Scaling laws and approximate expressions for the dynamic magnetic susceptibility of Brownian nanoparticles

We present simplified expressions for the out-of-phase component of the dynamic susceptibility χ″ of lognormal-sized magnetic nanoparticles under Brownian rotation. These expressions are based on transforming the general integral functions used for χ″ in the convolution of gaussian functions. χ″ can thus be expressed as a sum of gaussians with parameters directly related to those of the size distribution and to the saturation magnetization. The gaussian fit of χ″(ω) (where ω is the ac field frequency) is a simpler way to determine these structural and magnetic parameters as it avoids fitting χ″(ω) to an integral function. The expressions derived for χ″ suggest that χ″T data collapses in a ωη(T)/T scale (where T is the temperature and η the fluids viscosity), which is confirmed by numerical calculations. We also discuss the limits of validity of these approximations in real systems where both Néel and Brownian relaxation mechanisms coexist and we present further approximations for the relation of ω_χ with the average volume (being ω_χ the frequency at which χ″ is maximum). The ωη(T)/T scale can be used to qualitatively evaluate the dominance of the Brownian relaxation mechanism.     

Low-frequency complex magnetic susceptibility of magnetic composite microspheres in colloidal dispersion

A procedure is presented to determine the permanent magnetic dipole moment of composite microspheres containing magnetic nanoparticles with a blocked magnetic dipole moment. The composite particles are dispersed in a solvent, and the complex magnetic susceptibility is measured from 0.1 to 1000 Hz using a highly sensitive new setup. Composite particles with a permanent magnetic dipole moment are revealed by a characteristic frequency that corresponds to the Brownian rotation of the microspheres. From measured susceptibility spectra, we calculate the permanent magnetic dipole moment of recently developed cobalt ferrite-doped silica and latex microspheres.     

Flux relaxation phenomena in the presence of weak AC magnetic fields

Relaxation of flux profile and magnetisation due to non-linear vortex diffusion in a superconducting slab settled in a parallel-to-the-surface DC and superimposed weak AC magnetic fields is studied for several kinds of the non-linear vortex diffusivity, corresponding to different possible shapes of the current–voltage characteristics of the superconductor. The evolution of the dynamic vortex response on applied weak AC field due to flux relaxation process is studied and relaxation characteristics of the AC magnetic susceptibility are calculated. The flux creep rate and magnetisation decay are shown to be enhanced significantly in the case of strongly non-linear regime of vortex diffusion if even rather weak AC magnetic field is applied. The possibility of ‘dynamical melting' of the vortex lattice occurring at rather high levels of the induced current density (j>j_c) is also demonstrated.     

Comparison of transport and magnetic AC losses in Bi-2223/Ag tapes — the role of superconducting core geometry

AC losses were measured by 4-probe transport method and by external magnetization method in three samples of Bi-2223/Ag tape: a multifilamentary tape with separated filaments, another multifilamentary tape with ‘bridges' between filaments, and a two-shell tape. The transport losses agreed with those calculated using I_c from DC experiment. Magnetization experiments gave indications about the various paths of induced currents. For the tape with well separated filaments the main part of screening current closes inside individual filaments. Additional screening of the whole filamentary zone involves the normal metal matrix, leading to frequency dependent losses. In the case of tape with ‘bridged' filaments, supercurrents interconnect the filaments into bundles whose screening (and loss) is frequency-independent. Matching the experimental data indicates that a typical bundle was composed of 8 filaments. Magnetic losses of the two-shell tape were explained by a model for magnetization of superconducting wire with elliptical cross-section.     

Even harmonics of AC susceptibility in some sintered pellets of high temperature superconductors

The real (χ′ _n) and imaginary (χ″ _n) parts of even harmonic susceptibility (n⩽6) are measured as a function of external DC field (H _dc) in the field increasing (H↑) and decreasing (H↑) cycle. Hysteresis is observed betweenH↑ andH↓ cycles. In theH↓ cycle, at a field,H _comp=4·2G, bothχ′ andχ″ of all the even harmonics vanish indicating a true cancellation of fields in the intergrain region (H _eff≈0) caused by the balance betweenH _dc and the remanent magnetization of the grains. The position of the extrema and the zero of the various harmonics undergo a shift proportional to the remanent magnetization of the grains at that particular field.     

Evidence of new high-pressure magnetic phases in Fe–Pt Invar alloy

To investigate the magnetic properties of disordered Fe₇₀Pt₃₀ Invar alloy under high pressure, measurements of the real part of the AC susceptibility (χ) were made under pressure up to 7.5 GPa in the temperature range 4.2–385 K using a cubic anvil high-pressure apparatus. The Curie temperature (T_C) decreased with increasing pressure, and then, two new high-pressure magnetic phases appeared. These results show that the ferromagnetism of Fe–Pt Invar alloy becomes weaker, and the antiferromagnetic interaction becomes dominant with increasing pressure.     

Kinetics of the phase transition in an isotropic liquid crystalline dimer subjected to a deep temperature quench

Kinetics of the ordered phase growth in a liquid crystalline azomethine dimer under a deep temperature quench was studied using a polarizing optical microscope at different cooling rates. The nematic droplets revealed in the optical images across the phase transition were treated statistically and the resulting statistical size distributions were described using principles of irreversible thermodynamics. After analysis of the mean droplet diameter evolving with time, two regimes of the nematic phase growth were recognized: (i) nucleation and rapid nucleus growth and (ii) nucleus coarsening. Both regimes were quantitatively described with the universal scaling function.     

Dynamical spin susceptibility of the d–p model in the over doping region

Dynamical spin susceptibility χ^s(q,ω) of the d–p model in the over doping region is investigated by using the auxiliary boson technique. It includes higher order terms of the 1/N-expansion within the random phase approximation (RPA) of the local vertex, where frequency dependence of the quasi-particle interaction is taken into account. The incommensurate spin fluctuation is obtained due to the nesting effect in the low energy region (ωω^*), whereas the commensurate one in the high energy region (ωω^*), the characteristic energy ω^* is estimated to be about 30 meV. Both of the spin–lattice relaxation rate 1/T₁ and the spin–spin relaxation rate 1/T_g monotonically increase as T decreases, while the spin Knight shift K is almost independent of T.