By Fakharyar Khan
Introduction
The spin or angular momentum of an electron creates a magnetic field in a
certain direction. A full atomic orbital does not generate a magnetic field because the two electrons have equal and opposite fields which causes them to cancel out so only unpaired electrons can create a magnetic field. When an electric current or magnetic
field is applied to an object, many of the unpaired electrons will become aligned and form a stronger magnetic field called the magnetic moment. A domain is a region in the particle where all of the unpaired electrons are aligned. If all of the unpaired electrons of
a particle are aligned then the particle becomes single-domain. The direction of the magnetic field that will create a uniform alignment with the smallest amount of energy is called the easy axis of a particle. However, this magnetic field can create one of two
equally likely magnetic moments with opposite directions. Sufficiently small, single-domain nanoparticles (3 - 50 nm) exhibit an interesting property called superparamagnetism where the magnetization of a particle to flip from one magnetic moment to the other. There are two ways that nanoparticles can go through magnetic
reversal, one is through a process called the quantum spinning effect and the other is a much less understood process, magnetic avalanches.
It requires energy for an electron to reverse its direction and so the two
orientations are separated by an energy barrier. So there was a 50-50 chance of the electron going from one state to the other. Now that it has chosen one, the chance of going to the other state doesn’t immediately become zero so it does have a chance of
reversing its magnetic field in a phenomenon called the quantum spin tunneling effect. Since it’s probabilistic the time it takes for the entire particle to go through reversal could
be anywhere from nanoseconds to years.
When a superparamagnetic is placed in a magnetic field that points in the
direction opposite of the nanoparticle, it kickstarts a rapid magnetic reversal that finishes in milliseconds. The presence of the magnetic field creates potential energy within the
electrons called Zeeman energy that is released when the electron follows the direction of the field and becomes “relaxed”. This released energy turns into thermal energy 3 which then gives relaxes neighboring electrons which in turn releases more energy and
so on. The rapid energy increase characteristic of this process gives it the term magnetic avalanche. Experiments have shown that magnetic avalanches are analogous to combustion (Zeeman energy is like the chemical energy in atomic bonds) and behave
very similarly to them. This idea is called magnetic deflagration and in this paper I will present the research of scientists at the City University of New York.
Abstract
The researchers wanted to prove the theory of magnetic deflagration because this would allow them to study the behavior of chemical combustion by observing magnetic avalanches in molecular magnets. Combustion is a very complex process and
is difficult to create a reliable mathematical model on it. Studying magnetic deflagration is much more efficient than drawing conclusions from chemical combustion because
your object of study is destroyed after one experiment and is very hard to control whereas in magnetic deflagration, you can reset the magnetic field and have much more flexibility in manipulating the variables.
The researchers found evidence to support this theory by using microscopic hall effect sensors that would measure the strength of the magnetic fields produced by the nanoparticles. The hall effect sensors are conducting materials that when placed on a
magnet, its magnetic fields cause the electrons of the magnet that
pass through the sensor to curve. This is because the magnet’s
field interacts with the electron’s magnetic field which repels the
electron. Therefore, at one end of the hall sensor you have all of
these electrons and at the other end is nothing and this gradient
creates a voltage. The voltage is measured by the hall sensor which
can be used to find the strength of the magnetic field as it is directly proportional to the voltage.
The changes in the strength of the magnetic field can tell us how fast the magnetic
avalanche is going through the object which is called the velocity of propagation. For the
first sample, the researchers used eleven hall sensors that were spaced out in 40 um
intervals and laid them across a molecular magnet, Mn12 acetate that was fully
saturated (meaning its magnetic field was opposite that of the field they were going to
reverse it). The position of the hall sensor and the time it registered the peak voltage,
when looked across all eleven hall sensors, would give us the velocity of propagation.
This is because when peak voltage is reached, it means that all of the electrons going
through the hall sensor are being influenced by the magnetic field created by the
electrons that had already reversed their magnetic fields just like the front of an
avalanche. They then introduced a magnetic field with a strength of 4T and swung it
back and forth along the easy axis of the nanoparticle so that they could trigger the
avalanche.
Results and Analysis
The researchers measured the strength of the magnetic fields in gauss detected
by each of the eleven hall sensors as time (microseconds) went on. Since the hall sensor that was 160 um away from the beginning of the molecular magnet reached its peak first, the
avalanche must have started towards the beginning of the molecular magnet and made its way down. The inset is a graph of the position of the sensors over the time it took for the
sensors to reach peak voltage and by constructing a line of best fit for the data and measuring its slope, we can see that the velocity of propagation is approximately 12 m/s which is in the range of the speed of the flame front- 1-15 m/s. They found a positive correlation between the strength of the magnetic field and the velocities of propagation for fully saturated magnets and a weaker correlation for magnets with a lower saturation. However, when they compared the energy release per molecule with the velocity, for all of the samples and their different magnetic saturations, they all nearly collapsed into a single linear graph as shown
here. The x intercept indicates that that there is a certain amount of energy needed to kickstart magnetic deflagration just like with combustion. In fact, the energy released by a magnetic avalanche is very close to the energy released by combustion when temperature differences are taken into account (as magnetic deflagration is most easily triggered within the range of 250mK). In summation, the velocities of propagation of a flame front and a magnetic avalanche are very similar and they rely on the energy release per molecule in nearly the same way.
Critique and A New Proposal
Their experiment was very well thought out and they left very little room for
errors. But one thing I wanted to see in their experiment was them manipulating the field
sweep rate of the magnetic field, how fast the magnetic field is swung back and forth. I
would have used the same setup that they used for their experiment and use the field
sweep rate that they used for sample 1, 10mT/s, as my base case. I want to see how
increasing the field sweep rate will affect the velocity of propagation for the avalanche
and even its presence. I think that with an increasing rate, the magnetic field would be
much like moving your finger quickly through a fire. The electrons won’t have enough
time to be fully exposed to the magnetic field and “catch on fire". However, you could
also argue that with an increase in the speed of the magnetic field, the strength of the
field will increase as the velocity of the particle radiating the magnetic field increases.
But it should still not affect the electrons because the speed of the transfer of energy
can’t match the field sweep rate. I think that this experiment could give more evidence
for the theory of magnetic deflagration since it could show that the relationship between
the energy output per molecule and the transfer of energy for magnetic deflagration and
combustion are similar.