Hamiltonian of the S = 1/2 dimerized antiferromagnetic-ferromagnetic quantum spin chain $BaCu_2V_2O_8$

The novel quantum magnet ${\mathrm{BaCu}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$ was recently discovered to be a rare physical realization of a one-dimensional antiferromagnetic-ferromagnetic dimerized chain which displays strongly correlated phenomena at elevated temperatures [E. S. Klyushina et al., Phys. Rev. B 93, 241109(R) (2016)]. This paper presents an extended study of the Hamiltonian of ${\mathrm{BaCu}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$ at base temperature. Static susceptibility and inelastic neutron scattering data are compared to several theoretical models. An analytical relation for the dynamic structure factor of the complex unit cell of ${\mathrm{BaCu}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$ is derived and used to identify the intrachain exchange paths. Further analysis using the first moment of the dynamic structure factor was employed to determine the exchange path responsible for the intradimer interaction. This analysis reveals that the dimer chain is formed by a dominant antiferromagnetic exchange interaction ${J}_{\mathrm{intra}}=40.92\phantom{\rule{0.28em}{0ex}}\mathrm{meV}$ which is realized via the Cu-O-V(II)-O-Cu superexchange path and a weak ferromagnetic coupling ${J}_{\mathrm{inter}}=\ensuremath{-}11.97$ meV which arises within the copper-oxygen double plaquettes.