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Low-temperature specific heat (SH) is measured for the 12442-typeKCa$_2$Fe$_4$As$_4$F$_2$ single crystal under different magnetic fields. Aclear SH jump with the height of $\Delta C/T|_{T_c}$ = 130 mJ/mol K$^2$ isobserved at the superconducting transition temperature $T_c$. It is found thatthe electronic SH coefficient $\Delta\gamma (H)$ quickly increases when thefield is in the low-field region below 3 T and then considerably slows down theincrease with a further increase in the field, which indicates a rather stronganisotropy or multi-gap feature with a small minimum in the superconductinggap(s). The temperature-dependent SH data indicates the presence of the $T^2$term, which supplies further information and supports the picture with aline-nodal gap structure. Moreover, the onset point of the SH transitionremains almost unchanged under the field as high as 9 T, which is similar tothat observed in cuprates, and placed this system in the middle between the BCSlimit and the Bose-Einstein condensation.

Low temperature specific heat of 12442-type KCa_2Fe_4As_4F_2 single crystals