Large single-ion anisotropy and ferromagnetic intrachain interaction in four Ni-compounds of formula NiX2L2 with X = Cl,Br; L = N2C3H4, NC5H5

The specific heat has been measured of powdered samples of NiX₂L₂ (X = Cl, Br; L = pyrazole, pyridine), compounds which can be considered as weakly antiferromagnetically coupled ferromagnetic chains with large uniaxial single-ion anisotropy. The intrachain exchange constants and the zero-field splitting parameters for the four compounds have been deduced from the specific heat data, using accurate numerical calculations for the isotropic Heisenberg spin S = 1 linear chain model with uniaxial single-ion anisotropy.     

α-Fe2O3单离子磁晶各向异性的计算及Morin转变的解释

本文根据晶场理论计算了α-Fe₂O₃的单离子磁晶各向异性。采用点电荷模型,计及近邻及次近邻对晶场的贡献,并考虑到近邻O^2-离子对次近邻Fe³⁺离子的电屏蔽效应,在六级微扰近似下,得到单离子各向异性场H_si=102.3×10²Oe。这一结果结合Artman等人对磁偶极各向异性的计算,导出了α-Fe₂O₃的Morin转变温度T _关键词：     

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 [Ni₂(Medpt)₂(μ-ox)(H₂O)₂](ClO₄)₂·2H₂O (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.     

Amorphous rare-earth alloys: random-anisotropy antiferromagnetism

The model of randomly oriented single-ion uniaxial anisotropy field is extended to the case of antiferromagnetic exchange interaction between rare-earth ions. A self-consistent two-spin cluster approximation is used to calculate the magnetization curves for a model system of spin 1. The results are in good qualitative agreement with experimental data on amorphous RE_xCu_1?x and RE_xAg_1?x alloys (RE = Tb, Dy, Ho). In particular, the observed increase of the “coercive” field with increasing x in RE_xCu_1?x alloys is accounted for.     

Evaluation of the local anisotropy to exchange ratio D/J in amorphous DyxGd1−xNi

Values for the random anisotropy (D) and exchange (J) constants in amorphous Dy_xGd_1?xNi have been obtained from an analysis of the measured magnetization curves in terms of the H.P.Z. model. Within the molecular field approximation this model is suitable in high magnetic fields. In low fields, other properties, characteristic of random anisotropy systems, arise which are not taken into account in this model.     

磁共振法研究(Fe1-xCox)84Zr3.5Nb 3.5B8Cu1纳米晶薄带的磁各向异性

铁磁共振（FMR）实验研究(Fe_1-xCo_x)₈₄Zr_{3.5 Nb3.5B8Cu1（x=0.0,0.2,0.4,0.6, 0.8）合金薄 带的各向异性，易轴在薄带的横向方向,同等宽度样品 的各向异性常数K′随Co掺杂量的增加而减小, K′值在4.67×10^-5　J/m（x=0. 0）到 2.54×10^-5　J 关键词： 铁磁共振 各向异性常数 低场非共振信号 磁化过程}     

Effect of single ion anisotropy on the critical temperature of classical quasi-one-dimensional magnets

The effect of single ion anisotropy energy on the three-dimensional ordering temperature of a classical quasi-one-dimensional magnetic chain is estimated using a mean field approximation for the interchain coupling and a classical spin field model for a chain. Numerical results are presented for T_c as a function of the interchain and interchain exchange interactions and the single ion anisotropy.     

Magnetostriction of the NdCo5 uniaxial permanent magnet

Magnetostriction measurements, between ≈5 and 300 K, of powder magnetically aligned samples of the hexagonal compound NdCo₅, in strong pulsed magnetic fields up to 15 T are reported. The measurement have been performed parallel, perpendicular and at 45° to the alignment c-axis, for the field also applied in those directions. This set of measurements allows us to determine the six irreducible magnetoelastic modes: λ^α₁₁, λ^α₂₁, related to the strain dependence of the isotropic exchange, and λ^α₁₂, λ^α₂₂, λ^γ, λ^ϵ, related to the strain dependence of the crystalline field anisotropy energy. Anomalies on the strains, associated with the spin reorientation (SR) regime are observed, in particular at the temperatures of beginning, T_SR1, and end, T_SR2, of the SR. The thermal variation of the strains is explained by the standard magnetostriction model, including an ingredients: exchange striction (varying as m²_Nd), single-ion anisotropy (varying as m³_Nd), (where m_Nd is the reduc ed Nd sublattice magnetization), as well as an angular dependence of the form {sin²θ(H, T)−sin²θ(0, T)}, where θ(H, T) and θ(0, T), respectively, are the SR angles under field and spontaneous. The irreducible magnetoelastic coupling constants at 0 K have been estimated, although the point charge model is far from agreement with those results.     

Effect of single-ion uniaxial anisotropy on the phase diagrams of magnetic system in the presence of internal spin fluctuation

Basing on the two-spin-per-site Heisenberg model, the effect of single-ion uniaxial anisotropy on the phase diagrams of magnetic system in the presence of internal spin fluctuation has been investigated by use of the mean field theory. It was found that single-ion uniaxial anisotropy has important effect on the phase digrams. In the ferromagnetic case (J₃>0) the positive single-ion uniaxial anisotropies (D) suppress the internal spin fluctuation and raise the phase trasition temperature, and negative single-ion uniaxial anisotropies (D) increase the internal spin fluctuation and reduce the phase trasition temperature. In the antiferromagnetic case (J₃<0), there exist two critical values J_c1 and J_c2 (|J_c2|<|J_c1|) in the positive D values. In the |J₃|<|J_c2| range intra-spin exchange coupling prevails inter-spin exchange coupling, the positive D values suppress the internal spin fluctuation and raise the phase transition temperature. In the |J₃|>|J_c1| range the two sub-spins behave as a rigid spin and the positive D values make the reduction of the phase transition temperature. We also observe that the larger D values make the range of internal spin fluctuation to move towards the larger |J₃| range.     

Magnetic anisotropy of antiferromagnet (CH3)4NMnCl3

The parameters of the electron paramagnetic resonance (EPR) spectra of S ion pairs in diamagnetic crystals are analyzed. A relation between the spin Hamiltonian constants is established for solitary ions and pairs for (CH₃)₄NCdCl₃: Mn²⁺ crystals. In contrast to solitary ions, an additional contribution (which is a linear function of the exchange field) to the “single-ion” spin Hamiltonian constants appears in the case of pairs. It is shown that anisotropic exchange mechanisms do not play a significant part in the formation of the axial constant of the spin Hamiltonian for this crystal. Some aspects of the method of studying “single-ion” anisotropy predicted by the two-ion model are developed with the help of an isostructural diamagnetic analog with impurity concentration of the paramagnetic ions of a magnetically concentrated substance sufficiently high for observing the EPR spectrum of the pairs. It is found that the microscopic quantities determined partially from the EPR spectra for pairs and solitary Mn²⁺ ions in (CH₃)₄NCdCl₃ are in accord with the experimental value of the effective field for the (CH₃)₄NMnCl₃ crystal anisotropy which can be described primarily by the dipole and “single-ion” mechanisms of the exchange origin.     

Rare earth single-ion anisotropy and the magnetic structures of the RTiO3 perovskites: R = Tb,Dy, Ho,Er and Tm

Attention is drawn to common features in the magnetic structures of the isostructural RMO₃ phases where R = Tb, Dy, Ho, Er and Tm and M = Al, Ti, Cr, Fe and Co. The orientation of the rare earth magnetic moment with respect to the orthorhombic c-axis depends only on R. For R = Er and Tm the moments are parallel to the c-axis while for R = Tb, Dy and Ho they lie in the a-b plane. The in-plane moments are canted with respect to the a and b axes with both ferromagnetic and antiferromagnetic components and the canting angles are constant for a given R independent of M. Using symmetry arguments we show that the above systematics can be understood in terms of the rare earth single-ion anisotropy. Detailed calculations incorporating a crystal field of C_s symmetry determined for Er³⁺ in YAlO₃ and an isotropic molecular field of magnitude appropriate to the RTiO₃ compounds produce results in agreement with the experimental observations. Essentially the same results are obtained for a crystal field of D_4h symmetry. The B²₀O²₀ term in the crystal field Hamiltonian is identified as the factor which determines the orientation of the rare earth moment.     

Temperature evolution of spin-transfer switching in nonlocal spin valves with dipolar coupling

The spin-transfer effect has been achieved in nanoscale metallic nonlocal spin valves. A magnetic domain (∼70×150 nm²) in an extended wire can be switched by a pure spin current between 4.5 and 200 K. The dipolar coupling between the magnetic spin injector (F₁) and spin detector (F₂), the surface anisotropy of the thin F₂ layer, and the thermal instability of F₂ generates complex switching characteristics. Analysis of the results allows for detailed understanding of magnetic configurations during the current-sweep and the field-sweep measurements. The critical current (I_c) for spin-transfer switching gradually decreases as the temperature increases. The I_c⁺ for the transition from parallel (P) state to antiparallel (AP) state decreases faster than the I_c^‐ for the transition from AP to P due to the dipolar coupling. Above 200 K, the dipolar coupling and the thermal instability prevents a stable P state in the absence of an external field.     

Magnetoelastic coupling and spin reorientation in RECo5 uniaxial magnets (RE = Pr,Dy, Ho and Y). II

Magnetostriction measurements, between ≈ 5 and 300 K, of powder aligned samples of the uniaxial compounds RECo₅ (RE = Pr, Ho, Dy and Y) for strong applied magnetic fields up to 15 T are reported. The strains have been measured, parallel, perpendicular and at 45° form the c-axis, with the field applied also along these directions. These sets of measurements allow us to determine the six irreducible magnetoelastic coupling constants: λ^α₁₁, λ^α₂₁, related to the strain dependence of isotrop ic exchange, and λ^α₁₂, λ^α₂₂, λ^γ and λ^ϵ, describing the strain dependence of the magnetocrystalline anisotropy ene rgy. Anomalies on the strains, associated with the spin reorientation (SR) regime are observed. The thermal variation of the strains is well explained by the standard magnetostriction model, including as ingredients exchange striction and the single-ion anisotropic one, as well as a dependence on the angle of reorientation under field. The point charge model of the crystalline magnetoelastic field is far from agreement with the present results.     

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 [Ni₂(Medpt)₂(μ-ox)(H₂O)₂](ClO₄)₂·2H₂O (Medpt=methyl-bis(3-aminopropyl)amine).     

Effects of the single-ion anisotropy and dimerization on 1D spin-1 antiferromagnetic Heisenberg chain

One-dimensional quantum spin-1 antiferromagnetic Heisenberg chain (AFHC) with exchange anisotropy J_z, dimerization δ and single-ion anisotropy D∑_n(S_n^z)² was investigated on the basis of the continuum representation of the model Hamiltonian. Analytical results for the excitation spectrum, phase order and the phase fluctuation φ were derived in a self-consistent-harmonic-field approach. We studied the effects of the single-ion anisotropy and dimerization on two gaps by taking the different momentum cutoff α_i in two scalar field spaces H_i (i=1,2). The occurrences of richer phase transitions were understood in the viewpoints of the phase fluctuation and the z polar spin fluctuation. And the Gaussian critical line was given as J_z−D−πα₁δ=0.     

Anisotropy and relaxation processes of uniaxially oriented CoFe2O4 nanoparticles dispersed in PDMS

When a uniaxial magnetic field is applied to a non-magnetic dispersive medium filled with magnetic nanoparticles, they auto-assemble into thin needles parallel to the field direction, due to the strong dipolar interaction among them. We have prepared in this way magnetically oriented nanocomposites of nanometer-size CoFe₂O₄ particles in a polydimethylsiloxane polymer matrix, with 10% w/w of magnetic particles. We present the characteristic magnetic relaxation curves measured after the application of a magnetic field forming an angle α with respect to the needle direction. We show that the magnetic viscosity (calculated from the logarithmic relaxation curves) as a function of α presents a minimum at α=0, indicating slower relaxation processes associated with this configuration of fields. The results seems to point out that the local magnetic anisotropy of the nanoparticles is oriented along the needles, resulting in the macroscopic magnetic anisotropy observed in our measurements.     

Magnetic-field-induced quantum criticality in a spin-<Emphasis Type="Italic">S</Emphasis> planar ferromagnet with single-ion anisotropy

The effects of single-ion anisotropy on quantum criticality in a d-dimensional spin-S planar ferromagnet is explored by means of the two-time Green’s function method. We work at the Tyablikov decoupling level for exchange interactions and the Anderson-Callen decoupling level for single-ion anisotropy. In our analysis a longitudinal external magnetic field is used as the non-thermal control parameter and the phase diagram and the quantum critical properties are established for suitable values of the single-ion anisotropy parameter D. We find that the single-ion anisotropy has sensible effects on the structure of the phase diagram close to the quantum critical point. However, for values of the uniaxial crystal-field parameter below a positive threshold, the conventional magnetic-field-induced quantum critical scenario remains unchanged.     

Effects of ion doping on magnetism of antiferromagnetic nanoparticles

Based on the Heisenberg model including single-ion anisotropy and using a Green's function technique we have studied the influence of doping effects on magnetization M, Neel temperature T_N and coercive field H_c of antiferromagnetic nanoparticles. We have shown that the experimentally obtained room temperature magnetization M is due to surface or/and doping effects in antiferromagnetic nanoparticles.     

Magnetic dipolar interaction in ultrathin films: Structural and size effects

A previously introduced formalism for calculating magnetic dipolar anisotropy energy ΔU in atomic layered structures is further developed. Numerical results are presented for ultrathin films with different close-packed (face centered cubic (FCC) [1 1 1]) and non-close-packed (FCC [0 0 1] and body centered cubic (BCC) [0 0 1]) structures. Structural effects become apparent in the magnetocrystalline dipolar anisotropy energy ΔU_L when the ratio between the interlayer separation c and the 2D lattice constant a is changed. Despite the long-range character of the dipolar interaction, it is shown that the number of significantly interacting layers, conventially called coupled layers, is limited and depends on the structural aspect ratio c/a. The slope in the observed linear dependence between ΔU_L and the inverse of the film thickness t is explained by the number of the so-called coupled layers, and not by a surface contribution to volume values. Size effects appearing in ΔU are unambiguously distinguished from structural effects. Effective anisotropy energy ΔU_eff and ΔU are presented for Co [0 0 0 1] and Ni [0 0 1] ultrathin films. It is verified that the dipolar interaction makes an important contribution to ΔU_eff, but the spin reorientation transition is determined by non-dipolar interactions. The former favors the magnetization switching only when the size aspect ratio d/t, with d the characteristic lateral dimension of the film, is sufficiently small. Applications to other layered arrays of magnetic dipoles are straightforward.     

A multisublattice magnetic phase induced by external field in a singlet magnet

The theory of magnetization in a longitudinal magnetic field is developed for an easy-plane multisublattice antiferromagnet with a singlet ground state and a strong single-ion anisotropy exceeding the magnitude of exchange interaction. The magnetic-field-induced phase transition from the singlet (magnetically dis-ordered) state to a multisublattice antiferromagnetic state represents a displacive magnetic phase transition. At T=0, this transition proceeds continuously and belongs to second-order phase transitions, while at T ≠0, the behavior changes to jumplike and the process becomes the first-order phase transition.