Weak three-dimensional coupling of Heisenberg quantum spin chains in SrCuTe${}_2$O${}_6$

The magnetic Hamiltonian of the Heisenberg quantum antiferromagnet SrCuTe${}_2$O${}_6$ is studied by inelastic neutron scattering technique on powder and single crystalline samples above and below the magnetic transition temperatures at 8 K and 2 K. The high temperature spectra reveal a characteristic diffuse scattering corresponding to a multi-spinon continuum confirming the dominant quantum spin-chain behavior due to the third neighbour interaction J${}_{intra}$ = 4.22 meV (49 K). The low temperature spectra exhibits sharper excitations at energies below 1.25 meV which can be explained by considering a combination of weak antiferromagnetic first nearest neighbour interchain coupling J${}_1$ = 0.17 meV (1.9 K) and even weaker ferromagnetic second nearest neighbour J${}_2$ = -0.037 meV (-0.4 K) or a weak ferromagnetic J${}_2$ = -0.11 meV (-1.3 K) and antiferromagnetic J${}_6$ = 0.16 meV (1.85 K) giving rise to the long-range magnetic order and spin-wave excitations at low energies. These results suggest that SrCuTe${}_2$O${}_6$ is a highly one-dimensional Heisenberg system with three mutually perpendicular spin-chains coupled by a weak ferromagnetic J${}_2$ in addition to the antiferromagnetic J${}_1$ or J${}_6$ presenting a contrasting scenario from the highly frustrated hyper-hyperkagome lattice (equally strong antiferromagnetic J${}_1$ and J${}_2$) found in the iso-structural PbCuTe${}_2$O${}_6$.