Spin liquid
Encyclopedia
In solid-state physics
, spin liquid (quantum spin liquid, QSL) denotes a state of matter
, where local permanent magnetic moments
are present in the material, but do not show any sign of ordering down to the lowest temperatures despite comparable strong antiferromagnetic
interactions.
Even though many theories study spin liquids, no definite spin-liquid material has been found yet, although there are a few possible spin liquid candidates under investigation.
if there exist competing exchange interactions that can not all be satisfied at the same time leading to a large degeneracy of the system's ground state. A triangle of Ising spins (meaning the only possible orientations of the spins are "up" and "down"), which interact antiferromagnetically, is a simple example for frustration. In the ground state, two of the spins can be antiparallel but the third one can not. This leads to an increase of possible orientations (six in this case) of the spins in the ground state, enhancing fluctuations and thus suppressing magnetic ordering.
Some frustrated materials with different lattice structures and their Curie-Weiss temperature are listed in the table. All of them are proposed spin liquid candidates.
electron spins form a spin 0 singlet due to the antiferromagnetic interaction. If every spin
in the system is bound like this, the state of the system as a whole has spin 0 too and is
non-magnetic. The two spins forming the bond are maximally entangled, while not being
entangled with the other spins.
If all spins are distributed to certain localized static bonds, this is called a valence bond solid (VBS).
There are two things that still distinguish a VBS from a spin liquid: First, by ordering the
bonds in a certain way, the lattice symmetry is usually broken, which is not the case for a
spin liquid. Second, this ground state lacks long-range entanglement. To achieve this,
quantum mechanical fluctuations of the valence bonds must be allowed, leading to a ground
state consisting of a superposition of many different partitionings of spins into valence
bonds. If the partitionings are equally distributed, there is no preference for any specific
partitioning ("valence bond liquid"). This kind of ground state wavefunction
was proposed by P. W. Anderson in 1973 as the ground state of spin liquids and is called a
resonating valence bond (RVB) state. These states are of great theoretical interest as
they are proposed to play a key role in high-temperature superconductor physics.
may vary in different materials. Ground states with large contributions of long range
valence bonds have more low-energy spin excitations, as those valence bonds are easier to
break up. On breaking, they form two free spins. Other excitations rearrange the valence bonds, leading to low-energy excitations even for short-range bonds.
Very special about spin liquids is, that they support exotic excitations, meaning
excitations with fractional quantum numbers. A prominent example is the excitation of
spinon
s which are neutral in charge and carry spin
.
In spin liquids, a spinon is created if one spin is not paired in a valence bond. It can move by rearranging nearby valence bonds at low energy cost.
, which is defined as
where
is the Curie-Weiss temperature and 
is the temperature below magnetic order begins to develop.
One of the most direct evidence for absence of magnetic ordering give NMR
or µSR experiments. If there is a local magnetic field present, the nuclear or muon spin would be affected which can be measured. 1H-NMR
measurements on κ-(BEDT-TTF)2Cu2(CN)3 have shown no sign of magnetic ordering down to 32 mK, which is four orders of magnitude smaller than the coupling constant
J≈250 K between neighboring spins in this compound.
Further investigations include:
Solid-state physics
Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the large-scale properties of solid materials result from...
, spin liquid (quantum spin liquid, QSL) denotes a state of matter
State of matter
States of matter are the distinct forms that different phases of matter take on. Solid, liquid and gas are the most common states of matter on Earth. However, much of the baryonic matter of the universe is in the form of hot plasma, both as rarefied interstellar medium and as dense...
, where local permanent magnetic moments
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
are present in the material, but do not show any sign of ordering down to the lowest temperatures despite comparable strong antiferromagnetic
Antiferromagnetism
In materials that exhibit antiferromagnetism, the magnetic moments of atoms or molecules, usuallyrelated to the spins of electrons, align in a regular pattern with neighboring spins pointing in opposite directions. This is, like ferromagnetism and ferrimagnetism, a manifestation of ordered magnetism...
interactions.
Even though many theories study spin liquids, no definite spin-liquid material has been found yet, although there are a few possible spin liquid candidates under investigation.
Frustrated magnetic moments
Localized spins are frustratedGeometrical frustration
In condensed matter physics, the term geometrical frustration means a phenomenon in which the geometrical properties of the crystal lattice or the presence of conflicting atomic forces forbid simultaneous minimization of the interaction energies acting at a given site.This may lead to highly...
if there exist competing exchange interactions that can not all be satisfied at the same time leading to a large degeneracy of the system's ground state. A triangle of Ising spins (meaning the only possible orientations of the spins are "up" and "down"), which interact antiferromagnetically, is a simple example for frustration. In the ground state, two of the spins can be antiparallel but the third one can not. This leads to an increase of possible orientations (six in this case) of the spins in the ground state, enhancing fluctuations and thus suppressing magnetic ordering.
Some frustrated materials with different lattice structures and their Curie-Weiss temperature are listed in the table. All of them are proposed spin liquid candidates.
| Material | Lattice |  |
|---|---|---|
| κ-(BEDT-TTF)2Cu2(CN)3 | anisotropic triangular | -375 |
| ZnCu3(OH)6Cl2 (herbertsmithite) | Kagomé Kagome lattice A kagome lattice is an arrangement of laths composed of interlaced triangles such that each point where two laths cross has four neighboring points... |
-241 |
| BaCu3V2O8(OH)2 (vesignieite) | Kagomé Kagome lattice A kagome lattice is an arrangement of laths composed of interlaced triangles such that each point where two laths cross has four neighboring points... |
|
| Na4Ir3O8 | Hyperkagomé | -650 |
| Cu-(1,3-benzenedicarboxylate) | Kagomé Kagome lattice A kagome lattice is an arrangement of laths composed of interlaced triangles such that each point where two laths cross has four neighboring points... |
-33 |
| Rb2Cu3SnF12 | Kagomé Kagome lattice A kagome lattice is an arrangement of laths composed of interlaced triangles such that each point where two laths cross has four neighboring points... |
Resonating valence bonds (RVB)
To build a ground state without magnetic moment, valence bond states can be used, where twoelectron spins form a spin 0 singlet due to the antiferromagnetic interaction. If every spin
in the system is bound like this, the state of the system as a whole has spin 0 too and is
non-magnetic. The two spins forming the bond are maximally entangled, while not being
entangled with the other spins.
If all spins are distributed to certain localized static bonds, this is called a valence bond solid (VBS).
There are two things that still distinguish a VBS from a spin liquid: First, by ordering the
bonds in a certain way, the lattice symmetry is usually broken, which is not the case for a
spin liquid. Second, this ground state lacks long-range entanglement. To achieve this,
quantum mechanical fluctuations of the valence bonds must be allowed, leading to a ground
state consisting of a superposition of many different partitionings of spins into valence
bonds. If the partitionings are equally distributed, there is no preference for any specific
partitioning ("valence bond liquid"). This kind of ground state wavefunction
was proposed by P. W. Anderson in 1973 as the ground state of spin liquids and is called a
resonating valence bond (RVB) state. These states are of great theoretical interest as
they are proposed to play a key role in high-temperature superconductor physics.
Excitations
The valence bonds do not have to be formed by nearest neighbors only and their distributionsmay vary in different materials. Ground states with large contributions of long range
valence bonds have more low-energy spin excitations, as those valence bonds are easier to
break up. On breaking, they form two free spins. Other excitations rearrange the valence bonds, leading to low-energy excitations even for short-range bonds.
Very special about spin liquids is, that they support exotic excitations, meaning
excitations with fractional quantum numbers. A prominent example is the excitation of
spinon
Spinon
Spinons are one of two quasiparticles, along with holons, that electrons in solids are able to split into during the process of spin–charge separation, when extremely tightly confined at temperatures close to absolute zero....
s which are neutral in charge and carry spin
.In spin liquids, a spinon is created if one spin is not paired in a valence bond. It can move by rearranging nearby valence bonds at low energy cost.
Identification in Experiments
Since there is no single experimental feature that identifies a material as a spin liquid, several experiments have to be conducted to gain information on different properties which characterize a spin liquid. An indication is given by a large value of the frustration parameter, which is defined aswhere
is the Curie-Weiss temperature and is the temperature below magnetic order begins to develop.One of the most direct evidence for absence of magnetic ordering give NMR
NMR
NMR may refer to:Applications of Nuclear Magnetic Resonance:* Nuclear magnetic resonance* NMR spectroscopy* Solid-state nuclear magnetic resonance* Protein nuclear magnetic resonance spectroscopy* Proton NMR* Carbon-13 NMR...
or µSR experiments. If there is a local magnetic field present, the nuclear or muon spin would be affected which can be measured. 1H-NMR
NMR
NMR may refer to:Applications of Nuclear Magnetic Resonance:* Nuclear magnetic resonance* NMR spectroscopy* Solid-state nuclear magnetic resonance* Protein nuclear magnetic resonance spectroscopy* Proton NMR* Carbon-13 NMR...
measurements on κ-(BEDT-TTF)2Cu2(CN)3 have shown no sign of magnetic ordering down to 32 mK, which is four orders of magnitude smaller than the coupling constant
Heisenberg model
The Heisenberg model can refer to two models in statistical mechanics:*Heisenberg model , a classical nearest neighbour spin model*Heisenberg model , a model where the spins are treated quantum mechanically using Pauli matrices....
J≈250 K between neighboring spins in this compound.
Further investigations include:
- Specific heat measurements give information about the low-energy density of states, which can be compared to theoretical models.
- Thermal transport measurements can determine if excitations are localized or itinerant.
- Neutron scattering gives information about the nature of excitations and correlations (e.g. spinonSpinonSpinons are one of two quasiparticles, along with holons, that electrons in solids are able to split into during the process of spin–charge separation, when extremely tightly confined at temperatures close to absolute zero....
s). - Reflectance measurements can uncover spinonSpinonSpinons are one of two quasiparticles, along with holons, that electrons in solids are able to split into during the process of spin–charge separation, when extremely tightly confined at temperatures close to absolute zero....
s, which couple via emergent gauge fields to the electromagnetic field, giving rise to a power-law optical conductivity.