  We report a measurement of the strange axial coupling constant $g_A^s$ using
atmospheric neutrino data at KamLAND. This constant is a component of the axial
form factor of the neutral-current quasielastic (NCQE) interaction. The value
of $g_A^s$ significantly changes the ratio of proton and neutron NCQE cross
sections. KamLAND is suitable for measuring NCQE interactions as it can detect
nucleon recoils with low-energy thresholds and measure neutron multiplicity
with high efficiency. KamLAND data, including the information on neutron
multiplicity associated with the NCQE interactions, makes it possible to
measure $g_A^s$ with a suppressed dependence on the axial mass $M_A$, which has
not yet been determined. For a comprehensive prediction of the neutron emission
associated with neutrino interactions, we establish a simulation of particle
emission via nuclear deexcitation of $^{12}$C, a process not considered in
existing neutrino Monte Carlo event generators. Energy spectrum fitting for
each neutron multiplicity gives $g_A^s =-0.14^{+0.25}_{-0.26}$, which is the
most stringent limit obtained using NCQE interactions without $M_A$
constraints. The two-body current contribution considered in this analysis
relies on a theoretically effective model and electron scattering experiments
and requires future verification by direct measurements and future model
improvement.
