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

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 ωk∼Sσ2(S+σ)Jk2 with J the ferromagnetic coupling; and the gap between the two branches is estimated to be △ ∼ J. The Bose-Einstein condensation indicates a ferromagnetic ground state with magnetization mtotz=N(S+σ). At low temperature, the spin correlation length is inversely proportional to temperature (T), the susceptibility behaviors as χ=a1∗1T2+a2∗1T, and the specific heat has the form of C=c1∗T−c2∗T+c3∗T32, 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.