Magnetic blocking temperatures of magnetite calculated with a three-dimensional micromagnetic model

We present an analysis of thermal stability of magnetic remanence in fine grains of magnetite (grain size d = 15-120 nm). In order to model incoherent transitions between single-domain (SD) and pseudo-sing;le-domain (PSD) magnetization configurations, we employ a three-dimensional constrained minimization method proposed by Enkin and Williams [1994]. Using this approach, one can track in detail the transition from one local energy minimum state into another by constraining the magnetization vectors of appropriate cells in a discrete model. For each particle, we obtain the energy barriers E-B(T) from 25 degrees to 578 degrees C. Magnetic blocking temperatures (T-B) are calculated by integrating E-B(T) for two extreme cooling schedules representing laboratory and geological timescales. The computed blocking temperatures for laboratory timescales are in excellent agreement with the experimentally determined blocking temperatures for magnetite by Dunlop [1973b]. The results of our computations are summarized as relaxation time versus blocking temperature curves, which deviate from the curves of Pullaiah et al. [1975] for particles with grain sizes in the SD-PSD transition region. A consequence of the dependence of T-B on timescale is that some PSD size particles are blocked in vortex states on geologic timescales but are blocked in the SD state on laboratory timescales. Paleointensity determinations with the Thellier method on such samples can therefore underestimate the paleofield. The superparamagnetic to SD threshold size d(S) is determined as 50 nm for cubic grains, whereas a small aspect ratio of q = 1.1 is sufficient to depress d(S) to 27 nm. SD particles of magnetite with small shape anisotropy and cubic grains with 58 nm equal to or less than d equal to or less than 72 nm are reliable carriers of paleomagnetic information.