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Ferrimagnetism in delta chain with anisotropic ferromagnetic and antiferromagnetic interactions

We consider analytically and numerically an anisotropic spin-$\frac{1}{2}$ delta-chain (sawtooth chain) in which exchange interactions between apical and basal spins are ferromagnetic and those between basal spins are antiferromagnetic. In the limit of strong anisotropy of exchange interactions this model can be considered as the Ising delta chain with macroscopic degenerate ground state perturbed by transverse quantum fluctuations. These perturbations lift the ground state degeneracy and the model reduces to the basal XXZ spin chain in the magnetic field induced by static apical spins. We show that the ground state of such model is ferrimagnetic. The excitations of the model are formed by ferrimagnetic domains separated by domain walls with a finite energy. At low temperatures the system is effectively divided into two independent subsystems, the apical subsystem described by the Ising spin-$\frac{1}{2}$ chain and the basal subsystem described by the XXZ chain with infinite $zz$ interactions.