Single-ion Anisotropy Constant Research Articles

Existence conditions of surface spin waves in ferromagnetic nanowires and nanoparticles

A theoretical treatment of spin-wave excitations in ferromagnetic wires and particles in the presence of single-ion surface anisotropy is developed within the framework of the matrix theory. Two different models of surface anisotropy are considered, one of which assumes the anisotropy axes are perpendicular to the surfaces (current model) and the other one with a single selected axis for the whole system (Aharoni model). The results obtained indicate the possibility of the existence of surface exchange spin waves in ferromagnetic nanowires and nanoparticles in both models. However, under assumptions of the Aharoni model, this occurs only for the surface anisotropy of the proper sign (the single ion anisotropy constant at the surface of the wire or particle has to be negative, D<0), while under the assumptions of the current model, in the grains the surface states are always present, but—depending on the sign of D—they are localized at different faces. Therefore, both models are hardly distinguishable when applied to wires, but essentially nonequivalent when used to describe grains. It is suggested that resonance experiments on small magnetic grains should point out which of these models can be applied.

Temperature dependence of uniaxial magnetic anisotropy constants and spin-reorientation transition in the single-ion one-sublattice system

Based on an effective parameter method in the mean-field approximation, the temperature dependence of the single-ion anisotropy constants in the uniaxial one-sublattice system has been exhaustively studied within the three-constant approximation to the anisotropy free energy. Another important basis of our investigation is the connection between the experimentally measured anisotropy constants and the theoretically more fundamental anisotropy coefficients. A significant concept of anisotropy flow is introduced to detect all the possible types of spin-reorientation transitions driven by temperature evolution in the system. Seven types of temperature dependence of the first anisotropy constant and 14 types of spin-reorientation transitions are discovered in this one-sublattice system. Phase diagrams for these temperature behaviors and the spin-reorientation transitions are given by means of analytical and numerical calculations.

Influence of single-ion anisotropy fluctuations on temperature-driven reorientation transition in two-dimensional ferromagnets

The influence of single-ion anisotropy fluctuations on the temperature-driven reorientation transition in two-dimensional ferromagnets is studied. We show that in the presence of the spatial fluctuations of the single-ion anisotropy constants, the temperature-driven perpendicular to in-plane reorientation transition should be a continuous transition, and there are temperature regions in which both the perpendicular and in-plane magnetization are nonzero, in agreement with experimental observations.

Study of the special point in the surface phase diagram of a semi-infinite Ising ferromagnet

The phase diagrams of the semi-infinite Ising ferromagnet with decorated magnetic (spin- S) and nonmagnetic atoms on the surface are investigated within the framework of the effective-field theory. In particular, the critical properties of the special point in the surface phase diagram are examined numerically by changing the coupling constants, the single-ion anisotropy constant D on the spin- S ( S> 1 2 ) atom, the value of S and the concentration p of magnetic atoms. We find many characteristic features in the behaviour, such as the phenomenon depending on whether S is a half-integer or an integer.

Tuning the spin Hamiltonian ofNi(C2H8N2)2NO2ClO4by external pressure: A neutron-scattering study

We report an inelastic neutron scattering study of antiferromagnetic spin dynamics in the Haldane chain compound Ni(C2H8N2)2NO2ClO4 (NENP) under external hydrostatic pressure P = 2.5 GPa. At ambient pressure, the magnetic excitations in NENP are dominated by a long-lived triplet mode with a gap which is split by orthorhombic crystalline anisotropy into a lower doublet centered at $\Delta_\perp\approx$ 1.2meV and a singlet at $\Delta_\parallel\approx$ 2.5meV. With pressure we observe appreciable shifts in these levels, which move to $\Delta_\perp{(2.5GPa)}\approx$ 1.45 meV and $\Delta_\parallel(2.5GPa)\approx$ 2.2meV. The dispersion of these modes in the crystalline c-direction perpendicular to the chain was measured here for the first time, and can be accounted for by an interchain exchange J'_c approximately 3e-4*J which changes only slightly with pressure. Since the average gap value $\Delta_H\approx$ 1.64 meV remains almost unchanged with P, we conclude that in NENP the application of external pressure does not affect the intrachain coupling J appreciably, but does produce a significant decrease of the single-ion anisotropy constant from D/J = 0.16(2) at ambient pressure to D/J = 0.09(7) at P = 2.5 GPa.

Determination of the single-ion anisotropy in Cd 1− xCo xS using optical Faraday rotation technique at T = 80 mK

The single-ion anisotropy constant D of Co 2+ in Cd 1− x Co x S was determined from a magnetization step which was detected using optical Faraday rotation technique. Experiments were performed in a dilution refrigerator at a temperature of approximately 80mK. Analysis of the data gave D/ k B = 0.96 ± 0.02 K.

Spin waves in crystals with linear magnetoelectric interactions

Abstract Spin waves in crystals with linear magnetoelectric properties are analysed theoretically. Considerations are restricted to systems without spontaneous electric polarizations and to the case when the magnetoelectric properties can be described effectively by single-ion anisotropy constants and g-factor, which depend linearly on electric field. Coupled states of spin waves with photons as well as with collective electronic excitations are also analysed.

High Field Magnetization Process of anS=1 One-Dimensional Antiferromagnet NENP

High field magnetization measurements have been performed for NENP at low temperatures in steady fields up to 12 T and in pulsed fields up to 40 T. The magnetization for both directions parallel and perpendicular to the chain axis is extremely small in low fields and increases abruptly above the critical field B c // =9.8±0.2 T and B c ⊥ =13.1±0.3 T. This result indicates that the ground state of NENP is nonmagnetic, that is, singlet and becomes magnetic above the critical field due to the crossover between the singlet and magnetic excited states, consistent with Haldane's prediction. The magnetization data are analyzed on the basis of the Tsvelik theory. The two gaps and the single-ion anisotropy constant are estimated to be E 1 =14.2±0.3 K, E 2 =26.8±1.8 K and D ≈7 K. Using the values of E 1 and E 2 , the Haldane gap for D =0 is evaluated to be E G =(0.39±0.2)| J |. This value is in good agreement with the estimation of the Haldane gap from the Monte Carlo simulation. The Tsvelik theory satisfactorily explains the field dependence of the magnetization for NENP.

Impurity Susceptibility in the Ising-LikeAntiferromagnet CoCl22H2O

The impurity susceptibility of Mn 2+ in antiferromagnetic CoCl 2 2H 2 O single crystal has been investigated using the ac-susceptibility method. Experimental results indicate that Mn 2+ impurity spin couples weakly with host Co 2+ spins and behaves as a localized paramagnetic spin in accord with the ESR results with the single ion anisotropy constant D of -0.13 cm -1 and local effective field H E of 36.7 kOe.

Electron spin resonance in the diluted uniaxial antiferromagnet Mg 1- xFe xCl 2

We report electron spin resonance experiments at millimeter and submillimeter wavelengths performed on single crystal samples of the randomly diluted uniaxial antiferromagnet Mg 1- x Fe x Cl 2. Four resonance modes are observed in the x = 0.554 sample, three of which are assigned to the antiferromagnetic, in-phase ferromagnetic and out-of-phase ferromagnetic resonances, respectively. From the concentration dependence of the resonance frequency of the in-phase ferromagnetic mode, an accurate value for the single ion anisotropy constant is obtained (|D| = 6.3 cm −1).

EPR linewidth (T >~ Tg) in amorphous transition-metal-metalloid spin glasses: Theory.

A microscopic theory of the paramagnetic linewidth and line shift for an amorphous transition-metal--metalloid alloy spin glass has been given in the Mori-Kawasaki formalism. The linewidth has been calculated as being due to random single-ion anisotropy and the magnetic dipole-dipole anisotropic interaction, which are considered to be small perturbations. The contribution of the single-ion anisotropy has been found to be smaller. While it is noted that for T>${T}_{g}$ there is no static component of the random dipolar magnetic field the dynamic component of this field does exist. Taking the point of view of Souletie and Tholence [Phys. Rev. B 32, 516 (1985)] that the autocorrelation time of the dynamic component increases as the temperature is lowered to ${T}_{g}$ and attains the saturation value of 2\ensuremath{\pi}/w at T=${T}_{g}$(w), we predict that at this temperature the EPR response should be an inhomogeneously broadened Voigt line shape. The very limited data available have been compared with a rough numerical estimate of the linewidth at ${T}_{g}$(w) and reasons have been suggested for the lack of good agreement. At higher temperature the dynamic component will be partially averaged out by the EPR probe and the linewidth is expected to be less and the line shape more Lorentzian. It has been found that the critical part of the linewidth and line shift for all frequencies should obey dynamic scaling down to and including ${T}_{g}$(w). Also their temperature and frequency dependence shows trends similar to those for the canonical spin glasses. It is noted that more detailed data on the line shape close to ${T}_{g}$(w) and accurate determination of the single-ion anisotropy constant are needed for a check on the above predictions. A justification has been given for the applicability of the Mori-Kawasaki formalism at least for the higher frequencies. The regime of applicability of the theory is expected to be about T\ensuremath{\gtrsim}1.25${T}_{g}$.

On the theory of optical properties of anisotropic magnetic crystals in external magnetic field

The calculation of dielectric permeability tensor which are based on the theory of excitons in magnetoordered crystal are made. The dipole exciton energies of crystal are obtained and their dependence on external magnetic field H at arbitrary relation between exchange and single-ion anisotropy constants is established. Refractive index of tetragonal antiferromagnetic is determined and it is shown that it (index) is an odd function of H for a light polarized transverse to the fourth-order symmetry axis of crystal.

Thermal and magnetic studies of the nearly one-dimensional antiferromagnetic system CsNiBr 3

Magnetic susceptibility, specific heat and 133Cs magnetic resonance measurements in a single crystal of CsNiBr 3 are reported. The data reveal two magnetic transitions separating the paramagnetic phase from the antiferromagnetic ground state. At the higher transition temperature T N2 = (14.25 ± 0.05)K a net magnetic moment is observed only along the hexagonal c-axis, while only below the lower transition temperature T N1 = (11.75 ± 0.05)K a perpendicular component of the magnetic moment appears also. Above T N2 CsNiBr 3 can be described as a one-dimensional antiferromagnet with intrachain exchange interaction J k B = −(17.0 ± 0.2) K and single-ion anisotropy constant D k B ≊ −1.5 K . Below T N1 , the data are consistent with the non-colinear triangular structure of the Ni 2+ moments proposed previously for the isomorphic crystal CsNiCl 3. A reduced value of the zero-temperature susceptibility over the classical value is found and atrributed to the zero point deviations.

Observation of Tetragonal Optical Spectra of Divalent Nickel-Ion in Ba2NiF6

Optical absorption studies of the quadratic-layer antiferromagnets K 2 NiF 4 , Rb 2 NiF 4 and Ba 2 NiF 6 in the regions of electronic transitions have been performed from the magnetic anisotropic point of view. A Ni 2+ energy spectrum reflecting a tetragonal crystalline field was observed in Ba 2 NiF 6 , while cubic spectra were obtained in K 2 NiF 4 and Rb 2 NiF 4 . From the observed tetragonal splitting energy of 3 T 2 g ( 3 F ) band, the single ion anisotropy constant D of Ni 2+ in Ba 2 NiF 6 was determined as fairly large value of -15.4±1.8 cm -1 and -12.8±1.8 cm -1 at 300 K and 90 K, respectively.

Localized Magnons in a Heisenberg Ferromagnet with an Anisotropic Impurity Spin

Localized magnons around an impurity spin in a linear Heisenberg ferromagnet are investigated up to three-magnon states. The easy axis of the host spins is assumed to be in the z direction, while that of the impurity spin is in the x y plane. Two- and three-magnon localized states are obtained by the method similar to that of the one-magnon problem. It can be applicable over the whole intensity region of the single-ion anisotropy constant D ' of the impurity spin. In case of large D ', the ground state is a one-magnon localized state when the magnitude S ' of the impurity spin is 1; while, for S '=3/2, the ground state may be a one- or more-than-one-magnon localized state depending on relative magnitudes of the single-ion anisotropy of the host spins, host-host exchange interactions, and impurity-host exchange interactions.

Ground state properties of the Schrodinger model of ferromagnetism

A system is considered described by the hamiltonian H=- Sigma i,jJijPij- Sigma i,j,k,l(i not=k,l;j not=k,l) JijklPijPkl-...-g mu BH Sigma iSiz+D Sigma iSiz2 where Pij is the spin S Schrodinger exchange operator, H is an external magnetic field and D the single-ion anisotropy constant, and its ground state properties studied. In particular for S=1 at T=0 it is found that the magnetization m=0 for D>g mu B mod H mod while for D<g mu B mod H mod , m=H/ mod H mod , the ground states being non-degenerate.

AXIAL ANISOTROPY IN THE TERBIUM-HOLMIUM SYSTEM

The axial magnetic anisotropy has been studied in the Ho-Tb alloy system, by measuring the magnetic susceptibility of single crystals in fields up to 16 kOe and at temperatures between 80 K and 700 K. At high temperatures the inverse susceptibility varies linearly with temperature, but a significant curvature develops as the Neel temperature is approached. The single ion anisotropy constant D is positive for the whole system and varies slightly non-linearly with concentration. The temperature dependence of this variation has been studied. Furthermore the variation of the effective Bohr magneton number, the Neel temperature and the Curie temperature have been measured.

Spin waves in antiferromagnetic FeF2

Spin-wave dispersion in antiferromagnetic FeF2 has been investigated by inelastic neutron scattering using a chopper time-of-flight spectrometer. The single mode observed has a relatively flat dispersion curve rising from 53 cm-1 at the zone centre to 79 cm-1 at the zone boundary. A spin Hamiltonian which includes a single-ion anisotropy constant D (Hsi=-DSiz2), three exchange parameters Jl(Hex12=JlS1.S2) and dipolar interactions has been fitted to the measured energies. The authors find D=6.46 (+0.29, -0.10) cm-1, J1 (coupling neighbouring ions along the c axis)=-0.048 (+or-0.060) cm-1, j2 (coupling neighbouring ions at the corner and body centre of the cell)=+3.64(+or-0.10) cm-1, and J3 (coupling neighbouring ions along the a axis)=+0.194 (+0.060) cm-1.

Neutron-Scattering Determination of Spin-Wave Dispersion Relations in FeF2

Spin-wave dispersion in antiferromagnetic FeF2 has been investigated by inelastic neutron scattering at 4.2°K. Incident neutrons of 122 cm−1 energy were used to excite spin waves in a {010} plane, and the energies of the scattered neutrons determined by time-of-flight techniques. The single mode observed has a rather flat dispersion lying between 53 and 79 cm−1. The measured energies were fitted to a theoretical expression to determine values for the single ion anisotropy constant D, (Hsi=−DSiz2), and the exchange interactions between the ions Jl, (Hex12=J lS1·S2). We find D = 6.46(+0.29, −0.10) cm−1, J1 (coupling neighboring ions along the c axis) = −0.048 (±0.060) cm−1, J2 (coupling neighboring ions at the corner and body center of the cell) = +3.64(±0.10) cm−1, and J3 (coupling neighboring ions along the a axis) = +0.194(±0.060) cm−1.