Observation of confinment in condensed matter systems

It is well known that baryons are made of quarks. However, these quarks can not be directly observed due to a phenomenon called 'aymptotic freedom' or say 'confinement', which arises becasuse of increasing force strength with separation. It is interesting that, such confinement is not exclusive to high energy physics. It was recently observed occuring to condensed matter systems. This gives another example on how concepts are shared between various fields in physics.

a, The region between two spinons (domain walls) on a chain consists of reversed spins (coloured in red); if this chain is coupled antiferromagnetically to another chain, as in a spin ladder, these reversed spins cost energy owing to their parallel alignment with the spins on the neighbouring chain. This energy cost, which is proportional to the separation of the spinons, acts to confine the spinons. b,c, The structure of CaCu₂O₃ for the a–b plane (b) and the a–c plane (c). CaCu₂O₃ has orthorhombic symmetry with space group Pmmn and lattice parameters a=9.949 Å, b=4.078 Å and c=3.460 Å at T=10 K. The magnetic Cu²⁺ ions have spin=1/2 and are represented by the red spheres; they are coupled to each other by superexchange interactions through the O²⁻ ions (blue spheres) and the Cu–O bonds are represented by the solid black lines; the Ca²⁺ ions are not shown. The lattice parameters are shown in grey as well as the rung distance d_rung, which is approximately one third of the a lattice parameter. The structure consists of copper oxide layers stacked along the c direction, the ladders lie within this plane running parallel to b and neighbouring ladders are shifted by half a unit cell in a. The dotted black lines indicate the separate ladder units and the inter- and intraladder exchange interactions are labelled. The coupling along the legs, J_leg, occurs through superexchange interactions mediated by oxygen; the Cu–O–Cu bond angle is 180^°, giving rise to strong antiferromagnetic coupling (according to the Goodenough–Kanamori–Anderson rules). In contrast, the Cu–O–Cu bond along the rungs is 123^° and therefore J_rung is expected to be substantially weaker although still antiferromagnetic. In addition, a weak antiferromagnetic interaction, J_diag, is predicted between opposite copper ions within each plaquette of the ladder. The ladders are coupled together by a number of weaker interactions. Within the a–b plane, Cu²⁺ ions on neighbouring ladders are connected through Cu–O–Cu bonds that are 90^°, giving rise to a weak ferromagnetic J_inter. Note that J_inter is frustrated and competes with the much stronger J_leg; thus, its energy cancels in the Hamiltonian to first order. Weak interladder couplings J_c1 and J_c2 are also expected between ladders in the c direction. Finally, in common with other planar copper oxide materials, CaCu₂O₃ is expected to have a four-spin cyclic exchange interaction, J_cyclic, coupling the four copper ions that form each plaquette. Quantum chemistry calculations give the following exchange constants for CaCu₂O₃: J_leg=−147 to −134 meV; J_rung=−15 to −11.3 meV; J_cyclic=4 meV; J_inter<24 meV; J_diag=−0.2 meV; J_c1=0.1 meV; J_c2=0.8 meV (refs 19, 20). Susceptibility data fitted to a spin-1/2 Heisenberg chain model without other interactions provide good agreement with the data and suggest that J_leg is indeed the dominant interaction and has a value of −168 meV (ref. 22).

Nature Physics 6, 50 - 55 (2009)