Effective Spin-1 Research Articles

Spin-dependent vibronic response of a carbon radical ion in two-dimensional WS2

Atomic spin centers in 2D materials are a highly anticipated building block for quantum technologies. Here, we demonstrate the creation of an effective spin-1/2 system via the atomically controlled generation of magnetic carbon radical ions (CRIs) in synthetic two-dimensional transition metal dichalcogenides. Hydrogenated carbon impurities located at chalcogen sites introduced by chemical doping are activated with atomic precision by hydrogen depassivation using a scanning probe tip. In its anionic state, the carbon impurity is computed to have a magnetic moment of 1 μB resulting from an unpaired electron populating a spin-polarized in-gap orbital. We show that the CRI defect states couple to a small number of local vibrational modes. The vibronic coupling strength critically depends on the spin state and differs for monolayer and bilayer WS2. The carbon radical ion is a surface-bound atomic defect that can be selectively introduced, features a well-understood vibronic spectrum, and is charge state controlled.

Dynamical properties of the Haldane chain with bond disorder

By using Lanczos exact diagonalization and quantum Monte Carlo combined with stochastic analytic continuation, we study the dynamical properties of the S = 1 antiferromagnetic Heisenberg chain with different strengths of bond disorder. In the weak disorder region, we find weakly coupled bonds which can induce additional low-energy excitation below the one-magnon mode. As the disorder increases, the average Haldane gap closes at δΔ ∼ 0.5 with more and more low-energy excitations coming out. After the critical disorder strength δc ∼ 1, the system reaches a random-singlet phase with prominent sharp peak at ω = 0 and broad continuum at ω > 0 of the dynamic spin structure factor. In addition, we analyze the distribution of random spin domains and numerically find three kinds of domains hosting effective spin-1/2 quanta or spin-1 sites in between. These “spins” can form the weakly coupled long-range singlets due to quantum fluctuation which contribute to the sharp peak at ω = 0.

Weak Singularities of the Isothermal Entropy Change as the Smoking Gun Evidence of Phase Transitions of Mixed-Spin Ising Model on a Decorated Square Lattice in Transverse Field.

The magnetocaloric response of the mixed spin-1/2 and spin-S () Ising model on a decorated square lattice is thoroughly examined in presence of the transverse magnetic field within the generalized decoration-iteration transformation, which provides an exact mapping relation with an effective spin-1/2 Ising model on a square lattice in a zero magnetic field. Temperature dependencies of the entropy and isothermal entropy change exhibit an outstanding singular behavior in a close neighborhood of temperature-driven continuous phase transitions, which can be additionally tuned by the applied transverse magnetic field. While temperature variations of the entropy display in proximity of the critical temperature a striking energy-type singularity , two analogous weak singularities can be encountered in the temperature dependence of the isothermal entropy change. The basic magnetocaloric measurement of the isothermal entropy change may accordingly afford the smoking gun evidence of continuous phase transitions. It is shown that the investigated model predominantly displays the conventional magnetocaloric effect with exception of a small range of moderate temperatures, which contrarily promotes the inverse magnetocaloric effect. It turns out that the temperature range inherent to the inverse magnetocaloric effect is gradually suppressed upon increasing of the spin magnitude S.

Nonergodic dynamics of the one-dimensional Bose-Hubbard model with a trapping potential

We investigate nonergodic behavior of the one-dimensional Bose-Hubbard model, which emerges in the unitary quantum dynamics starting with initial-state $|\ensuremath{\psi}(0)\ensuremath{\rangle}=|\ensuremath{\cdots}2020\ensuremath{\cdots}\ensuremath{\rangle}$ in the presence of a trapping potential. We compute the level spacing statistic, the time evolution of the number imbalance between the odd and the even sites, and the entanglement entropy in order to show that the system exhibits nonergodicity in a strongly interacting regime. The trapping potential enhances nonergodicity even when the trapping potential is weak compared to the hopping energy. We derive the effective spin-1/2 $XXZ$ Hamiltonian for the strongly interacting regimes by using a perturbation method. On the basis of the effective Hamiltonian, we show that the trapping potential is effectively strengthened by the on-site interaction, leading to the enhancement of the nonergodic behavior. We also calculate the real-time dynamics under the effective Hamiltonian and find that the entanglement entropy grows logarithmically in time.

Field-induced quantum spin disordered state in spin-1/2 honeycomb magnet Na2Co2TeO6

Spin-orbit coupled honeycomb magnets with the Kitaev interaction have received a lot of attention due to their potential of hosting exotic quantum states including quantum spin liquids. Thus far, the most studied Kitaev systems are 4d/5d-based honeycomb magnets. Recent theoretical studies predicted that 3d-based honeycomb magnets, including Na2Co2TeO6 (NCTO), could also be a potential Kitaev system. Here, we have used a combination of heat capacity, magnetization, electron spin resonance measurements alongside inelastic neutron scattering (INS) to study NCTO’s quantum magnetism, and we have found a field-induced spin disordered state in an applied magnetic field range of 7.5 T < B (⊥ b-axis) < 10.5 T. The INS spectra were also simulated to tentatively extract the exchange interactions. As a 3d-magnet with a field-induced disordered state on an effective spin-1/2 honeycomb lattice, NCTO expands the Kitaev model to 3d compounds, promoting further interests on the spin-orbital effect in quantum magnets.

Gapped ground state in a spin- 12 frustrated square lattice

We present a model compound with a spin-1/2 frustrated square lattice, in which three ferromagnetic (F) interactions and one antiferromagnetic (AF) compet. Considering the effective spin-1 formed by the dominant F dimer, this square lattice can be mapped to a spin-1 spatially anisotropic triangular lattice. The magnetization curve exhibits gapped behavior indicative of a dominant one-dimensional (1D) AF correlation. In the field-induced gapless phase, the specific heat and magnetic susceptibility show a phase transition to an ordered state with 2D characteristics. These results indicate that the spin-1 Haldane state is extended to the 2D system. We demonstrate that the gapped ground state observed in the present spin-1/2 frustrated square lattice originates from the one-dimensionalization caused by frustration.

Survival of itinerant excitations and quantum spin state transitions in YbMgGaO4 with chemical disorder

A recent focus of quantum spin liquid (QSL) studies is how disorder/randomness in a QSL candidate affects its true magnetic ground state. The ultimate question is whether the QSL survives disorder or the disorder leads to a “spin-liquid-like” state, such as the proposed random-singlet (RS) state. Since disorder is a standard feature of most QSL candidates, this question represents a major challenge for QSL candidates. YbMgGaO4, a triangular lattice antiferromagnet with effective spin-1/2 Yb3+ions, is an ideal system to address this question, since it shows no long-range magnetic ordering with Mg/Ga site disorder. Despite the intensive study, it remains unresolved as to whether YbMgGaO4 is a QSL or in the RS state. Here, through ultralow-temperature thermal conductivity and magnetic torque measurements, plus specific heat and DC magnetization data, we observed a residual κ0/T term and series of quantum spin state transitions in the zero temperature limit for YbMgGaO4. These observations strongly suggest that a QSL state with itinerant excitations and quantum spin fluctuations survives disorder in YbMgGaO4.

Stripe-yz magnetic order in the triangular-lattice antiferromagnet KCeS2

Yb- and Ce-based delafossites were recently identified as effective spin-1/2 antiferromagnets on the triangular lattice. Several Yb-based systems, such as NaYbO2, NaYbS2, and NaYbSe2, exhibit no long-range order down to the lowest measured temperatures and therefore serve as putative candidates for the realization of a quantum spin liquid. However, their isostructural Ce-based counterpart KCeS2 exhibits magnetic order below T N = 400 mK, which was so far identified only in thermodynamic measurements. Here we reveal the magnetic structure of this long-range ordered phase using magnetic neutron diffraction. We show that it represents the so-called ‘stripe-yz’ type of antiferromagnetic order with spins lying approximately in the triangular-lattice planes orthogonal to the nearest-neighbor Ce–Ce bonds. No structural lattice distortions are revealed below T N, indicating that the triangular lattice of Ce3+ ions remains geometrically perfect down to the lowest temperatures. We propose an effective Hamiltonian for KCeS2, based on a fit to the results of ab initio calculations, and demonstrate that its magnetic ground state matches the experimental spin structure.

Magnetic properties of the Ising-like rare earth pyrosilicate: D-Er2Si2O7

Ising-like spin-1/2 magnetic materials are of interest for their ready connection to theory, particularly in the context of quantum critical behavior. In this work we report detailed studies of the magnetic properties of a member of the rare earth pyrosilicate family, D-Er2Si2O7, which is known to display a highly anisotropic Ising-like g-tensor and effective spin-1/2 magnetic moments. We used powder neutron diffraction, powder inelastic neutron spectroscopy (INS), and single crystal AC susceptibility to characterize its magnetic properties. Neutron diffraction enabled us to determine the magnetic structure below the known transition temperature (T N = 1.9 K) in zero field, confirming that the magnetic state is a four-sublattice antiferromagnetic structure with two non-collinear Ising axes, as was previously hypothesized. Our powder INS data revealed a gapped excitation at zero field, consistent with anisotropic (possibly Ising) exchange. An applied field of 1 T produces a mode softening, which is consistent with a field-induced second order phase transition. To assess the relevance of D-Er2Si2O7 to the transverse field Ising model, we performed AC susceptibility measurements on a single crystal with the magnetic field oriented in the direction transverse to the Ising axes. This revealed a transition at 2.65 T at 0.1 K, a field significantly higher than the mode-softening field observed by powder INS, showing that the field-induced phase transitions are highly field-direction dependent as expected. These measurements suggest that D-Er2Si2O7 may be a candidate for further exploration related to the transverse field Ising model.

Anomalous fractional quantization in the kagomelike Heisenberg ladder: Emergence of the effective spin-1 chain

We study a Kagome-like spin-$1/2$ Heisenberg ladder with competing ferromagnetic (FM) and antiferromagnetic (AFM) exchange interactions. Using the density-matrix renormalization group based calculations, we obtain the ground state phase diagram as a function of the ratio between the FM and AFM exchange interactions. Five different phases exist. Three of them are spin polarized phases; an FM phase and two kinds of ferrimagnetic (FR) phases (referred to as FR1 and FR2 phases). The spontaneous magnetization per site is $m=1/2$, $1/3$, and $1/6$ in the FM, FR1, and FR2 phases, respectively. This can be understood from the fact that an effective spin-1 Heisenberg chain formed by the upper and lower leg spins has a three-step fractional quantization of the magnetization per site as $m=1$, $1/2$, and $0$. In particular, an anomalous "intermediate" state $m=1/2$ of the effective spin-1 chain with the reduced Hilbert space of a spin from $3$ to $2$ dimensional is highly unexpected in the context of conventional spin-1 physics. Thus, surprisingly, the effective spin-1 chain behaves like a spin-1/2 chain with SU(2) symmetry. The remaining two phases are spin-singlet phases with translational symmetry breaking in the presence of valence bond formations. One of them is octamer-siglet phase with a spontaneous octamerization long-range order of the system, and the other is period-4 phase characterized by the magnetic superstructure with a period of four structural unit cells. In these spin-singlet phases, we find the coexistence of valence bond structure and gapless chain. Although this may be emerged through the order-by-disorder mechanism, there can be few examples of such a coexistence.

Rare-earth pyrocoboltates [formula omitted]Co2O7 (R = Ce, Yb): Effective spin-[formula omitted] antiferromagnetic insulators with strong geometrical frustration

The two new rare-earth pyrocoboltates R2Co2O7 (R = Ce, Yb) adopt the layered monoclinic Ca2Nb2O7-type structure with the space group P21(No. 4). Both compounds have been investigated by DC magnetic susceptibility χdc(T), AC magnetic susceptibility χac(T) and isothermal magnetization M(B) measurements. The observed effective magnetic moment of Ce2Co2O7 indicates a contribution from the Co sublattice while that of Yb2Co2O7 is mainly from the localized 4f13 electronic configuration of Yb3+ ion. A magnetic ordering of the antiferromagnetic-type is observed in Ce2Co2O7 at TN≃ 34 K. This ordering is accompanied by the opening of a magnetic spectral gap, Δ=57.7 K (~ 5.0 meV) in the spin-wave spectrum and it survives in an external magnetic field of 7 T. In addition to the transition at TN,χac(T) measurements reveal a dome-like feature centered at ≃ 20 K in high frequency which indicates the presence of possible short-range correlation. In Yb2Co2O7, a magnetic phase transition is observed below TN=2.94 K, which is suppressed below 1.9 K in an external magnetic field of 3 T. In the low-T region where the crystal electric field effects can be neglected, an effective spin-1/2 state is realized in Yb2Co2O7, with a Landé-g factor of 3.76 which is comparable to values observed from electron spin resonance (ESR) measurements on related systems. In addition, M(B) of Yb2Co2O7 shows a metamagnetic-like feature at a critical field of HC≈2.5 T. Signatures from both compounds reveal the presence of strong magnetic frustrations with frustration index f of 9.17 and 15.12 for Ce2Co2O7 and Yb2Co2O7, respectively.

Frustrated spin-1/2 dimer compound K2Co2(SeO3)3 with easy-axis anisotropy

Magnetic susceptibility, magnetization, and specific-heat measurements under both in-plane and out-of-plane field on ${\mathrm{K}}_{2}{\mathrm{Co}}_{2}{(\mathrm{Se}{\mathrm{O}}_{3})}_{3}$ single crystals are reported. The Co dimers in this compound, which are made from face-sharing effective spin-1/2 $\mathrm{Co}{\mathrm{O}}_{6}$ octahedra, sit on the corners of a geometrically frustrating triangular planar lattice. No long-range magnetic ordering is found down to 0.35 K, which, together with the large negative Curie-Weiss temperature obtained from fitting the temperature-dependent magnetic susceptibility, indicates that the system is magnetically frustrated. Analysis of the field and orientation dependence of the magnetic and thermodynamic properties suggests the presence of an easy-axis anisotropy. The magnetic fluctuations present due to geometric frustration are more resistant to an in-plane field than a perpendicular-to-plane field.

Quantum Phase Transitions in an Yb-based Semiconductor YbCuS2 with an Effective Spin-1/2 Zigzag Chain

Magnetic properties of an Yb-based semiconductor YbCuS2 with a zigzag chain of Yb3+ ions were studied. The Curie–Weiss behavior of the magnetic susceptibility χ(T) indicates antiferromagnetic interaction and an isolated Kramers doublet ground state with effective spin-1/2. Magnetic specific heat Cm/T exhibits a sharp peak at TO = 0.95 K, where the magnetic entropy is 20% of R ln 2, indicating strong magnetic fluctuations. In magnetic fields, TO is robust for B < 4 T, and it shifts to higher temperatures but reverses downward for B ≥ 7 T. Below TO, a magnetization plateau manifests itself at around 6 T which is followed by transitions at 9.1 and 15.6 T. The phase diagram suggests that nontrivial phases arise from magnetic frustration in the Yb zigzag chain.

Adiabatic preparation of entangled, magnetically ordered states with cold bosons in optical lattices

We analyze a scheme for preparation of magnetically ordered states of two-component bosonic atoms in optical lattices. We compute the dynamics during adiabatic and optimized time-dependent ramps to produce ground states of effective spin Hamiltonians, and determine the robustness to decoherence for realistic experimental system sizes and timescales. Ramping parameters near a phase transition point in both effective spin-1/2 and spin-1 models produces entangled spin-symmetric states that have potential future applications in quantum enhanced measurement. The preparation of these states and their robustness to decoherence is quantified by computing the quantum Fisher information (QFI) of final states. We identify that the generation of useful entanglement should in general be more robust to heating than it would be implied by the state fidelity, with corresponding implications for practical applications.

Possible itinerant excitations and quantum spin state transitions in the effective spin-1/2 triangular-lattice antiferromagnet Na2BaCo(PO4)2

The most fascinating feature of certain two-dimensional (2D) gapless quantum spin liquid (QSL) is that their spinon excitations behave like the fermionic carriers of a paramagnetic metal. The spinon Fermi surface is then expected to produce a linear increase of the thermal conductivity with temperature that should manifest via a residual value (κ0/T) in the zero-temperature limit. However, this linear in T behavior has been reported for very few QSL candidates. Here, we studied the ultralow-temperature thermal conductivity of an effective spin-1/2 triangular QSL candidate Na2BaCo(PO4)2, which has an antiferromagnetic order at very low temperature (TN ~ 148 mK), and observed a finite κ0/T extrapolated from the data above TN. Moreover, while approaching zero temperature, it exhibits series of quantum spin state transitions with applied field along the c axis. These observations indicate that Na2BaCo(PO4)2 possibly behaves as a gapless QSL with itinerant spin excitations above TN and its strong quantum spin fluctuations persist below TN.

Nature of intermediate magnetization plateaus of a spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice resembling a triangulated kagome lattice.

The spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice is exactly solved in a magnetic field within the framework of the generalized star-triangle transformation and the method of exact recursion relations. The generalized star-triangle transformation establishes an exact mapping correspondence with the effective spin-1/2 Ising model on a triangular Husimi lattice with a temperature-dependent field, pair and triplet interactions, which is subsequently rigorously treated by making use of exact recursion relations. The ground-state phase diagram of a spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice, which bears a close resemblance with a triangulated kagomé lattice, involves, in total, two classical and three quantum ground states manifested in respective low-temperature magnetization curves as intermediate plateaus at 1/9, 1/3, and 5/9 of the saturation magnetization. It is verified that the fractional magnetization plateaus of quantum nature have character of either dimerized or trimerized ground states. A low-temperature magnetization curve of the spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice resembling a triangulated kagome lattice may exhibit either no intermediate plateau, a single 1/3 plateau, a single 5/9 plateau, or a sequence of 1/9, 1/3, and 5/9 plateaus depending on a character and relative size of two considered coupling constants.

Roles of easy-plane and easy-axis XXZ anisotropy and bond alternation in a frustrated ferromagnetic spin- 12 chain

The spin-$1/2$ Heisenberg chain with a ferromagnetic first-neighbor exchange coupling $J_1$ and an antiferromagnetic second-neighbor $J_2$ has a Haldane dimer ground state with an extremely small spin gap. Thus, the ground state is readily altered by perturbations. Here, we investigate the effects of XXZ exchange magnetic anisotropy of both the easy-axis and easy-plane types and an alternation in $J_1$ on the ground state, the spin gap, and magnetic properties of the frustrated ferromagnetic spin-$1/2$ chain. It is found that there are two distinct dimerized spin-gap phases, in one of which the spin gap and the magnetic susceptibility are extremely small around the SU(2) symmetric case and in the other they are moderately large far away from the SU(2) symmetric case. A small alternation in the amplitude of $J_1$ rapidly shortens the pitch of spin correlations towards the four-spin periodicity, as in the limit of $J_1/J_2\to0$. These effects are not sufficient to quantitatively explain overall experimentally observed magnetic properties in the quasi-one-dimensional spin-gapped magnetoelectric cuprate Rb$_2$Cu$_2$Mo$_3$O$_{12}$ that exhibits ferroelectricity stabilized by a magnetic field. Our results are also relevant to Cs$_2$Cu$_2$Mo$_3$O$_{12}$, where the ferromagnetic intrachain and antiferromagnetic interchain order has recently been found, in a single chain level. We also reveal the nature of symmetry-protected topological phase transitions in the model by mapping onto effective spin-1 chain models.

Geometric driving of two-level quantum systems

We investigate a class of cyclic evolutions for %the cyclic evolution of driven two-level quantum systems (effective spin-1/2) with a particular focus on the geometric characteristics of the driving and their specific imprints on the quantum dynamics. By introducing the concept of geometric field curvature for any field trajectory in the parameter space we are able to unveil underlying patterns in the overall quantum behavior: the knowledge of the field curvature provides a non-standard and fresh access to the interrelation between field and spin trajectories, and the corresponding quantum phases acquired in non-adiabatic cyclic evolutions. In this context, we single out setups in which the driving field curvature can be employed to demonstrate a pure geometric control of the quantum phases. Furthermore, the driving field curvature can be naturally exploited to introduce the geometrical torque and derive a general expression for the total quantum phase acquired in a cycle. Remarkably, such relation allows to access the mechanisms controlling the changeover of the quantum phase across a topological transition and to disentangle the role of the spin and field topological windings. As for implementations, we discuss a series of physical systems and platforms to demonstrate how the geometric control of the quantum phases can be realized for pendular field drivings. This includes setups based on superconducting islands coupled to a Josephson junction and inversion asymmetric nanochannels with suitably tailored geometric shapes.

Magnetic behavior of a ferroferrimagnetic ternary alloy AB_{ρ}C_{1-ρ} with a selective site disorder: Case study of a mixed-spin Ising model on a honeycomb lattice.

Phase transitions, compensation phenomenon, and magnetization of a ferroferrimagnetic ternary alloy AB_{ρ}C_{1-ρ} composed of three different kinds of magnetic ions A, B, and C with the spin magnitudes 1/2, 1, and 3/2 are examined within the framework of a mixed-spin Ising model on a honeycomb lattice with a selective annealed site disorder on one of its two sublattices. It is supposed that the first sublattice of a bipartite honeycomb lattice is formed by the spin-1/2 magnetic ions, while the sites of the second sublattice are randomly occupied either by the spin-1 magnetic ions with a probability ρ or the spin-3/2 magnetic ions with a probability 1-ρ, both being subject to a uniaxial single-ion anisotropy. The model under investigation can be exactly mapped into an effective spin-1/2 Ising model on a triangular lattice through the generalized star-triangle transformation. For a specific concentration of the spin-1 (spin-3/2) magnetic ions, it is shown that the ferroferrimagnetic version of the studied model may display a compensation temperature at which the total magnetization vanishes below a critical temperature. The critical temperature strikingly may also become independent of the concentration of the randomly mixed spin-1 and spin-3/2 magnetic ions for a specific value of a uniaxial single-ion anisotropy. The spontaneous magnetic order may be notably restored at finite temperatures through the order-by-disorder mechanism above a disordered ground state, which results in an anomalous temperature dependence of the total magnetization with double reentrant phase transitions.

Magnetic phases of orbital bipartite optical lattices

In the Hamburg cold atom experiment with orbital states in an optical lattice, s- and p-orbital atomic states hybridize between neighboring sites. In this work we show how this alternation of sites hosting s- and p-orbital states gives rise to a plethora of different magnetic phases, quantum and classical. We focus on phases whose properties derive from frustration originating from a competition between nearest and next nearest neighboring exchange interactions. The physics of the Mott insulating phase with unit filling is described by an effective spin-1/2 Hamiltonian showing great similarities with the J1–J2 model. Based on the knowledge of the J1–J2 model, supported by numerical simulations, we discuss the possibility of a quantum spin liquid phase in the present optical lattice system. In the superfluid regime we consider the parameter regime where the s-orbital states can be adiabatically eliminated to give an effective model for the p-orbital atoms. At the mean-field level we derive a generalized classical XY model, and show that it may support maximum frustration. When quantum fluctuations can be disregarded, the ground state should be a spin glass.