One-dimensional Quantum Magnets Research Articles

Quantum spin helices more stable than the ground state: Onset of helical protection

Topological magnetic structures are promising candidates for resilient information storage. An elementary example is spin helices in one-dimensional easy-plane quantum magnets. To quantify their stability, we numerically implement the stochastic Schr\"odinger equation and time-dependent perturbation theory for spin chains with fluctuating local magnetic fields. We find two classes of quantum spin helices that can reach and even exceed ground-state stability: spin-current-maximizing helices and, for fine-tuned boundary conditions, the recently discovered ``phantom helices.'' Beyond that, we show that the helicity itself (left or right rotating) is even more stable. We explain these findings by separated helical sectors and connect them to topological sectors in continuous spin systems. The resulting helical protection mechanism is a promising phenomenon for stabilizing helical quantum structures, e.g., in ultracold atoms and solid-state systems. We also identify a third type of phantom helix in the system.

Spatiotemporal Crossover between Low- and High-Temperature Dynamical Regimes in the Quantum Heisenberg Magnet.

The stranglehold of low temperatures on fascinating quantum phenomena in one-dimensional quantum magnets has been challenged recently by the discovery of anomalous spin transport at high temperatures. Whereas both regimes have been investigated separately, no study has attempted to reconcile them. For instance, the paradigmatic quantum Heisenberg spin-1/2 chain falls at low temperature within the Tomonaga-Luttinger liquid framework, while its high-temperature dynamics is superdiffusive and relates to the Kardar-Parisi-Zhang universality class in 1+1 dimensions. This Letter aims at reconciling the two regimes. Building on large-scale matrix product state simulations, we find that they are connected by a temperature-dependent spatiotemporal crossover. As the temperature T is reduced, we show that the onset of superdiffusion takes place at longer length and timescales ∝1/T. This prediction has direct consequences for experiments including nuclear magnetic resonance: it is consistent with earlier measurements on the nearly ideal Heisenberg S=1/2 chain compound Sr_{2}CuO_{3}, yet calls for new and dedicated experiments.

Quantum criticality and excitations of a long-range anisotropic XY chain in a transverse field

The critical breakdown of a one-dimensional quantum magnet with long-range interactions is studied by investigating the high-field polarized phase of the anisotropic XY model in a transverse field for the ferromagnetic and antiferromagnetic cases. While for the limiting case of the isotropic long-range XY model we can extract the elementary one-quasiparticle dispersion analytically and calculate two-quasiparticle excitation energies quantitatively in a numerical fashion, for the long-range Ising limit as well as in the intermediate regime we use perturbative continuous unitary transformations on white graphs in combination with classical Monte Carlo simulations for the graph embedding to extract high-order series expansions in the thermodynamic limit. This enables us to determine the quantum-critical breakdown of the high-field polarized phase by analyzing the gap closing including associated critical exponents and multiplicative logarithmic corrections. In addition, for the ferromagnetic isotropic XY model we determined the critical exponents $z$ and $\ensuremath{\nu}$ analytically by a bosonic quantum-field theory.

Magnetic phase diagram of the linear quantum ferro-antiferromagnet Cs2Cu2Mo3O12

A single-crystal sample of the frustrated quasi one-dimensional quantum magnet Cs$_{2}$Cu$_{2}$Mo$_{3}$O$_{12}$ is investigated by magnetic and thermodynamic measurements.A combination of specific heat and magnetic torque measurements maps out the entire $H$-$T$ phase diagram for three orientations.Remarkably, a new phase emerges below the saturation field, irrespective of the crystal orientation. It is suggested that the presaturation phase represents spin-nematic order or other multi-magnon condensate. The phase diagrams within the long-range ordered dome are qualitatively different for each geometry. In particular, multiple transitions are identified in the field along the chain direction.

Dispersions of many-body Bethe strings

Complex bound states of magnetic excitations, known as Bethe string, were predicted almost a century ago to exist in one-dimensional quantum magnets 1. The dispersions of the string states have so far remained the subject of intensive theoretical studies 2-7. By performing neutron scattering experiments on the one-dimensional Heisenberg-Ising antiferromagnet SrCo2V2O8 in high longitudinal magnetic fields, we reveal in detail the dispersion relations of the string states over the full Brillouin zone, as well as their magnetic field dependences. Furthermore the characteristic energy, the scattering intensity and linewidth of the observed string states exhibit excellent agreement with our precise Bethe Ansatz calculations. Our results establish the important role of string states in the quantum spin dynamics of one-dimensional systems, and will invoke studies of their dynamical properties in more general many-body systems.

One- and three-dimensional quantum phase transitions and anisotropy in Rb2Cu2Mo3O12

Single crystal samples of the frustrated quasi one-dimensional quantum magnet Rb$_{2}$Cu$_{2}$Mo$_{3}$O$_{12}$ are investigated by magnetic, thermodynamic, and electron spin resonance (ESR) measurements. Quantum phase transitions between the gapped, magnetically ordered and fully saturated phases are observed. Surprisingly, the former has a distinctive three-dimensional character, while the latter is dominated by one-dimensional quantum spin fluctuations. The entire $H$-$T$ phase diagram is mapped out and found to be substantially anisotropic. In particular, the lower critical fields differ by over 50\% depending on the direction of applied field, while the upper ones are almost isotropic, as is the magnetization above saturation. The ESR spectra are strongly dependent on field orientation and point to a helical structure with a rigidly defined spin rotation plane.

Chirality-driven ferroelectricity in LiCuVO4

Chirality or the handedness of objects is of prime importance in life science, biology, chemistry, and physics. It is also a major symmetry ingredient in frustrated magnets revealing spin-spiral ground states. Vector-chiral phases, with the twist (either clock- or counter clock-wise) between neighboring spins being ordered, but with disorder with respect to the angles between adjacent spins, have been predicted almost five decades ago. Experimental proofs, however, are rare and controversial. Here, we provide experimental evidence for such a phase in LiCuVO4, a one-dimensional quantum magnet with competing ferromagnetic and antiferromagnetic interactions. The vector-chiral state is identified via a finite ferroelectric polarization arising at temperatures well above the multiferroic phase exhibiting long-range three-dimensional spin-spiral and polar order. On increasing temperatures, spin order becomes suppressed at TN, whereas chiral long-range order still exist, leaving a temperature window with chirality-driven ferroelectricity in the presence of an external magnetic field.

Coupling of Spinons with Defects and Phonons in the Spin Chain Compound Ca_{2}CuO_{3}.

Extrinsic spinon scattering by defects and phonons instead of intrinsic spinon-spinon coupling is responsible for resistive magnetic heat transport in one-dimensional (1D) quantum magnets. Here we report an investigation of the elusive extrinsic effect in the 1D Heisenberg S=1/2 spin chain compound Ca_{2}CuO_{3}, where the defect concentration is determined from the measured specific heat and first-principles calculations are used to separate the lattice component of the measured thermal conductivity to isolate a large magnetic contribution (κ_{m}). The obtained temperature-dependent spinon-defect and spinon-phonon mean free paths can enable a quantitative understanding of both κ_{m} and the spinon-induced spin Seebeck effect.

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).

Variational model for one-dimensional quantum magnets

A new variational technique for investigation of the ground state and correlation functions in 1D quantum magnets is proposed. A spin Hamiltonian is reduced to a fermionic representation by the Jordan–Wigner transformation. The ground state is described by a new non-local trial wave function, and the total energy is calculated in an analytic form as a function of two variational parameters. This approach is demonstrated with an example of the XXZ-chain of spin-1/2 under a staggered magnetic field. Generalizations and applications of the variational technique for low-dimensional magnetic systems are discussed.

Enhancement and destruction of spin-Peierls physics in a one-dimensional quantum magnet under pressure

The application of pressure can induce transitions between unconventional quantum phases in correlated materials. The inorganic compound TiOCl, composed of chains of S=1/2 Ti ions, is an ideal realization of a spin-Peierls system with a relatively simple unit cell. At ambient pressure, it is an insulator due to strong electronic interactions (a Mott insulator). Its resistivity shows a sudden decrease with increasing pressure, indicating a transition to a more metallic state which may coincide with the emergence of charge density wave order. Therefore, high pressure studies of the structure with x-rays are crucial in determining the ground-state physics in this quantum magnet. In ambient pressure, TiOCl exhibits a transition to an incommensurate nearly dimerized state at $T_{c2}=92$ K and to a commensurate dimerized state at $T_{c1}=66$ K. Here, we discover a rich phase diagram as a function of temperature and pressure using x-ray diffraction on a single crystal in a diamond anvil cell down to $T=4$ K and pressures up to 14.5 GPa. Remarkably, the magnetic interaction scale increases dramatically with increasing pressure, as indicated by the high onset temperature of the spin-Peierls phase. At $\sim$7 GPa, the extrapolated onset of the spin-Peierls phase occurs above $T=300$ K, indicating a quantum singlet state exists at room temperature. Further comparisons are made with the phase diagrams of related spin-Peierls systems that display metallicity and superconductivity under pressure.

Experimental observation of Bethe strings

Almost a century ago, string states-complex bound states of magnetic excitations-were predicted to exist in one-dimensional quantum magnets. However, despite many theoretical studies, the experimental realization and identification of string states in a condensed-matter system have yet to be achieved. Here we use high-resolution terahertz spectroscopy to resolve string states in the antiferromagnetic Heisenberg-Ising chain SrCo2V2O8 in strong longitudinal magnetic fields. In the field-induced quantum-critical regime, we identify strings and fractional magnetic excitations that are accurately described by the Bethe ansatz. Close to quantum criticality, the string excitations govern the quantum spin dynamics, whereas the fractional excitations, which are dominant at low energies, reflect the antiferromagnetic quantum fluctuations. Today, Bethe's result is important not only in the field of quantum magnetism but also more broadly, including in the study of cold atoms and in string theory; hence, we anticipate that our work will shed light on the study of complex many-body systems in general.

Possible quadrupolar nematic phase in the frustrated spin chain LiCuSbO4 : An NMR investigation

The frustrated one-dimensional (1D) quantum magnet LiCuSbO$_4$ is one rare realization of the $J_1-J_2$ spin chain model with an easily accessible saturation field, formerly estimated to 12~T. Exotic multipolar nematic phases were theoretically predicted in such compounds just below the saturation field, but without unambiguous experimental observation so far. In this paper we present extensive experimental research of the compound in the wide temperature (30mK$-$300K) and field (0$-$13.3T) range by muon spin rotation ($\mu$SR), $^7$Li nuclear magnetic resonance (NMR) and magnetic susceptibility (SQUID). $\mu$SR experiments in zero magnetic field demonstrate the absence of long range 3D ordering down to 30mK. Together with former heat capacity data [S.E. Dutton \emph{et al}, Phys. Rev. Lett. 108, 187206 (2012)], magnetic susceptibility measurements suggest short range correlated vector chiral phase in the field range $0-4$T. In the intermediate field values (5$-$12T), the system enters in a 3D ordered spin density wave phase with 0.75$\mu_B$ per copper site at lowest temperatures (125mK), estimated by NMR. At still higher field, the magnetization is found to be saturated above 13T where the spin lattice $T_1^{-1}$ relaxation reveals a spin gap estimated to 3.2(2)K. We narrow down the possibility of observing a multipolar nematic phase to the range 12.5$-$13T.

Dynamic Correlations in One-Dimensional Quantum Magnets at Finite Temperature

Dynamic Correlations in One-Dimensional Quantum Magnets at Finite Temperature

Theoretical investigation of the behavior of CuSe2O5 compound in high magnetic fields

Based on the analytical and numerical approaches, we investigate thermodynamic properties of CuSe2O5 compound at high magnetic fields which is a candidate for the strong intra-chain interaction in quasi one-dimensional (1D) quantum magnets. Magnetic behavior of the system can be described by the 1D spin-1/2 XXZ model in the presence of the Dzyaloshinskii–Moriya (DM) interaction. Under these circumstances, there is one quantum critical field in this compound. Below the quantum critical field the spin chain system is in the gapless Luttinger liquid (LL) regime, whereas above it one observes a crossover to the gapped saturation magnetic phase. Indications on the thermodynamic curves confirm the occurrence of such a phase transition. The main characteristics of the LL phase are gapless and spin–spin correlation functions decay algebraic. The effects of zero-temperature quantum phase transition are observed even at rather high temperatures in comparison with the counterpart compounds. In addition, we calculate the Wilson ratio in the model. The Wilson ratio at a fixed temperature remains almost independent of the field in the LL region. In the vicinity of the quantum critical field, the Wilson ratio increases and exhibits anomalous enhancement.

Microscopic observation of magnon bound states and their dynamics

The existence of bound states of elementary spin waves (magnons) in one-dimensional quantum magnets was predicted almost 80 years ago. Identifying signatures of magnon bound states has so far remained the subject of intense theoretical research, and their detection has proved challenging for experiments. Ultracold atoms offer an ideal setting in which to find such bound states by tracking the spin dynamics with single-spin and single-site resolution following a local excitation. Here we use in situ correlation measurements to observe two-magnon bound states directly in a one-dimensional Heisenberg spin chain comprising ultracold bosonic atoms in an optical lattice. We observe the quantum dynamics of free and bound magnon states through time-resolved measurements of two spin impurities. The increased effective mass of the compound magnon state results in slower spin dynamics as compared to single-magnon excitations. We also determine the decay time of bound magnons, which is probably limited by scattering on thermal fluctuations in the system. Our results provide a new way of studying fundamental properties of quantum magnets and, more generally, properties of interacting impurities in quantum many-body systems.

Low-Temperature Dynamics of Magnons in a Spin-1/2Ladder Compound

We have used a combination of neutron resonant spin-echo and triple-axis spectroscopies to determine the energy, fine structure, and linewidth of the magnon resonance in the model spin-1/2 ladder antiferromagnet IPA-CuCl(3) at temperatures T≪Δ(0)/k(B), where Δ(0) is the spin gap at T=0. In this low-temperature regime we find that the results deviate substantially from the predictions of the nonlinear sigma model proposed as a description of magnon excitations in one-dimensional quantum magnets and attribute these deviations to real-space and spin-space anisotropies in the spin Hamiltonian as well as scattering of magnon excitations from a dilute density of impurities. These effects are generic to experimental realizations of one-dimensional quantum magnets.

Spin–lattice coupling driven ferroelectric transition in one-dimensional organic quantum magnets

We propose a theoretical quantum spin model for a one-dimensional (1D) spin-Peierls (SP) system to describe its ferroelectricity driven by the spin–lattice coupling, and further investigate the ferroelectric (FE) SP transition for a known 1D organic donor–acceptor charge transfer compound, which was experimentally proved to show ferroelectricity, by means of many-body Green's function theory. It is found that the transition temperature (Tc), polarization (P) and dielectric constant are in agreement with experimental results. Meanwhile, it is shown that the two-site thermal entanglement entropy is a good indicator of a FE transition. In addition, the potential magnetoelectric behavior is taken into account. On the one hand, when the magnetic field is turned on, it makes P and Tc decrease, and drives the FE transition from the second order to the first order. Nevertheless, the FE dimerized-singlet state may collapse for high enough magnetic fields, leading to the restoration of paraelectric uniform stack of donor–acceptor. On the other hand, as the electric field is applied along the chain, the FE phase is evidenced by the electric polarization (P)–field (E) hysteresis loops. It is also found that the magnetization M decreases but the polarization P can be enhanced with increasing electric field, which makes the FE transition exhibit crossover behavior, since the electrostatic energy predominates over the spin–lattice coupling.

Antiferromagnetic spin-12chains in(NO)Cu(NO3)3: A microscopic study

We report on the microscopic model of the recently synthesized one-dimensional quantum magnet $(\text{NO})\text{Cu}{({\text{NO}}_{3})}_{3}$. Applying density-functional-theory band-structure calculations, we obtain a leading antiferromagnetic exchange coupling $J\ensuremath{\simeq}200\text{ }\text{K}$, which runs via ${\text{NO}}_{3}$ groups forming spin chains along the $b$ direction. Much weaker couplings ${J}^{\ensuremath{'}}\ensuremath{\simeq}2\text{ }\text{K}$ link the chains into layers in a nonfrustrated manner. Our calculations do not support the earlier conjecture on an anisotropic frustrated square lattice physics in $(\text{NO})\text{Cu}{({\text{NO}}_{3})}_{3}$. In contrast, the model of uniform spin chains leads to a remarkably good fit of the experimental magnetic susceptibility data, although the low-temperature features of the intrinsic magnetic susceptibility measured by electron spin resonance might call for extension of the model. We outline possible experiments to observe the suggested long-range magnetic ordering in $(\text{NO})\text{Cu}{({\text{NO}}_{3})}_{3}$ and briefly compare this compound to other spin-$\frac{1}{2}$ uniform-chain systems.

Incommensurate Magnetic Order and Dynamics Induced by Spinless Impurities inYBa2Cu3O6.6

We report an inelastic-neutron-scattering and muon-spin-relaxation study of the effect of 2% spinless (Zn) impurities on the magnetic order and dynamics of YBa(2)Cu(3)O(6.6), an underdoped high-temperature superconductor that exhibits a prominent spin pseudogap in its normal state. Zn substitution induces static magnetic order at low temperatures and triggers a large-scale spectral-weight redistribution from the magnetic resonant mode at 38 meV into uniaxial, incommensurate spin excitations with energies well below the spin pseudogap. These observations indicate a competition between incommensurate magnetic order and superconductivity close to a quantum critical point. Comparison to prior data on La(2-x)Sr(x)CuO(4) suggests that this behavior is universal for the layered copper oxides and analogous to impurity-induced magnetic order in one-dimensional quantum magnets.