Ordering and partial ordering in holmium titanate and related systems

Abstract

We take another look at two compounds which have been discussed as possible realizations of ``spin ice'', namely holmium titanate and dysprosium titanate. As we have earlier observed, holmium titanate does not display ice-like behaviour at low temperatures because the long ranged dipolar interactions between spins are strong compared to the nearest neighbour interactions. We show, analytically, that the true ground state of this system must be fully ordered, but simulations only reach partially ordered states because there are infinite energy barriers separating these from the true ground state. We also show that the true ground state of our model of dysprosium titanate is also fully ordered, and offer some explanations as to why simulations and experiments show ice-like behaviour. We discuss the effect on these systems of an applied magnetic field. Finally, we discuss several other models which show similar partial or full ordering in their ground states, including the well known Ising model on the fcc lattice.

10 pages, latex, 16 eps figures

References in corpus (2)

• Dipolar Interactions and Origin of Spin Ice in Ising Pyrochlore Magnets
• Ising pyrochlore magnets: Low temperature properties, ice rules and beyond

Cited by in corpus (27)

• Spin Ice State in Frustrated Magnetic Pyrochlore Materials
• Spin Correlations in Ho${}_2$Ti${}_2$O${}_7$: a Dipolar Spin Ice System
• Artificial square ice and related dipolar nanoarrays
• Why spin ice obeys the ice rules
• Low Temperature Spin Freezing in Dy2Ti2O7 Spin Ice
• Generic quantum spin ice
• Thermodynamic Properties of the Dipolar Spin Ice Model
• Higgs transition from a magnetic Coulomb liquid to a ferromagnet in Yb_2Ti_2O_7
• Theory of the [111] magnetization plateau in spin ice
• Realizing Colloidal Artificial Ice on Arrays of Optical Traps
• Zero Point Entropy in Stuffed Spin Ice
• Magnetization process of spin ice in a [111] magnetic field
• Removing the spin ice cap: magnetic ground states of rare earth tripod kagome lattice Mg${}_2$RE${}_3$Sb${}_3$O${}_{14}$ (RE = Gd, Dy, Er)
• Quantum-Classical Reentrant Relaxation Crossover in Dy2Ti2O7 Spin-Ice
• Short-range Magnetic interactions in the Spin-Ice compound Ho${}_2$Ti${}_2$O${}_7$
• Quantum and thermal spin relaxation in diluted spin ice: Dy(2-x)MxTi2O7 (M = Lu, Y)
• Non-monotonic zero point entropy in diluted spin ice
• Dirty Spin Ice: The Effect of Dilution on Spin Freezing in Dy2Ti2O7
• New physics in frustrated magnets: Spin ices, monopoles, etc
• Comment on "Short-range magnetic interactions in the spin-ice compound Ho2Ti2O7"
• Of chain-based order and quantum spin liquids in dipolar spin ice
• Spin ice behavior in Dy2Sn2-xSbxO7+x/2 and Dy2NbScO7
• Neutron Scattering Study of the Spin Correlation in the Spin Ice System Ho2Ti2O7
• Effect of long-and short-range interactions on the thermodynamics of dipolar spin ice
• Frustrated Ising model on the garnet lattice
• Exact Continuum Representation of Long-range Interacting Systems and Emerging Exotic Phases in Unconventional Superconductors
• Phase Transition and Monopoles Densities in a Nearest Neighbors Two-Dimensional Spin Ice Model