Near-infrared medium-resolution spectra of seven bright brown dwarfs are presented. The spectra were obtained with the Infrared Camera (IRC) on board the infrared astronomical satellite AKARI, covering 2.5--5.0 um with a spectral resolution of approximately 120. The spectral types of the objects range from L5 to T8, and enable us to study the spectral evolution of brown dwarfs. The observed spectra are in general consistent with the predictions from the previous observations and photospheric models. We find that the CO fundamental band around 4.6 um is clearly seen even in the T8 dwarf 2MASS J041519-0935, confirming the presence of non-equilibrium chemical state in the atmosphere. We also identify the CO_2 fundamental stretching-mode band at 4.2 um for the first time in the spectra of late-L and T-type brown dwarfs. We analyze the observed spectra by comparing with the predicted ones based on the Unified Cloudy Model (UCM). Although overall spectral energy distributions (SEDs) can be reasonably fitted with the UCM, observed CO and CO_2 bands in late-L and T-dwarfs are unexpectedly stronger than the model predictions assuming local thermodynamical equilibrium (LTE). We examine the vertical mixing model and find that this model explains the CO band at least partly in the T-dwarfs 2MASS J041519-0935 and 2MASS J055919-1404. The CO fundamental band also shows excess absorption against the predicted one in the L9 dwarf SDSS J083008+4828. Since CO is already highly abundant in the upper photospheres of late-L dwarfs, the extra CO by vertical mixing has little effect on the CO band strengths, and the vertical mixing model cannot be applied to this L-dwarf. A more serious problem is that the significant enhancement of the CO_2 4.2 um band in both the late-L and T dwarfs cannot be explained at all by the vertical mixing model. The enhancement of the CO_2 band remains puzzling.
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