Vacancy-induced spin textures and their interactions in a classical spin liquid

Motivated by experiments on the archetypal frustrated magnet SrCr<SUB>9p</SUB>Ga<SUB>12−9p</SUB>O<SUB>19</SUB> (SCGO), we study the classical Heisenberg model on the pyrochlore slab (kagomé bilayer) lattice with site dilution x=1−p. This allows us to address generic aspects of the physics of nonmagnetic vacancies in a classical spin liquid. We explicitly demonstrate that the pure (x=0) system remains a spin liquid down to the lowest temperatures, with an unusual nonmonotonic temperature dependence of the susceptibility, which even turns diamagnetic for the apical spins between the two kagome layers. For x>0 but small, the low-temperature magnetic response of the system is most naturally described in terms of the properties of spatially extended spin textures that cloak an “orphan” S=3/2 Cr<SUP>3+</SUP> spin in direct proximity to a pair of missing sites belonging to the same triangular simplex. In the T→0 limit, these orphan-texture complexes each carry a net magnetization that is exactly half the magnetic moment of an individual spin of the undiluted system. Furthermore, we demonstrate that they interact via an entropic temperature-dependent pairwise exchange interaction J<SUB>eff</SUB>(T,⃗r)∼TJ(⃗r√T) that has a logarithmic form at short distances and decays exponentially beyond a thermal correlation length ξ(T)∼1/√T. The sign of J<SUB>eff</SUB> depends on whether the two orphan spins belong to the same kagome layer or not. We provide a detailed analytical account of these properties using an effective field theory approach specifically tailored for the problem at hand. These results are in quantitative agreement with large-scale Monte Carlo numerics