Effective spin-1/2 exchange interactions in Tb${}_2$Ti${}_2$O${}_7$

Abstract

We derive an effective spin-1/2 exchange model for non-Kramers Tb${}^{3+}$ states in the pyrochlore Tb${}_2$Ti${}_2$O${}_7$. The four anisotropic nearest-neighbour exchange constants, as well as next-neighbour exchange constants are derived for the effective model. This work goes beyond the independent tetrahedra model by considering all nearest-neighbour exchange paths on the pyrochlore lattice. Estimates of the exchange constants reveal that Tb${}_2$Ti${}_2$O${}_7$ is described by a quantum spin ice Hamiltonian.

arXiv comment10 pages, 2 figures

References in corpus (24)

• Magnetic Monopoles in Spin Ice
• Quantum Excitations in Quantum Spin Ice
• Coulombic Quantum Liquids in Spin-1/2 Pyrochlores
• Magnetic and Thermodynamic Properties of the Collective Paramagnet-Spin Liquid Pyrochlore Tb2Ti2O7
• Dynamically-Induced Frustration as a Route to a Quantum Spin Ice State in Tb2Ti2O7 via Virtual Crystal Field Excitations and Quantum Many-Body Effects
• Er2Ti2O7: Evidence of Order by Disorder in a Frustrated Antiferromagnet
• Generic quantum spin ice
• Definitive Evidence for Order-by-Quantum-Disorder in Er2Ti2O7
• Quantum order by disorder and accidental soft mode Er2Ti2O7
• Phonon and crystal field excitations in geometrically frustrated rare earth titanates
• Structural distortion and the spin liquid state in Tb2Ti2O7
• Magnetoelastic excitations in the pyrochlore spin liquid Tb${}_2$Ti${}_2$O${}_7$
• Structural Fluctuations in the Spin Liquid State of Tb2Ti2O7
• Long-range order and spin-liquid states of polycrystalline Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$
• Magnetic order, magnetic correlations and spin dynamics in the pyrochlore antiferromagnet Er2Ti2O7
• Energetic selection of ordered states in a model of the Er2Ti2O7 frustrated pyrochlore XY antiferromagnet
• Antiferromagnetic Spin Ice Correlations at (1/2,1/2,1/2) in the Ground State of the Pyrochlore Magnet Tb2Ti2O7
• Spin liquid correlations, anisotropic exchange and symmetry breaking in Tb2Ti2O7
• Quantum spin configurations in Tb2Ti2O7
• Magnetoelastics of a spin liquid: X-ray diffraction studies of Tb2Ti2O7 in pulsed magnetic fields
• Low-temperature magnetization in geometrically frustrated Tb2Ti2O7
• Neutron spectroscopic study of crystal field excitations in Tb2Ti2O7 and Tb2Sn2O7
• Vibrating-coil magnetometry of the spin liquid properties of Tb2Ti2O7
• Nature of finite-temperature transition in anisotropic pyrochlore Er2Ti2O7

Cited by in corpus (3)

• Theory of multiple--phase competition in pyrochlore magnets with anisotropic exchange, with application to Yb2Ti2O7, Er2Ti2O7 and Er2Sn2O7
• Living on the edge : ground-state selection in quantum spin-ice pyrochlores
• Antiferro-quadrupolar correlations in the quantum spin ice candidate Pr2Zr2O7