Superparamagnetic relaxation

Usually, it is assumed that the magnetic anisotropy in nanoparticles is uniaxial with the magnetic anisotropy energy given by the simple expression 

In studies of superparamagnetic relaxation the blocking temperature is defined as the temperature at which the relaxation time equals the time scale of the experimental technique. Thus, the blocking temperature is not uniquely defined, but depends on the experimental technique that is used for the study of superparamagnetic relaxation. In Mossbauer spectroscopy studies of samples with a broad distribution of relaxation times, the average blocking temperature is commonly defined as the temperature where half of the spectral area is in a sextet and half of it is in a singlet or a doublet form. 

When a magnetic field, B, is applied to a ferromagnetic or ferrimagnetic particle with magnetic moment, p, the magnetic energy has a contribution from the Zeeman term 

Even for applied magnetic fields below 1 T, the Zeeman energy may be larger than the anisotropy energy. Above the blocking temperature application of a 

For fiB 2KV, there is only one energy minimum, i.e. there is no energy barrier between different magnetization directions [57], and the fluctuations of the magnetic hyperfine field can therefore be considered fast compared to Tm- The induced magnetic hyperfine field is then proportional to the induced magnetization. Using 

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Figure 6.13 shows the Mossbauer spectra of ferritin [51], which is an iron-storage protein consisting of an iron-rich core with a diameter around 8 nm with a structure similar to that of ferrihydrite and which is surrounded by a shell of organic material. At 4.2 K essentially all particles contribute to a magnetically split component, but at higher temperatures the spectra show the typical superposition of a doublet and a sextet with a temperature dependent area ratio. At 70 K the sextet has disappeared since all particles have fast superparamagnetic relaxation at this temperature. 

The height of the energy barrier between the forward and reverse states is the product of the particle volume, V, and the anisotropy constant Kefr (which is, to some extent, a function of particle size). Superparamagnetic relaxation occurs when the thermal energy of the particles exceeds the activation energy barrier between the spin states and so allows rapid, spontaneous fluctuations between these states. The effect of these spin reversals is that the observed magnetic field is reduced or even absent. 

Because the appearance of the superparamagnetic effect depends on the particle size and on the anisotropy constant, it is often displayed at room temperature by iron oxides <10 nm in size, for example, soil iron oxides. Superparamagnetic relaxation may be counteracted by lowering the temperature and thereby increasing x. Superparamagnetic particles will usually be ordered below a blocking temperature,Tb, which is ... 

Owing to its small particle size and poor crystallinity, the mineral feroxyhyte (5 -FeOOH) is superparamagnetic at room temperature. Superparamagnetic relaxation is also observed for small particles of the synthetic compound, which had a Bhf at 4.2 K of 51.3 T (Carlson Schwertmann, 1980). 

Contam. Hydrol. 17 347-363 Morup, S. Tronc, E. (1994) Superparamagnetic relaxation of weakly interacting particles. Phys. Rev. Letters 72 3278-3281 Morup, S. Dumesic, A. Tops0e, H. (1980)... 

This section is based mostly on the results presented in Ref. 78 and is arranged in the following way. In Section III.B.l we note mentioned the problem of superparamagnetic relaxation, which has been already tackled by means of the Kramers method, in the in Section II.A), and show how to obtain the analytical solution (in the form of asymptotic series) for the micromagnetic Fokker-Planck equation in the uniaxial case. In Section III.B.l the perturbative... 

Coffey WT, Crothers DSF, Dormann JL, Geoghegan LJ, Kalmykov YP, Waldron JT, Wickstead AW (1995a) Effect of an obliqne magnetic field on the superparamagnetic relaxation time. Phys Rev B 52 15951-15965... 

Garcia-Palacios JL, Svedlindh P (2001) Derivation of the basic system equations governing superparamagnetic relaxation by the use of the adjoint Fokker-Planck operator. Phys Rev B 63 172417-1-172417/4... 

Jambor JL, Dutrizac JE (1998) Occurrence and constitution of natural and synthetic ferrihydrite, a widespread iron oxyhydroxide. ChemRev 98 2549-2585 files DC, Atherton DL (1984) Theory of ferromagnetic hysteresis (invited). J Appl Phys 55 2115-2120 Jones DH, Srivastava KKP (1989) A re-examination of models of superparamagnetic relaxation. J Magnet Magnetic Mater 78 320-328... 

Morup S, Topsoe H, Lipka J (1976) Modified theory for Mossbauer spectra of superparamagnetic particles Application to Fe304. J Physique, Colloque C6, Suppln° 12 C6-287-C6-291 Morup S, Tronc E (1994) Superparamagnetic relaxation of weakly interacting particles. Phys Rev Lett 72 3278-3281... 

Morup, S. "Paramagnetic and Superparamagnetic Relaxation Phenomena studied by Mossbauer Spectroscopy", Polyteknisk Forlag, Lyngby 1981. 

Small-particle samples of MnFe204 show superparamagnetic relaxation effects [81]. 

Meisel W (1994) Hyperfine Interact 92 1213 Mitra S (1992) Applied Mossbauer spectroscopy, physics and chemistry of earth, Vol 18. Pergamon, Oxford, New York, Seoul, Tokyo Moon PB (1950) Ptoc Phys Soc 63 1189 Morup S (1981) Paramagnetic and superparamagnetic relaxation phenomena studied by Mossbauer spectroscopy. Polyteknisk Forlag, Lyngby... 

Superparamagnetic relaxation Transition from blocked to superpara magnetic regime... 

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