Investigation of magnetic structure on (C$_{5}$H$_{12}$N)CuBr$_{3}$ system on the basis of DFT study and orbital interaction*

The (C$_{5}$H$_{12}$N)CuBr$_{3}$ compound crystallizes in the monoclinic group C2/c. Magnetic susceptibility data down to 1.8 K can be well fitted for the antiferromagnetic spin-1/2 chain, giving the intrachain magnetic coupling constant J$_{\mathrm{intra}} \approx $ $-$17 K. At zero field, (pipH)CuBr3 shows 3D order below T$_{\mathrm{N}}$ $=$ 1.68 K. Calculated by the mean-field theory, the interchain coupling constant J$_{\mathrm{inter}} = -$0.91 K is obtained and the ordered magnetic moment is about 0.23 $\mu_{\mathrm{B}}$. However, the interchain interaction should be strong unlike experimental observation. From the analysis of local structure, the J$_{\mathrm{inter}}$ spin dimer show the possibility of good orbital overlap via Cu-O...O-Cu path in which angle for Cu-O...O-Cu is 161$^{\circ}$ indicating strong interchain interaction via Cu-O...O-Cu path. The magnetic structure of (C$_{5}$H$_{12}$N)CuBr$_{3}$ system in terms of orbital interaction could anticipated by two-leg spin ladder which such spin ladders interact ferromagnetically to form ladder. In this study, we evaluated spin exchange interactions of (pipH)CuBr$_{3}$ based on DFT calculations to find the magnetic structure of this system. As a consequence, the J$_{\mathrm{inter}}$ interaction is strong and the magnetic structure of this system, indeed, is described by two-leg spin ladder.