Skyrmion Lattices in Antiferromagnetic Systems Daniel C. Cabra Universidad Nacional de La Plata Argentina Collaborators: Pierre Pujol, Université de Toulouse Diego Rosales, Mauricio Sturla, Santiago Osorio, Universidad de La Plata IIP Natal, August 2017 Outline • Introduction • A bit of history • Skyrmions in experiments • Ferromagnetic models and Dzyaloshinskii-Moriya • Antiferromagnetic triangular model • New state of matter: AF-SkX • Phase diagram in a magnetic field • Low energy Hamiltonian • Conclusions and future work Skyrmions History: * 1962, T.H.R. Skyrme (The Skyrme model) * 1975, Belavin-Polyakov (Baby) Skyrmions in the Non-linear sigma model NLSM Topological charge These states may have lower energy if inversion symmetry is broken Dzyaloshinskii-Moriya interactions Two-dimensional (baby) Skyrmions In two dimensions we have R2 -> S2 and spin variables span S2 i.e. we care about π2(S2) = Z Analogy with S1 π1(S1) = Z Skyrmion Lattices Type II SC - Vortex Lattice - Abrikosov A.A. Abrikosov, Soviet Physics JETP 1957 Nobel Prize 2003 Where to find Skyrmion lattices? * 1985 I. Klebanov Skyrmion lattice in nuclear matter * 1989 Bogdanov-Yablonskii Skyrmion lattice in a 2D ferromagnet * 1993 Sondi et al. Skyrmions in Quantum Hall effect systems * 1995 Fertig et al. Skyrmion crystals * 1998 T.L. Ho Spinor Bose–Einstein condensates * 2011 Fukuda-Zumer Quasi 2D SkX in Liquid crystals Skyrmions lattices are ubiquitous! Since 2009, 1000 ArXiv papers contain the word “Skyrmion”, more than 100 with “SkX” Chiral magnets: Theory and experiment * 1989 Bogdanov-Yablonskii Predicted a Skyrmion lattice in a 2D ferromagnet * 2009 Mühlbauer et al Observed it in MnSi Phase diagram Mean-field analysis of Another case: Fe1-xCoxSi, theory and experiment W. Münzer et al. PRB (2010) x = 0.2, 0.25,… Small angle neutron scattering -> six-fold symmetry Theory Heisenberg exchange Dzyaloshinskii-Moriya originates from spin-orbit couplings (allowed if inversion symmetry is broken) Competes with exchange which tends to either align (FM) or anti-align (AFM) spins Phases with DM and J If we add J in 2D Ferromagnetic models in square lattices Nagaosa et al. Ginzburg-Landau These models explain fairly well the experimental observations DM and AF exchange AF Skyrmions FM nanodisks AF-coupled Yet another example (without DM interactions!) T. Okubo et al (PRL 2012) have shown that a triangular lattice with FM J1 and J3= -1/3 J1 SkX shows up (inversion symmetry is preserved) Antiferromagnetic Triangular Lattice • KT Phase transition via dissociation of Z2 vortices • Both phases are massive, kBTc/J approx. 0.3 • Order parameter -> vorticity function Antiferromagnetic Triangular Lattice • Kawamura-Miyashita (1984) -> Z2 vortices • Dombre-Read (1989) -> SO(3) NLM Now: π2(SO(3)) = 0 and π1(SO(3)) = Z2 Antiferromagnetic triangular lattice Possible new state of matter: AF-SkX The model The lattice AF-SkX state Looked by sublattice The complete phase diagram (from Monte Carlo simulations) Magnetization and susceptibility Chirality T-h phase diagram Specific heat Static spin structure factor Finite size analysis Low energy effective action Reproducing the phase diagram T (D) ≃ 6.57 J/D − 1.95 Dynamics Coupling to a 1D wire Coupling to fermions and transport • Motome et al (PRL 2017) ! “bi-skyrmions” Similar to Ying Zhang et al, in (Mn1−xNix)65Ga35 x = 0.5 A Centrosymmetric Biskyrmion Magnetic Nanodomain at 100–340 K Ying Zhang et al, in (Mn1−xNix)65Ga35 x = 0.5 Conclusions and Future Work • In Antiferromagnetic systems a new structure shows up: AF-Skyrmion lattice Z_2 vortex lattice • Stability of topologically charged states • Deformed skyrmions (in progress) • Interest: * Data storage (1 or 0) * Spin and electron transport * Skyrmion superconductivity (?) (Baskaran) “Skyrmionics” Advertisement SCHOOL AND WORKSHOP 2018 LATIN AMERICAN WORKSHOP IN CONDENSED MATTER: NOVEL PHASES IN STRONGLY CORRELATED SYSTEMS August 29th September 7th 2018 Directors: • Daniel Barci Universidade do Estado do Rio de Janeiro • Daniel Cabra University of La Plata, Argentina. • Pierre Pujol University Paul Sabatier, Toulouse, France • Daniel Stariolo Universidade Federal Fluminense, Niterói .