Spin Waves

Magnetism of the kind that sticks fridge magnets to your fridge — we call this permanent magnetism — occurs in nature as a result of an interesting mechanical property of electrons called spin. The spin of an an electron is said to be either up or down. Although it is a quantum mechanical property that does not have an exact classical analogue, we can think of spin a little bit like the angular momentum of a spinning top with electrons with up spin rotating counter-clockwise and electrons with down spin rotating clockwise.

An electron is essentially an extremely small magnet, and the direction of the spin can be thought of as determining whether its “North pole” is pointing up or down.

The electrons inside a magnetic material like iron are arranged in a regular pattern called a “spin lattice”. If we apply an external magnetic field to this lattice, the electron spins align with the magnetic field. If, furthermore, we give them a small amount of energy — which might come, for example, from small thermal fluctuations in the system — the spins will precess around the direction of the applied field just like a gyroscope.

As well as having the capacity to precess about their fixed positions, the electron spins in a magnetic material can interact with one another. There are two important interactions: the so-called magnetic dipole interaction which is analogous to the interaction between two macroscopic bar magnets, and a quantum mechanical effect called the exchange interaction. The exchange interaction does not have a classical analogue: it occurs as a result of the rules that govern the symmetries of overlapping electronic wavefunctions. The dipole interaction is weak but long range while the exchange interaction is strong but very short range.

The existence of the interaction between adjacent spins in a magnetic material gives life to the phenomenon known as the spin wave.

Spin waves are most easily visualised in one dimension. Consider a chain of spins (i.e. little magnets), all precessing about an applied magnetic field and interacting with one another through the dipole and exchange interactions introduced above. Imagine what happens if we “knock” one of the spins: the “knock” moves along the chain of spins just like a wave — a spin wave.

Like other types of waves, spin waves have a certain frequency and wavelength. In the laboratory, we can create spin waves at microwave frequencies (typically a few gigahertz).

Just like conventional electrical signals, spin wave signals can be created in the spin-wave analogue of electrical circuits: pieces of magnetic material addressed using small current-carrying antennae.

 Spin waves, excited by sending a microwave signal to the antenna, propagate in the YIG waveguide. YIG stands for yttrium iron garnet, which is a magnetic insulator. GGG stands for gadolinium gallium garnet, which is a substrate material for YIG. The red arrow shows the direction of a fixed, strong magnetic field, needed to produce a spin wave. The white arrow shows the direction of spin-wave propagation.

The study of spin waves not only gives us insight into the physics of spins, waves and magnetism, but also has the potential to catalyse the development of new technologies such as more efficient computers and whole new platforms for computing.

In particular, unlike the currents of electrons that carry signals in conventional computers, spin waves can travel over long distances inside certain magnetic insulators without generating any heat. This is an extremely attractive attribute in the context of the development of next-generation computing systems.

Apart from microwaves, spin waves also couple with light. Since spin waves can interact with both microwaves and light, they hold promise for converting information or signals between microwaves and light.