Attached is a numerically simulated magnetization in 15x2cm FeNi sample, rapidly cooled from Curie temperature.
a. The magnetization is parallel to the local direction of the magnetic field, therefore the paper and iron dust would procuce a similar picture if placed on top of this sample.
b. Equilibrium configuration is a result of such things as a competition between exchange and dipole-dipole interactions for a given shape.
c. The loss of precise magnetization is more or less a smooth function of temperature. Since Fe has Curie temperature of about 1000K (700C) it is not that noticable at the room temperature, but becomes an essnetial issue when you heat any sample to 500-600C. Initial magnetization, i.e. whether magnetized or unmagnetized iron has been used, becomes at this point mostly irrelevant.
d. The attached simulation was performed in the absence of external fields. Earth's magnetic field is truly irrelevant since it is extremely small; on the other hand the presence of other magnets like magnetized anvil and so on could have made the magnetization to be more uniform.
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