Exchange interactions in two-state systems: rare earth pyrochlores

Abstract

The general form of the nearest neighbour exchange interaction for rare earth pyrochlores is derived based on symmetry. Generally, the rare earth angular momentum degeneracy is lifted by the crystal electric field (CEF) into singlets and doublets. When the CEF ground state is a doublet that is well-separated from the first excited state the CEF ground state doublet can be treated as a pseudo-spin of some kind. The general form of the nearest neighbour exchange interaction for pseudo-spins on the pyrochlore lattice is derived for three different types of pseudo-spins. The methodology presented in this paper can be applied to other two-state spin systems with a high space group symmetry.

10 pages; submitted to J. Phys.: Condensed Matter

References in corpus (8)

• Dynamically-Induced Frustration as a Route to a Quantum Spin Ice State in Tb2Ti2O7 via Virtual Crystal Field Excitations and Quantum Many-Body Effects
• Definitive Evidence for Order-by-Quantum-Disorder in Er2Ti2O7
• Rods of Neutron Scattering Intensity in Yb2Ti2O7: Compelling Evidence for Significant Anisotropic Exchange in a Magnetic Pyrochlore Oxide
• Structural distortion and the spin liquid state in Tb2Ti2O7
• Energetic selection of ordered states in a model of the Er2Ti2O7 frustrated pyrochlore XY antiferromagnet
• Antiferro-quadrupolar correlations in the quantum spin ice candidate Pr2Zr2O7
• The quantum origins of moment fragmentation in Nd2Zr2O7
• Order by Disorder and Energetic Selection of the Ground State in the XY Pyrochlore Antiferromagnet Er2Ti2O7. An Inelastic Neutron Scattering Study

Cited by in corpus (5)

• Competing $U(1)$ and ${\mathbb{Z}}_2$ dipolar-octupolar quantum spin liquids on the pyrochlore lattice: application to Ce${}_2$Zr${}_2$O${}_7$
• Exact diagonalization for spin-1/2 spin ice pyrochlores
• Phase Diagram of a Spin-ice Kondo Lattice Model in a Breathing Pyrochlore Lattice
• Quantum Spin Liquids in Pyrochlore Magnets With Non-Kramers Local Moments
• Analytic description of spin waves in dipolar/octupolar pyrochlore magnets