Magnetization and magnetic phase diagrams of a spin-1/2 ferrimagnetic diamond chain at low temperature

We used the Jordan-Wigner transform and the invariant eigenoperator method to study the magnetic phase diagram and the magnetization curve of the spin-1/2 alternating ferrimagnetic diamond chain in an external magnetic field at finite temperature. The magnetization versus external magnetic field curve exhibits a 1/3 magnetization plateau at absolute zero and finite temperatures, and the width of the 1/3 magnetization plateau was modulated by tuning the temperature and the exchange interactions. Three critical magnetic field intensities H_\rm CB, H_\rm CE and H_\rm CS were obtained, in which the H_\rm CB and H_\rm CE correspond to the appearance and disappearance of the 1/3 magnetization plateau, respectively, and the higher H_\rm CS correspond to the appearance of fully polarized magnetization plateau of the system. The energies of elementary excitation \hslash \omega _\sigma,k\,\,(\sigma =1, 2, 3) present the extrema of zero at the three critical magnetic fields at 0 K, i.e., \left \hslash \omega _3,k\left(H_\rm CB \right) \right_\min=0, \left \hslash \omega _2,k\left(H_\rmCE \right) \right_\max=0 and \left \hslash \omega _2,k\left(H_\rmCS \right) \right_\min=0, and the magnetic phase diagram of magnetic field versus different exchange interactions at 0 K was established by the above relationships. According to the relationships between the system's magnetization curve at finite temperatures and the critical magnetic field intensities, the magnetic field-temperature phase diagram was drawn. It was observed that if the magnetic phase diagram shows a three-phase critical point, which is intersected by the ferrimagnetic phase, the ferrimagnetic plateau phase, and the Luttinger liquid phase, the disappearance of the 1/3 magnetization plateau would inevitably occur. However, the 1/3 magnetization plateau would not disappear without the three-phase critical point. The appearance of the 1/3 magnetization plateau in the low temperature region is the macroscopic manifestations of quantum effect.