This is the second post in a two-part introduction to quantum spin liquids. Read the first part if you haven’t already:
Today we will explore some characteristics of the RVB state and current research on QSLs.
fractional excitations
Recall our superposition of all possible singlet arrangements. If an experimentalist forces a single spin to orient a certain direction (by applying a field for example), the spin will be pulled out of its quantum singlet. The rest of the spins will arrange in new singlets.
This forms a quasiparticle called a spinon which can travel throughout the material much like a hole can in semiconductor physics.1
Let’s assume the spins in our system have a magnitude of 1/2, which would be true for electrons. In this case, our system would have had 0 net spin to start, and it now has a net spin of 1/2. Thus, our spinon is a 1/2 spin excitation. Since the net spin of the system changed by a non-integer value, a spinon is an example of a fractional excitation.
Fractional excitations are unique because, in most cases, an excitation changes a single spin from -1/2 to 1/2 or vice versa, leading an integer change in overall spin.
disorder at low temperatures
A key characteristic of QSLs is their spin disorder at low temperatures. Spin disorder in and of itself is not a unique property; heat any magnetic material up enough, and thermal excitations will disorder the spins. Usually though, you can cool a sample sufficiently for its spins to reorder in an aligned ground state.
However, in QSLs, the ground state is the RVB state we discussed in the first post. Thus, theoretically, no matter how cool you make the material, the spins exist in a disordered, degenerate state.
in QSLs, L is for liquid??
Let’s understand the liquid in quantum spin liquid by making magnetic analogies to all three familiar phases of matter: solids, liquids, and gases.
“solids”
In magnetic materials, antiferromagnetic or ferromagnetic materials would be analogous to solids. These materials have spins that are strictly aligned and happy to stay in place. This is akin to the restrained motion of molecules in solids.
“gases”
In contrast, paramagnetic materials are analogous to gases, since thermal excitations cause spins to move stochastically, independent from neighboring spins. This is much like the movement of individual ideal gas molecules.
“liquids”
Finally, let’s see how QSLs are analogous to liquids. The RVB state allows for excitations like spinons and visons that travel through the material like ripples in liquids.2 Spins have some freedom, but unlike paramagnetic materials, spins are not completely independent; they are held in a superpositions of singlets. This is analogous to how the molecules of liquids have stronger interactions than those of a gas.
real-life examples
Insofar, we have approached QSLs from a mostly theoretical perspective. However, since Anderson’s proposal, a lot of research has been done to find or create QSLs.
kagome lattices
Recall that a frustrated spin system is a prerequisite for the quantum spin liquid state. One of the most frustrated lattice structures is the kagome lattice, made of corner-adjacent triangles.
herbertsmithite
Fortunately, certain compounds naturally form this crystal structure. Herbertsmithite has become a quintessential example of a Kagome lattice, and its pure form is often used in QSL research.
Work on herbertsmithite has been promising for Anderson’s theories. Norman’s 2016 colloquium paper states:
Of particular note was the report in 2005 by Dan Nocera’s group of the synthesis of herbertsmithite, composed of a lattice of copper ions sitting on a kagome lattice, which indeed does not order down to the lowest measured temperature despite the existence of a large exchange interaction of 17 meV.
This low temperature disorder implies the existence of an RVB state, validating the quantum spin liquid state. More work is being done to better understand spins in herbertsmithite and other prospective QSLs. Additionally, active research focuses on how doping QSLs could lead to new superconducting materials.
conclusion
QSLs RVB state leads to interesting properties like fractional excitations and low temperature spin disorder. Experimental attempts to verify real-life QSLs have been moderately successful, but cutting edge research continues to explore the dynamics and applications of quantum spin liquids.
A “hole” is the absence of an electron. As nearby electrons fill this void, they leave behind a void of their own. Thus, the hole can be said to “move” around.
There are also quasiparticles named visons which I do not understand yet (feel free to leave a comment or link to resources if you know more)