Three-dimensional Spin System Research Articles

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.

Magnetization-direction-tunable spin coupling in kagome magnet LiMn6Sn6

The LiMn6Sn6-type of RMn6Sn6 kagome magnet, a room temperature intrinsic ferromagnet with a large anomalous Hall conductivity, has recently been shown to have magnetic-field-direction-dependent electronic structure due to the possible interplay between magnetism and band topology. In this work, we demonstrate magnetic moment direction tunable spin coupling from 3D-Ising type in in-plane spin orientation to 3D-Heisenberg type in out-of-plane spin orientation in kagome magnet LiMn6Sn6, which will further enhance the physics and functionality of LiMn6Sn6. Magnetization measurement of LiMn6Sn6 single crystal revealed paramagnetic to ferromagnetic (PM-FM) phase transition at around 381 K and an easy magnetization axis along the ab-plane (H‖ab). The comprehensive analysis of magnetization isotherms measured in the vicinity of Tc yields the asymptotic critical exponents β, γ, and δ as 0.323, 1.169 and 4.72 for H‖ ab, and 0.350, 1.37, and 4.77 for (H‖ c). These critical exponents satisfy the scaling relation and scaling equation of the magnetic state predicted by scaling theory. The critical exponents obtained are consistent with those found using the renormalization group theory approach for a three-dimensional Ising spin system with spin ordered in an easy in-plane axis (H ⊥ c). However, when the H is applied parallel to the c-axis (H‖ c), the spin coupling changes to a three-dimensional Heisenberg type. Consequently, the origin of ferromagnetism and long-range spin interaction are investigated by DFT first-principles calculations. The calculating result reveals that the Mn3-Mn3 interlayer FM coupling mediated by the super-exchange interaction via Sn2 honeycomb layers sandwiched between the two Mn3 layers is responsible for the macroscopic magnetization in LiMn6Sn6. At the same time, the magnetic couplings between Sn2Li and Mn3 layers play an important role in stabilizing the long-range ferromagnetic ordering.

Broken-Symmetry Ground States of the Heisenberg Model on the Pyrochlore Lattice

The spin-1/2 Heisenberg model on the pyrochlore lattice is an iconic frustrated three-dimensional spin system with a rich phase diagram. Besides hosting several ordered phases, the model is debated to possess a spin-liquid ground state when only nearest-neighbor antiferromagnetic interactions are present. Here, we contest this hypothesis with an extensive numerical investigation using both exact diagonalization and complementary variational techniques. Specifically, we employ a RVB-like many-variable Monte Carlo ansatz and convolutional neural network quantum states for (variational) calculations with up to $4\times 4^3$ and $4 \times 3^3$ spins, respectively. We demonstrate that these techniques yield consistent results, allowing for reliable extrapolations to the thermodynamic limit. Our main results are (1) the determination of the phase transition between the putative spin-liquid phase and the neighboring magnetically ordered phase and (2) a careful characterization of the ground state in terms of symmetry-breaking tendencies. We find clear indications of spontaneously broken inversion and rotational symmetry, calling the scenario of a featureless quantum spin-liquid into question. Our work showcases how many-variable variational techniques can be used to make progress in answering challenging questions about three-dimensional frustrated quantum magnets.

Charge-transfer driven ferromagnetism in a disordered three-dimensional 3d-5d spin system

A three-dimensional disordered spin system consisting of 3d transition metal ion Mn4+ with strong electronic correlations and heavy 5d transition metal ion Ir4+ has been investigated in form of a perovskite thin film. The studied compound of the composition SrMn0.5Ir0.5O3 does not exist as bulk or single crystal, but can be stabilized by epitaxy onto SrTiO3 single crystals as fully disordered double perovskite by pulsed laser deposition. As measured by X-ray circular dichroism, the ground state of this material is ferromagnetic with both, Mn and Ir, spins aligned in parallel. This unusual ground state can be qualitatively explained by charge-transfer driven magnetic exchange involving Mn eg-state and Ir t2g-state, with no evidence of spin–orbit coupling in Ir. Due to the coexistence of competing magnetic interactions and randomness in the system, spin-glass features are observed at low temperatures.

Quantum criticality in a three-dimensional spin system at zero field and pressure

We report spontaneous appearance of antiferromagnetic order in a model gapped quantum paramagnet Ni(Cl$_{1-x}$Br$_x$)$_2$$\cdot$4SC(NH$_2$)$_2$ induced by a change in bromine concentration x. This transition is qualitatively similar to a z = 1 magnetic quantum critical point. However, the observed critical scaling of thermodynamic and magnetic properties has rather unusual critical exponents.

Self-Induced Glassiness and Pattern Formation in Spin Systems Subject to Long-Range Interactions.

We study the glass formation in two- and three-dimensional Ising and Heisenberg spin systems subject to competing interactions and uniaxial anisotropy with a mean-field approach. In three dimensions, for sufficiently strong anisotropy the systems always modulate in a striped phase. Below a critical strength of the anisotropy, a glassy phase exists in a finite range of temperature, and it becomes more stable as the system becomes more isotropic. In two dimensions the criticality is always avoided and the glassy phase always exists.

Neutron spin-echo study of the critical dynamics of spin-52antiferromagnets in two and three dimensions

We report a neutron spin-echo study of the critical dynamics in the $S=5/2$ antiferromagnets MnF$_2$ and Rb$_2$MnF$_4$ with three-dimensional (3D) and two-dimensional (2D) spin systems, respectively, in zero external field. Both compounds are Heisenberg antiferromagnets with a small uniaxial anisotropy resulting from dipolar spin-spin interactions, which leads to a crossover in the critical dynamics close to the N\'eel temperature, $T_N$. By taking advantage of the $\mu\text{eV}$ energy resolution of the spin-echo spectrometer, we have determined the dynamical critical exponents $z$ for both longitudinal and transverse fluctuations. In MnF$_2$, both the characteristic temperature for crossover from 3D Heisenberg to 3D Ising behavior and the exponents $z$ in both regimes are consistent with predictions from the dynamical scaling theory. The amplitude ratio of longitudinal and transverse fluctuations also agrees with predictions. In Rb$_2$MnF$_4$, the critical dynamics crosses over from the expected 2D Heisenberg behavior for $T\gg T_N$ to a scaling regime with exponent $z = 1.387(4)$, which has not been predicted by theory and may indicate the influence of long-range dipolar interactions.

Phase diagrams of one-, two-, and three-dimensional quantum spin systems

We study the bipartite entanglement per bond to determine characteristic features of the phase diagram of various quantum spin models in different spatial dimensions. The bipartite entanglement is obtained from a tensor network representation of the ground state wave-function. Three spin-1/2 models (Ising, XY, XXZ, all in a transverse field) are investigated. Infinite imaginary-time evolution (iTEBD in 1D, ‘simple update’ in 2D and 3D) is used to determine the ground states of these models. The phase structure of the models is discussed for all three dimensions.

The gonihedric paradigm extension of the Ising model

In this paper we review a recently suggested generalization of the Feynman path integral to an integral over random surfaces. The proposed action is proportional to the linear size of the random surfaces and is called gonihedric. The convergence and the properties of the partition function are analyzed. The model can also be formulated as a spin system with identical partition functions. The spin system represents a generalization of the Ising model with ferromagnetic, antiferromagnetic and quartic interactions. Higher symmetry of the model allows to construct dual spin systems in three and four dimensions. In three dimensions the transfer matrix describes the propagation of closed loops and we found its exact spectrum. It is a unique exact solution of the three-dimensional statistical spin system. In three and four dimensions, the system exhibits the second-order phase transitions. The gonihedric spin systems have exponentially degenerated vacuum states separated by the potential barriers and can be used as a storage of binary information.

Phase diagrams of one-, two-, and three-dimensional quantum spin systems derived from entanglement properties

We study the bipartite entanglement per bond to determine characteristic features of the phase diagram of various quantum spin models in different spatial dimensions. The bipartite entanglement is ...

Influence of disorder on critical ageing in 3D Ising model

Abstract It is considered the non-equilibrium critical evolution of three-dimensional pure and site-diluted spin systems described by Ising model from high-temperature initial state with displaying some features, such as ageing and violation of the fluctuation–dissipation theorem. The Monte Carlo simulation results obtained for systems with the spin concentration varying in a wide range are given.

Localized and propagating excitations in gapped phases of spin systems with bond disorder

Using the conventional $T$-matrix approach, we discuss gapped phases in one-, two-, and three-dimensional (3D) spin systems (both with and without a long-range magnetic order) with bond disorder and with weakly interacting bosonic elementary excitations. This work is motivated by recent experimental and theoretical activity in spin-liquid-like systems with disorder and in the disordered interacting boson problem. In particular, we apply our theory to both paramagnetic low-field and fully polarized high-field phases in dimerized spin-$\frac{1}{2}$ systems and in integer-spin magnets with large single-ion easy-plane anisotropy $\mathcal{D}$ with disorder in exchange coupling constants (and/or $\mathcal{D}$). The elementary excitation spectrum and the density of states are calculated in the first order in defects concentration $c\ensuremath{\ll}1$. In 2D and 3D systems, the scattering on defects leads to a finite damping of all propagating excitations in the band except for states lying near its edges. We demonstrate that the analytical approach is inapplicable for states near the band edges and our numerical calculations reveal their localized nature. We find that the damping of propagating excitations can be much more pronounced in considered systems than in magnetically ordered gapless magnets with impurities. In 1D systems, the disorder leads to localization of all states in the band, while those lying far from the band edges (short-wavelength excitations) can look like conventional wave packets.

Dipolar needles in the microcanonical ensemble: Evidence of spontaneous magnetization and ergodicity breaking

We have studied needle-shaped three-dimensional classical spin systems with purely dipolar interactions in the microcanonical ensemble, using both numerical simulations and analytical approximations. We have observed spontaneous magnetization for different finite cubic lattices. The transition from the paramagnetic to the ferromagnetic phase is shown to be of first order. For two lattice types we have observed magnetization flips in the phase transition region. In some cases, gaps in the accessible values of magnetization appear, a signature of the ergodicity breaking found for systems with long-range interactions. We analytically explain these effects by performing a nontrivial mapping of the model Hamiltonian onto a one-dimensional Ising model with competing antiferromagnetic nearest-neighbor and ferromagnetic mean-field interactions. These results hint at performing experiments on isolated dipolar needles in order to verify some of the exotic properties of systems with long-range interactions in the microcanonical ensemble.

Information-theoretic approach to ground-state phase transitions for two- and three-dimensional frustrated spin systems

The information-theoretic observables entropy (a measure of disorder), excess entropy (a measure of complexity), and multi-information are used to analyze ground-state spin configurations for disordered and frustrated model systems in two and three dimensions. For both model systems, ground-state spin configurations can be obtained in polynomial time via exact combinatorial optimization algorithms, which allowed us to study large systems with high numerical accuracy. Both model systems exhibit a continuous transition from an ordered to a disordered ground state as a model parameter is varied. By using the above information-theoretic observables it is possible to detect changes in the spatial structure of the ground states as the critical point is approached. It is further possible to quantify the scaling behavior of the information-theoretic observables in the vicinity of the critical point. For both model systems considered, the estimates of critical properties for the ground-state phase transitions are in good agreement with existing results reported in the literature.

The Magnetic Properties of Mixed Ferrimagnetic Spin System

Based on Monte Carlo (MC) simulation, the magnetization behavior of mixed ferrimagnetic spin system with single-ion anisotropy under external field is investigated. It is assumed that the element of the mixed system is composed of spin-1 and spin-3/2 by turns. The simulated results indicate that there exist the magnetization curves at the ground state on the one-dimensional spin chain, two-dimensional spin system as well as three-dimensional spin system. It found that the size, anisotropy constant and spin configurations influence evidently the magnetic properties of the mixed system. Moreover, the magnetic plateaus and the phase diagrams of the systems can be well interpreted in terms of the simple calculation of energy.

Singlet Ground State and Magnetic Interactions in New Spin Dimer System Ba3Cr2O8

We have successfully synthesized Ba 3 Cr 2 O 8 and investigated its crystal structure and magnetic properties. The crystal structure consists of Ba 2 + cations and isolated CrO 4 3- tetrahedra; magnetic chromium ions exist as rare Cr 5 + (3 d 1 , S = 1/2). An S = 1/2 compound Ba 3 Cr 2 O 8 was found to be a three-dimensional quantum spin system with a singlet ground state of dimer origin. From the analysis of magnetic susceptibility and high-field magnetization data, excitation gap is evaluated as Δ/ k B = 16.1 K and intra- and interdimer exchange interactions are estimated as J 0 / k B = 25.0 K and J '/ k B = 7.7 K, respectively. Comparing with a similar spin dimer compound Ba 3 Mn 2 O 8 , Ba 3 Cr 2 O 8 has a more dominant intradimer interaction.

Field-induced Bose-Einstein condensation of interacting dilute magnons in three-dimensional spin systems: A renormalization-group study

We use the Renormalization Group method to study the magnetic field influence on the Bose-Einstein condensation of interacting dilute magnons in three dimensional spin systems. We first considered a model with SU(2) symmetry (universality class $z=1$) and we obtain for the critical magnetic field a power law dependence on the critical temperature, $[H_c(T)-H_c(0)]\sim T^2$. In the case of U(1) symmetry (universality class $z=2$) the dependence is different, and the magnetic critical field depends linearly on the critical temperature, $[H_c(T)-H_c(0)]\sim T$. By considering a more relevant model, which includes also the system's anisotropy, we obtain for the same symmetry class a $T^{3/2}$ dependence of the magnetic critical field on the critical temperature. We discuss these theoretical predictions of the renormalization group in connection with experimental results reported in the literature.

Influence of the phase separation effect on low-field magnetic properties of La 1−xBa xMnO 3

Magnetic susceptibility, χ ( T ) , is investigated in ceramic La 1− x Ba x MnO 3 (LBMO) with x = 0.02 – 0.25 in the range of fields B = 10 – 80 G and temperatures T = 5 – 310 K . All samples exhibit a paramagnetic (PM) to ferromagnetic (FM) transition with T C increasing with x from 177 K ( x = 0.02 ) to 295 K ( x = 0.25 ) and magnetic irreversibility decreasing below T C with increasing x . In the PM phase an interval of the Curie–Weiss behavior of χ ( T ) with an effective Bohr magneton number, p eff ∼ 30 – 40 , is observed above T 1 ∼ 260 – 290 K . Below T 1 and down to T cr ∼ 190 – 220 K the susceptibility follows the scaling law χ - 1 ( T ) - χ - 1 ( T C ) ∼ ( T / T C - 1 ) γ with γ = γ 1 ≈ 1.4 corresponding to a three-dimensional (3D) Heisenberg spin system. Below T cr, χ ( T ) obeys the same scaling law as for T > T cr , but with another value of γ = γ 2 ≈ 1.7 – 1.8 , characteristic of a 3D percolation system. The temperature dependence of the susceptibility observed in the PM phase is explained by small FM particles embedded in the host LBMO matrix above T 1. The size of these particles increases between T 1 and T cr up to nanometer scale, forming critical percolation clusters below T cr. The magnetic irreversibility is connected to a mixed, FM and cluster-glass, phase.

Critical dynamics of three-dimensional spin systems with long-range interactions

A field-theoretic description of critical behavior of Ising systems with long-range interactions is obtained by using the Padé-Borel summation technique in the two-loop approximation directly in the three-dimensional space. It is shown that long-range interactions affect the relaxation time of the system.

Crossover behavior in three-dimensional dilute spin systems.

We study the crossover behaviors that can be observed in the high-temperature phase of three-dimensional dilute spin systems, using a field-theoretical approach. In particular, for randomly dilute Ising systems we consider the Gaussian-to-random and the pure-Ising-to-random crossover, determining the corresponding crossover functions for the magnetic susceptibility and the correlation length. Moreover, for the physically interesting cases of dilute Ising, XY, and Heisenberg systems, we estimate several universal ratios of scaling-correction amplitudes entering the high-temperature Wegner expansion of the magnetic susceptibility, of the correlation length, and of the zero-momentum quartic couplings.