Specific heat of Sr₄Ru₃O₁₀

We have measured the specific heat of single crystals of the triple-layer Ruddlesden-Popper material, Sr₄Ru₃O₁₀, grown both in an image furnace (IF) and by flux-growth. The flux grown (FG) sample has a sharp mean-field-like anomaly at the onset of magnetic order, T _C=102K, but a much broader anomaly, indicative of residual heterogeneity, is observed for the IF sample. Even for the FG sample, however, the anomaly is at least an order of magnitude smaller than one would expect for complete ordering of the spins. Neither sample exhibits an anomaly at T _M∼50K, where magnetic measurements suggest that basal plane antiferromagnetism sets in. Anomalous behavior (e.g., consistent with a term in the specific heat ∝T^3/2 as would be observed for a three-dimensional ferromagnet with weak exchange) is observed at low temperatures for both samples, indicative of the unusual magnetic order in this material.