The resonance decay function method in the determination of the pre-factor of the Néel relaxation time of single-domain nanoparticles

In its simple form, the relaxation time of the Néel relaxation process of the magnetic moment of single-domain particles is given by τ N =τ 0 N exp( σ), σ being the ratio of anisotropy energy to thermal energy. The pre-factor, τ 0 N , is normally given a value of 10 −9 s, but values ranging from 10 −8 to 10 −12 s have been reported in literature. Here, by means of the field and frequency dependence of the complex magnetic susceptibility, χ( ω, H) =χ′( ω, H) −iχ″( ω, H), of a magnetic fluid sample, in the MHz–GHz range, in conjunction with the determination of the sample decay function, b( t), the pre-factor τ 0 N is determined. b( t) is readily obtained through the inverse Fourier transformation relationship, which exists between b( t) and χ″( ω). ► Experimental technique centred on the measurement of the complex magnetic susceptibility, χ( ω, H) =χ′( ω, H) −iχ″( ω, H). ► Precessional decay time of the Landau–Lifshitz equations is evaluated. ►Néel pre-factor, τ 0 N , determined for single-domain magnetite particles of mean diameter 10 nm. ► After-effect function, b( t), obtained through the relationship, which exists between b( t) and χ″( ω).