Looking for ghost particles in a frustrated world

In some of the many types of objects and events involving electrons, it is helpful to think that these particles are made up of three smaller particles, called spinons, holons and orbitons. Physicists call these supposedly imaginary particles quasiparticles. By assuming that they exist, we get to simplify our calculations of the electrons’ behaviour in these environments. Another example of a quasiparticle is the phonon – carriers of sound energy in solid materials.

One such object, and en exotic one at that, is a spin liquid. These are actually solid materials that are magnets, but are incapable of aligning the spins of their constituent electrons in one consistent way. In conventional ferromagnets, the electrons’ spins are aligned all in the same direction in the presence of a magnetic field. In antiferromagnets, the spins are aligned in an alternating pattern. But in spin liquids, in the presence of a magnetic field, the alignment of electron spins constantly changes in a dynamic pattern. Such materials are said to be frustrated – in that even when they have a reason to be aligned, some other forces intervene to keep them changing.

Think of ripples in a closed tank of water bouncing between the walls: the height of the waves would be analogous to the extent to which the electrons’ spins are aligned. See this short 2017 video by the CENN Nanocenter, Slovenia, for a visual description.

When studying spin liquids, scientists have found that it is useful to assume that each electron is made of a spinon and a holon. The spinon carries the electron’s spin and the holon carries the charge. (The orbiton is there but not involved.) Physicists have elucidated the need for such quasiparticles through experiments in which electrons were subjected to extreme physical conditions. In 2009, researchers set up an experiment in which electrons would jump from the surface of a metal to a very narrow wire, in a chamber held only a few fractions above absolute zero. When they jumped, the particles suddenly found themselves with much less room to move around, especially to not get too close to the other electrons (since like charges repel). As a result, the electrons became more distended, in a manner of speaking, as their spinons and holons moved apart to adapt to their surroundings. Such spin-charge separation is rare but has been documented. (See also a similar results reported in 2006.)

Now, in a new study (preprint here), physicists have reported yet more evidence, of a different kind, that the spinon-holon model is both legitimate and useful.

Physicists from Princeton University, New Jersey, created a spin liquid in a crystal of ruthenium chloride. This is not simple: the crystal, first made ultra-pure, had to be maintained at 0.5 K (-272.65º C) inside a magnetic field of 7.3-11 tesla (at least 1.2-million-times as strong as Earth’s magnetic field) – the environment in which a stable spin liquid arises in this material. Next, they applied a small amount of heat along “one edge” of the crystal, and began recording its thermal conductivity – its ability to conduct heat.

When a magnetic field is applied to certain materials in one direction, a temperature gradient, i.e. heat flow, emerges in the perpendicular direction. This is called the thermal Hall effect, and the material’s ability to conduct this heat is its thermal Hall conductivity (symbol κ, lowercase kappa).

According to a previously published theory, the presence of spinons in the material should show up as an oscillating pattern on a graph showing κ versus the magnetic field.

Source: https://arxiv.org/abs/2102.11410

This pattern is an analogue of the Shubnikov-de Haas effect: the electrons of a metal, a semimetal or certain semiconductors oscillate if the material is at a very low temperature and in the presence of an intense magnetic field. (However, the mechanism of action between these materials and spin liquids is different.)

The physicists observed that in the ruthenium chloride crystal, the value of κ oscillated along one direction as long as the magnetic field stayed between 7.3 and 11 tesla, confirming the presence of spinons and their relation to the spin liquid state. They also observed the period of oscillation – the time taken to complete one oscillation – varied in proportion to the inverse of the applied magnetic field. That is, if the magnetic field was weakened by some amount, the period would increase by a proportionate amount. This was an anomalous pattern; the researchers called it a “paradox” in their paper.

Does this mean spinons are real?

There’s a two-part answer to this question, and neither arises from the new paper but from what we already know about quasiparticles, and particles in general. But in the end, yes, they could be real.

The first part is that instead of pondering the existence of quasiparticles, it may be more useful for us to discard the importance we accord to fundamental particles. We were taught in school that fundamental particles are indivisible. But what we know to be fundamental depends on the energy scale at which we probe these particles. Consider a closed tank of water that you keep heating. First, the liquid will vaporise, and at some point the compounds in the vapour will break apart. Next, the atoms themselves will disintegrate into their constituent particles. If you kept heating the tank (while preserving its structural integrity) for a long time, at some point, with sophisticated instruments, you may be able to observe the protons and neutrons come apart into quarks and gluons.

For many decades, we thought protons and neutrons were fundamental particles – until we developed methods to observe their behaviour at higher and higher energies. And at one point, using ultra-sophisticated machines like the Large Hadron Collider, we discovered the state of matter called a quark-gluon plasma. As physicist Vijay Shenoy of the Indian Institute of Science, Bengaluru, told me in 2017:

Something may look fundamental to us at scales of energies that are accessible to us – but if we probe at higher energy scales, we may see that it is also made up of other even more fundamental things (neutrons/protons are really quarks held together by gluons). We will then say that the original ‘fundamental particle’ is a quasiparticle excitation of the system of ‘even more fundamental things’! You could actually ask where this will end, at what energy scales… We really do not know the answer to this question. This is why the concept of a ‘fundamental particle’ is not a very useful concept in physics.

Second: Physicists studying particles use quantum field theory (QFT) to make sense of the particles’ properties and behaviour. And in QFT, what we know to be ‘particles’ are really excitations – clumps of energy – of an underlying energy field. For example, electrons are excitations of an electric field; photons are excitations of an electromagnetic field; the hypothetical gravitons are excitations of a gravity field; and so on. In Shenoy’s words (emphasis in the original):

An excitation is called a particle if, for a given momentum of the excitation, there is a well-defined energy. Quite remarkably, this definition of a particle embodies what we conventionally think of as a particle: small hard things that move about. … A ‘quasiparticle’ excitation is one that is very nearly a particle-like excitation: for the given momentum, it is a small spread of energy about some average value. The manifestation is such that, for practical purposes, if you watch this excitation over longer durations, it will behave like a particle in an experiment.

Taking both parts together, it seems that instead of asking which parts are ‘fundamental’ and which are ‘imaginary’, it has been more fruitful for physicists to focus on the energy fields that give rise to all excitations in the first place.