On the use of ferromagnetic resonance to determine the ferromagnetic-spin glass transition line —Temperature dependence of linewidths

We report temperature dependence of FMR linewidths (Γ) for a set of amorphous Fe_yNi_80?yP₁₄B₆ alloys. The linewidths show maxima as a function of T. However, the temperatures (T_m) corresponding to the maxima not only differ from the low field freezing temperatures reported earlier but also depend on microwave frequency. We contend that the T_m ′s should not be used to identify the zero-field ferromagnetic-spin glass transition line.     

Temperature dependence of ferromagnetic resonance in permalloy/NiO exchange-biased films

The temperature dependencies of the ferromagnetic resonance (FMR) linewidth and the resonance field-shift have been investigated for NiO/NiFe exchange-biased bilayers from 78 K to 450 K. A broad maximum in the linewidth of 500 Oe, solely due to the exchange-bias, is observed at ≈150 K when the magnetic field is applied along the film plane. When the magnetic field is applied perpendicular to the film plane, the maximum in the linewidth is less pronounced and amounts to 100 Oe at the same temperature. Such a behavior of the FMR linewidth is accompanied with a monotonic increase in the negative resonance field-shift with decreasing temperature. Our results are compared with the previous experimental FMR and Brillouin light scattering data for various ferromagnetic/antiferromagnetic (FM/AF) structures, and suggest that spin dynamics (spin-wave damping and anomalous resonance field-shift) in the FM/AF structures can be described in a consistent way by a single mechanism of the so-called slow-relaxation.     

Theory of ferromagnetic polariton linewidths

The interaction between magnons and photons which is responsible for magnetic polariton formation is expressed in terms of second quantized operators, and it is confirmed that the polariton dispersion curve obtained by diagonalizing the Hamiltonian is the same as that found classically. A term describing relaxation of the polariton by the two magnon mechanism which is often dominant in ferromagnetic resonance is then introduced. The lineshape function for inelastic light scattering is calculated by a Greens function technique. On the assumption that the lineshape can be approximated as a Lorentzian an expression for the linewidth is derived. The linewidth is zero when the polariton frequency Ω lies outside the magnon manifold, and increases discontinuously from zero at w = ¦γ¦H₀, where H₀ is the (internal) static field.     

Temperature dependence of the linewidths of shallow impurity spectral lines

A pronounced broadening of shallow donor transition linewidths in GaAs and CdTe by a factor of 2-2·5 on raising the sample temperature from 4 K to 10 K is reported. At low temperatures such impurity lines are inhomogeneously broadened by the Stark effect due to random electric fields arising from the ionized impurities in the crystal. The experimental observation is analysed and explained in terms of the temperature dependent spatial correlation between ionized donors and acceptors in the crystal.     

Temperature dependence of ferromagnetic anisotropy energy in cubic crystals

The magnetic anisotropy constant K₁ for cubic ferromagnetic crystals has been discussed based on the general expressions derived by Yang for hexagon crystals. By matching the experimental data, we obtained

$\text{K}{}_1\text{(T,H)}\text{K}{}_1\text{(0,0)}\text{=?6.14}\text{I}\text{?}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{(T,H) + 3.36}\text{I}\text{?}\text{9}\text{2}\text{(T,H) + 4.88m}{}^2\text{(T,H) ?1.10[}\text{I}\text{?}\text{5}\text{2}\text{(T,H)]}{}^2$

for nickel, and $\text{K}{}_1\text{(T,H)/K}{}_1\text{(0,0)=I}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ for iron, where Î_{$\text{5}\text{2}$} and Î_{$\text{9}\text{2}$} are the hyperbolic bessel functions of order 2 and 4 respectively and m is the reduced magnetization. Both expressions have a theoretical basis.     

Frequency dependence of the ferromagnetic resonance width in magneto-impedance measurements

Giant magneto-impedance has shown large sensitivities that are of great interest in practical applications. Above certain frequencies the ferromagnetic resonance controls the magneto-impedance behavior, and the resonance width limits the maximum achievable magneto-impedance ratio. In this work we present the evolution of the resonance width as a function of the frequency, determined through magneto-impedance and microwave absorption measurements on a NiFe–Au multilayer thin film. The width of the resonance can be fitted to a curve in the form of Δf∼f⁻¹. This is explained by means of a simple model taking into account all inhomogeneities in the sample through a Gaussian distribution of anisotropy fields, as suggested by the shape of the hysteresis loop.     

Reaction dependence of nuclear decay linewidths

Various light- and heavy-ion reactions, 20 < E < 100 MeV, have been used to study the reaction dependence of α-decay widths for ⁸Be¹(2 ⁺ , 2.9 MeV) and ¹⁶O¹(1^?, 9.6 MeV). Although slight differences (< 20 %) are found for the observed line shapes (Γ), the resonance widths inferred (Γ_R) are self-consistent and indicate little if any reaction dependence (< 10 %). Near a decay threshold one may expect Γ < Γ_R by 20 % or more, however, and thus care must be taken in comparing decay widths inferred from nuclear reactions with those from scattering resonances. Reduced formal α-decay widths of γ_λ² = 680 ± 100 keV (s = 4.8 fm) and γ_λ² = 350 ± 50 keV(s = 5.4 fm), corresponding to θ_λ² = 0.50 and θ_λ² = 0.49 are deduced for ⁸Be¹(2 ⁺ , 2.9 MeV) and ¹⁶O¹(1^?, 9.6 MeV) using the nuclear-reaction Γ_R values and a particular set of α-nucleus potentials.     

The dependence of susceptibility on the high-frequency field at ferromagnetic resonance

The dependence of the uniform precession amplitude and susceptibility at ferromagnetic resonance on the high-frequency fieldh is discussed on the basis of an equation for the energy balance and classical equations for the spin wave amplitudes. The dependence (h) is first determined in the lowest non-linear approximation. According to these calculations, the initial decline of the susceptibility differs from Schlömann's quadratic law. The influence of other nonlinear interactions between spin wavesk0 is then discussed on a certain special assumption of the type of two-magnon scattering. It is shown that such interactions can lead to the appearance of a maximum in the h.f. field dependence of the uniform precession amplitude.     

Directional dependence of vortex core resonance in a square-shaped ferromagnetic dot

The resonant property of the magnetic vortex confined in a square-shaped ferromagnetic dot has been investigated. We showed that the field dependence of the resonant frequency has a unique directional dependence originating from a four-fold rotational symmetry of the square. The resonant frequency is found to be strongly modulated by the magnetic field along the diagonal direction although the magnetic field applied along the side of the square hardly modified the resonant frequency. The modulation ratio of the resonant frequency defined by the ratio between minimum and maximum frequencies for the vortex resonance was found to be tuned by the lateral dimension of the square. These unique frequency tunabilities controlled by the magnitude and the direction of the magnetic field may provide additional functions in the application of the magnetic vortex systems.     

Temperature dependence of the electronic quasiparticle structure of ferromagnetic Gd.

We propose a theory, which combines a one-electron bandstructure calculation with a many body treatment, to explain temperature effects in the electronic excitation spectrum of ferromagnetic 4f-systems like Gd. In the ferromagnetic phase the quasiparticle density of states reacts sensitively on temperature variations, in particular a striking shift of order 0.4 eV of the lower conduction band edge to smaller energies upon cooling below T_c is predicted and should be observable in a photoemission experiment.     

Angular dependence of the ferromagnetic resonance spectrum in continuous/heterogeneous multilayers

We present here a study of the angular dependence of the ferromagnetic resonance (FMR) spectra in trilayers formed by two continuous ferromagnetic layers, Fe and Ni₈₀Fe₂₀ (permalloy), separated by a granular film of Fe(x)–SiO₂(1–x). The study of the Fe/Fe-SiO₂/Ni₈₀Fe₂₀ trilayer was made for an Fe volume concentration x=0.75 and two thicknesses (t=1 and 18 nm) of the granular layer. One microwave absorption line is in general found close to the field expected for Fe, while the other is coincident with the resonance field of permalloy. However, the Fe-like absorption is considerably wider than what is usually observed in pure Fe films, which suggests the presence of a strong exchange interaction between this layer and the granular spacer. The angular dependence of the resonance field and the line width could be very well fitted with a model that assumes an effective in-plane anisotropy for each layer, indicating that the shape anisotropy dominates the angular response of both modes. When the excitation frequency is increased, the line width of the permalloy-like mode increases by a similar factor. The width of the Fe-like mode is very similar at different frequencies because of the effect of the granular layer.     

Temperature dependence of the cyclotron resonance in graphene

The dynamic conductivity of graphene in a magnetic field under the conditions of cyclotron resonance has been calculated. The effect of the temperature on cyclotron resonance has been analyzed. So-called multiple resonances have been considered. A dimensionless quantity determining the width and amplitude of the cyclotron peak in the conductivity has been found. Coulomb corrections to the electronic spectrum have been discussed.     

Temperature dependence of exchange bias and coercivity in ferromagnetic/antiferromagnetic bilayers

A model for the temperature dependence of exchange bias and coercivity in epitaxial ferromagnetic (FM)/ antiferromagnetic (AFM) bilayers is developed. In this model, the interface coupling includes two contributions, the direct coupling and the spin-flop coupling. The temperature dependence arises from the thermal disturbance to the system, involved in the thermal fluctuations of magnetization of AFM grains and the temperature modulation of the relevant magnetic parameters. In addition, the randomness of original orientations of easy axes of AFM grains after field cooling is taken into account. A self-consistent calculation scheme is proposed and numerical treatment is carried out. The results show that the temperature dependence of exchange bias and coercivity is closely related to the sizes of AFM grains and the interface exchange coupling constants. Especially, the exchange bias will have a peak and the blocking temperature will increase if the spin-flop coupling plays a role. On the other hand, the original orientation distribution of easy axes of AFM grains will affect exchange bias and coercivity prominently. The prediction has been well supported by experiments.Received: 12 May 2004, Published online: 31 August 2004PACS: 75.30.Et Exchange and superexchange interactions - 75.50.Ee Antiferromagnetics - 75.30.Gw Magnetic anisotropy     

Frequency dependence of ferromagnetic resonance in amorphous magnets: Ferromagnetic and reentrant alloys

We report measurements on magnetic resonance in a number of transition metal-glass former complexes. Data were taken over a wide range of frequencies (2–35 GHz) and temperatures (2–300 K). In the ferromagnetic regime all the systems have a term in their linewidth which points strongly to noncolinearity of spin in glassy magnets even in a nominally saturated state. At low temperatures, in the reentrant alloys, there is a characteristic exponential term describing the increase in linewidth, with reducing T. Such a contribution appears in most random spin systems. There is no adequate microscopic picture to account for many of the results.     

Temperature dependence of superparamagnetic resonance of iron oxide nanoparticles

Nanoparticles of maghemite (γ-Fe₂O₃) are formed in a sol–gel silicate glass with a molar ratio Fe/Si of 2% by a treatment at 1000°C for 6 h. Electron paramagnetic resonance spectrum at 300 K shows a relatively narrow sharp line at g_eff≈2. As the temperature lowers to 5 K, the apparent resonance field decreases and the linewidth considerably increases. We develop a theoretical formalism based on a distribution of diameters or volumes of the nanoparticles following a lognormal. The nanoparticles are considered as single magnetic domains with random orientations of magnetic moments and thermal fluctuations of anisotropic axes. The individual line shape function is derived from the damped precession equation of Landau–Lifshitz. An appropriate linewidth expression is put forward, which account for the averaging of the fluctuations of orientations of the magnetic moments with respect to the magnetic field and to the magnetic anisotropy axes. A single set of parameters provides good fits to the spectra recorded at the different temperatures. The low-temperature blocking of the nanoparticle magnetic moments has been clearly evidenced in the resonance absorption intensity and the blocking temperature of the assembly of nanoparticles (averaged over the distribution in the nanoparticle volume) has been evaluated as 90 K.     

Power dependence of Brillouin linewidths in a silica fiber

We report the dependence of Brillouin linewidths on the pump power below the threshold of Brillouin lasing in a silica fiber. The Stokes Brillouin shift in a silica fiber is nearly unchanged, and its linewidth decreases with increasing pump power. However, the anti-Stokes Brillouin shift becomes smaller and its linewidth larger with increasing pump power. We explain these experimental results by the distributed fluctuating source model.     

Temperature dependence electron spin resonance spectra of a magnetic fluid

ESR spectra of a laboratory synthesized kerosene base magnetic fluid containing ultrafine magnetic particles (average diameter of 100A) of Zn_0.1 Fe_0.9Fe₂O₄ are recorded at different temperatures. A narrow signal was observed above the melting point of the carrier liquid (200 K) which can be attributed to a very small volume fraction of superparamagnetic particles in the system. The peak-to-peak line width for both low and high field cooled configurations show an increase with decreasing temperature. This observed behaviour has been explained by considering various energy terms which contribute to the line width.