Quantum criticality and universal scaling of a quantum antiferromagnet

Abstract

Quantum effects dominate the behaviour of many diverse materials. Of particular current interest are those systems in the vicinity of a quantum critical point (QCP). Their physical properties are predicted to reflect those of the nearby QCP with universal features independent of the microscopic details. The prototypical QCP is the Luttinger liquid (LL) which is of relevance to many quasione-dimensional materials. The magnetic material KCuF 3 realizes an array of weakly-coupled spin chains (or LLs) and thus lies close to but not exactly at the Luttinger liquid quantum critical point. By using inelastic neutron scattering we have collected a complete data set of the magnetic correlations of KCuF 3 as a function of momentum, energy, and temperature. The LL description is found to be valid over an extensive range of these parameters, and departures from this behaviour at high and low energies and temperatures have been identified and explained.The concept of a quantum critical point 1,2 -a zero temperature phase transition between quantum ground states -provides an attractive approach for describing regions dominated by quantum mechanics in condensed matter. In its vicinity universal behaviors are predicted that are independent of the microscopic details of the system. An example of this is universal energy/temperature (E/T) scaling of the collective response of the system -a phenomenon that has received heightened attention due to its observation in both cuprate high-temperature superconductors 3,4,5 and unconventional metals 6,7,8 . By exploiting the powerful mathematics of scaling, the aim is to set up systematic expansions of the physical properties about these special points thus explaining the quantum-dominated behaviour found in a diverse range of systems. In quasi-onedimensional quantum magnets experimental and theoretical techniques 9 are now sufficiently advanced to study these ideas and methods in depth. Here we consider the generic problem of an array of one-dimensional systems weakly coupled together into three dimensions.Quantum critical states in one-dimension (1D) are thought to apply to systems as diverse as carbon nanotubes, stripes in cuprate high-temperature superconductors, and spin chains 10,11 . The prototypical example is the spin-1/2 (S=1/2) Heisenberg antiferromagnetic chain (HAFC) which maps onto the Luttinger liquid QCP. Here the magnetic ions possess spin angular momentum of 1/2, and interact with their nearest neighbours via antiferromagnetic Heisenberg exchange couplings in only one crystallographic direction. This system fails to develop long-range Néel ordering (where + Present address -Clarendon

Kitaev's exact solution approximated

“…At higher energies the spectra more closely resemble that predicted for the Kitaev spin liquid. This partitioning of energy scales is very similar to that found in magnetically ordered quasi-1D spin chain systems like KCuF 3 , where the high energy behavior reflects that of the free fractionalized spin-1/2 particles of the spin liquid state inherent to 1D, but at low energies there is a crossover to spectra that reflect the ordered state 12 .…”

Lattice and magnetic instabilities in Cu3Bi(SeO3)2OGnezdilov1, Pashkevich2, Lemmens3 et al. 2017Phys. Rev. B235190View full textAdd to dashboardCite

“…The origin of the magnetic signal is discussed from the point of view of Fano resonance and scattering on longitudinalmagnons. 11,12,13 The symmetry analysis supports both mechanisms. In addition, the anomalies observed in the magnetic specific heat C(T) and the permittivity ε(T) confirm our conclusions.…”

Longitudinal magnetic dynamics and dimensional crossover in the quasi-one-dimensional spin-12Heisenberg antiferromagnetKCuF3Lake1, Tennant2, Nagler3 2005Phys. Rev. B5611600View full textAdd to dashboardCite

“…We must however take into account that the NSF data is less reliable than the SF data, due to the phonon contamination and the greater uncertainties in the background subtraction and it is probably not possible to determine from the data whether or not a transverse continuum is present. The continuum in the low temperature antiferromagnetically ordered phase of KCuF 3 has been previously observed [5,10] and an estimate of its lower edge, given by the onset of the energy/temperature scaling predicted for the magnetic correlations of an ideal ID spin-1/2, Heisenberg antiferromagnet [32], was found to be 26 meV [10]. There are similarities between the low temperature phase of KCuF 3 and the spin-Peierls phase in CuGeO 3 where a gapped dimer mode is observed, separated by a further gap from a continuum [33].…”

“…Using unpolarized neutron scattering the dynamical response for all energy, wavevector and temperature scales has been sampled [10]. A damped mode attributed to the longitudinal mode was discovered in the 3D magnetically ordered phase with a wavevector and frequency dependence closely following predictions [11].…”