Combined study of Schwinger-boson mean-field theory and linearized tensor renormalization group on Heisenberg ferromagnetic mixed spin (S, σ) chains

Xin Yan, 1 Zhen-Gang Zhu, 1,2,a and Gang Su1,a

1Theoretical Condensed Matter Physics and Computational Materials Physics Laboratory, College of Physical Sciences, University of Chinese Academy of Sciences, P. O. Box 4588, Beijing 100049, China

2School of Electronics, Electric and Communication Engineering, University of Chinese Academy of Science, Beijing 100049, China

The Schwinger-boson mean-field theory (SBMFT) and the linearized tensor renormalization group (LTRG) methods are complementarily applied to explore the thermodynamics of the quantum ferromagnetic mixed spin (S, σ) chains. It is found that the system has double excitations, i.e. a gapless and a gapped excitation; the low-lying spectrum can be approximated by ω_k ∼ Sσ/2(S+σ) Jk² with J the ferromagnetic coupling; and the gap between the two branches is estimated to be △ ∼ J. The BoseEinstein condensation indicates a ferromagnetic ground state with magnetization m_tot^z = N(S + σ). At low temperature, the spin correlation length is inversely proportional to temperature (T), the susceptibility behaviors as χ = a₁∗( 1/T² )+a₂ ∗1/T， and the specific heat has the form of C = c₁∗√ T − c₂ ∗ T + c₃ ∗ (T) ^3/2 , with ai (i = 1,2) and ci (i = 1,2,3) the temperature independent constants. The SBMFT results are shown to be in qualitatively agreement with those by the LTRG numerical calculations for S = 1 and σ = 1/2. A comparison of the LTRG results with the experimental data of the model material MnIINiII(NO2)4(en)2(en = ethylenediamine), is made, in which the coupling parameters of the compound are obtained. This study provides useful information for deeply understanding the physical properties of quantum ferromagnetic mixed spin chain materials