  We theoretically investigate spin-lattice coupling (SLC) effects on the
in-field ordering properties of classical Heisenberg antiferromagnets on the
breathing pyrochlore lattice. Here, we use the two possible simplified models
describing the effect of local lattice distortions on the spin ordering via the
SLC, the bond-phonon and site-phonon models. It is found by means of Monte
Carlo simulations that in both models, the $\frac{1}{2}$ plateau shows up in
the magnetization curve being relatively robust against the breathing
bond-alternation, although magnetic long-range orders (LRO's) are realized only
in the site-phonon model. In the bond-phonon model, additional further neighbor
interactions are necessary to induce a magnetic LRO. In the site-phonon model,
it is also found that in addition to the low-field, middle-field 1/2-plateau,
and high-field phases appearing on both the uniform and breathing pyrochlore
lattices, various types of unconventional phases which can be viewed as LRO's
in units of tetrahedron are induced by the breathing bond-alternation just
below the 1/2 plateau and the saturation field. The occurrence of these
tetrahedron-based orders could be attributed to the nature characteristic of
the breathing pyrochlore lattice, i.e., the existence of the nonequivalent
small and large tetrahedra. Experimental implications of our result are also
discussed.
