1 / 21

Spontaneous Hexagon Organization in Pyrochlore Lattice

Spontaneous Hexagon Organization in Pyrochlore Lattice. Jung Ho on Han & Chenglong Jia (Sung Kyun Kwan University). Examples of Frustrated Lattice - Triangular. Ground state of Heisenberg model. Mean-field theory predicts long-range spin ordering

badrani
Download Presentation

Spontaneous Hexagon Organization in Pyrochlore Lattice

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Spontaneous Hexagon Organization in Pyrochlore Lattice JungHoon Han & Chenglong Jia (Sung Kyun Kwan University)

  2. Examples of Frustrated Lattice - Triangular Ground state of Heisenberg model Mean-field theory predicts long-range spin ordering with for nearest neighbors

  3. More Examples - Kagome Mean-field theory predicts but this is insufficient to define a unique ground state Macroscopic degeneracy of (N=number of triangles) Absence of LRO, despite local spin ordering

  4. 3D Frustrated Lattice - Pyrochlore Tetrahedron as a building block Ground state condition for each tetrahedron Lee et al. Nature 02 Canals & Lacroix, PRB00

  5. 3D Frustrated Lattice - Pyrochlore indeterminate!! -> No local rigidity of spins Continuous manifold of ground states highly susceptible to perturbation!!

  6. Experiments on Pyrochlore – ZnCr2O4 Below Tc S.H.Lee et al. PRL, 2000 : Spins on Cr3+(S=3/2) order antiferromagnetically at as first-order transition, acccompanied by cubic-to-tetragonal distortion.

  7. : Neutron scattering of paramagnetic state at Structure factor consistent with hexagon spin cluster (spin-loop director) Above Tc S.H.Lee et al. Nature, 2002 Experiments on Pyrochlore – ZnCr2O4

  8. Theory of spin-Peierls transition by Tschernyshyov, Moessner, and Sondhi TMS, PRL, 2002 TMS, PRB, 2002 Elongation (contraction) of a tetrahedron along an axis And collinear antiferromagnetic spins is the ground state

  9. uj Rij j ui i Theory of Spin-Lattice Coupling Experimental fact: Short-range spin correlation persists at temperatures above transition (“Hexagon protectorate”) A “glue” is needed to protect correlation within a hexagon Perhaps it comes from spin-lattice coupling Exchange integral depends only on relative distance of ions:

  10. Lattice-Coupled Antiferromagnetic Spin Model Spin and lattice are coupled through magneto-striction effect (Pytte, PRB 1974) Lattice displacement related to local spin-spin correlation by

  11. Spin Lattice Antiferomagnetic Spins on a Hexagon Ring Each hexagon can “Shrink” to minimize exchange energy Spins are collinear antiferromagnet (Holstein-Primakoff boson analysis of spin-lattice model)

  12. “Hidden geometry” of Pyrochlore (S.H.Lee et al. Nature 2002) Pyrochlore can be decomposed in terms of hexagons, instead of tetrahedra Each site belongs to one and only one hexagon Four hexagon types of different orientations Non-overlapping hexagons form a lattice

  13. Neutrons scatter off hexagons (S.H.Lee, nature 02) Extrapolated correlation length remains finite

  14. Interpreting Experiments as spin-lattice coupling Invoking spin-lattice coupling, each independent hexagon shrinks, taking advantage of finite lattice stiffness and lowering exchange energy Nearby spin-loop directors are orthogonal, to be consistent with uniform contraction of hexagons

  15. Spins within a hexagon are collinearSpins of nearby hexagons are orthogonal Director-Director Interaction

  16. Emergence of 3-states Potts Model R G B

  17. Projecting onto a Kagome plane …

  18. A picture of paramagnetic state in ZnCr2O4 Spin-lattice interaction leads to enhanced singlet (collinear antiferromagnet) tendency within a hexagon Residual spin-lattice interaction leads to orthogonality of nearby directors (3-states Potts model) At finite temperature, thermal fluctuations smear out the inter-hexagon interaction, spin-spin correlation remains confined to a single hexagon Further lowering temperature might lead to condensation of spin-loop directors, but it appears that a tetragonal distortion pre-empts this possibility in ZnCr2O4

  19. Spin-Lattice Coupling in Other Frustrated Lattices Local rigidity of spin-spin correlation leads to absence of lattice distortion within our model

  20. YMnO3 There is direct evidence of coupling between spin and lattice Distortion of triangular lattice of Mn ions takes place Reason remains unclear yet

  21. Outlook Spin-lattice coupling is the likely reason for the formation of a “super-structure” in frustrated lattices Different types of super-structures (hexagon vs. tetrahedron) may compete in a given lattice

More Related