Non-coplanar orders & phase diagram of Kagome Kondo Lattice model

Shivam Ghosh, Christopher L. Henley Cornell University

HFM 2014 –Cambridge U.K.

Pat O’ Brien, Michael Lawler Binghamton University

Kondo Lattice Model - route to finding non-coplanar orders

Electrons mediatelong ranged oscillatoryRKKY interactions

What spin order minimizes{Jij}? Is it non-coplanar?

{J ij}

(A

rbit

rary

unit

s) Filling (n)

(Martin & Batista 2008,Akagi & Motome 2012Chern 2010)

Filling (n)

K

Γ

√3×√3

From RKKY interactions to spin orders

F.T. {Jij} to get 3×3 J(q)

Construct {Si} fromdominant q modes

Consider RKKY at n=1/3

But coplanar order. Other fillings?

{J ij}

(arb

itra

ry u

nit

s)

Predicting spin orders in the RKKY limit

Evolution of optimal mode connected to F.S. Qopt is insufficient to specify spin order on Kagome

K

M

Γ

K

ΓΓ

Track Qopt (filling)

Kagome 1st B.Z.

Get a variety of non-coplanar incommensurate states!

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)

Decompose

in to sublattices Spin config. mixture many Fourier modesSimplify: 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

Filling

1/3 5/120 0.05

Incommensuratetwists of Ferrolocked at Q=0

“Twisted”√3×√3

Locally ferroSkyrmion textures

√3×√3 Cuboc1(Messio 2012)

3Q

0.180.2 0.53 0.59

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