Gap Structure of 12442-Type KCa_2(Fe_1-xCo_x)_4As_4F_2 (x = 0, 0.1) Revealed by Temperature Dependence of Lower Critical Field

We report an in-depth investigation on the out-of-plane lower critical field H_\rm c1 of the KCa_2(Fe_1-xCo_x)_4As_4F_2 (12442-type, x = 0, 0.1). The multi-gap feature is revealed by the kink in the temperature-dependent H_\rm c1(T) curve for the two samples with different doping levels. Based on a simplified two-gap model, the magnitudes of the two gaps are determined to be \varDelta_1 = 1.2 meV and \varDelta_2 = 5.0 meV for the sample with x = 0, \varDelta_1 =  0.86 meV and \varDelta_2 = 2.8 meV for that with x = 0.1. With the cobalt doping, the ratio of energy gap to critical transition temperature (\varDelta/k_\rm BT_\rm c) remains almost unchanged for the smaller gap and is suppressed by 20% for the larger gap. For the undoped KCa_2Fe_4As_4F_2, the obtained gap sizes are generally consistent with the results of angle-resolved photoemission spectroscopy experiments.