Understanding Length Scales for Magnetic 

Coupling in Thin Film Topological Insulators

Jyotsna Rao

Montgomery Blair High School

Mentor: Alexander Grutter

NIST Center for Neutron Research
Thin Film Topological Insulators

● Insulators in interior

● Metallic and conductive surface state

● Layered structure

○ (Bi-Sb)2Te3
Band Structure

● Combining of orbitals in bonding 

creates molecular orbitals with 

many different energy levels

● When electrons can move around, 

there is conduction

● Topological insulators have surface 

states for electrons to move 

through 
Quantum Anomalous Hall Effect

● Quantum Anomalous Hall Effect: 

Quantized edge conduction

○ 2D electronic material

○ Magnetic

○ Topological 

● QAHE allows dissipationless 

transport

○ Around edge of material

● Applications in low power devices
Why does raising magnetic ordering temperature not raise 

QAHE temperature?

● QAHE disappears at less than 1K

● Magnetization seen at up to 400K

● Theory: QAHE very sensitive to defects and inhomogeneity

● Goal: Magnetize TI while minimizing defects

○ High quality interfaces

○ Separate dopants from surface state

○ Raise QAHE temperature?
How can we magnetize?

● Doping with chromium

● Grow TI on MTI

● Grow TI on magnet

Cr:TI TI

Cr:TI

TI

● TI on MTI reduces defects

○ No dopants in TI

○ No rough interface
Samples

● Grown on substrate

○ Easier to handle

○ Fewer defects

● TI layer adjacent to 

MTI layer

○ MTI layer magnetism 

affects TI

● Thickness range for TI

○ 1 nm

○ 3 nm

○ 6 nm Substrate: GaAs

MTI: Cr-(Bi,Sb)2Te3

TI: (Bi,Sb)2Te3

Cap: Te, Te2O3
X-Ray Reflectometry

● Beam of X-rays shot at sample

● Measure intensity of reflected beam

● Fit resulting data

● X-rays interact with electrons in sample
Polarized Neutron Reflectometry

● Similar to X-ray reflectometry

○ Neutrons are also waves

● Neutrons interact with nucleus

● Neutrons give information about magnetism in sample

○ Spin up and down neutrons interact slightly differently

Q (nm-1)

Reflectivity (Arb. Units)
Fitting

● Vary parameters for each layer of sample

○ Thickness

○ Roughness

○ SLD

● Gives depth and magnetic profiles
X-Ray Results
Neutron Results
Alternative Fit
Another Sample

 Substrate MTI TI Te Cap 
Conclusions

● Structural depth profiles ✔

● Magnetic depth profiles ✔

● Chrome dopant locations ??

● Some evidence of magnetized 

undoped TI layer

○ Need more statistical analysis

● X-ray reflectometry so far 

not sensitive enough to 

detect chromium dopants

● Neutrons may be able to 

differentiate between Cr:TI 

and TI

Substrate MTI TI Te Cap 
Next Steps

● Probe chrome dopants with synchrotron

● More chrome dopants?

● Different capping material

 Substrate MTI TI Te Cap Te Oxide 

 
Acknowledgements 

● Alexander Grutter

● David Hoogerheide

● Julie Borchers

● Yamali Hernandez

● SHIP 

● NCNR

● CHRNS
Topological Order

● Topological invariant: Property of an object which 

remains invariant regardless of transformations

● TI have topological invariants 

○ Invariants not change as long as material is an insulator

○ Invariant broken at surface boundary → metallic surface state

○ Topological invariant caused by electrons’ wavefunctions
Hall Effect

● Hall Effect: Voltage transverse to current in applied magnetic 

field

● Anomalous Hall Effect: Hall effect is much stronger in 

ferromagnetic materials

○ Voltage without applied magnetic field
Quantum Anomalous Hall Effect

● Quantum Hall Effect: Quantized values of Hall conductance

○ Low temperatures (~0K)

○ Strong magnetic field

○ 2D electronic materials

● Quantum Anomalous Hall Effect: 

Quantized values of Hall conductance

○ Low temperatures (~0K)

○ 2D electronic materials

○ Magnetic

○ Topological 

● QAHE allows dissipationless 

transport
LP2984

 Substrate MTI TI Te Cap Te Oxide 
LP2984

 Substrate TI Te Cap Te Oxide 
LP2985

 Substrate MTI TI Te Cap Air
LP2985

 Substrate MTI TI Te Cap Te Oxide Ice Air
Profiles