Color ice states, weathervane modes, and order by disorder in the bilinear-biquadratic pyrochlore Heisenberg antiferromagnet

Abstract

We study the pyrochlore Heisenberg antiferromagnet with additional positive biquadratic interaction in the semiclassical limit. The classical ground state manifold of the model contains an extensively large family of non-coplanar spin states known as "color ice states". Starting from a color ice state, a subset of spins may rotate collectively at no energy cost. Such excitation may be viewed in this three-dimensional system as a "membrane-like" analog of the well-known weathervane modes in the classical kagome Heisenberg antiferromagnet. We investigate the weathervane modes in detail and elucidate their physical properties. Furthermore, we study the order by disorder phenomenon in this model, focusing on the role of harmonic fluctuations. Our computationally-limited phase space search suggests that quantum fluctuations select three different states as the magnitude of the biquadratic interaction increases relative to the bilinear interaction, implying a sequence of phase transitions solely driven by fluctuations.

arXiv comment14 pages, 9 figures. New results included. Phase diagram discussion streamlined

References in corpus (35)

• Properties of a classical spin liquid: the Heisenberg pyrochlore antiferromagnet
• Low-temperature properties of classical, geometrically frustrated antiferromagnets
• Order by distortion and string modes in pyrochlore antiferromagnet
• Spin Driven Jahn-Teller Distortion in a Pyrochlore system
• Half-magnetization plateau stabilized by structural distortion in the antiferromagnetic Heisenberg model on a pyrochlore lattice
• Ordering in the pyrochlore antiferromagnet due to Dzyaloshinsky-Moriya interactions
• Octupolar ordering of classical kagome antiferromagnets in two and three dimensions
• Quantum stabilization of 1/3-magnetization plateau in Cs_2CuBr_4
• Field induced ordering in highly frustrated antiferromagnets
• Quantum Selection of Order in an $XXZ$ Antiferromagnet on a Kagomé Lattice
• Classical antiferromagnet on a hyperkagome lattice
• Nematic, vector-multipole, and plateau-liquid states in the classical O(3) pyrochlore antiferromagnet with biquadratic interactions in applied magnetic field
• Ground State Phase Diagram of Generic XY Pyrochlore Magnets with Quantum Fluctuations
• Partial order from disorder in a classical pyrochlore antiferromagnet
• Dipolar order by disorder in the classical Heisenberg antiferromagnet on the kagome lattice
• Order and excitations in large-$S$ kagomé-lattice antiferromagnets
• Order-by-Disorder in the XY Pyrochlore Antiferromagnet Revisited
• Quantum stabilization of classically unstable plateau structures
• Ising Like Order by Disorder In The Pyrochlore Antiferromagnet with Dzyaloshinskii-Moriya Interactions
• Phase competition in the double-exchange model on the frustrated pyrochlore lattice
• Order by disorder and gauge-like degeneracy in quantum pyrochlore antiferromagnet
• Classical Heisenberg antiferromagnet on a garnet lattice: a Monte Carlo simulation
• Effective Hamiltonian for the Pyrochlore antiferromagnet: semiclassical derivation and degeneracy
• Spin Hamiltonian, {Order Out of a Coulomb Phase} and Pseudo-Criticality in the Highly Frustrated Pyrochlore Heisenberg Antiferromagnet FeF${}_3$}
• Order and Disorder in AKLT Antiferromagnets in Three Dimensions
• Classical heisenberg antiferromagnet away from the pyrochlore lattice limit: entropic versus energetic selection
• Fictitious excitations in the classical Heisenberg antiferromagnet on the kagome lattice
• A Bionic Coulomb Phase on the Pyrochlore Lattice
• Orbital ice: an exact Coulomb phase on the diamond lattice
• Anharmonic Ground state selection in the pyrochlore antiferromagnet
• Symmetry considerations on the magnetization process of the Heisenberg model on the pyrochlore lattice
• Emergent quantum phases in a frustrated J1-J2 Heisenberg model on hyperhoneycomb lattice
• Four-coloring model and frustrated superfluidity in the diamond lattice
• "Switching" of Magnetic Anisotropy in a fcc Antiferromagnet with Direction-Dependent Interactions
• A strong coupling theory for electron-mediated interactions in double-exchange models

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• Inelastic Neutron Scattering Study of the Spin Dynamics in the Breathing Pyrochlore System LiGa0.95In0.05Cr4O8
• The quantum spin quadrumer