# Realization of a Tomonaga-Luttinger liquid in YbAlO_{3}

18. Februar 2019

In condensed matter physics, among the large number of well-studied theoretical models there are some that have very rare experimental realization. This is valid even for the simplest models like the one-dimensional (1D) antiferromagnetic (AFM) quantum spin ½ chains. This model can be well described by the exotic Tomonaga-Luttinger liquid (TLL) theory and exhibits exceptional properties, such as strong quantum fluctuations and the presence of so-called “spinons”. What are spinons? In conventional 3D magnets, in which the AFM ground state consists of a periodic arrangement of magnetic moments, an elementary excitation can be represented as a wave of small deflections of these moments from their initial position, or as a quasiparticle known as magnon which carries spin momentum *S* = 1. On the other hand, in the 1D case the situation is different: a magnon is “fractionalized” into two fermionic quasiparticles known as *“*spinons”. The process of creation of a spinons pair is schematically illustrated in Fig.1. These spinons can propagate freely (deconfined) along the AFM chain at temperature above the ordering temperature *T*_{N} (Fig.1 b,c) while the presence of an effective internal field due to the intrachain interactions at *T* < *T*_{N} confines the spinons (Fig.1 d) because their propagation will cost energy.

Recently, an international team of scientists from USA, China, Ukraine and Germany (MPI-CPfS Dresden) has demonstrated that, in the rare-earth quantum magnet YbAlO_{3} (with an AFM ordering temperature *T*_{N} = 0.88 K), the TLL is experimentally realized. This was done by a combination of thermodynamic (at MPI-CPfS in Dresden) and spectroscopic (at Oak Ridge National Laboratory) measurements. The low-temperature magnetization measurements revealed a very strong uniaxial anisotropy of the Yb moments, which is induced by a combination of spin-orbit coupling and crystalline electrical field effect. On the other hand, results of inelastic neutron scattering above the ordering temperature show a gapless spinon continuum, dispersive along the direction of the Yb chains, indicating that the collective magnetic behavior is dominated by the highly isotropic Yb-Yb exchange interaction and forms a TLL state. Note that the combination of highly anisotropic magnetic moment of Yb and isotropic Yb-Yb exchange interaction is among the unique properties of YbAlO_{3 }giving a rise to its unusual behavior and rich excitation spectra.

With decreasing temperature, a dipole-diople intrachain interaction confines the spinons and induces a simple long-range AFM ordering of the Yb moments. The application of a magnetic field, at first, creates an exotic longitudinal spin-density-wave phase, and with further increasing, destroys the long-range order at the *quantum critical point (QCP)*. Most remarkably, thermodynamic properties of YbAlO_{3} near the *QCP* follow a universal behavior and the analysis of the scaling behavior and critical exponents indicates that the *QCP* is a free fermion fixed point, consistently with expectation for in the 1D TLL.

Results of presented study demonstrate that *f*-electron-based magnets can provide an experimental platform for realization of different aspects of quantum magnetism, such as spinon confinement-deconfinement transition and a quantum critical TLL behavior. More details can be found in https://doi.org/10.1038/s41467-019-08485-7.

NS / CPfS