Ising Like Order by Disorder In The Pyrochlore Antiferromagnet with Dzyaloshinskii-Moriya Interactions

Abstract

It is shown that the mechanism of order out of disorder is at work in the antisymmetric pyrochlore antiferromagnet. Quantum as well as thermal fluctuations break the continuous degeneracy of the classical ground state manifold and reduce its symmetry to ${\mathbb{Z}}_3\times {\mathbb{Z}}_2$. The role of anisotropic symmetric exchange is also investigated and we conclude that this discrete like ordering is robust with respect to these second order like interactions. The antisymmetric pyrochlore antiferromagnet is therefore expected to order at low temperatures, whatever the symmetry type of its interactions, in both the classical and semi classical limits.

6 pages. 9 figures

References in corpus (13)

• Low-temperature properties of classical, geometrically frustrated antiferromagnets
• Order by distortion and string modes in pyrochlore antiferromagnet
• Symmetry breaking due to Dzyaloshinsky-Moriya interactions in the kagome lattice
• Quantum phase transition induced by Dzyaloshinskii-Moriya in the kagome antiferromagnet
• Order induced by dipolar interactions in a geometrically frustrated antiferromagnet
• Ordering in the pyrochlore antiferromagnet due to Dzyaloshinsky-Moriya interactions
• Magnetic ordering in Gd2Sn2O7: the archetypal Heisenberg pyrochlore antiferromagnet
• Theory of paramagnetic scattering in highly frustrated magnets with long-range dipole-dipole interactions: The case of the Tb2Ti2O7, pyrochlore antiferromagnet
• Orbital order in classical models of transition-metal compounds
• Order by disorder and gauge-like degeneracy in quantum pyrochlore antiferromagnet
• Field-Driven Transitions in the Dipolar Pyrochlore Antiferromagnet Gd${}_2$Ti${}_2$O${}_7$
• Structural phase transitions in geometrically frustrated antiferromagnets
• Frustrated Order by Disorder: the Pyrochlore Antiferromagnet with Bond Disorder

Cited by in corpus (32)

• Frustrated quantum rare-earth pyrochlores
• 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
• Frustration and anisotropic exchange in ytterbium magnets with edge-shared octahedra
• Are multiphase competition & order-by-disorder the keys to understanding Yb2Ti2O7?
• Rank-2 $U(1)$ spin liquid on the breathing pyrochlore lattice
• Anisotropic exchange within decoupled tetrahedra in the quantum breathing pyrochlore Ba3Yb2Zn5O11
• Kinetically Inhibited Order in a Diamond-Lattice Antiferromagnet
• Order-by-disorder near criticality in $XY$ pyrochlore magnets
• Generic nearest-neighbour kagome model: XYZ & Dzyaloshinskii-Moriya, and comparison to pyrochlore
• Magnon interactions in the frustrated pyrochlore ferromagnet Yb${}_2$Ti${}_2$O${}_7$
• Unravelling competing microscopic interactions at a phase boundary: a single crystal study of the metastable antiferromagnetic pyrochlore Yb${}_2$Ge${}_2$O${}_7$
• Competing phases and topological excitations of spin-one pyrochlore antiferromagnets
• Fluctuation-Driven Selection at Criticality in a Frustrated Magnetic System: the Case of Multiple-k Partial Order on the Pyrochlore Lattice
• Classical and quantum phases of the pyrochlore $S=1/2$ magnet with Heisenberg and Dzyaloshinskii-Moriya interactions
• Modulated Helical Metals at Magnetic Domain Walls of Pyrochlore Iridium Oxides
• Reentrance of disorder in the anisotropic shuriken Ising model
• Behavior of the breathing pyrochlore lattice Ba${}_3$Yb${}_2$Zn${}_5$O${}_{11}$ in applied magnetic field
• Selection of factorizable ground state in a frustrated spin tube: Order by disorder and hidden ferromagnetism
• State selection in frustrated magnets
• Chiral magnetism and helimagnons in a pyrochlore antiferromagnet
• Color ice states, weathervane modes, and order by disorder in the bilinear-biquadratic pyrochlore Heisenberg antiferromagnet
• Anisotropic exchange and non-collinear antiferromagnets on a noncentrosymmetric fcc structure as in the half-Heuslers
• Effects of "stuffing" on the atomic and electronic structure of the pyrochlore Yb${}_2$Ti${}_2$O${}_7$
• Dynamical Signatures of Rank-2 $U(1)$ Spin Liquids
• Frustrated Magnetism of Pharmacosiderite Comprising Tetrahedral Clusters Arranged in the Primitive Cubic Lattice
• Human-machine collaboration: ordering mechanism of rank-2 spin liquid on breathing pyrochlore lattice
• The quantum spin quadrumer
• Analytical theory of pyrochlore cooperative paramagnets
• Helimagnons in a chiral ground state of the pyrochlore antiferromagnets
• Quantum Coulomb Liquids of Different Rank in the Breathing Pyrochlore Antiferromagnet
• Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice