Spin Correlations of Geometrically Frustrated Magnetic System

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Geometrically frustrated spin systems have been investigated for decades because of their fascinating magnetic properties. An Ising model on a cubic pyrochlore lattice consisting of spins parallel to local [111] easy axes was shown to exhibit macroscopic degeneracy in the ground states in the same way as the proton disorder in water ice does. The local easy axis, nearest-neighbor (NN) exchange interaction, and the geometry of corner sharing tetrahedra give rise to frustration in this system. Since the local spin configuration of the ground states simulates the "ice rule" in water ice, the Ising model is referred to as "spin ice". By applying magnetic fields to the NN spin-ice model the macroscopic degeneracy of the ground states can be partly or fully lifted depending on the field direction and magnitude. For a field parallel to a [111] direction, along which the pyrochlore lattice is alternating stacking of kagome and triangular layers, the field with intermediate strengths partly lifts the degeneracy and simultaneously induces decoupling of spins between the layers (kagome ice).Frustrated behavior attributable to the NN ferromagnetic spin-ice model was discovered in pyrochlore oxides, e.g.R_2Ti_2O_7, R_2Sn_2O_7 (R=Dy, Ho). Although spins in these oxides interact dominantly by the dipolar interaction, Monte Carlo (MC) simulation studies showed that the dipolar interaction brings about an effective NN ferromagnetic coupling. In this work, we performed neutron scattering experiments on Dy_2Ti_2O_7 with field along [111] in the conjectured kagome ice regime, aiming at microscopic demonstration of the kagome ice state. We compared the neutron data with MC simulations based on the dipolar interacting model. The simulations reproduce the main characteristics of the kagome ice : the residual entropy, the spin correlations close to the wave vector (2/3,-2/3, 0), and the field-induced dimensional reduction, being consistent with observations.