Uniaxial Single-ion Anisotropy Research Articles

Spin-wave analysis of the spin-1 Heisenberg antiferromagnet with uniaxial single-ion anisotropy in a field

Spin-wave approaches are explored for the spin-1 Heisenberg antiferromagnet with uniaxial single-ion anisotropy in a field. In the spin-flop region a standard $1/S$ expansion with canted quantization axes gives good results for small anisotropies or near the saturated ferromagnetic boundary. It is shown analytically that the formulation respects the Goldstone theorem through second order in $1/S$. For the square lattice case, we find that in the quantum paramagnetic phase a two-boson formulation gives good results at large anisotropies. Near the boundary of the quantum paramagnetic phase, neither approach gives good results and a more generalized approach is needed.

Mixed spin-1/2 and spin-1 Ising model with uniaxial and biaxial single-ion anisotropy on the Bethe lattice

Abstract The mixed spin-1/2 and spin-1 Ising model on the Bethe lattice with both uniaxial as well as biaxial single-ion anisotropy terms is solved exactly by combining star-triangle and triangle-star mapping transformations with exact recursion relations. Magnetic properties (magnetization, phase diagrams, and compensation phenomenon) are investigated in detail. Particular attention is focused on the effect of uniaxial and biaxial single-ion anisotropies that basically influence the magnetic behavior of the spin-1 atoms.

Spin canting in a Dy-based single-chain magnet with dominant next-nearest-neighbor antiferromagnetic interactions

We investigate theoretically and experimentally the static magnetic properties of single crystals of the molecular-based single-chain magnet of formula ${[\text{Dy}{(\text{hfac})}_{3}\text{NIT}({\text{C}}_{6}{\text{H}}_{4}\text{OPh})]}_{\ensuremath{\infty}}$ comprising alternating ${\text{Dy}}^{3+}$ and organic radicals. The magnetic molar susceptibility ${\ensuremath{\chi}}_{M}$ displays a strong angular variation for sample rotations around two directions perpendicular to the chain axis. A peculiar inversion between maxima and minima in the angular dependence of ${\ensuremath{\chi}}_{M}$ occurs on increasing temperature. Using information regarding the monomeric building block as well as an ab initio estimation of the magnetic anisotropy of the ${\text{Dy}}^{3+}$ ion, this ``anisotropy-inversion'' phenomenon can be assigned to weak one-dimensional ferromagnetism along the chain axis. This indicates that antiferromagnetic next-nearest-neighbor interactions between ${\text{Dy}}^{3+}$ ions dominate, despite the large Dy-Dy separation, over the nearest-neighbor interactions between the radicals and the ${\text{Dy}}^{3+}$ ions. Measurements of the field dependence of the magnetization, both along and perpendicularly to the chain, and of the angular dependence of ${\ensuremath{\chi}}_{M}$ in a strong magnetic field confirm such an interpretation. Transfer-matrix simulations of the experimental measurements are performed using a classical one-dimensional spin model with antiferromagnetic Heisenberg exchange interaction and noncollinear uniaxial single-ion anisotropies favoring a canted antiferromagnetic spin arrangement, with a net magnetic moment along the chain axis. The fine agreement obtained with experimental data provides estimates of the Hamiltonian parameters, essential for further study of the dynamics of rare-earth-based molecular chains.

Ground-state phase diagram of an (S, S') = (1, 2) spin-alternating chain with competing single-ion anisotropies

Employing various numerical methods, we determine the ground-state phase diagram of an (S, S') = (1, 2) spin-alternating chain with antiferromagnetic nearest-neighboring exchange interactions and uniaxial single-ion anisotropies. The resulting phase diagram consists of eight kinds of phases including two phases which accompany the spontaneous breaking of the translational symmetry and a ferrimagnetic phase in which the ground-state magnetization varies continuously with the uniaxial single-ion anisotropy constants for the S=1 and S =2 spins. The appearance of these three phases is attributed to the competition between the uniaxial single-ion anisotropies of both spins.

Finite-size scaling of string order parameters characterizing the Haldane phase

We have developed a numerical procedure to clarify the critical behavior near a quantum phase transition by analyzing a multipoint correlation function characterizing the ground state. This work presents a successful application of this procedure to the string order parameter of the $S=1$ $XXZ$ chain with uniaxial single-ion anisotropy. The finite-size string correlation function is estimated by the density-matrix renormalization-group method. We focus on the gradient of the inverse-system-size dependence of the correlation function on a logarithmic plot. This quantity shows that the finite-size scaling sensitively changes at the critical point. The behavior of the gradient with increasing system size is divergent, is stable at a finite value, or rapidly decreases to zero when the system is in the disordered phase, at the critical point, or in the ordered phase, respectively. The analysis of the finite-size string correlation functions allows precise determination of the boundary of the Haldane phase and estimation of the critical exponent of the correlation length. Our estimates of the transition point and the critical exponents, which are determined only by the ground-state quantities, are consistent with results obtained from the analysis of the energy-level structure. Our analysis requires only the correlation functions of several finite sizes under the same condition as a candidate for the long-range order. The quantity is treated in the same manner irrespective of the kind of elements which destroy the order concerned. This work will assist in the development of a method for directly observing quantum phase transitions.

Breakdown of an intermediate plateau in the magnetization process of anisotropic spin-1 Heisenberg dimer: Theory vs. experiment

The magnetization process of the spin-1 Heisenberg dimer model with the uniaxial or biaxial single-ion anisotropy is particularly investigated in connection with recent experimental high-field measurements performed on the single-crystal sample of the homodinuclear nickel(II) compound [ Ni 2 ( Medpt ) 2 ( μ - ox ) ( H 2 O ) 2 ] ( ClO 4 ) 2 · 2 H 2 O (Medpt=methyl-bis(3-aminopropyl)amine). The results obtained from the exact numerical diagonalization indicate a striking magnetization process with a marked spatial dependence on the applied magnetic field for arbitrary but finite single-ion anisotropy. It is demonstrated that the field range, which corresponds to an intermediate magnetization plateau emerging at a half of the saturation magnetization, basically depends on a single-ion anisotropy strength as well as a spatial orientation of the applied field. The breakdown of the intermediate magnetization plateau is discussed at length in relation to the single-ion anisotropy strength.

Phase transition and magnetic properties of a bond-diluted mixed spin-1 and spin- Ising model with the uniaxial and biaxial single-ion anisotropy

The effective-field theory with a probability distribution technique that accounts for the self-spin correlation functions is used to study the phase diagrams and magnetic properties of a bond-diluted mixed spin- and spin-1 Ising model with the uniaxial and biaxial single-ion anisotropy on a simple cubic structure. It is found that the phase diagrams of the system can exhibit re-entrant phenomena for certain values of the concentration p and uniaxial and biaxial single-ion anisotropy, D0/J, Dx/J and Dy/J. We have also studied the effect of these parameters on the existence of the tricritical behavior.

Parallel Susceptibility of Thin Ferromagnetic Films within Many-Body Green's Function Theory

Parallel susceptibility of the quantum Blume{Capel model for ferromagnetic fllms is calculated within the Green function theory. The Hamiltonian includes a Heisenberg term with the difierent surface exchange coupling with respect to bulk, an external magnetic fleld, a second-order uniaxial single-ion anisotropy, and the exchange anisotropy. The importance of collective excitations is demonstrated by comparing with result calculated within mean fleld approximation.

One-Third Magnetization Plateau in an Anisotropic (S,S')=(1,2) Spin-Alternating Chain

Employing numerical methods, we study the ground-state magnetization curve of a ( S , S ')=(1,2) spin-alternating chain with uniaxial single-ion anisotropies, where S =1 and S '=2 spins are alternating and coupled antiferromagnetically. Special attention is paid to the magnetization plateau, the one-third plateau, which appears at one third of the saturation magnetization in the ground-state magnetization curve. We find that three kinds of one-third plateaux appear, one of which has a quantum nature, while the remaining two have a classical (Ising) nature. We determine the one-third plateau phase diagram on the D 2 versus D 1 plane, where D 1 ( D 2 ) is the ratio of the single-ion anisotropy constant for the S =1 ( S '=2) spin to the exchange interaction constant. This phase diagram consists of a phase boundary line between the quantum and classical one-third plateau states as well as three phase boundary lines between the one-third plateau and plateauless states. We emphasize that there is no phase trans...

Spin Supersolid in an Anisotropic Spin-One Heisenberg Chain

We consider an S=1 Heisenberg chain with strong exchange (Delta=J(z)/J(perpendicular)) and single-ion uniaxial anisotropy (D) in a magnetic field (B) along the symmetry axis. The low-energy spectrum is described by an effective S=1/2 XXZ model that acts on two different low-energy sectors for a finite range of fields. The vacuum of each sector exhibits Ising-like antiferromagnetic ordering coexisting with the finite spin stiffness obtained from the exact solution of the XXZ model. In this way, we demonstrate the existence of a spin supersolid phase. We also compute the full Delta-B quantum phase diagram using a quantum Monte Carlo method.

Phase diagram of uniaxial antiferromagnetic particles: Field perpendicular to the easy axis

We consider a spherical uniaxial antiferromagnetic particle in the presence of an external magnetic field perpendicular to its easy axis. The model is described by a classical Heisenberg Hamiltonian including a single-ion uniaxial anisotropy, where the magnetic moments of the particle are represented by continuous spin vectors. We employ mean-field calculations and Monte Carlo simulations to determine the phase diagram of the system. The phase diagram in the plane field versus temperature is obtained for particles with radii ranging from three up to twelve spacing lattice units. We have seen that a particle with more than nine shells behaves as a true thermodynamic system. We find the explicit dependence of the zero temperature critical field and the Néel temperature on the diameter of the particle. At low temperatures, we have also shown that, for particles with three or more shells, the critical field follows a T 2 law, which is in agreement with the predictions of the spin-wave theory, when the field is perpendicular to the easy axis.

Exact solution of the mixed-spin Ising model on a decorated square lattice with two different kinds of decorating spins on horizontal and vertical bonds

The mixed spin-(1/2, S_B, S_C) Ising model on a decorated square lattice with two different kinds of decorating spins S_B and S_C placed on its horizontal and vertical bonds, respectively, is exactly solved by establishing a precise mapping relationship with the corresponding spin-1/2 Ising model on an anisotropic square (rectangular) lattice. The effect of uniaxial single-ion anisotropy acting on both types of decorating spins S_B and S_C is examined in particular. If decorating spins S_B and S_C are integer and half-odd-integer, respectively, or if the reverse is the case, the model under investigation displays a very peculiar critical behavior beared on the spontaneously ordered 'quasi-1D' spin system, which appears as a result of the single-ion anisotropy strengthening. We have found convincing evidence that this remarkable spontaneous ordering virtually arises even though all integer-valued decorating spins tend towards their 'non-magnetic' spin state S=0 and the system becomes disordered only upon further increase of the single-ion anisotropy. The single-ion anisotropy parameter is also at an origin of various temperature dependences of the total magnetization when imposing the pure ferrimagnetic or the mixed ferro-ferrimagnetic character of the spin arrangement.

Heisenberg-type ferromagnetic films with a sandwich structure

Abstract Green’s function theory is applied to an alternating two-element multilayer ferromagnetic film. The Hamiltonian is based on the Heisenberg model with a second-order uniaxial single-ion anisotropy and with the interaction between the layer in the interfaces. Magnetization and the phase transition in such system are derived for several sets of material parameters.

1/3 magnetization plateau in a one-dimensional anisotropic ferrimagnet

Using mainly numerical methods, we investigate the ground-state magnetization curve of a mixed spin chain with uniaxial single-ion anisotropies, where S = 1 and S = 2 spins are alternating and coupled antiferromagnetically. Special attention is paid to the magnetization plateau, the 1/3-plateau, which appears at one third of the saturation magnetization in the magnetization curve. It is found that there appear three kinds of 1/3-plateaux, one of which has a quantum nature, while the remaining two have a classical (Ising) nature.

Thermodynamic properties of small magnetic particles

We investigate the equilibrium magnetic properties of a simple cubic small ferromagnetic particle under an external magnetic field. Although the particle is small, it can not be considered as a single-domain unit. The magnetic moments are represented by unitary spin vectors and we consider ferromagnetic interactions between nearest-neighbor spins. The coupling between spins is given in terms of the classical Heisenberg Hamiltonian and we also include a Zeeman contribution and a single-ion uniaxial anisotropy. The size of the particle changes from one to twelve lattice spacings. We employ in our study mean-filed calculations and Monte Carlo simulations. The magnetization and susceptibility curves as a function of temperature show that an uniaxial anisotropy can mimic a ferromagnetic or an antiferromagnetic coupling, depending on the angle between the external magnetic field and the easy axis.

Quantum dynamics of the Néel vector in the antiferromagnetic molecular wheelCsFe8

The inelastic neutron scattering (INS) spectrum is studied for the antiferromagnetic molecular wheel $\mathrm{Cs}{\mathrm{Fe}}_{8}$, in the temperature range $2--60\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, and for transfer energies up to $3.6\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. A qualitative analysis shows that the observed peaks correspond to the transitions between the $L$-band states, from the ground state up to the $S=5$ multiplet. For a quantitative analysis, the wheel is described by a microscopic spin Hamiltonian (SH), which includes the nearest-neighbor Heisenberg exchange interactions and uniaxial easy-axis single-ion anisotropy, characterized by the constants $J$ and $D$, respectively. For a best-fit determination of $J$ and $D$, the $L$ band is modeled by an effective SH, and the effective SH concept extended such as to facilitate an accurate calculation of INS scattering intensities, overcoming difficulties with the dimension of the Hilbert space. The low-energy magnetism in $\mathrm{Cs}{\mathrm{Fe}}_{8}$ is excellently described by the generic SH used. The two lowest states are characterized by a tunneling of the N\'eel vector, as found previously, while the higher-lying states are well described as rotational modes of the N\'eel vector.

Non-universal critical behaviour of a mixed-spin Ising model on the extended Kagomé lattice

The mixed spin-1/2 and spin-3/2 Ising model on the extended Kagome lattice is solved by establishing a mapping correspondence with the eight-vertex model. When the parameter of uniaxial single-ion anisotropy tends to infinity, the model system becomes exactly solvable as the staggered eight-vertex model satisfying the free-fermion condition. The critical points within this manifold can be characterized by critical exponents from the standard Ising universality class. The critical points within another subspace of interaction parameters, which corresponds to a coexistence surface between two ordered phases, can be approximated by corresponding results of the uniform eight-vertex model satisfying the zero-field condition. This coexistence surface is bounded by a line of bicritical points that have non-universal continuously varying critical indices.

Magnetic behavior of a spin-1 dimer: model system for homodinuclear nickel(II) complexes

Magnetic behavior of a spin-1 Heisenberg dimer is analysed in dependence on the both uniaxial single-ion anisotropy and XXZ exchange anisotropy in a zero- as well as non-zero longitudinal magnetic field. A complete set of eigenfunctions and eigenvalues of the total Hamiltonian is presented together with an exact analytical expression for the Gibbs free energy, longitudinal magnetization, longitudinal and transverse susceptibility. The obtained theoretical results are compared with the relevant experimental data of [Ni 2(Medpt) 2( μ-ox)(H 2O) 2](ClO 4) 2·2H 2O (Medpt=methyl-bis(3-aminopropyl)amine).

Exact results of a mixed spin-1/2 and spin- S Ising model on a bathroom tile (4–8) lattice: Effect of uniaxial single-ion anisotropy

Effect of uniaxial single-ion anisotropy upon magnetic properties of a mixed spin-1/2 and spin- S ( S ⩾ 1 ) Ising model on a bathroom tile (4–8) lattice is examined within the framework of an exact star-triangle mapping transformation. Particular attention is focused on the phase diagrams established for several values of the quantum spin number S. It is shown that the mixed-spin bathroom tile lattice exhibits very similar phase boundaries as the mixed-spin honeycomb lattice whose critical points are merely slightly enhanced with respect to the former ones. The influence of uniaxial single-ion anisotropy upon the total magnetization vs. temperature dependence is particularly investigated as well.

One-dimensionalS=1 Spin–Orbital Model with Uniaxial Single-Ion Anisotropy

We investigate ground-state properties of a one-dimensional S=1 spin-orbital model with or without uniaxial single-ion anisotropy. By means of the density matrix renormalization group method, we compute the ground-state energy, the magnetization curves and the correlation functions. We discuss how the ground-state properties depend on the two exchange couplings for orbital and spin sectors. The phase diagram obtained is compared with that for the S=1/2 model. We also address the effect of uniaxial single-ion anisotropy.