Two-dimensional Heisenberg Ferromagnet Research Articles

Vortices and magnetic structures of the target type in a two-dimensional ferromagnet with anisotropic exchange

Various types of magnetic structure in a two-dimensional Heisenberg ferromagnet are considered in a continuum approximation. The effect of anisotropic exchange and single-ion anisotropy on the vortex structure is analyzed. A new type of static magnetic structure (“target”) is predicted and investigated in an easy-plane ferromagnet.

Theoretical Methods in Low-Dimensional Magnetism and Their Application to 3He Films

Two theoretical methods are proposed to describe analytically the thermodynamics of a two-dimensional quantum Heisenberg ferromagnet on a triangular lattice at all temperatures. The first method is based on the generalization of 2+e-expansion and the second one—on the modified random-phase approximation. In the low-temperature limit both methods yield a correct temperature behavior of thermodynamic functions, which is consistent with Dyson's theory. The obtained results can be used for interpretation of the experimentally observed heat capacity of the second 3He layer solid in the ferromagnetic regime.

Pressure-induced change of the interlayer exchange interaction from ferromagnetic to antiferromagnetic in CS2CuF4 observed by neutron scattering experiments up to 2 GPa

Neutron scattering experiments on the two-dimensional Heisenberg ferromagnets Cs2 CuF4 and K2CuF4 have been performed around 2 ∼ 3 GPa over 1·4–15 K. At ambient pressure both the intralayer and the interlayer exchange interactions in these two compounds are ferromagnetic. At about 2 GPa, the interlayer exchange coupling in Cs2 CuF4 is found to change from ferromagnetic to antiferromagnetic, while the ferromagnetic intralayer exchange interaction is maintained. Contrary to Cs2CuF4, the ferromagnetism in K2Cuf4 is not destroyed by pressure up to 9 GPa, that was confirmed in the early study of the magnetic susceptibility measurements.

Calorimetric and Magnetic Studies on a Ferromagnetic Phase Transition of the Metal-Assembled Complex MnCu(obbz)·H2O

Abstract Heat capacities of the metal-assembled ferromagnet MnCu(obbz)·H2O (obbz = oxamidobis(benzoato)) have been measured in the temperature region between 0.1 and 301 K by adiabatic calorimetry. A broad phase transition due to the three-dimensional ferromagnetic ordering was observed around 17 K. Above the transition temperature, a heat capacity tail arising from the short-range order characteristic of a low-dimensional magnet was found. The enthalpy and entropy gained by the phase transition are 227 J mol-1 and 12.7 J K-1 mol-1, respectively. This entropy acquisition is very close to the value Rln 5 ( = 13.4 J K-1 mol-1) expected for the spin manifold of the spin quantum number S = 2 ground state, where R stands for the gas constant. The thermal anomaly above the transition temperature can be accounted for in terms of the S = 2 two-dimensional ferromagnetic Heisenberg model rather than the one- or three-dimensional models. This suggests that this complex can be regarded as a two-dimensional ferrimagnet, in which strong antiferromagnetic interaction exists between a pair of Mn(II) (S = 5/2) and Cu(II) (S = 1/2) but the magnetic coupling between the pairs is very weak. Magnetic measurements for the complex revealed a bend of the hysteresis loop above the transition temperature and a magnetic relaxation below the transition temperature. These results lead to the conclusion that the broadness of the phase transition may be attributed to superparamagnetism caused by the fact that the present complex is prepared only in a fine powder.

Low-Temperature Heat Capacities and Ferromagnetic Phase Transition of the Organic Free Radical Ferromagnet, 4-(4-Chlorobenzylideneamino)-2,2,6,6-tetramethylpiperidin-1-oxyl (CATMP)

Abstract Heat capacities of the organic free radical ferromagnet, 4-(4-chlorobenzylideneamino)-2,2,6,6-tetramethylpiperidin-1-oxyl (CATMP) have been measured in the temperature range between 0.1 and 311 K. A ferromagnetic phase transition was observed at 0.28 K and a heat capacity hump was found above the transition temperature. This hump is due to the short-range order characteristic of low-dimensional magnetic spin systems. The enthalpy and entropy gains due to the ferromagnetic phase transition were estimated to be 4.06 J mol-1 and 5.71 J K-1 mol-1, respectively. This entropy agrees well with the theoretical value Rln 2 ( = 5.76 J K-1 mol-1) expected for the magnetic entropy of a spin system with the spin quantum number S = 1/2, where R is the gas constant. The heat capacity hump above the transition temperature is well accounted for in terms of the S = 1/2 two-dimensional ferromagnetic Heisenberg model of square lattice with the intralayer exchange interaction J/kB = 0.42 K, where the spin Hamiltonian H = -2JSi·Sj is adopted and kB stands for the Boltzmann constant. The analysis of the magnetic heat capacities below the transition temperature on the basis of the spin wave theory clarified that the magnetic system settles down in three-dimensional ferromagnetic order below the transition temperature with the interlayer exchange interaction J′/kB = 0.024 K.

Localized modes in two-dimensional square anisotropic ferromagnets with a hole

By using the path-integral method with a $\mathrm{SU}(2)$ coherent-state basis, two-dimensional anisotropic Heisenberg ferromagnets bearing a fixed magnetic hole are investigated with particular attention paid to interplaying between the intrinsic nonlinearity and the extrinsic structural disorder due to hole doping. Detailed numerical calculations are made for s-like localized modes to determine their eigenfrequencies and profiles as a function of a nonlinearity parameter and various anisotropic exchange parameters. A localized magnetic vortex is found in the neighborhood of a hole. Analytical and numerical analyses on their time evolution show two kinds of localized modes separately; one is mobile under certain conditions and intrinsic due to the nonlinearity, and the other is immobile and extrinsic due to the fixed magnetic hole.

Hierarchical structure of domain walls in magnetic layers

I discuss thin magnetic layers in the context of a two-dimensional ferromagnetic Heisenberg spin system. In the low energy regime it is shown that the system follows a Belavin-Polyakov type of equation. It is argued that unlike in traditional systems where these equations occur only under uniform boundary conditions, the boundary conditions in this case are less restrictive, allowing for a new family of solutions. These solutions consist of magnetic domains of spins that are oriented at relative opposite directions. The boundaries between regions are sharp on the continuous scale but within a domain wall the magnetization changes orientation continuously from one ground state to another. All the magnetic energy in the system is shown to concentrate along the domain walls. It is therefore argued that most favorable for the walls is to rearrange in a hierarchical or fractal fashion because such an arrangement lowers the overall energy density. It is suggested that this hierarchical structure of magnetic domain boundaries should be observable by magnetic force microscopy. Recent results suggest that such configurations may also dominate the structure of domain walls in magnetostrictive materials and magnetic nanotubes.

Differential approximants: An accurate interpolation from high-temperature series expansions to low-temperature behavior in two-dimensional ferromagnets

We introduce biased differential approximants to high-temperature series expansions of the susceptibility in two-dimensional Heisenberg ferromagnets, taking into account the exponential divergence at low temperature. They provide a remarkable continuous description of the susceptibility from high temperature down to the low-temperature regime.

1/Nexpansion for two-dimensional quantum ferromagnets

The magnetization of a two-dimensional ferromagnetic Heisenberg model, which represents a quantum Hall system at filling factor $\ensuremath{\nu}=1,$ is calculated employing a large $N$ Schwinger boson approach. Corrections of order $1/N$ to the mean-field $(N=\ensuremath{\infty})$ results for both the $\mathrm{SU}(N)$ and the $\mathrm{O}(N)$ generalization of the bosonized model are presented. The calculations are discussed in detail and the results are compared with quantum Monte Carlo simulations as well as with recent experiments. The $\mathrm{SU}(N)$ model describes both Monte Carlo and experimental data well at low temperatures, whereas the $\mathrm{O}(N)$ model is much better at moderate and high temperatures.

Magnetic phase transitions ofCrCl3graphite intercalation compound

Magnetic phase transitions of stage-2 ${\mathrm{CrCl}}_{3}$ graphite intercalation compound have been studied using ac superconducting quantum interference device (SQUID) magnetic susceptibility and dc SQUID magnetization. This compound is a two-dimensional (2D) Heisenberg ferromagnet with small $\mathrm{XY}$ anisotropy and very weak antiferromagnetic interplanar exchange interaction: interplanar exchange interaction $J$ $(=5.86\ifmmode\pm\else\textpm\fi{}0.05\mathrm{K}),$ effective anisotropy field ${H}_{A}^{\mathrm{out}}(=193\mathrm{Oe}),$ and ${H}_{E}^{\ensuremath{'}}(=51\mathrm{Oe}).$ This compound undergoes magnetic transitions at ${T}_{c1}(=11.5\mathrm{K}),$ ${T}_{c2}(=10.3--10.5\mathrm{K}),$ ${T}_{c3}(=8.67--9.70\mathrm{K}),$ and ${T}_{g}(=5.7--7\mathrm{K}).$ Below ${T}_{c1}$ a 2D ferromagnetic long-range order with spin component along the $c$ axis appears, forming an axial ferromagnetic phase. Below ${T}_{c2}$ a 2D ferromagnetic long-range order of spin component perpendicular to the $c$ axis appears, forming an oblique phase. Below ${T}_{c3}$ there appears a 3D antiferromagnetic order accompanying spin-glass-like behavior. Below ${T}_{g}$ the system enters into a reentrant spin glass phase arising from the competition between a ferromagnetic ${\mathrm{Cr}}^{3+}{\ensuremath{-}\mathrm{C}\mathrm{r}}^{3+}$ interaction and possible antiferromagnetic ${\mathrm{Cr}}^{2+}{\ensuremath{-}\mathrm{C}\mathrm{r}}^{2+}$ interactions. The role of ${\mathrm{Cr}}^{2+}$ spins with Ising symmetry may be crucial for the axial ferromagnetic and oblique phases.

Theory of quantum nonlinear localized modes in quantum lattices

A theory of quantum nonlinear localized modes is developed for three kinds of spatially discrete quantum systems, Bose lattices, Heisenberg spin systems and Frenkel excitons, by employing the coherent state path integral formulation. Applying the stationary-phase approximation leads to nonlinear lattice equations in c-number forms, in which the intrinsic nonlinearity of the quantum systems is incorporated to all orders. The general theory is illustrated by solving the obtained nonlinear equations both analytically and numerically to show the existence of stationary self-localized magnons in one-dimensional Heisenberg antiferromagnets and moving nonlinear localized modes in two-dimensional Heisenberg ferromagnets containing a hole.

Pressure-induced magnetic phase transition in the two-dimensional Heisenberg ferromagnet K 2CuF 4

A pressure-induced magnetic phase transition in K 2CuF 4 was investigated up to 13 GPa. We observed a sudden decrease in the Curie temperature starting from 7 GPa and a large decrease in the susceptibility above 10 GPa. High-pressure powder X-ray diffraction studies were also made at room temperature up to 14 GPa to investigate such a drastic change in magnetism from structural point of view. A structural phase transition was observed at around 9.5 GPa, above which the CuF 6 octahedra were found to be in the ferrodistortive (FD) order with the elongated axes in the basal plane. As magnetic and structural changes occur at nearly the same pressure, the observed change in the magnetism suggests a ferromagnetic-to-antiferromagnetic phase transition resulting from the distortive change in the basal plane if the critical pressure is assumed not to change so much in the temperature range investigated.

Change of Magnetism in the Two-Dimensional Heisenberg FerromagnetK2CuF4Observed at High Pressures

The mechanism responsible for determining the exchange interaction to be ferromagnetic or antiferromagnetic in Cu 2+ compounds is closely correlated with the antiferrodistortive (AFD) or ferrodistortive (FD) order of Cu 2+ hole orbitals. One of the representative two-dimensional Heisenberg ferromagnets, K 2 CuF 4 , has an ideal AFD orbital ordering. To investigate the possibility of the magnetic phase transition due to a change in the orbital ordering from AFD to FD at high pressures, susceptibility measurements of this compound have been made under various pressures up to 13 GPa over the temperature range from 1.5 to 18 K. A sudden decrease in the Curie temperature starting from 7 GPa was observed. Furthermore, a large decrease in the susceptibility was observed at pressures above 10 GPa. These results indicate a pressure induced ferromagnetic to antiferromagnetic phase transition occurring at about 8–9 GPa as a result of a change of orbital state from AFD to FD order.

Pressure Effect on the Curie Temperature and Inter- Molecular Interactions in Organic Ferromagnet β -Phase p-Npnn

Abstract The magnetic properties of the β -phase p-NPNN have been investigated by the simultaneous observation of heat capacity and ac-susceptibility under hydrostatic pressures in magnetic fields. A drastic reduction of the Curie temperature from 0.61 K at an ambient pressure to 0.35 K at 7.2 kbar has been observed. The magnetic heat capacity under 7.2 kbar shows a characteristic shoulder of a two-dimensional Heisenberg ferromagnet with spin S-½, just above the heat capacity peak. By the application of weak external fields up to 1 kOe, the peak disappears and the shoulder grows its height and shifts to higher temperatures, as in the case of one-dimensional Heisenberg ferromagnets in external fields.

Temperature-dependent magnetization of fcc Fe/Cu(001) studied by spin-polarized appearance potential spectroscopy

The temperature-dependent magnetic properties of room-temperature-grown fcc iron films on Cu(001) were investigated by means of spin-polarized appearance potential spectroscopy. The Curie temperatures are strongly reduced in relation to the bulk value of ferromagnetic bcc iron and show an unusual dependence on coverage. In addition, the shape of the magnetization curves exhibits distinct differences in various regions of film thickness. While the thinnest ferromagnetic films (2 and 2.5 monolayers) represent almost ideal two-dimensional anisotropic Heisenberg ferromagnets, coverages between 6 and 8 monolayers exhibit linear and, without remagnetizing the sample, irreversible temperature dependences approaching the magnetic phase transition. The magnetic peculiarities of metastable fcc iron are attributed to the critical influence of structural properties.

Magnetic field dependence of the nuclear magnetization of3He films adsorbed on graphite in the ferromagnetic regime

The nuclear magnetic susceptibility of3He films adsorbed on graphite in the ferromagnetic regime has been measured for different values of the magnetic field. The results are discussed in the framework of the spin wave theory of finite size two-dimensional Heisenberg ferromagnets.

Self consistent harmonic approximation in theXY model

We discuss the use of the self consistent harmonic approximation applied to the two-dimensional classical anisotropic Heisenberg ferromagnet. The Kosterlitz-Thouless transition temperature for the isotropic antiferromagnet in a uniform magnetic field, applied perpendicular to the xy plane, is obtained.

Magnetism of the β-Phase p-Nitrophenyl Nitronyl Nitroxide Crystal

Abstract The ferromagnetism of β-phase p-nitrophenyl nitronyl nitroxide has been established by various measurements at an ambient pressure. To get further insight into the magnetic interactions, the pressure effect on the magnetic and thermal properties has been examined in the pressure range of 0–7.7 kbar. Important feature of the results is twofold. One is a reduction of the Curie temperature with applied pressure. This suggests that the exchange interactions are mainly responsible for determination of the Curie temperature. Dipolar couplings are estimated to be too small to explain the observed Curie temperature. The other is the lowering of the lattice dimensionality. The heat capacity curve under the pressure of 7.2 kbar coincides with the theory for a two-dimensional Heisenberg ferromagnet above the Curie temperature. This suggests that the interactions between the neighboring ac-plane are more affected by compression of the crystal.

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.

Normal modes of vortices in easy-plane ferromagnets.

We investigate the linear spin-wave spectrum of two-dimensional easy-plane classical Heisenberg ferromagnets in the presence of a vortex, using numerical diagonalization on small systems. The spectra of normal modes for both in-plane and out-of-plane vortices are determined, for square, triangular, and hexagonal lattices. Some of the modes show a strong localization of their amplitudes near the center of the vortex. Moreover, we investigate a particular mode that drives the crossover in the static vortex structure from purely in-plane to a vortex with well-localized out-of-plane component as the easy-plane character of the system is reduced below a certain threshold.