Quantum phase diagram of a frustrated spin- 12 system on a trellis ladder

We study an isotropic Heisenberg spin-$\frac{1}{2}$ model on a trellis ladder which is composed of two ${J}₁\ensuremath{-}{J}₂$ zigzag ladders interacting through antiferromagnetic rung coupling ${J}₃$. ${J}₁$ and ${J}₂$ are ferromagnetic zigzag spin interaction between two legs and antiferromagnetic interaction along each leg of a zigzag ladder. A quantum phase diagram of this model is constructed using the density matrix renormalization group method and linearized spin-wave analysis. In the small ${J}₂$ limit, a short-range striped collinear phase is found in the presence of ${J}₃$, whereas, in the large ${J}₂/{J}₃$ limit, a noncollinear quasi-long-range phase is found. The system shows a short-range noncollinear state in the large ${J}₃$ limit. The short-range-order phase is the dominant feature of this phase diagram. We also show that the results obtained by DMRG and linearized spin-wave analysis show a similar phase boundary between the collinear striped and noncollinear short-range phases, and the collinear phase region shrinks with increasing ${J}₃$. We apply this model to understand the magnetic properties of ${\mathrm{CaV}}₂{\mathrm{O}}₅$ and also fit the experimental data of susceptibility and magnetization. We note that ${J}₃$ is a dominant interaction in this material, whereas ${J}₁$ and ${J}₂$ are approximately half of ${J}₃$. The variation of magnetic specific heat capacity as a function of temperature for various external magnetic fields is also predicted.