Spin-spin Correlation Research Articles

Critical spin dynamics of Heisenberg ferromagnets revisited

We calculate the dynamic structure factor $S (\boldsymbol{k},\omega)$ in the paramagnetic regime of quantum Heisenberg ferromagnets for temperatures $T$ close to the critical temperature $T_c$ using our recently developed functional renormalization group approach to quantum spin systems. In $d=3$ dimensions we find that for small momenta $\boldsymbol{k}$ and frequencies $\omega$ the dynamic structure factor assumes the scaling form $S(\boldsymbol{k},\omega) = (\tau T G (\boldsymbol{k})/\pi)\Phi (k\xi, \omega\tau)$, where $ G (\boldsymbol{k})$ is the static spin-spin correlation function, $\xi$ is the correlation length, and the characteristic time-scale $\tau$ is proportional to $\xi^{5/2}$. We explicitly calculate the dynamic scaling function $\Phi (x,y)$ and find satisfactory agreement with neutron scattering experiments probing the critical spin dynamics in EuO and EuS. Precisely at the critical point where $\xi = \infty$ our result for the dynamic structure factor can be written as $S (\boldsymbol{k},\omega) = (\pi\omega_k)^{-1} T_c G (\boldsymbol{k}) \Psi_c (\omega/\omega_k)$, where $\omega_k \propto k^{5/2}$. We find that $\Psi_c(\nu)$ vanishes as $\nu^{-13/5}$ for large $\nu$, and as $\nu^{3/5}$ for small $\nu$. While the large-frequency behavior of $\Psi_c (\nu)$ is consistent with calculations based on mode-coupling theory and with perturbative renormalization group calculations to second order in $\epsilon = 6-d$, our result for small frequencies disagrees with previous calculations. We argue that up until now neither experiments nor numerical simulations are sufficiently accurate to determine the low-frequency behavior of $\Psi_c (\nu)$. We also calculate the low-temperature behavior of $S ( \boldsymbol{k},\omega)$ in one- and two dimensional ferromagnets and find that it satisfies dynamic scaling with exponent $z=2$ and exhibits a pseudogap for small frequencies.

Relaxor–super-paraelectric behaviour and crystal-field–driven spin-phonon coupling in pyrochlore Eu2Ti2O7

The temperature-dependent Raman spectroscopy and dielectric property of pyrochlore Eu2Ti2O7 have been investigated. The appearance of additional phonon modes below 200 K is observed suggesting a local structural change. The anomalous softening of the phonon modes and existence of crystal-field-induced short-range magnetic ordering below 150 K unveiled the possible spin-phonon coupling. The signature behaviour of a dipolar glassy-relaxor state and super-paraelectric nature has been demonstrated. Additional dielectric anomaly at lower temperature, below 40 K, related to spin-spin correlation has also been reported.

Evidence for Magnetic Fractional Excitations in a Kitaev Quantum-Spin-Liquid Candidate α-RuCl3

It is known that α-RuCl3 has been studied extensively because of its proximity to the Kitaev quantum-spin-liquid (QSL) phase and the possibility of approaching it by tuning the competing interactions. Here we present the first polarized inelastic neutron scattering study on α-RuCl3 single crystals to explore the scattering continuum around the Γ point at the Brillouin zone center, which was hypothesized to be resulting from the Kitaev QSL state but without concrete evidence. With polarization analyses, we find that, while the spin-wave excitations around the M point vanish above the transition temperature T N, the pure magnetic continuous excitations around the Γ point are robust against temperature. Furthermore, by calculating the dynamical spin-spin correlation function using the cluster perturbation theory, we derive magnetic dispersion spectra based on the K–Γ model, which involves with a ferromagnetic Kitaev interaction of –7.2 meV and an off-diagonal interaction of 5.6 meV. We find this model can reproduce not only the spin-wave excitation spectra around the M point, but also the non-spin-wave continuous magnetic excitations around the Γ point. These results provide evidence for the existence of fractional excitations around the Γ point originating from the Kitaev QSL state, and further support the validity of the K–Γ model as the effective minimal spin model to describe α-RuCl3.

Weak Ferromagnetism in a One-Orbital Double-Exchange Model with Ising Spins for Cerium Oxides

Cerium oxides (ceria) are materials that exhibit weak, room-temperature ferromagnetism without d-electrons. The latter are usually responsible for magnetism in a variety of other oxide compounds, but the underlying mechanism for such a magnetic response in ceria without the d-electrons (d0-magnetism) is still under debate. A possible explanation is Zener double-exchange, where itinerant electrons polarize the localized spins via Hund-coupling as they hop from site to site. Here, we report magnetization and spin-spin correlation results using various values of the Hund-coupling in a one-orbital double-exchange model with Ising spins. In the real material with formula CeO2−x, the oxygen-deficient sites are denoted by x. These sites are related to the density of tetravalent cerium spins (the Ising spin background in our model), which we denoted as and set at N=0.50 in our simulations. Our results at this value of localized spin concentration show ferromagnetic tendencies at low carrier densities (n=0.25). However, ferromagnetism is lost at intermediate carrier concentrations (n=0.50) due to charge localization at high temperatures, as evident from density of states calculations and Monte Carlo snapshots. To our knowledge, our study based on a realistic Zener-type double exchange mechanism is a first in the study of magnetism in cerium oxides. Our results are also consistent with previous studies using similar Hamiltonians in the context of diluted magnetic semiconductors, where Heisenberg spins were used.

Spin- S impurities with XXZ anisotropy in a spin- 12 Heisenberg chain

We study the effect of anisotropy of spin-$S$ impurities on an antiferromagnetic SU(2) Heisenberg chain. The magnetic impurities are assumed to have an XXZ-type anisotropic exchange with its neighboring sites. First, using density-matrix renormalization group technique. we examine spin-spin correlation function, instability of N\'eel order, and local spin susceptibility in the presence of a single spin-$S$ impurity. Based on the results, we find that the types of spin-$S$ impurities are classified into two groups: $\rm(\hspace{.18em}i\hspace{.18em})$ nonmagnetic and $S=1$ impurities enhance only short-range antiferromagnetic correlation and $\rm(\hspace{.08em}ii\hspace{.08em})$ $S=1/2$ and $S>1$ impurities can, in contrast, stabilize a long-range N\'eel order in the disordered SU(2) Heisenberg chain. Then, we focus on the case of $S=1/2$ impurity as a representative of $\rm(\hspace{.08em}ii\hspace{.08em})$ and investigate the evolution of some experimentally observable quantities such as magnetization, specific heat, and magnetic susceptibility, as a function of concentration and XXZ anisotropy strength of the impurity. We confirm that the N\'eel order is induced in the bulk spin chain in the presence of finite amount of easy-axis XXZ $S=1/2$ impurities. Furthermore, we recover some of the aforementioned features using cluster mean-field theory, which allows us to present results on experimentally accessible quantities at finite temperatures. Interestingly, in the presence of uniform magnetic field, the total magnetization exhibits a pseudo-gap behavior for low values of applied field. We also discuss the dependence of NMR spectrum on various XXZ impurities and identify that the spin state of Co impurity in SrCu$_{0.99}$Co$_{0.01}$O$_2$ is $S = 3/2$.

Connecting Complex Electronic Pattern Formation to Critical Exponents

Scanning probes reveal complex, inhomogeneous patterns on the surface of many condensed matter systems. In some cases, the patterns form self-similar, fractal geometric clusters. In this paper, we advance the theory of criticality as it pertains to those geometric clusters (defined as connected sets of nearest-neighbor aligned spins) in the context of Ising models. We show how data from surface probes can be used to distinguish whether electronic patterns observed at the surface of a material are confined to the surface, or whether the patterns originate in the bulk. Whereas thermodynamic critical exponents are derived from the behavior of Fortuin–Kasteleyn (FK) clusters, critical exponents can be similarly defined for geometric clusters. We find that these geometric critical exponents are not only distinct numerically from the thermodynamic and uncorrelated percolation exponents, but that they separately satisfy scaling relations at the critical fixed points discussed in the text. We furthermore find that the two-dimensional (2D) cross-sections of geometric clusters in the three-dimensional (3D) Ising model display critical scaling behavior at the bulk phase transition temperature. In particular, we show that when considered on a 2D slice of a 3D system, the pair connectivity function familiar from percolation theory displays more robust critical behavior than the spin-spin correlation function, and we calculate the corresponding critical exponent. We discuss the implications of these two distinct length scales in Ising models. We also calculate the pair connectivity exponent in the clean 2D case. These results extend the theory of geometric criticality in the clean Ising universality classes, and facilitate the broad application of geometric cluster analysis techniques to maximize the information that can be extracted from scanning image probe data in condensed matter systems.

Magnetization dynamics in the XX spin chain model via multiparticle state

We consider a multiparticle fermionic state to study the magnetization dynamics in an XX spin chain model. The advantage this state provides is the freedom in choosing the initial magnetization profile at each spin site. We characterize the $t=0$ properties of this state, in particular, the probability for the state to have $n$ fermions, fidelity, the two-point and the four-point correlators, and spin-spin correlations. The dynamics of the domain-wall state formed by considering the ground states with magnetizations ${m}_{0}$ and $\ensuremath{-}{m}_{0}$ in the left and right half of the chain, respectively, results in the growth of a flat plateau $(m=0)$ away from the origin. In contrast, the magnetization dynamics of the domain wall state initialized via the multiparticle state reveals the absence of such a region. Our studies of the particle-number fluctuation for the multiparticle state with all sites having identical magnetization reveals linear dependence with respect to the system size, as opposed to the $lnl$ dependence which is obtained for the ground state with the same magnetization.

Antiferromagnetic and ferromagnetic spintronics and the role of in-chain and inter-chain interaction on spin transport in the Heisenberg ferromagnet

Spin-transport and current-induced torques in ferromagnet heterostructures given by a ferromagnetic domain wall are investigated. Furthermore, the continuum spin conductivity is studied in a frustrated spin system given by the Heisenberg model with ferromagnetic in-chain interaction J_1<0 between nearest neighbors and antiferromagnetic next-nearest-neighbor in-chain interaction J_2>0 with aim to investigate the effect of the phase diagram of the critical ion single anisotropy D_c as a function of J_2 on conductivity. We consider the model with the moderate strength of the frustrating parameter such that in-chain spin-spin correlations that are predominantly ferromagnetic. In addition, we consider two inter-chain couplings J_{perp ,y} and J_{perp ,z}, corresponding to the two axes perpendicular to chain where ferromagnetic as well as antiferromagnetic interactions are taken into account.

Arrested Phase Separation in Double-Exchange Models: Large-Scale Simulation Enabled by Machine Learning.

We present large-scale dynamical simulations of electronic phase separation in the single-band double-exchange model based on deep-learning neural-network potentials trained from small-size exact diagonalization solutions. We uncover an intriguing correlation-induced freezing behavior as doped holes are segregated from half filled insulating background during equilibration. While the aggregation of holes is stabilized by the formation of ferromagnetic clusters through Hund's coupling between charge carriers and local magnetic moments, this stabilization also creates confining potentials for holes when antiferromagnetic spin-spin correlation is well developed in the background. The dramatically reduced mobility of the self-trapped holes prematurely disrupts further growth of the ferromagnetic clusters, leading to an arrested phase separation. Implications of our findings for phase separation dynamics in materials that exhibit colossal magnetoresistance effect are discussed.

Thermodynamics of three-dimensional Kitaev quantum spin liquids via tensor networks

We study the 3D Kitaev and Kitaev-Heisenberg models, respectively, on the hyperhoneycomb and hyperoctagon lattices, both at zero and finite-temperature, in the thermodynamic limit. Our analysis relies on advanced tensor network (TN) simulations based on graph projected entangled-pair states (gPEPS). We map out the TN phase diagrams of the models and characterize their underlying gapped and gapless phases both at zero and finite temperature. In particular, we demonstrate how cooling down the hyperhoneycomb system from high temperature leads to fractionalization of spins to Majorana fermions and gauge fields that occurs in two separate temperature regimes, leaving their fingerprint on specific heat as a double-peak feature as well as on other quantities such as the thermal entropy, spin-spin correlations, and bond entropy. Using the Majorana representation of the Kitaev model, we further show that the low-temperature thermal transition to the Kitaev quantum spin liquid (QSL) phase is associated with the nontrivial Majorana band topology and the presence of Weyl nodes, which manifests itself via nonvanishing Chern number and finite thermal Hall conductivity. Beyond the pure Kitaev limit, we study the 3D Kitaev-Heisenberg (KH) model on the hyperoctagon lattice and extract the full phase diagram for different Heisenberg couplings. We further explore the thermodynamic properties of the magnetically-ordered regions in the KH model and show that, in contrast to the QSL phase, here the thermal phase transition follows the standard Landau symmetry-breaking theory.

Driven quantum spin chain in the presence of noise: Anti-Kibble-Zurek behavior

We study defect generation in a quantum XY-spin chain arising due to the linear drive of the many-body Hamiltonian in the presence of a time-dependent fast Gaussian noise. The main objective of this work is to quantify analytically the effects of noise on the defect density production. In the absence of noise, it is well known that in the slow sweep regime, the defect density follows the Kibble-Zurek (KZ) scaling behavior with respect to the sweep speed. We consider time-dependent fast Gaussian noise in the anisotropy of the spin-coupling term $[{\ensuremath{\gamma}}_{0}=({J}_{1}\ensuremath{-}{J}_{2})/({J}_{1}+{J}_{2})]$ and show via analytical calculations that the defect density exhibits anti-Kibble-Zurek (AKZ) scaling behavior in the slow sweep regime. In the limit of large chain length and long time, we calculate the entropy and magnetization density of the final decohered state and show that their scaling behavior is consistent with the AKZ picture in the slow sweep regime. We have also numerically calculated the sublattice spin correlators for finite separation by evaluating the Toeplitz determinants and find results consistent with the KZ picture in the absence of noise, while in the presence of noise and slow sweep speeds the correlators exhibit the AKZ behavior. Furthermore, by considering the large $n$-separation asymptotes of the Toeplitz determinants, we further quantify the effect of the noise on the spin-spin correlators in the final decohered state. We show that while the correlation length of the sublattice correlator scales according to the AKZ behavior, we obtain different scaling for the magnetization correlators.

High Temperature Superconductivity in a Lightly Doped Quantum Spin Liquid.

We have performed density-matrix renormalization group studies of a square lattice t-J model with small hole doping, δ≪1, on long four and six-leg cylinders. We include frustration in the form of a second-neighbor exchange coupling, J_{2}=J_{1}/2, such that the undoped (δ=0) "parent" state is a quantum spin liquid. In contrast to the relatively short range superconducting (SC) correlations that have been observed in recent studies of the six-leg cylinder in the absence of frustration, we find power-law SC correlations with a Luttinger exponent, K_{SC}≈1, consistent with a strongly diverging SC susceptibility, χ∼T^{-(2-K_{SC})} as the temperature T→0. The spin-spin correlations-as in the undoped state-fall exponentially suggesting that the SC "pairing" correlations evolve smoothly from the insulating parent state.

Quantum impurity models using superpositions of fermionic Gaussian states: Practical methods and applications

The coherent superposition of nonorthogonal fermionic Gaussian states has been shown to be an efficient approximation to the ground states of quantum impurity problems [Bravyi and Gosset, Commun. Math. Phys. 356, 451 (2017)]. We propose a practical approach for performing a variational calculation based on such states. Our method is based on approximate imaginary-time equations of motion that decouple the dynamics of each Gaussian state forming the ansatz. It is independent of the lattice connectivity of the model and the implementation is highly parallelizable. To benchmark our variational method, we calculate the spin-spin correlation function and R\'enyi entanglement entropy of an Anderson impurity, allowing us to identify the screening cloud and compare to density matrix renormalization group calculations. Secondly, we study the screening cloud of the two-channel Kondo model, a problem difficult to tackle using existing numerical tools.

Short-Range Berezinskii-Kosterlitz-Thouless Phase Characterization for the q-State Clock Model.

Beyond the usual ferromagnetic and paramagnetic phases present in spin systems, the usual q-state clock model presents an intermediate vortex state when the number of possible orientations q for the system is greater than or equal to 5. Such vortex states give rise to the Berezinskii-Kosterlitz-Thouless (BKT) phase present up to the XY model in the limit . Based on information theory, we present here an analysis of the classical order parameters plus new short-range parameters defined here. Thus, we show that even using the first nearest neighbors spin-spin correlations only, it is possible to distinguish the two transitions presented by this system for q greater than or equal to 5. Moreover, the appearance at relatively low temperature and disappearance of the BKT phase at a rather fix higher temperature is univocally determined by the short-range interactions recognized by the information content of classical and new parameters.

Turbulent relaxation after a quench in the Heisenberg model

We predict the emergence of turbulent scaling in the quench dynamics of the two-dimensional Heisenberg model for a wide range of initial conditions and model parameters. In the isotropic Heisenberg model, we find that the spin-spin correlation function exhibits universal scaling consistent with a turbulent energy cascade. When the spin rotational symmetry is broken by an easy-plane exchange anisotropy, we find a dual cascade of energy and an emergent conserved charge associated to transverse magnetization fluctuations. The scaling exponents are estimated analytically and agree with numerical simulations using phase space methods. We also define the range of initial conditions and model parameters (energy, magnetization, and spin number $S$) that lead to a turbulent cascade. The universal character of the cascade, insensitive to microscopic details or initial conditions, suggests that turbulence in spin systems can be broadly realized in cold atom and solid-state experiments.

Itinerant magnetism of chromium under pressure: a DFT+DMFT study

We consider electronic and magnetic properties of chromium, a well-known itinerant antiferromagnet, by a combination of density functional theory (DFT) and dynamical mean-field theory (DMFT). We find that electronic correlation effects in chromium, in contrast to its neighbors in the periodic table, are weak, leading to the quasiparticle mass enhancement factor m*/m ≈ 1.2. Our results for local spin-spin correlation functions and distribution of weights of atomic configurations indicate that the local magnetic moments are not formed. Similarly to previous results of DFT at ambient pressure, the non-uniform magnetic susceptibility as a function of momentum possesses close to the wave vector Q H = (0, 0, 2π/a) (a is the lattice constant) sharp maxima, corresponding to Kohn anomalies. We find that these maxima are preserved by the interaction and are not destroyed by pressure. Our calculations qualitatively capture a decrease of the Néel temperature with pressure and a breakdown of itinerant antiferromagnetism at pressure of ∼9 GPa in agreement with experimental data, although the Néel temperature is significantly overestimated because of the mean-field nature of DMFT.

Dissipative spin dynamics in hot quantum paramagnets

We use the functional renormalization approach for quantum spin systems developed by Krieg and Kopietz [Phys. Rev. B $\mathbf{99}$, 060403(R) (2019)] to calculate the spin-spin correlation function $G (\boldsymbol{k}, \omega )$ of quantum Heisenberg magnets at infinite temperature. For small wavevectors $\boldsymbol{k} $ and frequencies $\omega$ we find that $G ( \boldsymbol{k}, \omega )$ assumes in dimensions $d > 2$ the diffusive form predicted by hydrodynamics. In three dimensions our result for the spin-diffusion coefficient ${\cal{D}}$ is somewhat smaller than previous theoretical predictions based on the extrapolation of the short-time expansion, but is still about $30 \%$ larger than the measured high-temperature value of ${\cal{D}}$ in the Heisenberg ferromagnet Rb$_2$CuBr$_4\cdot$2H$_2$O. In reduced dimensions $d \leq 2$ we find superdiffusion characterized by a frequency-dependent complex spin-diffusion coefficient ${\cal{D}} ( \omega )$ which diverges logarithmically in $d=2$, and as a power-law ${\cal{D}} ( \omega ) \propto \omega^{-1/3}$ in $d=1$. Our result in one dimension implies scaling with dynamical exponent $z =3/2$, in agreement with recent calculations for integrable spin chains. Our approach is not restricted to the hydrodynamic regime and allows us to calculate the dynamic structure factor $S ( \boldsymbol{k} , \omega )$ for all wavevectors. We show how the short-wavelength behavior of $S ( \boldsymbol{k}, \omega )$ at high temperatures reflects the relative sign and strength of competing exchange interactions.

Quenching of Isovector and Isoscalar Spin-M1 Excitation Strengths in N = Z Nuclei

Spin-M1 excitations of nuclei are important for describing neutrino reactions in supernovae or in neutrino detectors since they are allowed transitions mediated by neutral current neutrino interactions. The spin-M1 excitation strength distributions in self-conjugate N=Z nuclei were studied by proton inelastic scattering at forward angles for each of isovector and isoscalar excitations as reported in H. Matsubara et al., Phys. Rev. Lett. 115, 102501 (2015). The experiment was carried out at the Research Center for Nuclear Physics, Osaka University, employing a proton beam at 295 MeV and the high-resolution spectrometer Grand Raiden. The measured cross-section of each excited state was converted to the squared nuclear matrix elements of spin-M1 transitions by applying a unit cross-section method. Comparison with predictions by a shell-model has revealed that isoscalar spin-M1 strengths are not quenched from the prediction although isovector spin-M1 strengths are quenched similarly with Gamow-Teller strengths in charged-current reactions. This finding hints at an important origin of the quenching of the strength relevant to neutrino scattering, that is, the proton-neutron spin-spin correlation in the ground state of the target nucleus. In this manuscript we present the details of the unit cross-section method used in the data analysis and discuss the consistency between the quenching of the isoscalar magnetic moments and that of the isoscalar spin-M1 strengths.

Artificial out-of-plane Ising antiferromagnet on the kagome lattice with very small farther-neighbor couplings

Despite their simple formulation, short range classical antiferromagnetic Ising models on frustrated lattices give rise to exotic phases of matter, in particular due to their macroscopic ground state degeneracy. Recent experiments on artificial spin systems comprising arrays of chirally coupled nanomagnets provide a significant strengthening of the nearest neighbour couplings compared to systems with dipolar-coupled nanomagnets. This opens the way to design artificial spin systems emulating Ising models with nearest neighbour couplings. In this paper, we compare the results of an extensive investigation with tensor network and Monte Carlo simulations of the nearest- and further-neighbour ($J_1-J_2-J_{3||}$) kagome Ising antiferromagnet with the experimental spin-spin correlations of a kagome lattice of chirally coupled nanomagnets. Even though the ratios between the further neighbour couplings and the nearest neighbour coupling estimated from micromagnetic simulations are much smaller than for dipolar-coupled nanomagnets, we show that they still play an essential role in the selection of the correlations.

Parallel Simulation of Two-Dimensional Ising Models Using Probabilistic Cellular Automata

We study the numerical simulation of the shaken dynamics, a parallel Markovian dynamics for spin systems with local interaction and transition probabilities depending on the two parameters q and J that “tune” the geometry of the underlying lattice. The analysis of the mixing time of the Markov chain and the evaluation of the spin-spin correlations as functions of q and J, make it possible to determine in the (q, J) plane a phase transition curve separating the disordered phase from the ordered one. The relation between the equilibrium measure of the shaken dynamics and the Gibbs measure for the Ising model is also investigated. Finally two different coding approaches are considered for the implementation of the dynamics: a multicore CPU approach, coded in Julia, and a GPU approach coded with CUDA.