  The magnetic excitation spectrum and Hamiltonian of the quantum magnet
BaCuTe2O6 is studied by inelastic neutron scattering (INS) and density
functional theory (DFT). INS on powder and single crystal samples reveals
overlapping spinon continuua - the spectrum of an antiferromagnetic spin-1/2
spin chain - due to equivalent chains running along the a, b, and c directions.
Long-range magnetic order onsets below TN = 6.3 K due to interchain
interactions, and is accompanied by the emergence of sharp spin-wave
excitations which replace the continuua at low energies. The spin-wave spectrum
is highly complex and was successfully modelled achieving excellent agreement
with the data. The extracted interactions reveal an intrachain interaction, J3
= 2.9 meV, while the antiferromagnetic hyperkagome interaction J2, is the
sub-leading interaction responsible for coupling the chains together in a
frustrated way. DFT calculations reveal a similar picture for BaCuTe2O6 of
dominant J3 and sub-leading J2 antiferromagnetic interactions and also indicate
a high sensitivity of the interactions to small changes of structure which
could explain the very different Hamiltonians observed in the sister compounds
SrCuTe2O6 and PbCuTe2O6.
