The Effect of FM Inter-ladder coupling in spin-1/2 AFM two-Leg Ladders in the presence of a magnetic field: Quantum Monte Carlo Study

We study the effect of inter-ladder ferromagnetic (FM) coupling in spin-1/2 two-leg ladders with antiferromagnetic (AFM) legs and rungs interactions using the stochastic series expansion quantum Monte Carlo. We have compared the results with the experimental measurement on Sr${}_{14-x}$Ca${}_x$Cu${}_{24}$O${}_{41}$ cuprate which is the candidate for spin-1/2 AFM two-leg ladders with FM inter-ladder interaction. A remarkable asymptotic behavior of susceptibility is observed at very low temperature. In the absence of the magnetic field, thermodynamic behavior of an individual spin-1/2 two-leg ladder is similar to coupled one up to $-0.5J_{leg}$ interaction. But, the gaped phase is not clear in the $J_{in}=-0.2J_{leg}$ of FM coupled two-leg ladder even at low magnetic fields, which shows that the inter-ladder FM interaction can induce a new quantum ordered gapless phase at zero temperature.