  We theoretically investigate effects of lattice distortions on the spin
ordering of classical Heisenberg antiferromagnets on the breathing pyrochlore
lattice. In the model, local lattice distortions originating from the site
vibration are taken into account to yield effective spin interactions via the
spin-lattice coupling (SLC). The breathing lattice-alternation is characterized
by the ratio of the nearest-neighbor interaction for large tetrahedra to that
for small ones, J'/J. It is found by Monte Carlo simulations that the system
exhibits a first-order transition into four different types of collinear
magnetic ordered states. In the uniform case (J'/J=1), the state realized at
stronger SLC is cubic-symmetric characterized by the (1/2,1/2,1/2) magnetic
Bragg peaks, while the one at weaker SLC is tetragonal-symmetric characterized
by the (1,1,0) ones. With increasing the breathing distortion (decreasing
J'/J), the ordering pattern of the (1/2,1/2,1/2) state becomes non-cubic with
its magnetic Bragg reflections almost unchanged, while the (1,1,0) state is
robust. The non-cubic state peculiar to the breathing pyrochlores is further
categorized into two types. We demonstrate that these two non-cubic orderings
result in the massive degeneracy of the ground state and that the associated
residual entropy per spin takes characteristic values of k_B ln(4)/16 and k_B
ln(6)/16. Experimental implications of the results are discussed.
