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

Abstract

Motivated by experiments on the archetypal frustrated magnet SrCr${}_{9p}$Ga${}_{12-9p}$O${}_{19}$ (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 non-magnetic 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 {\em non-monotonic} 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${}^{3+}$ spin in direct proximity to a pair of missing sites belonging to the same triangular simplex. In the $T\to 0$ 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 {\em temperature dependent} {\em pair-wise exchange interaction} $J_{eff}(T,\vec{r})\sim T\mathcal{J}(\vec{r}\sqrt{T})$ that has a logarithmic form at short-distances and decays exponentially beyond a thermal correlation length $\xi (T)\sim 1/\sqrt{T}$. The sign of $J_{eff}$ 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.

two-column PRB format; 21 pages; 14 .eps figures. v2: a minor typo fixed

References in corpus (4)

• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Unusual liquid state of hard-core bosons on the pyrochlore lattice
• Spin Dynamics in Pyrochlore Heisenberg Antiferromagnets
• Large-scale Monte Carlo simulations of the isotropic three-dimensional Heisenberg spin glass

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