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