Quantum phase transition and thermodynamic properties of a fourfold magnetic periodic system

•The antiferromagnetic interaction-magnetic field phase diagrams are constructed.•The magnetization per site makes different contribution to the 1/2 plateau.•The spectral functions for different magnetic interactions are studied.•We investigate the gapless or gapped low-lying excitations at low temperatures.

Based on the experimental synthesis of organic compound verdazyl radical ββ-3-(2,6-dichlorophenyl)-1,5-diphenylverdazyl, consisting of four antiferromagnetic couplings, we study the magnetic properties and thermodynamic behaviors for different antiferromagnetic interactions using Green’s function theory. Under different fields, there are five regimes containing two gapless phases and three magnetization plateaus (M=0, 1/2 and saturated magnetization) distinguished by four critical lines, which are evidenced by the two-site entanglement entropy and closely related to the energy spectra. In addition, we calculate the susceptibility and specific heat, to demonstrate the low-lying excitations at low temperatures. It will provide guidance for us to synthesize varieties of unconventional magnetic materials, and stimulate future studies on quantum spin systems.