Thermoremanent magnetization
Encyclopedia
When an igneous rock cools, it acquires a thermoremanent magnetization (TRM) from the Earth's field. TRM can be much larger than it would be if exposed to the same field at room temperature (see isothermal remanence). This remanence can also be very stable, lasting without significant change for millions of years. TRM is the main reason that paleomagnetists are able to deduce the direction and magnitude of the ancient Earth's field.
could be magnetized by heating until it was red hot and then quenched in water. While quenching it was oriented in the Earth's field to get the desired polarity. In 1600, William Gilbert published De Magnete
(1600), a report of a series of meticulous experiments in magnetism. In it, he described the quenching of a steel rod in the direction of the Earth's field, and he may have been aware of the Chinese work.
In the early 20th century, a few investigators found that igneous rocks had a remanence
that was much more intense than remanence acquired in the Earth's field without heating; that heating rocks in the Earth's magnetic field could magnetize them in the direction of the field; and that the Earth's field had reversed its direction in the past.
of the minerals carrying it. A TRM can also be partially demagnetized by heating up to some lower temperature 
and cooling back to room temperature. A common procedure in paleomagnetism
is stepwise demagnetization, in which the sample is heated to a series of temperatures
, cooling to room temperature and measuring the remaining remanence in between each heating step. The series of remanences can be plotted in a variety of ways, depending on the application.
(below the Curie temperature), applying a magnetic field and cooling to a temperature 
, then cooling the rest of the way to room temperature in zero field.
and 
are two non-overlapping temperature intervals. Suppose that 
is a pTRM that is acquired by cooling the sample to room temperature, only switching the field 
on while the temperature is in interval 
; 
has a similar definition. The Thellier laws are
If these laws hold for any non-overlapping temperature intervals
and 
, the sample satisfies the Thellier laws.
that is independent of magnetic field for small fields. No irreversible changes occur at temperatures below 
. If the resulting TRM is heated in zero field, it becomes superparamagnetic again at an unblocking temperature 
that is equal to 
. Then it is easy to verify that reciprocity, independence and additivity hold. It only remains for linearity to be satisfied for all the Thellier laws to be obeyed.
History
As early as the eleventh century, the Chinese were aware that a piece of ironIron
Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series. It is the most common element forming the planet Earth as a whole, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust...
could be magnetized by heating until it was red hot and then quenched in water. While quenching it was oriented in the Earth's field to get the desired polarity. In 1600, William Gilbert published De Magnete
De Magnete
De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure is a scientific work published in 1600 by the English physician and scientist William Gilbert and his partner Aaron Dowling...
(1600), a report of a series of meticulous experiments in magnetism. In it, he described the quenching of a steel rod in the direction of the Earth's field, and he may have been aware of the Chinese work.
In the early 20th century, a few investigators found that igneous rocks had a remanence
Remanence
Remanence or remanent magnetization is the magnetization left behind in a ferromagnetic material after an external magnetic field is removed. It is also the measure of that magnetization. Colloquially, when a magnet is "magnetized" it has remanence...
that was much more intense than remanence acquired in the Earth's field without heating; that heating rocks in the Earth's magnetic field could magnetize them in the direction of the field; and that the Earth's field had reversed its direction in the past.
Demagnetization of TRM
It has long been known that a TRM can be removed if it is heated above the Curie temperature of the minerals carrying it. A TRM can also be partially demagnetized by heating up to some lower temperature and cooling back to room temperature. A common procedure in paleomagnetismPaleomagnetism
Paleomagnetism is the study of the record of the Earth's magnetic field in rocks. Certain minerals in rocks lock-in a record of the direction and intensity of the magnetic field when they form. This record provides information on the past behavior of Earth's magnetic field and the past location of...
is stepwise demagnetization, in which the sample is heated to a series of temperatures
, cooling to room temperature and measuring the remaining remanence in between each heating step. The series of remanences can be plotted in a variety of ways, depending on the application.Partial TRM
If a rock is later re-heated (as a result of burial, for example), part or all of the TRM can be replaced by a new remanence. If it is only part of the remanence, it is known as partial thermoremanent magnetization (pTRM). Because numerous experiments have been done modeling different ways of acquiring remanence, pTRM can have other meanings. For example, it can also be acquired in the laboratory by cooling in zero field to a temperature (below the Curie temperature), applying a magnetic field and cooling to a temperature , then cooling the rest of the way to room temperature in zero field.The Thellier laws
The ideal TRM is one that can record the magnetic field in such a way that both its direction and intensity can be measured by some process in the lab. Thellier showed that this could be done if pTRM's satisfied four laws. Suppose that and are two non-overlapping temperature intervals. Suppose that is a pTRM that is acquired by cooling the sample to room temperature, only switching the field on while the temperature is in interval ; has a similar definition. The Thellier laws are
- Linearity:
and 
are proportional to 
when 
is not much larger than the present Earth's field. - Reciprocity:
can be removed by heating through temperature interval 
, and 
through 
. - Independence:
and 
are independent. - Additivity: If
is acquired by turning the field on in both temperature intervals, 
.
If these laws hold for any non-overlapping temperature intervals
and , the sample satisfies the Thellier laws.A simple model for the Thellier laws
Suppose that a sample has a lot of magnetic minerals, each of which has the following property: It is superparamagnetic until the temperature reaches a blocking temperature that is independent of magnetic field for small fields. No irreversible changes occur at temperatures below . If the resulting TRM is heated in zero field, it becomes superparamagnetic again at an unblocking temperature that is equal to . Then it is easy to verify that reciprocity, independence and additivity hold. It only remains for linearity to be satisfied for all the Thellier laws to be obeyed.