Two-dimensional Isotropic Heisenberg 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.

Frustrated honeycomb-lattice bilayer quantum antiferromagnet in a magnetic field: Unconventional phase transitions in a two-dimensional isotropic Heisenberg model

We consider the spin-1/2 antiferromagnetic Heisenberg model on a bilayer honeycomb lattice including interlayer frustration in the presence of an external magnetic field. In the vicinity of the saturation field, we map the low-energy states of this quantum system onto the spatial configurations of hard hexagons on a honeycomb lattice. As a result, we can construct effective classical models (lattice-gas as well as Ising models) on the honeycomb lattice to calculate the properties of the frustrated quantum Heisenberg spin system in the low-temperature regime. We perform classical Monte Carlo simulations for a hard-hexagon model and adopt known results for an Ising model to discuss the finite-temperature order-disorder phase transition that is driven by a magnetic field at low temperatures. We also discuss an effective-model description around the ideal frustration case and find indications for a spin-flop-like transition in the considered isotropic spin model.

Magnon spectrum in ferromagnets with a skyrmion

The analysis of the spin wave excitations in two-dimensional isotropic Heisenberg ferromagnet is performed with a single skyrmion in the ground state. We employ the ideas of semiclassical quantization method, duly modified for the use of the lattice model and Maleyev-Dyson boson representation of spin operators. The resulting Schr\"odinger equation for magnons describes the dispersion and wave functions of spin-wave excitations with strictly non-negative spectrum. In contrast to usual ferromagnet, we demonstrate the existence of three zero modes, corresponding to conformal symmetries spontaneously violated by the skyrmion configuration.

Magnetic phase diagram ofBa3CoSb2O9as determined by ultrasound velocity measurements

Using high-resolution sound velocity measurements we have obtained a very precise magnetic phase diagram of ${\mathrm{Ba}}_{3}{\mathrm{CoSb}}_{2}{\mathrm{O}}_{9}$, a material that is considered to be an archetype of the spin-$\frac{1}{2}$ triangular-lattice antiferromagnet. Results obtained for the field parallel to the basal plane (up to 18 T) show three phase transitions, consistent with predictions based on simple two-dimensional isotropic Heisenberg models and previous experimental investigations. The phase diagram obtained for the field perpendicular to the basal plane clearly reveals an easy-plane character of this compound and, in particular, our measurements show a single first-order phase transition at ${H}_{c1}=12.0$ T which can be attributed to a spin flop between an umbrella-type configuration and a coplanar $V$-type order where spins lie in a plane perpendicular to the $ab$ plane. At low temperatures, softening of the lattice within some of the ordered phases is also observed and may be a result of residual spin fluctuations.

Stabilization of Long-Range Order by Additional Anisotropic Spins in Two-Dimensional Isotropic Heisenberg Antiferromagnets —A Possible Model of an Organic Compound with Magnetic Anions—

We examine a two-dimensional (2D) coupled antiferromagnetic (AF) Heisenberg model that consists of two subsystems: an isotropic S = 1/2 spin subsystem with strong AF exchange interactions (main system), and a uniaxial S = 5/2 spin subsystem with weak exchange interactions. This model is an example in which additional semiclassical degrees of freedom affect a quantum system; it also describes a possible stabilization mechanism of AF long-range order (LRO) in the 2D organic compound λ-(BETS)2FeCl4, where BETS stands for bis(ethylenedithio)tetraselenafulvalene. Previous experimental studies have revealed that 3d spins on FeCl4 anions passively follow the AF LRO of the π-electron system in the BETS layers, although the AF LRO is stabilized by the 3d spins themselves. To explain this paradoxical behavior, we examine a scenario in which the uniaxial anisotropy of the 3d spins stabilizes the AF LRO on an isotropic 2D π-spin system. We extend Green’s function theory, called the Tyablikov approximation, to the present system, which describes spin-wave excitations and is consistent with the Mermin–Wagner theorem. It is shown that even extremely weak interactions with the uniaxial subsystem efficiently stabilize the AF LRO in the main system, even in the absence of AF exchange interactions in the uniaxial subsystem. The AF LRO is triggered by the uniaxial subsystem, but the sublattice magnetization remains smaller than that of the main system in the high-temperature region. These results are consistent with experimental data for λ-(BETS)2FeCl4 and λ-(BETS)2GaCl4; the latter does not have the 3d spins and does not exhibit the AF LRO.

A quantum Mermin–Wagner theorem for quantum rotators on two-dimensional graphs

This is the first of a series of papers considering symmetry properties of quantum systems over 2D graphs or manifolds, with continuous spins, in the spirit of the Mermin–Wagner theorem [N. D. Mermin and H. Wagner, “Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models,” Phys. Rev. Lett. 17, 1133–1136 (1966)]10.1103/PhysRevLett.17.1133. In the model considered here (quantum rotators), the phase space of a single spin is a d-dimensional torus M, and spins (or particles) are attached to sites of a graph \documentclass[12pt]{minimal}\begin{document}$(\Gamma ,\mathcal {E})$\end{document}(Γ,E) satisfying a special bi-dimensionality property. The kinetic energy part of the Hamiltonian is minus a half of the Laplace operator −Δ/2 on M. We assume that the interaction potential is C2-smooth and invariant under the action of a connected Lie group \documentclass[12pt]{minimal}\begin{document}${\tt G}$\end{document}G (i.e., a Euclidean space \documentclass[12pt]{minimal}\begin{document}${\mathbb {R}}^{d^{\prime }}$\end{document}Rd′ or a torus M′ of dimension d′ ⩽ d) on M preserving the flat Riemannian metric. A part of our approach is to give a definition (and a construction) of a class of infinite-volume Gibbs states for the systems under consideration (the class \documentclass[12pt]{minimal}\begin{document}$\mathfrak {G}$\end{document}G). This class contains the so-called limit Gibbs states, with or without boundary conditions. We use ideas and techniques originated from papers [R. L. Dobrushin and S. B. Shlosman, “Absence of breakdown of continuous symmetry in two-dimensional models of statistical physics,” Commun. Math. Phys. 42, 31–40 (1975)10.1007/BF01609432; C.-E. Pfister, “On the symmetry of the Gibbs states in two-dimensional lattice systems,” Commun. Math. Phys. 79, 181–188 (1981)10.1007/BF01942060; J. Fröhlich and C. Pfister, “On the absence of spontaneous symmetry breaking and of crystalline ordering in two-dimensional systems,” Commun. Math. Phys. 81, 277–298 (1981)10.1007/BF01208901; B. Simon and A. Sokal, “Rigorous entropy-energy arguments,” J. Stat. Phys. 25, 679–694 (1981)10.1007/BF01022362; D. Ioffe, S. Shlosman and Y. Velenik, “2D models of statistical physics with continuous symmetry: The case of singular interactions,” Commun. Math. Phys. 226, 433–454 (2002)]10.1007/s002200200627 in combination with the Feynman–Kac representation, to prove that any state lying in the class \documentclass[12pt]{minimal}\begin{document}$\mathfrak {G}$\end{document}G (defined in the text) is \documentclass[12pt]{minimal}\begin{document}${\tt G}$\end{document}G-invariant. An example is given where the interaction potential is singular and there exists a Gibbs state which is not \documentclass[12pt]{minimal}\begin{document}${\tt G}$\end{document}G-invariant. In the next paper, under the same title we establish a similar result for a bosonic model where particles can jump from a vertex i ∈ Γ to one of its neighbors (a generalized Hubbard model).

Discrete double core skyrmions in magnetic thin films

We study the Belavin–Polyakov double core skyrmions in two-dimensional isotropic Heisenberg ferromagnets on a discrete square lattice by means of spin dynamic simulations using periodic boundaries conditions. It is also investigated the presence of external in-plane magnetic fields and lattice defects. We have shown that these discrete skyrmions not cylindrically symmetric have a high degree of stability, similar to their continuum counterparts, even if small spatial inhomogeneities are present into the system.

The method of exact diagonalization preserving the total spin and taking the point symmetry of the two-dimensional isotropic Heisenberg magnet into account

We propose a double-pass method of exact diagonalization of a finite cluster on the base of functions that have a definite total spin and transform by a definite irreducible representation of the point symmetry group of the lattice. We also propose the method for approximating the energy spectrum in the thermodynamic limit using the spectrum of the surrounding states, which increases the calculation accuracy leaving the cluster size invariant. The algorithm details are extensively illustrated with an example of clusters of spin 1/2 on a simple square lattice.

Spin Stiffness of 2D Isotropic Heisenberg Antiferromagnet

The spin stiffness of spin- two-dimensional isotropic Heisenberg antiferromagnet is calculated by a perturbation method based on the extended Schwinger–Boson mean-field theory. We arrive at a value of the spin stiffness, , which is in quite well agreement with experiments and the numerical results.

Vortex dynamics in two-dimensional antiferromagnets

Vortices or merons are the relevant topological solitons in a two-dimensional isotropic Heisenberg antiferromagnet immersed in a uniform magnetic field. The dynamics of such solitons is studied numerically within the discrete spin model as well as analytically within a continuum approximation based on a suitable extension of the nonlinear model. Vortex dynamics is affected rather profoundly by the applied field and acquires the characteristic features of the Hall effect of electrodynamics or the Magnus effect of fluid dynamics. In particular, a single vortex is always spontaneously pinned, two like vortices form a rotating bound state, and a vortex-antivortex pair undergoes Kelvin motion.

Thermodynamics of the two-dimensional Heisenberg ferromagnet in the framework of the renormalization-group approach

A method of describing the thermodynamic functions of two-dimensional isotropic Heisenberg ferromagnets based on a generalization of the 2 +e expansion is proposed. Interpolation formulas constructed in the framework of this approach make possible a smooth passage to the results obtained by the methods of high-temperature expansions.

Ground state of the two-dimensional isotropic antiferromagnetic Heisenberg model of S= 1/2 on a square lattice

An application of the method developed in our previous papers to a two-dimensional isotropic Heisenberg antiferromagnet of S= 1/2 on a square lattice is presented. A self-consistent independent spin-wave representation (SCISWR) is proposed in which we have performed the renormalization from both the dynamic and kinematics interaction and calculated the corrections from the correlation of the nearest-neighbour and next-nearest-neighbour sites. An anisotropy spin-wave excitation energy in unrestricted space is found self-consistently and has a gap. The difficulty of divergence of higher-order terms in usual spin-wave theory seems to have been overcome. Our calculation shows gives a ground-state energy E approximately=-0.659NJ.

Dynamic correlations in a classical two-dimensional Heisenberg antiferromagnet.

A Monte Carlo molecular-dynamics calculation of the dynamic structure function S(q,\ensuremath{\omega}) for the classical two-dimensional isotropic Heisenberg antiferromagnet is presented. For wave vectors near the antiferromagnetic Bragg point, S(q,\ensuremath{\omega}) is well described by a product of Lorentzians representing damped spin waves. For adequately low temperatures, the dependence of the spin-wave frequency and damping on wave vector and temperature are consistent with a dynamic scaling description of Chakravarty, Halperin, and Nelson. Even for higher temperatures a scaling description is quite well satisfied, but with a modified scaling frequency.

Long range order in the ground state of two-dimensional antiferromagnets

We show the existence of long range order in the ground state of the two-dimensional isotropic Heisenberg antiferromagnet for S⩾ 3 2 . The method yields also long range order in the ground state for the larger class of anisotropic quantum antiferromagnetic spin systems with or without transverse magnetic fields.

Phase diagrams and critical behavior of a two-dimensional anisotropic Heisenberg antiferromagnet

A classical $d=2$ anisotropic Heisenberg antiferromagnet is studied in the presence of a uniform magnetic field ($H$) along the easy axis. Ground-state properties are determined exactly, and expected low-temperature behavior is calculated for the antiferromagnetic state using first-order spin-wave theory and for the spin-flop state using a modification of the harmonic approximation used by Berezinski for the classical $\mathrm{XY}$ model. Extensive data are obtained from Monte Carlo simulations on $L\ifmmode\times\else\texttimes\fi{}L$ square lattices with periodic boundary conditions and nearest-neighbor coupling $\frac{{J}_{\ensuremath{\perp}}}{{J}_{\ensuremath{\parallel}}}=0.8$. The phase diagram agrees with the predictions of renormalization-group theory: The antiferromagnetic state is Ising-like, and the spin-flop phase shows behavior similar to the two-dimensional $\mathrm{XY}$ model and the two-dimensional isotropic Heisenberg model in a field. However, the existence of biconical or bicritical points at finite temperature could not be confirmed. Spin-wave therory and the modified harmonic-approximation theory for the spin-flop state are valid only at extremely low temperatures.

Magnetic excitations in diluted ferromagnets. II. Localisation and wavefunctions

For pt.I see ibid., vol.10, p.5035 (1977). The excitations in a diluted two-dimensional isotropic Heisenberg ferromagnet are investigated in detail. Spectra obtained by the recursion method and the moment-expansion method are presented and compared with each other. This makes clear the effect of the spatial extent of clusters. The wavefunctions are visualised and discussed in relation with the cluster extent in the system.

A Green's Function Treatment of a Ferromagnetic Layered System

A ferromagnetic layered spin-S system with an anisotropic exchange interaction is studied by the RPA Green's function method and the validity of the approximation is ascertained for a nearly two-dimensional Heisenberg system. The Curie temperature T, is given in terms of the ratio a of the interlayer exchange interaction to the intralayer one and of the exchange anisotropy 71, and is shown to be raised abruptly by a slight additional XY-like exchange anisotropy for the nearly two-dimensional isotropic Heisenberg model. The zero-point spin contraction increases as the system becomes XY-like and two-dimensional. For the nearly two-dimensional Heisenberg system the magnetization behaves like lv1,oc1-cT'12 in the vast intermediate temperature region, which amounts to (0.19~0.72) T, in the case of K 2CuF4 with a=0.00066 and the XY-like anisotropy of one percent, and the present theory IS m satisfactory agreement with the experimental results. § l. Introduction Magnetic layered systems with an anisotropic interaction present great interest­ mg problems not only experimentally but also theoretically, because the changes in the dimensionalities of the lattice and of the spin are connected closely with the

Degeneration of ferromagnetic phase in films

The anisotropic Heisenberg model of ferromagnetic films is investigated using the Green function method. A new type of approximation is applied for renormalizing the spin-wave energy. The renormalizing factor accounts for the magnetization and also for the transverse fluctuation of the magnetization, which makes it possible to describe the model correctly at all values of the anisotropy parameter, Delta , and the number of magnetic layers, n. In the special case of Delta =0 and n=1 (two-dimensional isotropic Heisenberg model), the approximation leads to the formulae obtained by Mubayi and Lange (1969) for describing the Stanley-Kaplan phase. It is concluded that the degeneration of the ferromagnetic phase (towards the Stanley-Kaplan phase) becomes observable when n<30 and Delta <0.001, simultaneously.