Theoretical and experimental studies of melting of the 1/3 magnetization plateau in a frustrated \(S=1/2\) antiferromagnetic trimerized quantum Heisenberg spin chain compound \(\hbox {Na}_2\hbox {Cu}_3\hbox {Ge}_4\hbox {O}_{12}\)

Abstract

We report the magnetization process of \(S=1/2\) Heisenberg antiferromagnetic \(J_1{-}J_1{-}J_2\) trimerized spin chain system (with frustration due to the next-nearest-neighbor interaction \(J_3\) within the trimer) under applied magnetic field by means of density-matrix renormalization group method. Here, \(J'\)s are the antiferromagnetic exchange interaction constants. Specifically, we explore the phenomenon of 1/3 magnetization plateau for the exchange coupling ratios \( \alpha = 0.18, \beta =0.18 \), and \(J_1=235\) K, where \(\alpha =J_2/J_1\), and \(\beta =J_3/J_1\) as found for the model compound \(\hbox {Na}_2\hbox {Cu}_3\hbox {Ge}_4\hbox {O}_{12}\). It is found that a wide 1/3 quantum magnetization plateau state (observed in ground state magnetization) gradually disappears with increasing temperature beyond a crossover temperature \(T_{co}\) due to thermal fluctuations. Based on numerical data, the width w(T) of the magnetization plateau is found to follow an exponential behave as \(\sim e^{-B/\sqrt{T_{co}-T}}\), where B is a constant and \(T_{co}\) is estimated to be \( \approx 60\) K. The occurrence of the 1/3 plateau is also seen through the field-induced energy gap in the energy-level spectrum of the system. The stability of the magnetization plateau state against the perturbation depends upon the size of the energy gap. Further, calculated isothermal magnetization results are compared with experimental high field magnetization data for the quasi-one-dimensional (1D) spin \(S=1/2\) trimer chain compound \(\hbox {Na}_2\hbox {Cu}_3\hbox {Ge}_4\hbox {O}_{12}\).