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Proximity effects on topological surface: TI/FM heterostructures - - PowerPoint PPT Presentation

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Proximity effects on topological surface: TI/FM heterostructures Ilya Eremin Theoretische Physik III, Ruhr-Uni Bochum NQS Workshop Kyoto, 20.11.2017 Collaborators: Flavio S. Nogueira Jagadeesh Moodera Ferhat Katmis IFW Dresden & RUB

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Proximity effects on topological surface: TI/FM heterostructures

Ilya Eremin Theoretische Physik III, Ruhr-Uni Bochum

NQS Workshop Kyoto, 20.11.2017

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Collaborators:

Flavio S. Nogueira IFW Dresden & RUB Jagadeesh Moodera MIT Ferhat Katmis MIT

NQS Workshop Kyoto, 20.11.2017

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Electrodynamics of the topological insulator

In a 3d+1 Z2 topological insulator (class AII ) there is another term (-term)

 

     B E     

     

rdt d c e A A rdt d c e S

3 2 2 3 2 2

2 4  

  • does not depend on the metric but only on the topology of the underlying space
  • serves as an alternative definition of the non-trivial topological insulator

X.-L. Qi, T. L. Hughes, and S.-C. Zhang, PRB 78, 195424 (2008) A.M. Essin, J. E. Moore, and D. Vanderbilt, PRL 102, 146805 (2009)

NQS Workshop Kyoto, 20.11.2017

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Electrodynamics of the topological insulator

  • the value of  is defined modulo 2
  • S is an integral over a total derivative (no effect for  = const.)
  • matters at interfaces and surfaces, where  changes
  • for strong topological insulator = ( possibility to classify TI even in

the presence of interactions)

 

     B E     

     

rdt d c e A A rdt d c e S

3 2 2 3 2 2

2 4  

Application of the Gauss-Theorem gives the CS term on the surface

 

    

   A A rdt d c e S

2 2 2

2 

NQS Workshop Kyoto, 20.11.2017

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Outline

  • FM insulator/TI heterostructures
  • Interaction effects at the interface: spontaneous

generation of the Chern-Simons term and RKKY interaction

  • Finite temperature effects: shift of Curie

temperature and Dzyloshinsky-Moriya interaction

NQS Workshop Kyoto, 20.11.2017

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ferromagnetic order in TI by doping with specific Elements (Mn,Fe,Cr…)

Exp.:Y. L. Chen et al., Science 329, 659 (2010); L. A. Wray et al., Nat. Phys. 7, 32 (2010); J. G. Checkelsky et al., Nat. Phys. 8, 729 (2012); S.-Y. Xu et al., Nat. Phys. 8, 616 (2012); Z. Wang et al., APL Mater.. (2015)

  • hard to separate the surface and the bulk phases
  • transport of a TI can be influenced by metallic overlayer or atoms
  • crystal defects, magnetic scattering centers, as well as impurity states

in the insulating gap

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Proximity induced symmetry breaking

S.V. Eremeev et al., PRB 88, 144430 (2014); JMMM 383 (2014; )Sci. Rep. 5 (2015)

NQS Workshop Kyoto, 20.11.2017

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  • EuS well behaved Heisenberg-like ferromagnetic insulator
  • Local time-reversal symmetry breaking at the interface
  • P. Wei et al. PRL 110, 186807 (2013);

Qi I. Yang et al., PRB 88, 081407(R) (2014) L.D. Alegria et al., Appl. Phys. Lett. 105, 053512 (2014) FMI(Y3Fe5O12)/TI: Lang et al., NanoLett. 14, 3459 (2014) Bi2Se3/Permalloy A. R. Melinik et al., Nature 511, 449 (2014)

NQS Workshop Kyoto, 20.11.2017

Proximity induced symmetry breaking: FM/TI heterostructure

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Proximity induced symmetry breaking Ferrimagnet/TI heterostructure

  • Anomalous Hall effect at room temperatures
  • TI surface is spin-polarized (Andreev reflection experiments)

Tang et al., Sci. Adv. 2017;3: e1700307 (2017)

NQS Workshop Kyoto, 20.11.2017

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FI/TI Interface

Out of plane magnetization: gapped Dirac spectrum In-plane magnetization: gapless Dirac spectrum

Mean-field type Hamiltonian at the interface

NQS Workshop Kyoto, 20.11.2017

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FI/TI Interface: vanishing out-of-plane magnetization

Add screened Coulomb interaction The full Lagrangian in terms of auxilary field a0

NQS Workshop Kyoto, 20.11.2017

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FI/TI Interface: Effective action

(a) recall the situation J≠0

  • Integrating out N fermionic degrees of freedom and expanding the

action in terms of the components of the vector field

  • expanding the action in terms of the components of the vector field

 

           

N i i i i eff

a a m m f f m x d J S

1 3 2

6 1 8

     

 

NQS Workshop Kyoto, 20.11.2017

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FI/TI Interface: Effective action

(a) recall the situation J≠0

  • The first (Maxwell) term contains a dimensional coefficient
  • the CS term is universal (depends on the sign of m), independent of the

scale transformations

 

           

N i i i i eff

a a m m f f m x d J S

1 3 2

6 1 8

     

 

NQS Workshop Kyoto, 20.11.2017

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FI/TI Interface: Effective action

(a) the situation J≠0, N is odd

  • Two-component Dirac fermions
  • the broken symmetries are TRS and mirror symmetry N=2n+1

2

, J     

NQS Workshop Kyoto, 20.11.2017

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FI/TI Interface: Landau-Lifshitz equations

(a) J≠0

  • I. Garate and M. Franz, Phys. Rev. Lett. 104, 146802 (2010)
  • T. Yokoyama, J. Zang, and N. Nagaosa, PRB 81, 241410(R) (2010);
  • Ya. Tserkovnyak and D. Loss PRL 108, 187201 (2012)

 Electric field associated with screened Coulomb potential Spin-Hall response

To get the full magnetization dynamics

   

 

 

2 2 2 2 2 2

! 4 2 2 n n n n n b u r L

z t FM

         

F.S. Nogueira and I. Eremin PRL109 (2012)

NQS Workshop Kyoto, 20.11.2017

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FI/TI Interface: Landau-Lifshitz equations

(a) J≠0

   

 

               

2 2 2 2

~ ~ 1 | | 6 1 8

z z t eff

n n m a a m m f f m rdt d NJ S

     

 

 

 

                E e n E n H n n

t z F eff t

m ZNJ 3 1 2

2

  

Landau-Lifshitz torque Magnetoelectric torque

i eff

n S  

  • Coupled to the equation determining the scalar potential

   

eff

S

F.S. Nogueira and I. Eremin PRL109 (2012)

NQS Workshop Kyoto, 20.11.2017

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Outline

  • FM insulator/TI heterostructures
  • Interaction effects at the interface: spontaneous

generation of the Chern-Simons term and RKKY interaction

  • Finite temperature effects: shift of Curie

temperature and Dzyloshinsky-Moriya interaction

NQS Workshop Kyoto, 20.11.2017

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FI/TI Interface: planar ferromagnet

 From effective action derive the propagator for the bosonic excitations (charge and spin fluctuations)  Compute the self-energy for the fermions and see what is the condition to have (0)≠0  once it is non-zero it means the breaking of TRS and parity (generation

  • f the Chern-Simons term)

NQS Workshop Kyoto, 20.11.2017

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Planar FM: self-consistent equation for the mass generation

NQS Workshop Kyoto, 20.11.2017

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Outline

  • FM insulator/TI heterostructures
  • Interaction effects at the interface: spontaneous

generation of the Chern-Simons term and RKKY interaction

  • Finite temperature and chemical potential effects:

Tc shift and Dzyloshinsky-Moriya Interaction (DMI)

NQS Workshop Kyoto, 20.11.2017

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Finite temperature effects: shift of Curie temperature at the interface and out-of-plane magnetic anisotropy

 FI/TI heterostructure

  • Bulk Curie Temperature for EuS, Tc=17K
  • At the interface the magnetization persists up to much higher

temperatures

NQS Workshop Kyoto, 20.11.2017

  • F. Katmis et al., Nature 533, 513 (2016)
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Finite temperature effects: shift of Curie temperature at the interface

NQS Workshop Kyoto, 20.11.2017

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Planar FM: RKKY type interaction on the interface between TI and FM

NQS Workshop Kyoto, 18.11.2017v

  • J. Kim et al., PRL 119, 027201 (2017)
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Finite temperature effects: shift of Curie temperature at the interface

NQS Workshop Kyoto, 20.11.2017

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Finite temperature effects: shift of Curie temperature at the interface

Magnetization at the interface is exponentially decaying in the bulk

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Effect of the temperatures on Chern Simons term

NQS Workshop Kyoto, 20.11.2017

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Effect of the temperatures on Chern Simons term

NQS Workshop Kyoto, 20.11.2017

F.S. Nogueira and I. Eremin, PRB 90, 014431 (2014); RRB 92, 224507 (2015)

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What happens above Curie temperature: generation of Dzyloshinsky-Moriya interaction

NQS Workshop Kyoto, 20.11.2017

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What happens above Curie temperature: generation of Dzyloshinsky-Moriya interaction (chemical potential is finite)

NQS Workshop Kyoto, 20.11.2017

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What happens above Curie temperature: generation of Dzyloshinsky-Moriya interaction

NQS Workshop Kyoto, 20.11.2017

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What happens above Curie temperature: generation of Dzyloshinsky-Moriya interaction

NQS Workshop Kyoto, 20.11.2017

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What happens above Curie temperature: generation of Dzyloshinsky-Moriya interaction

NQS Workshop Kyoto, 20.11.2017

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Conclusions

TI/FI heterostructure:

  • For interacting Dirac fermions coupled to an in-plane

exchange field there is a spontaneous breaking of parity and TRS due to a dynamical gap generation

  • Upward shift of the Curie temperature at the interface

due to RKKY and negative interface energy of Dirac fermions

  • Dynamical generation of the Dzyaloshinsky-Moriya

Interaction at the interface above Tc

Conclusions:

NQS Workshop Kyoto, 20.11.2017