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., $\left {{\hslash }\omega }_{{3,}k}\left(H_{\rm {CB}} \right) \right]_{{\min}}{=0}$, $\left \hslash \omega _{{2,}k}\left(H_{\rm{CE}} \right) \right]_{{\max}}{=0}$ and $\left {{\hslash }\omega }_{{2,k}}\left(H_{\rm{CS}} \right) \right]_{{\min}}{=0}$, 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.