Report

Non-coplanar orders & phase diagram of Kagome Kondo Lattice model Shivam Ghosh, Christopher L. Henley Cornell University Pat O’ Brien, Michael Lawler Binghamton University HFM 2014 –Cambridge U.K. Kondo Lattice Model - route to finding non-coplanar orders (Martin & Batista 2008 ,Akagi & Motome 2012 Chern 2010) {Jij} (Arbitrary units) Electrons mediate long ranged oscillatory RKKY interactions Filling (n) What spin order minimizes {Jij}? Is it non-coplanar? {Jij} (arbitrary units) From RKKY interactions to spin orders Filling (n) Consider RKKY at n=1/3 But coplanar order. Other fillings? F.T. {Jij} to get 3×3 J(q) K Γ Construct {Si} from dominant q modes √3×√3 Predicting spin orders in the RKKY limit Track Qopt (filling) Kagome 1st B.Z. K M Γ K Γ Evolution of optimal mode connected to F.S. Qopt is insufficient to specify spin order on Kagome Monte Carlo on RKKY couplings at for all n<2/3 Diagnostics real space :4 examples of spins at different fillings (All spin directions plotted with common origin, sublattices in different color) Get a variety of non-coplanar incommensurate states! Decompose in to sublattices Spin config. mixture many Fourier modes Simplify: project on to dominant mode “Purified state” Phase diagram in the RKKY limit Smoothly evolving phases with the same broken symmetries – Classified as a single phase Incommensurate Locally ferro twists of Ferro Skyrmion locked at Q=0 textures 0 0.05 0.18 0.2 “Twisted” √3×√3 Filling 1/3 √3×√3 5/12 0.53 0.59 3Q Cuboc1 (Messio 2012) RKKY limit of Kondo Lattice Model gives us a variety of complex non-coplanar orders. Survive at finite JK? Variational phase diagram of the Kondo Lattice model ( comm. orders also found by - K. Barros, J. Venderbose, G.-W. Chern, and C. D. Batista, private comm.) Variational phase diagram of the Kondo Lattice model Variational phase diagram of the Kondo Lattice model Three JK dependent regimes: JK: 0-2 RKKY limit : non-coplanar incommensurate JK: 2-10 non-coplanar commensurate & incomm JK>20 DE limit: Trivial Ferromagnetic favored