Magnetism and thermodynamics of spin-1∕2Heisenberg diamond chains in a magnetic field

Abstract

The magnetic and thermodynamic properties of spin-$1∕2$ Heisenberg diamond chains are investigated in three different cases: (a) ${J}_{1}$, ${J}_{2}$, ${J}_{3}>0$ (frustrated), (b) ${J}_{1}$, ${J}_{3}<0$, ${J}_{2}>0$ (frustrated), and (c) ${J}_{1}$, ${J}_{2}>0$, ${J}_{3}<0$ (nonfrustrated), where the bond coupling ${J}_{i}$ $(i=1,2,3)>0$ stands for an antiferromagnetic (AF) interaction, and $<0$ for a ferromagnetic (F) interaction. The density-matrix renormalization-group (DMRG) technique is invoked to study the properties of the system in the ground state, while the transfer-matrix renormalization-group (TMRG) technique is applied to explore the thermodynamic properties. The local magnetic moments, spin-correlation functions, and static structure factors are discussed in the ground state for the three cases. It is shown that the static structure factor $S(q)$ shows peaks at wave vectors $q=a\ensuremath{\pi}∕3$ $(a=0,1,2,3,4,5)$ for different couplings in a zero magnetic field, which, however, in the magnetic fields where the magnetization plateau with $m=1∕6$ pertains, exhibits the peaks only at $q=0$, $2\ensuremath{\pi}∕3$, and $4\ensuremath{\pi}∕3$, which are found to be couplings independent. The DMRG results of the zero-field static structure factor can be nicely fitted by a linear superposition of six modes, where two fitting equations are proposed. It is observed that the six modes are closely related to the low-lying excitations of the system. At finite temperatures, the magnetization, susceptibility, and specific heat show various behaviors for different couplings. The double-peak structures of the susceptibility, and specific heat against temperature are obtained, where the peak positions and heights are found to depend on the competition of the couplings. It is also uncovered that the $XXZ$ anisotropy of F and AF couplings leads the system of case (c) to display quite different behaviors. In addition, the experimental data of the susceptibility, specific heat, and magnetization for the compound ${\mathrm{Cu}}_{3}{(\mathrm{C}{\mathrm{O}}_{3})}_{2}{(\mathrm{O}\mathrm{H})}_{2}$ are fairly compared with our TMRG results.