Magnetic blocking temperatures of single‐domain grains during slow cooling

Abstract

Acquisition of TRM by a cooling assemblage of identical monodomain grains involves a transition from superparamagnetic to blocked behavior over a narrow but indefinite range of temperature. Blocking temperature may, nevertheless, be precisely defined by comparing the blocked magnetization, after cooling, with the curve of equilibrium magnetization against temperature. At the blocking temperature TB the relaxation time τ of the magnetization is of the same order as the cooling time constant θ, which is the time required for τ to increase by a factor e. An approximate analytic solution of the differential equation for magnetization in a cooling system gives for TB:ε (TB)/kT = 1n(1.78Cθ) where ε is the activation energy for rotation of magnetic moments, k is Boltzmann's constant, and C is the frequency factor (∼1010 Hz). Because ε varies with temperature, the cooling time constant θ is given by 1/θ = (1/kTB)(dε/dT ‐ ε/TB)dT/dt. The 95% blocking interval is about 7.2θ. For steady cooling it is reasonable to assume θ to be constant through this interval; small deviations from constancy have a negligible effect upon TB. In small external fields the variable grain geometry to be found within a real assemblage can be incorporated in a parameter ε0, which is the activation energy at O°C. Curves of ε0 against TB for magnetite and haematite, at cooling rates from 6°C per minute to 3°C per million years, show that (1) a change in ε0 by a factor of 2 corresponds to 12 orders of magnitude change in cooling rate and (2) for a broad distribution of grain sizes a large proportion of the size range will acquire their magnetization within 100°C–200°C of the Curie point. Using these curves, blocking temperature in cooling assemblages can be related to laboratory demagnetization temperatures; the differences are greater at slower cooling rates and lower temperatures and tend to zero as the Curie temperature is approached. Intensity of magnetization should increase by a few percent for each order of magnitude decrease in cooling rate. Magnetization acquired at temperatures near the Curie point should dominate in a chemically homogenous monodomain assemblage with a broad spread of grain sizes. Possible tests of the theory and its application to the determination of cooling history are discussed.