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

• in experiments

• Ferromagnetic models and Dzyaloshinskii-Moriya

• Antiferromagnetic triangular model

• New state of matter: AF-SkX

• Phase diagram in a magnetic

• 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 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 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)

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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