Fast Nuclear Spin Hyperpolarization of Phosphorus in Silicon
E. Sorte, W. Baker, D.R. McCamey, G. Laicher, C. Boehme, B. SaamDepartment of Physics, University of Utah
H0
Energy Splitting in Magnetic Field
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ms = 12 ,mI = 1
2
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ms = − 12 ,mI = 1
2
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ms = − 12 ,mI = − 1
2
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ms = 12 ,mI = − 1
2
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ˆ H = −μ e ⋅Ho − μN ⋅Ho + AI ⋅J
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Tx =1
Γx=
4πh2s5ρ
ω02kTresγ
2IA2
• Tx returns the spin populations n2 and n3 to thermal equilibrium with the phonon reservoir
1 D. Pines, J. Bardeen, C. Slichter, Phys. Rev. 106, 489 1957
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1
Tx
=2π
h
dk
2π( )3∫ δ hsk − hω0( ) Nk +1 1
2 δA Nk
2
Relaxation Times
n4
n3
n2
n1
1
1X
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T1 =1
Γ1
∝ e−
E
kTspin
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⇒
but
• T1 returns the spin populations n4 and n3 / n1 and n2 to thermal equilibrium with the lattice
Ee ≈ 240 GHz (electric Zeeman)
En ≈ 147 MHz (nuclear Zeeman)
A ≈ 117 MHz (hyperfine interaction)
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ωconduction band
valence band
phonons
Tspin (LH2 bath)
Tres
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hω > E res > kTspin
In general: Tres ≠ Tspin
Tres > TspinIn fact we want:
Temperature
• Constant illumination generates new charge carriers, leading to steady state with constant density of “hot” electrons
• As hot electrons cascade toward the lattice temperature, they emit phonons at constant rate.
G.Feher, Phys. Rev Lett 3, 135 (1959)
X
B=8.5T
1
1
Result = net nuclear antipolarization:
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P =(n1 + n2) − (n3 + n4 )
(n1 + n2) + (n3 + n4 )
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Tres >> Tspin
Mechanism
EDMR at T = 1.37 K Xe discharge lamp
EDMR at different temperatures
Experimental - EDMR
D. R. McCamey, J. van Tol, G. W. Morley, C. Boehme, eprint arXiv:0806.3429v1 (2008)
Comparison of polarization measured using EDMR vs EPR at different intensitiesof light (Hg discharge) at T = 3 K.
Hg discharge has higher spectral temperature, yielding higher polarizations(P=-24% at 3K vs -6% at 3K for Xe lamp) independent of intensity for most part.
Polarization with ESR 45% that measured with EDMR
Experimental - EDMR vs. ESR