Spin gap in Tl2Ru2O7 and the possible formation of Haldane chains in three-dimensional crystals

Dimensionality is one of the most important parameters of physical phenomena. Only two things determine the universality class of a phase transition: the dimensionality of a given system and the symmetry of the order parameter. In most cases, the dimensionality of a substance is predetermined by its crystal structure. Examples in which the effective dimensionality is reduced are quite rare. Here we show that the three-dimensional cubic system of Tl2Ru2O7 most probably evolves into a one-dimensional spin-one Haldane system with a spin gap below 120 K, accompanied by anomalies in the structure, resistivity and susceptibility. We argue that these anomalies are due to an orbital ordering of Ru 4d electrons, with a strong coupling among three degrees of freedom: orbital, spin and lattice. Our work provides a unique example of the spontaneous formation of Haldane system with an insight into the intriguing interplay of different degrees of freedom.