  We report a lattice QCD calculation of the strange quark contribution to the
nucleon's magnetic moment and charge radius. This analysis presents the first
direct determination of strange electromagnetic form factors including at the
physical pion mass. We perform a model-independent extraction of the strange
magnetic moment and the strange charge radius from the electromagnetic form
factors in the momentum transfer range of $0.051 \,\text{GeV}^2 \lesssim Q^2
\lesssim 1.31 \,\text{GeV}^2 $. The finite lattice spacing and finite volume
corrections are included in a global fit with $24$ valence quark masses on four
lattices with different lattice spacings, different volumes, and four sea quark
masses including one at the physical pion mass. We obtain the strange magnetic
moment $G^s_M(0) = - 0.064(14)(09)\, \mu_N$. The four-sigma precision in
statistics is achieved partly due to low-mode averaging of the quark loop and
low-mode substitution to improve the statistics of the nucleon propagator. We
also obtain the strange charge radius $\langle r_s^2\rangle_E = -0.0043
(16)(14)\,$ $\text{fm}^2$.
