Unconventional order in a low-dimensional magnet
The analogy between the behaviour of different quantum particles which have the same quantum nature is one of the most fascinating aspects of science. A simple but prominent example is the analogy between the behaviour of electrons (fermions) in a one-dimensional metal and spinons (fermions) in a one-dimensional quantum magnet. But, what are spinons?
It is generally known that magnetic fluctuations in conventional magnets can be seen as a wave of deflection of the magnetic moments out of the equilibrium. These waves are described by quantum mechanics as quasi-particles, known as magnons, which carry integer spin momentum S = 1 and therefore are bosons. However, in one-dimensional systems magnons decay (fractionalize) into two S = 1/2 spinon quasiparticles which are fermions. Their low-energy physics is described by the Tomonaga-Luttinger liquid of spinless fermions, similar to the conduction electrons in one-dimensional metals. Such Tomonaga-Luttinger liquid behavior has been observed in the quantum magnet YbAlO₃ (see press release: Realization of a Tomonaga-Luttinger liquid in YbAlO₃).
Recently, an international team of scientists from Germany (MPI CPfS Dresden), USA, China, Russia and Ukraine has studied YbAlO₃ by means of magnetization and neutron diffraction experiments supported by numerical calculations and has shown that the weak interchain coupling produces Umklapp scattering between the left- and right-moving spinons. Under finite magnetic fields Hz this stabilizes an „unconventional“ incommensurate spin-density wave order at the q = 2kF with kF being the Fermi wavevector. This mechanism is similar to Fermi surface nesting observed in metals. The Umklapp processes open a route to multiple coherent scattering of fermions, which results in the formation of satellites at integer multiples of the incommensurate fundamental wavevector Q = nq which were indeed measured by elastic neutron scattering. These results provide surprising and profound insight into band-structure control for emergent fermions in quantum materials and uncover a process of multiple fermion scattering in one-dimensional systems.