Techniques for Studying Skyrmion Excitations in a 2DES in Quantum Hall Effect Regime

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Techniques for Studying Skyrmion Excitations in a
2DES in Quantum Hall Effect Regime

• Presenter Liu, Shu-chen
• Department of Physics
• University of Florida
• January 7, 2002

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Integer Quantum Hall Effect (IQHE)

• Discovered by Klaus von Klitzing in 1980 with
  two-dimensional electron system (2DES) confined
  in a silicon MOSFET transistor.
• Landau level filling factor ? ( of electrons
  per unit area) / (degeneracy per unit area in
  each Landau level) nhc/eB? integer 1,2,3,
  
• 
  MOSFET GaAs/AlGaAs

I
(Stormer, 1999)
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Fractional Quantum Hall Effect (FQHE)

• Discovered with lower temperature (1.5K) and
  higher magnetic field (15T) by Dan Tsui and Horst
  Stormer in 1981.
• Hall resistance RH h/?e2
• (magnetoresistance R) has plateaus (deep
  minima) at
• ? p/(2p?1), p2,3,4,(prominent fractions)
• ? i ? 1/q, i1,2,3,(primary
  fractions)
• Can be explained as many-body problem.
• ?1/3 composite boson (CB) ?1/2 composite
  fermion (CF).

(Stormer, 1999)
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Spin wave versus Skyrmion excitations
Ferromagnet ground state (all spin up)
low-lying elementary excitations
one reversed spin
(Spin wave)
Skyrmion charged spin-texture excitations, CSTEs
lower B field, decrease nB
Spin split Landau levels
excited state
ground state
increasing B
(Barrett website)
The size of Skyrmions or the number of spin
flips per excitation depends on
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Optically Pumped Nuclear Magnetic Resonance
(OPNMR)
SAT a train of 90 RF pulses to saturate
the nuclear spin polarization ?L irradiation of
near IR polarized laser ?D(gt1s) without laser
irradiation in the dark DET detection of NMR
FID after one 90 pulse
Time Sequence
RF pulses
RF pulses
?L
SAT
?D
DET
Fermi contact hyperfine Interaction (DNP)
Electron interband transition
Nuclear polarization saturation
Nuclear spin diffusion
AlGaAs barriers
2DES
AlGaAs barriers
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Knight Shift peak-to-peak frequency splitting
between W and B.W 71Ga nuclei in GaAs
wells B 71Ga in AlxGa1-xAs barriers.
Nuclear spin polarization diffuses from W to B
with increasing ?L (nuclear spin-diffusion)
Nuclear spin-lattice relaxation in GaAs wells
with increasing ?D
B
W
?D0s, ?L2s (in the light)
71Ga OPNMR spectra of MQW in the dark (?L10s)
for different ?D (?1.20, ?56.7?, Btot9.39T,
T2.1K)
71Ga OPNMR spectra of MQW in the dark (?D1s)
for different ?L (?0.88, ?0?, Btot7.05T,
T1.9K)
(Science, Barrett ,1995)
(Science, Barrett ,1995)
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Knight Shift (KS) v.s. Electron Spin Polarization
(P)
Knight shift vs temperature at ?1/3 (?36.8?,
and 46.4?, Btot12T)
(Barrett ,1998)
71Ga OPNMR spectra at ?1/3 (?36.8?, Btot12T,
f0155.93MHz)
(Barrett ,1998)
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Knight Shift (KS) v.s. Landau Level Filling
Factor (?)
Existence of Skyrmions at ? 1
Ks (?) near ? 1 at T1.5K (Btot3.6263, 3.2589T)
Ks (?) near ? 1 at T1.55K (Btot7.05T)
(PRL, Barrett, 1995)
(PRL, Barrett ,1998)
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Conventional, Thermally Polarized NMR
Pulse Sequence
?/2
echo
4??/2 RF pulses
?
tR
?
?
At ?1, the local peak exists at 0.022,
but disappears at 0.037, so lt0.037
Recovery time tR dependence of NMR signal at
T1.5K, ?1(?0?)
(PRB, Melinte, 2001)
71Ga Ks(?) and P(?) at T1.5K Dashed line P(?)
at T0 single e- model
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Tilted-Field Magnetotransport Method
(PRL, Schmeller, 1995)
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Photoluminescence Method
?e electron spin polarization (from the
luminescence spectra) BN induced
nuclear-magnetic field The Skyrmion size, R
, is measured from the amplitude of
discontinuity of d ?e / d? at ?1 R 0.1 ? 0.3
for Ez / Ec 0.0108 (no Skyrmion), R
1.0 ? 0.3 for 0.0077, R 2.1 ? 0.3 for
0.0058, R 4.8 ? 0.3 for
0.0038 (sR1)
The skyrmion disappears at 0.011?0.001
(Kukushkin,1999)
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Heat Capacity Method
Pulse technique
The (Schottky) nuclear specific heat
0.047
Fraction of Ga and As nuclei in the quantum
wells coupling to the lattice
0.0370.043
(PRL, Melinte,1999)
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Electrically Detected ESR / Dynamic Nuclear
Polarization Method
Down-Field-Swept Microwave Dynamic Nuclear
Polarization Technique

• At constant T (not affect ?)
• No LL mixing and subband energy changes

(a) ?xx(B) near ?1 (B05.5T, f020.0GHz,
T2.50K) (b) ?xx(B) near ?1 (B05.5T, f032GHz,
T2.50K)
(Vitkalov, Bowers,1999)
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20-72 GHz Electrically Detected ENDOR Spectrometer
YIG Oscillator
10-18 GHz
Heliox 3He Probe
Doubling amp
Hall bar sample on goniometer
20-36 GHz
coax
modulator
rf coil
H0
20-36 GHz,12 Hz.
Doubling amp
40-72GHz,12Hz
10MW
coax
RF Synth.
Spectrometer
50 MHz
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Electron-Nuclear Cross Relaxation
Electron Spin Resonance (ESR) due to absorption
of microwave
Dynamic Nuclear Polarization Overhauser Effect
nmr
esr
esr
nmr
nucleus
electron
T0.3K, ?0?, ?1 at B02.9T inset
f032.48GHz, ?1, T1.7K, ?60?
(Vitkalov, Bowers,1999)
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(Vitkalov, Bowers,1999)
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Conclusion

• The relationship of the number of spin flips (s)
  and the dimensionless Zeeman energy ( ) is
  achieved in distinct techniques.
• 2. The results are not comparable in various
  methods due to different experimental conditions.
• 3. Need to work on one single sample and control
  all factors to be the same in the distinct
  techniques future work!

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Experiments to Do

• I. Test for Skyrmions
• 1. Measure "s" by tilted field technique in our
  samples.
• 2. Measure "s" by ESR/DNP method in the same
  samples.
• 3. Measure "s" by NMR or OP-NMR in same samples.
• 4. Compare results of all 3 techniques in the
  same sample.

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• II. Other EDESR experiments1. Measure
  modulation frequency dependence of
• EDESR signal as a function of
  temperature.    -- this will test if we are in
  the steady state, possibly
• measure the electron T1 directly.
• 2. Measure microwave power dependence of EDESR
• signal as a function of temperature.    --
  these tests will determine if saturation is
  occurring.

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Acknowledgement
Dr. Bowers Bowers group Bhavin, Anil,
Josh Thank you very much for your participation!

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The work has been accomplished in the past
year(2002)1. NMR signal acquisition software --
NMRdaq3.5.1.vi2. NMR spectrometer3. Literature
Survey report
The circuit layout in the NMR spectrometer
PTS
attenuator
cable jumper
1
2
splitter
Pin 15 SW
Pin 16 SW
S
REC
power Amp
TR
ADC channel 1
ADC channel 2
1
2
S
splitter
Pin 13 SW
pre-amp box probe
Amp
Amp
Amp