Low-dimensional Quantum Magnets Research Articles

(C5H9NH3)2CuBr4 : A metal-organic two-ladder quantum magnet

Low-dimensional quantum magnets are a versatile materials platform for studying the emergent many-body physics and collective excitations that can arise even in systems with only short-range interactions. Understanding their low-temperature structure and spin Hamiltonian is key to explaining their magnetic properties, including unconventional quantum phases, phase transitions, and excited states. We study the metal-organic coordination compound (C5H9NH3)2CuBr4 and its deuterated counterpart, which upon its discovery was identified as a candidate two-leg quantum (S=12) spin ladder in the strong-leg coupling regime. By growing large single crystals and probing them with both bulk and microscopic techniques, we deduce that two previously unknown structural phase transitions take place between 136 and 113 K. The low-temperature structure has a monoclinic unit cell that gives rise to two inequivalent spin ladders. We further confirm the absence of long-range magnetic order down to 30 mK and investigate the implications of this two-ladder structure for the magnetic properties of (C5H9NH3)2CuBr4 by analyzing our own specific-heat and susceptibility data. Published by the American Physical Society 2024

Momentum-resolved spin-conserving two-triplon bound state and continuum in a cuprate ladder

Studying multi-particle elementary excitations has provided unique access to understand collective many-body phenomena in correlated electronic materials, paving the way towards constructing microscopic models. In this work, we perform O K-edge resonant inelastic X-ray scattering (RIXS) on the quasi-one-dimensional cuprate {{{{{{rm{Sr}}}}}}}_{14}{{{{{{rm{Cu}}}}}}}_{24}{{{{{{rm{O}}}}}}}_{41} with weakly-doped spin ladders. The RIXS signal is dominated by a dispersing sharp mode ~ 270 meV on top of a damped incoherent component ~ 400-500 meV. Comparing with model calculations using the perturbative continuous unitary transformations method, the two components resemble the spin-conserving ΔS = 0 two-triplon bound state and continuum excitations in the spin ladders. Such multi-spin response with long-lived ΔS = 0 excitons is central to several exotic magnetic properties featuring Majorana fermions, yet remains unexplored given the generally weak cross-section with other experimental techniques. By investigating a simple spin-ladder model system, our study provides valuable insight into low-dimensional quantum magnetism.

Partitioning the Two-Leg Spin Ladder in Ba2Cu1-x Zn x TeO6: From Magnetic Order through Spin-Freezing to Paramagnetism.

Ba2CuTeO6 has attracted significant attention as it contains a two-leg spin ladder of Cu2+ cations that lies in close proximity to a quantum critical point. Recently, Ba2CuTeO6 has been shown to accommodate chemical substitutions, which can significantly tune its magnetic behavior. Here, we investigate the effects of substitution for non-magnetic Zn2+ impurities at the Cu2+ site, partitioning the spin ladders. Results from bulk thermodynamic and local muon magnetic characterization on the Ba2Cu1-x Zn x TeO6 solid solution (0 ≤ x ≤ 0.6) indicate that Zn2+ partitions the Cu2+ spin ladders into clusters and can be considered using the percolation theory. As the average cluster size decreases with increasing Zn2+ substitution, there is an evolving transition from long-range order to spin-freezing as the critical cluster size is reached between x = 0.1 to x = 0.2, beyond which the behavior became paramagnetic. This demonstrates well-controlled tuning of the magnetic disorder, which is highly topical across a range of low-dimensional Cu2+-based materials. However, in many of these cases, the chemical disorder is also relatively strong in contrast to Ba2CuTeO6 and its derivatives. Therefore, Ba2Cu1-x Zn x TeO6 provides an ideal model system for isolating the effect of defects and segmentation in low-dimensional quantum magnets.

Topological Defects Induced High-Spin Quartet State in Truxene-Based Molecular Graphenoids

Topological Defects Induced High-Spin Quartet State in Truxene-Based Molecular Graphenoids

Magnetic properties of the S = 52 anisotropic triangular chain compound Bi3FeMo2O12

Competing magnetic interactions in low-dimensional quantum magnets can lead to the exotic ground state with fractionalized excitations. Herein, we present our results on an S = 5/2 quasi-one-dimensional spin system Bi3FeMo2O12. The structure of Bi3FeMo2O12 consists of very well separated, infinite zig-zag S = 5/2 spin chains. The observation of a broad maximum around 10 K in the magnetic susceptibility suggests the presence of short-range spin correlations. Magnetic susceptibility data do not fit to S=5/2 uniform spin chain model due to the presence of 2nd nearest-neighbor coupling (J2) along with the 1st nearest-neighbor coupling J1 of the zig-zag chain. The electronic structure calculations infer that the value of J1 is comparable with J2 (J2/J1~1.1) with a negligible inter-chain interaction (J'/J ~ 0.01), implying that Bi3FeMo2O12 is a highly frustrated triangular chain system. The absence of magnetic long-range ordering down to 0.2 K is seen in the heat capacity data, despite a relatively large antiferromagnetic Curie-Weiss temperature of -40 K. The magnetic heat capacity follows nearly a linear behavior at low temperatures indicating that the S = 5/2 anisotropic triangular chain exhibits the gapless excitations.

Observation of fractional edge excitations in nanographene spin chains.

Fractionalization is a phenomenon in which strong interactions in a quantum system drive the emergence of excitations with quantum numbers that are absent in the building blocks. Outstanding examples are excitations with charge e/3 in the fractional quantum Hall effect1,2, solitons in one-dimensional conducting polymers3,4 and Majorana states in topological superconductors5. Fractionalization is also predicted to manifest itself in low-dimensional quantum magnets, such as one-dimensional antiferromagnetic S = 1 chains. The fundamental features of this system are gapped excitations in the bulk6 and, remarkably, S = 1/2 edge states at the chain termini7-9, leading to a four-fold degenerate ground state that reflects the underlying symmetry-protected topological order10,11. Here, we use on-surface synthesis12 to fabricate one-dimensional spin chains that contain the S = 1 polycyclic aromatic hydrocarbon triangulene as the building block. Using scanning tunnelling microscopy and spectroscopy at 4.5 K, we probe length-dependent magnetic excitations at the atomic scale in both open-ended and cyclic spin chains, and directly observe gapped spin excitations and fractional edge states therein. Exact diagonalization calculations provide conclusive evidence that the spin chains are described by the S = 1 bilinear-biquadratic Hamiltonian in the Haldane symmetry-protected topological phase. Our results open a bottom-up approach to study strongly correlated phases in purely organic materials, with the potential for the realization of measurement-based quantum computation13.

Large magnetic thermal conductivity induced by frustration in low-dimensional quantum magnets

We study the magnetic field-dependence of the thermal conductivity due to magnetic excitations in frustrated spin-1/2 Heisenberg chains. Near the saturation field, the system is described by a dilute gas of weakly-interacting fermions (free-fermion fixed point). We show that in this regime the thermal conductivity exhibits a non-monotonic behavior as a function of the ratio $\alpha= J_2/J_1$ between second and first nearest-neighbor antiferromagnetic exchange interactions. This result is a direct consequence of the splitting of the single-particle dispersion minimum into two minima that takes place at the Lifshitz point $\alpha=1/4$. Upon increasing $\alpha$ from zero, the inverse mass vanishes at $\alpha=1/4$ and it increases monotonically from zero for $\alpha \geq 1/4$. By deriving an effective low-energy theory of the dilute gas of fermions, we demonstrate that the Drude weight $K_{\rm th}$ of the thermal conductivity exhibits a similar dependence on $\alpha$ near the saturation field. Moreover, this theory predicts a transition between a two-component Tomonaga-Luttinger liquid and a vector-chiral phase at a critical value $\alpha=\alpha_c$ that agrees very well with previous density matrix renormalization group results. We also show that the resulting curve $K_{\rm th}(\alpha)$ is in excellent agreement with exact diagonalization (ED) results. Our ED results also show that $K_{\rm th}(\alpha)$ has a pronounced minimum at $\alpha\simeq 0.7$ and it decreases for sufficiently large $\alpha$ at lower magnetic field values. We also demonstrate that the thermal conductivity is significantly affected by the presence of magnetothermal coupling.

Magnetic and magneto-elastic couplings in the low-dimensional Heisenberg quantum magnet Cs2CuCl2Br2 with octahedral Cu coordination

Abstract In single crystals of the solid solution Cs2 CuCl 4 - x Br x ( 0 ⩽ x ⩽ 4 ), depending on the growth conditions, two structural modifications with a tetrahedral or an octahedral Cu environment can be realized. The border compounds (x = 0 and 4) with a tetrahedral Cu coordination have been recognized as model systems for quasi-2D frustrated anisotropic triangular quantum antiferromagnets. This holds true also for the newly discovered stoichiometric compounds with x = 1 and 2. In contrast, the systems exhibiting an octahedral Cu environment can be classified as quasi-2D ferromagnets characterized by ferromagnetic layers with a weak inter-layer coupling. Here we study the magnetic and magneto-elastic couplings for the low-dimensional Heisenberg quantum magnet Cs2CuCl2Br2 with octahedral Cu coordination. By applying magnetic susceptibility measurements under varying hydrostatic (He-gas) pressure, χ ( T , p ) , we determine the pressure dependence of the magnetic coupling constant ∂ J / ∂ p and estimate the magneto-elastic couplings ∂ J / ∂ ∊ v . These values are enhanced by almost one order of magnitude compared to Cs2CuCl2Br2 with tetrahedral Cu coordination.

Tomonaga\u2013Luttinger liquid behavior and spinon confinement in YbAlO3

Low dimensional quantum magnets are interesting because of the emerging collective behavior arising from strong quantum fluctuations. The one-dimensional (1D) S = 1/2 Heisenberg antiferromagnet is a paradigmatic example, whose low-energy excitations, known as spinons, carry fractional spin S = 1/2. These fractional modes can be reconfined by the application of a staggered magnetic field. Even though considerable progress has been made in the theoretical understanding of such magnets, experimental realizations of this low-dimensional physics are relatively rare. This is particularly true for rare-earth-based magnets because of the large effective spin anisotropy induced by the combination of strong spin–orbit coupling and crystal field splitting. Here, we demonstrate that the rare-earth perovskite YbAlO3 provides a realization of a quantum spin S = 1/2 chain material exhibiting both quantum critical Tomonaga–Luttinger liquid behavior and spinon confinement–deconfinement transitions in different regions of magnetic field–temperature phase diagram.

Interplay of Spin and Spatial Anisotropy in Low-Dimensional Quantum Magnets with Spin 1/2

Quantum Heisenberg chain and square lattices are important paradigms of a low-dimensional magnetism. Their ground states are determined by the strength of quantum fluctuations. Correspondingly, the ground state of a rectangular lattice interpolates between the spin liquid and the ordered collinear Néel state with the partially reduced order parameter. The diversity of additional exchange interactions offers variety of quantum models derived from the aforementioned paradigms. Besides the spatial anisotropy of the exchange coupling, controlling the lattice dimensionality and ground-state properties, the spin anisotropy (intrinsic or induced by the magnetic field) represents another important effect disturbing a rotational symmetry of the spin system. The S = 1/2 easy-axis and easy-plane XXZ models on the square lattice even for extremely weak spin anisotropies undergo Heisenberg-Ising and Heisenberg-XY crossovers, respectively, acting as precursors to the onset of the finite-temperature phase transitions within the two-dimensional Ising universality class (for the easy axis anisotropy) and a topological Berezinskii–Kosterlitz–Thouless phase transition (for the easy-plane anisotropy). Experimental realizations of the S = 1/2 two-dimensional XXZ models in bulk quantum magnets appeared only recently. Partial solutions of the problems associated with their experimental identifications are discussed and some possibilities of future investigations in quantum magnets on the square and rectangular lattice are outlined.

String orders in the Luttinger liquid phase of one-dimensional spin-1/2 systems

Luttinger liquid (LL) phase refers to a quantum phase which emerges in the ground state phase diagram of quite often low-dimensional quantum magnets as spin-1/2 XX, XYY and frustrated chains. It is believed that the quasi long-range order exists between particles forming the system in the LL phase. Here, at the first step we concentrate on the study of correlated spin particles in the one-dimensional (1D) spin-1/2 XX model which is exactly solvable. We show that the spin-1/2 particles form string orders with an even number of spins in the LL phase of the 1D spin-1/2 XX model. As soon as the transverse magnetic field is applied to the system, string orders with an odd number of spins induce in the LL phase. All ordered strings of spin-1/2 particles will be destroyed at the quantum critical transverse field, hc. No strings exist in the saturated ferromagnetic phase. At the second step we focus on the LL phase in the ground state phase diagram of the 1D spin-1/2 XYY and frustrated ferromagnetic models. We show that the even-string orders exist in the LL phase of the 1D spin-1/2 XYY model but in the LL phase of the 1D spin-1/2 frustrated ferromagnetic model we found all kind of strings. In addition, the existence of a clear relation between the long-distance entanglement and string orders in the LL phase is shown. Also, the effect of the thermal fluctuations on the behavior of the string orders is studied.

Low-dimensional quantum magnetism in Cu(NCS)2 : A molecular framework material

Low-dimensional magnetic materials with spin-$\frac{1}{2}$ moments can host a range of exotic magnetic phenomena due to the intrinsic importance of quantum fluctuations to their behavior. Here, we report the structure, magnetic structure and magnetic properties of copper(II) thiocyanate, Cu(NCS)$_2$, a one-dimensional coordination polymer which displays low-dimensional quantum magnetism. Magnetic susceptibility, electron paramagnetic resonance (EPR) spectroscopy, $^{13}$C magic-angle spinning nuclear magnetic resonance (MASNMR) spectroscopy, and density functional theory (DFT) investigations indicate that Cu(NCS)$_2$ behaves as a two-dimensional array of weakly coupled antiferromagnetic spin chains ($J_2 = 133(1)$ K, $\alpha = J_1/J_2 = 0.08$). Powder neutron-diffraction measurements confirm that Cu(NCS)$_2$ orders as a commensurate antiferromagnet below $T_\mathrm{N} = 12$ K, with a strongly reduced ordered moment (0.3 $\mu_\mathrm{B}$) due to quantum fluctuations.

Dimensional reduction by pressure in the magnetic framework material CuF2(D2O)2 (pyz): From spin-wave to spinon excitations

Metal organic magnets have enormous potential to host a variety of electronic and magnetic phases that originate from a strong interplay between the spin, orbital and lattice degrees of freedom. We control this interplay in the quantum magnet CuF$_2$(D$_2$O)$_2$pyz by using high pressure to drive the system through a structural and magnetic phase transition. Using neutron scattering, we show that the low pressure state, which hosts a two-dimensional square lattice with spin-wave excitations and a dominant exchange coupling of 0.89 meV, transforms at high pressure into a one-dimensional spin-chain hallmarked by a spinon continuum and a reduced exchange interaction of 0.43 meV. This direct microscopic observation of a magnetic dimensional crossover as a function of pressure opens up new possibilities for studying the evolution of fractionalised excitations in low dimensional quantum magnets and eventually pressure-controlled metal--insulator transitions.

Multi-triplet bound states and finite-temperature dynamics in highly frustrated quantum spin ladders

Low-dimensional quantum magnets at finite temperatures present a complex interplay of quantum and thermal fluctuation effects in a restricted phase space. While some information about dynamical response functions is available from theoretical studies of the one-triplet dispersion in unfrustrated chains and ladders, little is known about the finite-temperature dynamics of frustrated systems. Experimentally, inelastic neutron scattering studies of the highly frustrated two-dimensional material SrCu$_2$(BO$_3$)$_2$ show an almost complete destruction of the one-triplet excitation band at a temperature only 1/3 of its gap energy, accompanied by strong scattering intensities for apparent multi-triplet excitations. We investigate these questions in the frustrated spin ladder and present numerical results from exact diagonalization for the dynamical structure factor as a function of temperature. We find anomalously rapid transfer of spectral weight out of the one-triplet band and into both broad and sharp spectral features at a wide range of energies, including below the zero-temperature gap of this excitation. These features are multi-triplet bound states, which develop particularly strongly near the quantum phase transition, fall to particularly low energies there, and persist to all the way to infinite temperature. Our results offer valuable insight into the physics of finite-temperature spectral functions in SrCu$_2$(BO$_3$)$_2$ and many other highly frustrated spin systems.

When Ising meets Majorana

The topological degeneracy associated with Majorana edge states has been measured in a spin-1/2 chain of cobalt atoms, thereby opening new avenues in low-dimensional quantum magnetism.

Covalency effects reflected in the magnetic form factor of low-dimensional cuprates

We analyze the magnetic form factor of Cu$^{2+}$ in low-dimensional quantum magnets by taking the metal-ligand hybridization into account explicitly. In this analysis we use the form of magnetic Wannier orbitals, derived from the first-principles calculations, and identify the contributions of different atomic sites. Having performed local density approximation calculations for cuprates with different types of ligand atoms, we discuss the influence of the on-site Coulomb correlations on the structure of the magnetic orbital. The typical composition of Wannier functions for copper oxides, chlorides and bromides is defined and related to features of the magnetic form factor. We propose easy-to-use approximations of the partial orbital contributions to the magnetic form factor in order to give a microscopic explanation for the results obtained in previous first-principles studies.

Magnetic susceptibility of frustrated spin-s J1-J2 quantum Heisenberg magnets: High-temperature expansion and exact diagonalization data

Motivated by recent experiments on low-dimensional frustrated quantum magnets with competing nearest-neighbor exchange coupling J1 and next nearest-neighbor exchange coupling J2 we investigate the magnetic susceptibility of two-dimensional J1-J2 Heisenberg models with arbitrary spin quantum number s. We use exact diagonalization and high- temperature expansion up to order 10 to analyze the influence of the frustration strength J2/J1 and the spin quantum number s on the position and the height of the maximum of the susceptibility. The derived theoretical data can be used to get information on the ratio J2/J1 by comparing with susceptibility measurements on corresponding magnetic compounds.

Mild hydrothermal synthesis, isomorphous substitution, crystal structure characterization and magnetic properties of BaMP2O7 (M = Mn, Cu)

At mild hydrothermal conditions triclinic modifications of BaMP2O7 (M = Mn and/or Cu) have been succeeded. The method offers cheap, one step, impurity free and chemical flexible fabrication of family of metal phosphates that are potential low-dimensional quantum magnets. Partial isomorphous substitution of the Mn2+ by Cu2+ resulted into mixed-metal solid that has been structurally and magnetically characterized. Rietveld refinement study confirmed the structures and revealed the influence of transition metal substitution. The temperature-dependent magnetic measurements revealed that the system is paramagnetic in almost all temperature range and an apparent antiferromagnetic phase transition occurs around 5 K. Using the Curie–Weiss law, a Curie–Weiss temperature, θP = −11.0 K, and a Curie constant C = 3.39 emu K mol−1 was obtained. The small negative θP value and the χT behavior as a function of temperature reveal a weak antiferromagnetic interaction between the Cu2+/Mn2+magnetic centers.

Field-induced staggered moment stabilization in frustrated quantum magnets

For low-dimensional frustrated quantum magnets, the dependence of the staggered moment on a magnetic field is nonmonotonic: For small and intermediate fields, quantum fluctuations are gradually suppressed, leading to an increase of the staggered moment as a function of the field strength. For large applied magnetic fields, the classically expected field dependence is recovered, namely a monotonous decrease with increasing field strength. The staggered moment is eventually suppressed when reaching the fully polarized state at the saturation field. The quantitative analysis of this behavior is an excellent tool to determine the frustration parameter of a magnetic compound. We have developed a general finite-size scaling scheme for numerical exact-diagonalization data of low-dimensional frustrated magnets, which we apply to the recently measured field dependence of the magnetic neutron scattering intensity of Cu(pz)2(ClO4)2 in the framework of the S = 1/2 two-dimensional (2D) J 1–J 2 Heisenberg model. We also apply linear spin-wave theory to complement our numerical findings. Our results show that Cu(pz)2(ClO4)2 is a quasi-2D antiferromagnet with intermediate frustration J 2/J 1 = 0.2.

Phonon-magnon interaction in low dimensional quantum magnets observed by dynamic heat transport measurements.

Thirty-five years ago, Sanders and Walton [Phys. Rev. B 15, 1489 (1977)] proposed a method to measure the phonon-magnon interaction in antiferromagnets through thermal transport which so far has not been verified experimentally. We show that a dynamical variant of this approach allows direct extraction of the phonon-magnon equilibration time, yielding 400 μs for the cuprate spin-ladder system Ca(9)La(5)Cu(24)O(41). The present work provides a general method to directly address the spin-phonon interaction by means of dynamical transport experiments.