetic couplings within chains and very weak ones between chains. Strong frustration of magnetic interactions is combined with the presence of the electric polarization in tetrahedra chains in piipite. The uniqueness of magnetic structures of these minerals caused by peculiarities of their crystal structures has been discussed. Keywords: Frustrated quasi-one-dimensional antiferromagnets, tetrahedral spin chains, klyuchevskite K3Cu3(Fe0.82Al0.18)O2(SO4)4, piypite K4Cu4O2(SO4)4MeCl