Assume a spherical magnetic particles of radius R and magnetization value of M =

Question

Assume a spherical magnetic particles of radius R and magnetization value of M = 1000 emu/cm3 and exchange parameter A = 1 x 10-6 ergs/cm. For each of the following uniaxial magnetic anisotropy values K = 1 x 105 , 1 x 106 , and 1x 107 ergs/cm3 (assuming an attempt frequency of 10 GHz) calculate:

a) The zero-temperature coercive field (assuming the field is along the anisotropy axis).

b) The radius going from single-domain to multi-domain ground state (using the simplified expression in the notes). Will these answers overestimate or underestimate the critical radius and why? What calculation is needed to accurately calculate the critical radius.

c) The radius for the particle to be ferromagnetic at room temperature for time great than 1 sec.

please help! please answer only if you know all of the parts. Thank you!

Explanation / Answer

a)    The zero-temperature coercive field = 1000 * 1x 107/(1 x 106)

                                                                = 10000 T

b)   The radius going from single-domain to multi-domain   =   4.128 * 10-6 * 10000

                                                                                             = 0.04128 cm

These answers overestimate the critical radius due to larger magnetization .

c)    The radius for the particle to be ferromagnetic   =   5.263 * 10-4 * 1000

                                                                                   = 0.5263 cm

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