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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 (, ) 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 with the ferromagnetic coupling; and the gap between the two branches is estimated to be △ ∼ . The Bose-Einstein condensation indicates a ferromagnetic ground state with magnetization . At low temperature, the spin correlation length is inversely proportional to temperature (), the susceptibility behaviors as , and the specific heat has the form of , with ( = 1, 2) and ( = 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 = 1 and = 1/2. A comparison of the LTRG results with the experimental data of the model material ( )()( = ), 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.


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