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7.3 Ferromagnets & Single Molecule

To this point, we have been considering only molecular species that are paramagnetic. In other words, species that do not exhibit any kind of remnant or slow magnetization dynamics upon removal of an applied H (i.e., species for which the M vs. H plot looks like the line from point A to point B on the right-hand graph, and for which the plot of M vs. H is identical in the increasing and decreasing H directions.)

Many molecular species exhibit remnant magnetization (Mr), meaning that upon magnetization, followed by removal of the applied field, they retain a net with a specific orientation.

It requires application of a magnetic field in the opposite direction to demagnetize the material. The applied field required to demagnetize the material is called the coercive field (Hc).

Clearly, this is a hysteresis loop. At zero field, there are two possible values of Mr, one positive and one negative. The net magnetic moment can be oriented either “up” or “down” along a specific axis. Another way of looking at this is as a binary system, either a 1 or 0…so we can store digital data using the remnant magnetization (hard drives!)

In order for hysteresis to be possible, there must be axial magnetoanistropy, specifically easy-axis magnetoanisotropy. There must a unique axis along which the net moment can be easily aligned (either “up” or “down”) and it must require some amount of energy to “flip” the moment vector…in other words, there must be a hard plane in which it is more difficult to align the moment vector (an energy barrier to reversing the moment direction).

There are two possible ways in which the a molecular material can develop the requisite axial magnetoanistropy:

1) Cooperativity between microscopic moments – i.e., (etc.) 2) Significant /molecule – i.e., single molecule magnets (etc.)

Section 7.3 - 1 Ferromagnets and related types of

Ferromagnetism is a critical phenomenon involving a between a paramagnetic phase (above the so-called TC) and a magnetically ordered phase below the critical temperature, or so-called Curie temperature TC.

In order to treat ferromagnetism (and related phenomena, such as anti-ferromagnetism, ferrimagnetism, etc.) properly, we would require a good understanding of statistical mechanics, which is beyond the scope of this course.

At present, we will examine this phenomenon briefly and superficially.

First, it is prudent to not that a ferromagnet is NOT the same things as a paramagnet exhibiting zero-order energy splitting of electronic states due to exchange coupling!!

FERROMAGNETISM ≠ FERROMAGNETIC EXCHANGE COUPLING

In a ferromagnet:

• Microscopic (local) moments throughout the material tend to align parallel to one another, leading to a spontaneous permanent magnetization M in the absence of applied field H.

• HOWEVER, in this type of MACROSCOPIC system, it is energetically favorablefor moments to segregate into physical regions called DOMAINS.

• The domains need not be aligned with one another. In fact, in a “virgin” sample, that has never been subjected to a magnetic field, the alignment of the domain moments may actually completely cancel each other out and the sample may not exhibit a net spontaneous M.

• Application of an applied field H causes aligned domains to grow at the expense of misaligned domains. The resulting alignment persists when H is removed. (Note that the Earth’s magnetic field may be sufficient!)

• It takes energy to move domain walls, resulting in hysteresis.

Section 7.3 - 2

microcrystalline grains within a piece of NdFeB with magnetic domains made visible with a Kerr microscope. The domains are the light and dark stripes within each grain. –Wikipedia

Section 7.3 - 3 Single Molecule Magnets (SMMs) (etc)

Unlike ferromagnets, which rely on long-range ordering between many, many microscopic moments within a species, single molecule magnets exhibit remnant magnetization owing to properties arising from a single molecule, or possibly from a single ion in a molecule.

Again, to retain magnetization in zero field requires uniaxial magnetoanisotropy, i.e., a directional preference for the magnetic moment and an energy barrier that hinders randomization of its direction.

We have already looked at molecule-based magnetic anisotropy, but just to remind ourselves: • Magnetic anisotropy is the non-uniform distribution of magnetic properties in 3D.

Because SMMs are individual molecules, they must be treated using quantum mechanics, not (classical) statistical mechanics. This also means they are subject to physical phenomena that are uniquely quantum mechanical in nature (e.g., quantum tunneling).

For a species to exhibit SMM behavior (slow magnetization dynamics), two things are required:

1) an electronic arrangement with a non-zero S (or J) ground state (or at least a very low-lying S(or J) ≠ 0 state that is thermally populated at very low T) 2) easy-axis magnetic anisotropy (i.e., a large, negative value of D)

A (very oversimplified) equation to predict an energy barrier to “spin flipping” in an 2 SMM is given by D SZ . This is the energy difference between EMs = O and EMs = ±S.

QTM = Quantum Tunneling Mechanism of spin relaxtion.

Section 7.3 - 4 There are two ways in which relaxation (randomization of the moment orientation and loss of magnetization) can occur:

1) thermal activation – over the energy barrier 2) quantum tunneling – through the energy barrier

The QTM mechanism results in “steps” in the hysteresis loop.

These steps arise due to demagnetization via a QTM mechanism.

As the applied field H changes, the relative energy levels of the MS energy levels change. Those aligned parallel to the field have different energy from those aligned anti-parallel to the field!

Resonant magnetic tunneling can only occur when the energy levels on either side of the barrier are degenerate (i.e., at specific, periodic values of H).

While ferromagnetic domain is capable of storing a single bit of digital data (1s and 0s), an SMM is potentially capable of storing a quantum bit (qubit) of digital data (1, 0 and a probability distribution of all the possible states in between).

Two weakly coupled SMMs may function as a universal quantum computing gate (a CNOT gate to be accurate).

Section 7.3 - 5