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The European Physical Journal B

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 $$\hbox {Na}_2\hbox {Cu}_3\hbox {Ge}_4\hbox {O}_{12}$$

Sachin Kumar, Anup Kumar Bera, Amit Kumar, Y. Skourski, Seikh Mohammad Yusuf

Published Mar 1, 2025• 1 citation
Publisher

Abstract

Abstract We report the magnetization process of $$S=1/2$$ S = 1 / 2 Heisenberg antiferromagnetic $$J_1{-}J_1{-}J_2$$ J 1 - J 1 - J 2 trimerized spin chain system (with frustration due to the next-nearest-neighbor interaction $$J_3$$ J 3 within the trimer) under applied magnetic field by means of density-matrix renormalization group method. Here, $$J'$$ J ′ s are the antiferromagnetic exchange interaction constants. Specifically, we explore the phenomenon of 1/3 magnetization plateau for the exchange coupling ratios $$ \alpha = 0.18, \beta =0.18 $$ α = 0.18 , β = 0.18 , and $$J_1=235$$ J 1 = 235 K, where $$\alpha =J_2/J_1$$ α = J 2 / J 1 , and $$\beta =J_3/J_1$$ β = J 3 / J 1 as found for the model compound $$\hbox {Na}_2\hbox {Cu}_3\hbox {Ge}_4\hbox {O}_{12}$$ Na 2 Cu 3 Ge 4 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 $$T_{co}$$ 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 $$\sim e^{-B/\sqrt{T_{co}-T}}$$ ∼ e - B / T co - T , where B is a constant and $$T_{co}$$ T co is estimated to be $$ \approx 60$$ ≈ 60

DOI
10.1140/epjb/s10051-025-00891-9

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Theoretical and experimental studies of melting of the 1/3 magnetization plateau in a frustrated S=1/2S=1/2S=1/2 antiferromagnetic trimerized quantum Heisenberg spin chain compound Na2Cu3Ge4O12\hbox {Na}_2\hbox {Cu}_3\hbox {Ge}_4\hbox {O}_{12}Na2​Cu3​Ge4​O12​
Abstract We report the magnetization process of S=1/2S=1/2S=1/2 S = 1 / 2 Heisenberg antiferromagnetic J1−J1−J2J_1{-}J_1{-}J_2J1​−J1​−J2​ J 1 - J 1 - J 2 trimerized spin chain system (with frustration due to the next-nearest-neighbor interaction J3J_3J3​ J 3 within the trimer) under applied magnetic field by means of density-matrix renormalization group method. Here, J′J'J′ J ′ s are the antiferromagnetic exchange interaction constants. Specifically, we explore the phenomenon of 1/3 magnetization plateau for the exchange coupling ratios α=0.18,β=0.18\alpha = 0.18, \beta =0.18α=0.18,β=0.18 α = 0.18 , β = 0.18 , and J1=235J_1=235J1​=235 J 1 = 235 K, where α=J2/J1\alpha =J_2/J_1α=J2​/J1​ α = J 2 / J 1 , and β=J3/J1\beta =J_3/J_1β=J3​/J1​ β = J 3 / J 1 as found for the model compound Na2Cu3Ge4O12\hbox {Na}_2\hbox {Cu}_3\hbox {Ge}_4\hbox {O}_{12}Na2​Cu3​Ge4​O12​ Na 2 Cu 3 Ge 4 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 TcoT_{co}Tco​ 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 ∼e−B/Tco−T\sim e^{-B/\sqrt{T_{co}-T}}∼e−B/Tco​−T​ ∼ e - B / T co - T , where B is a constant and TcoT_{co}Tco​ T co is estimated to be ≈60 \approx 60≈60 ≈ 60
We investigate frustration-induced instabilities in a trimerized quantum spin chain motivated by recent experimental findings for the compound Na2_22​Cu3_33​Ge4_44​O12_{12}12​. Employing a cluster mean-field approach combined with Lanczos exact diagonalization, we analyze the ground-state and quantum-information properties of a Heisenberg model with competing interactions in a magnetic field. In the weakly frustrated regime, the system exhibits a robust 1/31/31/3 magnetization plateau associated with a collective ferrimagnetic-like trimer state. Increasing the next-nearest-neighbor intratrimer coupling drives a pronounced reorganization of spin correlations, leading to a crossover toward a doublon-like correlation regime and providing a static ground-state picture consistent with the composite excitations observed dynamically in trimerized chains. The resulting low-energy behavior can be interpreted in terms of weakly interacting emergent spins, offering a microscopic explanation for the extended stability of the magnetization plateau. Furthermore, through finite-size scaling analyses of the energy gap, von Neumann entanglement entropy, and fidelity susceptibility, we characterize the zero-field criticality of the model. Ultimately, our results suggest that frustration gives rise to qualitatively distinct quantum states and provide a microscopic framework for understanding the emergence of fractionalized excitations in trimerized quantum spin systems.
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Topologically nontrivial 1/31/31/3-magnetization plateau state in a spin-1/2 trimer chain
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