Low-dimensional Spin Systems Research Articles

Quantitative Disorder Effects in Low-Dimensional Spin Systems

The Imry–Ma phenomenon, predicted in 1975 by Imry and Ma and rigorously established in 1989 by Aizenman and Wehr, states that first-order phase transitions of low-dimensional spin systems are ‘rounded’ by the addition of a quenched random field coupled to the quantity undergoing the transition. The phenomenon applies to a wide class of spin systems in dimensions d≤2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d\\le 2$$\\end{document} and to spin systems possessing a continuous symmetry in dimensions d≤4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d\\le 4$$\\end{document}. This work provides quantitative estimates for the Imry–Ma phenomenon: in a cubic domain of side length L, we study the effect of the boundary conditions on the spatial and thermal average of the quantity coupled to the random field. We show that the boundary effect diminishes at least as fast as an inverse power of loglogL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\log \\log L$$\\end{document} in general two-dimensional spin systems. For systems possessing a continuous symmetry, we show that the boundary effect diminishes at least as fast as an inverse power of L in two and three dimensions and at least as fast as an inverse power of loglogL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\log \\log L$$\\end{document} in four dimensions. Finally, we establish a partial uniqueness results for translation-covariant Gibbs states, and prove that, for almost every realization of the random field, all such states must agree on the thermally-averaged value of the quantity coupled to the random field. Specific models of interest for the obtained results include the random-field q-state Potts model, the Edwards-Anderson spin glass model, and the random-field spin O(n) models.

Existence of long-range magnetic order in Heisenberg spin nanoribbons with edge modification

Long-range magnetic order appears on a side decorated Heisenberg spin nanoribbon at nonzero temperature, although no spontaneous magnetization exists in a one- or two-dimensional isotropic Heisenberg model at any nonzero temperature according to the Mermin–Wagner theorem. By use of the spin Green’s function method, we calculated the magnetizations of Heisenberg nanoribbons decorated by side spins with single-ion anisotropy and found that the system exhibits a nonzero transition temperature, whether the decorated edge spins of the system link together or separate from each other. When the width of the nanoribbon achieves infinite limit, the transition temperatures of the system tend to the same finite constant eventually whether one edge or both edges are decorated by side spins in the nanoribbon. The results reveal that the magnetism of a low-dimensional spin system is different from that of a three-dimensional spin system. When the single-ion anisotropy of edge spins in a Heisenberg spin nanoribbon can be modulated by an electric field experimentally, various useful long-range magnetic orders of the system can be obtained. This work can provide a detailed theoretical basis for designing and fabricating next-generation low-dimensional magnetic random-access memory.

Metamagnetism in a coordination polymer built of trimeric cobalt units and melamine.

A coordination polymer of linear trimeric cobalt units and melamine has been synthesized. The magnetic isotherms of violet coloured crystals as long as 400 μm show a field-induced transition in an external field of about 2 T at temperatures approximately below 2 K. It is addressed that by assuming the coexistent positive and negative exchange between the nearest-neighbour spins in the linear trimer, this metamagnetism can be interpreted as a transition from antiferromagnetic to ferromagnetic exchange within each trimeric spin cluster. Although weak inter-cluster or inter-chain exchange to yield a long-range magnetic order is another possible and often attributed origin of metamagnetism in low-dimensional spin systems, this study demonstrates the significance of the exchange flip within each cluster in clustered spin networks.

Spatiotemporal dynamics of classical and quantum density profiles in low-dimensional spin systems

We provide a detailed comparison between the dynamics of high-temperature spatiotemporal correlation functions in quantum and classical spin models. In the quantum case, our large-scale numerics are based on the concept of quantum typicality, which exploits the fact that random pure quantum states can faithfully approximate ensemble averages, allowing the simulation of spin-$1/2$ systems with up to $40$ lattice sites. Due to the exponentially growing Hilbert space, we find that for such system sizes even a single random state is sufficient to yield results with extremely low noise that is negligible for most practical purposes. In contrast, a classical analog of typicality is missing. In particular, we demonstrate that, in order to obtain data with a similar level of noise in the classical case, extensive averaging over classical trajectories is required, no matter how large the system size. Focusing on (quasi-)one-dimensional spin chains and ladders, we find a remarkably good agreement between quantum and classical dynamics. This applies not only to cases where both the quantum and classical model are nonintegrable, but also to cases where the quantum spin-$1/2$ model is integrable and the corresponding classical $s\to\infty$ model is not. Our analysis is based on the comparison of space-time profiles of the spin and energy correlation functions, where the agreement is found to hold not only in the bulk but also in the tails of the resulting density distribution. The mean-squared displacement of the density profiles reflects the nature of emerging hydrodynamics and is found to exhibit similar scaling for quantum and classical models.

Entanglement Negativity and Concurrence in Some Low-Dimensional Spin Systems.

The influence of magnon bands on entanglement in the antiferromagnetic XXZ model on a triangular lattice, which models the bilayer structure consisting of an antiferromagnetic insulator and normal metal, is investigated. This effect was studied in ferromagnetic as well as antiferromagnetic triangular lattices. Quantum entanglement measures given by the entanglement negativity have been studied, where a magnon current is induced in the antiferromagnet due to interfacial exchange coupling between localized spins in the antiferromagnet and itinerant electrons in a normal metal. Moreover, quantum correlations in other frustrated models, namely the metal-insulation antiferromagnetic bilayer model and the Heisenberg model with biquadratic and bicubic interactions, are analyzed.

Lattice distortion of oxygen monolayer on Ag(111) observed by scanning probe microscopy

Oxygen molecules (${\mathrm{O}}_{2}$) physically adsorbed on solid surfaces are of interest as low-dimensional spin systems. Monolayers of ${\mathrm{O}}_{2}$ adsorbed on an Ag(111) surface at a low density of less than 1 ML are observed at 4.5 K using scanning tunneling microscopy combined with atomic force microscopy with ${\mathrm{O}}_{2}$ terminated tips. Various domains with their specific density are mixed, each with different rotation angles to the substrate. The shape of the ${\mathrm{O}}_{2}$ lattice correlates with the rotation angle between the monolayer and the substrate. The domains with a rotation angle of greater than $1.{4}^{\ensuremath{\circ}}$ can be explained by the model of on-line coincidence, which had previously been confirmed only for organic molecules. The coincidence with the substrate naturally explains the observed lattice distortion quantitatively. On the other hand, in domains at the rotation angle near ${0}^{\ensuremath{\circ}}$, the lattice distortion is smaller than that of previous study that attributed it to spin. Nevertheless, the length of the shortest distance between two ${\mathrm{O}}_{2}$ implies antiferromagnetic order.

Combined unitary and symmetric group approach applied to low-dimensional Heisenberg spin systems

A novel combined unitary and symmetric group approach is used to study the spin-$\frac{1}{2}$ Heisenberg model and related Fermionic systems in a total spin-adapted representation, using a linearly-parameterised Ansatz for the many-body wave function. We show that a more compact ground-state wave function representation---indicated by a larger leading ground-state coefficient---is obtained when combining the symmetric group ${\mathcal{S}}_{n}$, in the form of permutations of the underlying lattice site ordering, with the cumulative spin coupling based on the unitary group $\mathrm{U}(n)$. In one-dimensional systems the observed compression of the wave function is reminiscent of block-spin renormalization group approaches, and allows us to study larger lattices (here taken up to 80 sites) with the spin-adapted full configuration interaction quantum Monte Carlo method, which benefits from the sparsity of the Hamiltonian matrix and the corresponding sampled eigenstates that emerge from the reordering. We find that in an optimal lattice ordering the configuration state function with highest weight already captures with high accuracy the spin-spin correlation function of the exact ground-state wave function. This feature is found for more general lattice models, such as the Hubbard model, and ab initio quantum chemical models, exemplified by one-dimensional hydrogen chains. We also provide numerical evidence that the optimal lattice ordering for the unitary group approach is not generally equivalent to the optimal ordering obtained for methods based on matrix-product states, such as the density-matrix renormalization group approach.

Unusual magnetization process and magnetocaloric effect in α-CoV2O6 driven by pulsed magnetic fields

In low-dimensional Ising spin systems, an interesting observation is the presence of step magnetization at low temperatures. Here we combine both DC and pulsed magnetic fields to study the 1/3 magnetization plateau and multiple steps in the Ising spin-chain material α-CoV2O6. Magnetization in pulsed fields is quite different from that in DC fields, showing multiple steps in an intermediate range of 4.2–6 K, inverted hysteresis below 4.2 K and asymmetric magnetization in negative fields below 11 K. We demonstrate that these unusual behaviors in magnetization are caused by the spin dynamics and the anomalous magnetocaloric effect (MCE) in α-CoV2O6, i.e., abrupt changes of sample temperature in adiabatic conditions. We successfully separate the influence between the intrinsic slow spin dynamics and the quasi-extrinsic temperature change. From the MCE, we find that some irreversible behavior is originated from the slow spin dynamics. Two different slow dynamics associated with the metastable steps are observed: one is sensitive to the slow field sweep rate at the order of ∼mT s−1 and weakly depends on temperature, while the other responds to the rapid field sweep rate of ∼kT s−1 and dominates at lowest temperature. We also distinguish that the metastable transition at H 4 is the first order and crucial for the ferrimagnetic to ferromagnetic transition. This study is useful to the understanding of multistep magnetization in α-CoV2O6 and sheds light on recent experimental findings of related compounds.

Generative neural samplers for the quantum Heisenberg chain.

Generative neural samplers offer a complementary approach to Monte Carlo methods for problems in statistical physics and quantum field theory. This paper tests the ability of generative neural samplers to estimate observables for real-world low-dimensional spin systems. It maps out how autoregressive models can sample configurations of a quantum Heisenberg chain via a classical approximation based on the Suzuki-Trotter transformation. We present results for energy, specific heat, and susceptibility for the isotropic XXX and the anisotropic XY chain are in good agreement with Monte Carlo results within the same approximation scheme.

Exact solution of two-dimensional (2D) Ising model with a transverse field: A low-dimensional quantum spin system

The exact solution of ferromagnetic two-dimensional (2D) Ising model with a transverse field, which can be used to describe the critical phenomena in low-dimensional quantum spin systems, is derived by equivalence between the ferromagnetic 2D Ising model with a transverse field and the ferromagnetic three-dimensional (3D) Ising model. The results obtained in this work can be extended to be suitable for the antiferromagnetic 2D Ising model with a transverse field in the cases without frustration.

Enhancement of magnetization plateaus in low-dimensional spin systems

We study the low-energy properties and, in particular, the magnetization process of a spin-1/2 Heisenberg $J_1-J_2$ sawtooth and frustrated chain (also known as zig-zag ladder) with a spatially anisotropic $g$-factor. We treat the problem both analytically and numerically while keeping the $J_2/J_1$ ratio generic. Numerically, we use complete and Lanczos diagonalization as well as the infinite time-evolving block decimation (iTEBD) method. Analytically we employ (non-)Abelian bosonization. Additionally for the sawtooth chain, we provide an analytical description in terms of flat bands and localized magnons. By considering a specific pattern for the $g$-factor anisotropy for both models, we show that a small anisotropy significantly enhances a magnetization plateau at half saturation. For the magnetization of the frustrated chain, we show the destruction of the $1/3$ of the full saturation plateau in favor of the creation of a plateau at half-saturation. For large anisotropies, the existence of an additional plateau at zero magnetization is possible. Here and at higher magnetic fields, the system is locked in the half-saturation plateau, never reaching full saturation.

Magnetization plateaus of spin- 12 system on a 5/7 skewed ladder

Magnetization plateaus are some of the most striking manifestations of frustration in low-dimensional spin systems. We present numerical studies of magnetization plateaus in the fascinating spin-1/2 skewed ladder system obtained by alternately fusing five- and seven-membered rings. This system exhibits three significant plateaus at $m = 1/4$, $1/2$ and $3/4$, consistent with the Oshikawa-Yamanaka-Affleck condition. Our numerical as well as perturbative analysis shows that the ground state can be approximated by three weakly coupled singlet dimers and two free spins, in the absence of a magnetic field. With increasing applied magnetic field, the dimers progressively become triplets with large energy gaps to excited states, giving rise to stable magnetization plateaus. Finite-temperature studies show that $m=1/4$ and $1/2$ plateaus are robust and survive thermal fluctuations while the $m=3/4$ plateau shrinks rapidly due to thermal noise. The cusps at the ends of a plateau follow the algebraic square-root dependence on $B$.

Experimental investigation of low dimensional spin system in metal oxides

Nano particles of SrCrO4 were manufactured by sol-gel technique. The crystal part ofSrCrO4 is monoclinic having space group P21/n. We calcined it at 950°C temperature. Its cand a lattice parameter are 6.77 and 7.08 which is very close to the reported ones. Ba and Cadoped SrCrO4 were also synthesized by sol-gel method by various concentrations for x= 0.2,0.4, 0.6 and 0.8. Doping samples also sintered at 950°C for 2 hours in order to obtain finepowder. Different characterization techniques such as XRD, Ultra-violet-Spectroscopy, PLSpectroscopy and FTIR Spectroscopy were used to analyze SrCrO4, Ba and Ca-dopedSrCrO4. XRD tells us about the crystal size and dislocation density of samples. The value of2? for the XRD patterns is ranging from 5 to 95. Four peaks are observed in the UV-spectraof SrCrO4 which occur at 350nm, 380nm, 700nm and 750nm. The UV band gap of SrCrO4is 3.25 eV. In PL spectra, two peaks are observed one at 480nm and other at 410nm. At480nm, the energy of emitted photons is 2.5eV, while at 410nm the emitted photons hasenergy of 3ev. In the FTIR analysis, the core modes frequently showed by CrO4 unit aresymmetric stretching bond (?1 (A1)), symmetric bending mode (?2 (E)), asymmetricstretching mode (?3 (F2)) and asymmetric bending mode (?4 (F2)).

Mixed system Cs3Cu3Cl8-xBrxOH with weakly connected Cu-triangles

To study the relationship between the properties of low-dimensional spin systems with weakly coupled Cu-triangles and their crystal structure, single crystals of Cs3Cu3Cl8OH (1) and the new Cs3Cu3Cl7.6Br0.4OH (2) were grown. Both compounds are isostructural and crystallize in a monoclinic structure with space group P21/c. The magnetic susceptibility of (1) shows a maximum at 2.23 K and of (2) at 2.70 K, which are attributed to antiferromagnetic phase transitions. Furthermore, the magnetization along the b-axis at 1.9 K for both compounds shows a spin-flop transition into a new antiferromagnetic phase. This transition occurs at 0.61 T for (1) and at 2.0 T for (2). The antiferromagnetic order can be suppressed by a magnetic field BC1 = 1.1 T for (1) and BC2 = 1.2 T for (2). First single crystal neutron diffraction measured on (1) at different temperatures reveals the magnetic signal on the top of the nuclear reflection at (−1 0 0). Its magnetic ordering temperature was found to be at TN1 = 2.12(3) K.

Classes of topological qubits from low-dimensional quantum spin systems

Topological phases of matter is a natural place for encoding robust qubits for quantum computation. In this work we extend the newly introduced class of qubits based on valence-bond solid models with SPT (symmetry-protected topological) order to more general cases. Furthermore, we define and compare various classes of topological qubits encoded in the bulk ground states of topological systems, including SSB (spontaneous symmetry-breaking), TOP (topological), SET (symmetry-enriched topological), SPT, and subsystem SPT classes. We focus on several features for qubits to be robust, including error sets, logical support, code distance and shape of logical gates. In particular, when a global U(1) symmetry is present and preserved, we find a twist operator that extracts the SPT order plays the role of a topological logical operator, which is suitable for global implementation.

Magnetocaloric effect as a signature of quantum level-crossing for a spin-gapped system

Recent research dealing with magnetocaloric effect (MCE) study of antiferromagnetic (AFM) low dimensional spin systems have revealed a number of fascinating ground-state crossover characteristics upon application of external magnetic field. Herein, through MCE investigation we have explored field-induced quantum level-crossing characteristics of one such spin system: (NCP), an AFM spin 1/2 dimer. Experimental magnetization and specific heat data are presented and the data have been employed to evaluate entropy, magnetic energy and magnetocaloric properties. We witness a sign change in magnetic Grüneisen parameter across the level-crossing field BC. An adiabatic cooling is observed at low temperature by tracing the isentropic curves in temperature-magnetic field plane. Energy-level crossover characteristics in NCP interpreted through MCE analysis are well consistent with the observations made from magnetization and specific heat data.

Sub-Kelvin (100 mK) time resolved electron paramagnetic resonance spectroscopy for studies of quantum dynamics of low-dimensional spin systems at low frequencies and magnetic fields.

This article presents a time-resolved electron paramagnetic resonance spectrometry setup designed to work at frequencies below 20 GHz and temperatures down to 50 mK. The setup consists of an on-chip microstrip resonator (Q < 100) placed in a dilution cryostat located within a superconducting 3D vector magnet. A housemade spin echo circuitry controlled by a microwave network analyzer, a pulse pattern generator, and an oscilloscope connects to the microstrip through a series of copper, stainless steel, and superconducting semirigid coaxial lines which are thermally anchored to the different cooling stages of the fridge by means of power attenuators, circulators, and a cryogenic amplifier. Spin echo experiments were performed at a 0.5-T magnetic field on a spin 1 2 paramagnetic coal marker sample mounted on a 15 GHz microstrip resonator at temperatures ranging from 100 to 800 mK. The results show an increase in echo signal intensity as temperature is decreased until saturation as theoretically expected in reaching 99% spin polarization at 100 mK. Our technique allows tuning of the spin system in the pure-state regime and minimizing dipolar fluctuations, which are the main contribution to decoherence in solid-state samples of single-molecule magnets (SMMs) - molecular spin systems that are currently being tested for applications in quantum computation. The achievement of full spin polarization at 100 mK will allow for coherent control over the time evolution of spin systems without the need for large magnetic fields (commonly used to polarize the dipolar bath at higher temperatures) and high frequencies.

Thermodynamics of evolutionary games.

How cooperation can evolve between players is an unsolved problem of biology. Here we use Hamiltonian dynamics of models of the Ising type to describe populations of cooperating and defecting players to show that the equilibrium fraction of cooperators is given by the expectation value of a thermal observable akin to a magnetization. We apply the formalism to the public goods game with three players and show that a phase transition between cooperation and defection occurs that is equivalent to a transition in one-dimensional Ising crystals with long-range interactions. We then investigate the effect of punishment on cooperation and find that punishment plays the role of a magnetic field that leads to an "alignment" between players, thus encouraging cooperation. We suggest that a thermal Hamiltonian picture of the evolution of cooperation can generate other insights about the dynamics of evolving groups by mining the rich literature of critical dynamics in low-dimensional spin systems.

On low-dimensional models at NMR line shape analysis in nanomaterial systems

We present a model of localized spin dynamics at room temperature for the low-dimensional solid-state spin system, which contains small ensembles of magnetic nuclei (N ~ 40). The standard spin Hamiltonian (XXZ model) is the sum of the Zeeman term in a strong external magnetic field and the magnetic dipole interaction secular term. The 19F spins in a single crystal of fluorapatite [Ca5(PO4)3F] have often been used to approximate a one-dimensional spin system. If the constant external field is parallel to the c axis, the 3D 19F system may be treated as a collection of many identical spin chains. When considering the longitudinal part of the secular term, we suggest that transverse component of a spin in a certain site rotates in a constant local magnetic field. This field changes if the spin jumps to another site. On return, this spin continues to rotate in the former field. Then we expand the density matrix in a set of eigenoperators of the Zeeman Hamiltonian. A system of coupled differential equations for the expansion coefficients then solved by straightforward numerical methods, and the fluorine NMR line shapes of fluorapatite for different chain lengths are calculated.

Optical phonon dynamics and electronic fluctuations in the Dirac semimetal Cd3As2

Raman scattering in the three-dimensional Dirac semimetal $\mathrm{C}{\mathrm{d}}_{3}\mathrm{A}{\mathrm{s}}_{2}$ shows an intricate interplay of electronic and phonon degrees of freedom. We observe resonant phonon scattering due to interband transitions, an anomalous anharmonicity of phonon frequency and intensity, as well as quasielastic $(E\ensuremath{\sim}0)$ electronic scattering. The latter two effects are governed by a characteristic temperature scale ${T}^{*}\ensuremath{\sim}100\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ that is related to mutual fluctuations of lattice and electronic degrees of freedom. A refined analysis shows that this characteristic temperature corresponds to the energy of optical phonons which couple to interband transitions in the Dirac states of $\mathrm{C}{\mathrm{d}}_{3}\mathrm{A}{\mathrm{s}}_{2}$. As electron-phonon coupling in a topological semimetal is primarily related to phonons with finite momenta, the back action on the optical phonons is only observed as anharmonicities via multiphonon processes involving a broad range of momenta. The resulting energy density fluctuations of the coupled system have previously only been observed in low dimensional or frustrated spin systems with suppressed long range ordering.