Pauli spin susceptibility in 2D electronsystem of (111) Si MOSFET.

Cryoconference 2010

Kapustin Aleksandra,b, A.A. Shashkina, V.T. Dolgopolova,M. Goiranb, H. Rakotob and Z.D. Kvonc

a Institute of Solid State Physics, Russian Academy of Science, Chernogolovka, Moscow region, 142432 Russia.

b Laboratoire National des Champs Magnetique Pulsees,31400 Toulouse,France.c Institute of Semiconductor Physics, Russian Academy of Science, Siberian branch, Novosibirsk, Russia.

Si MOSFETs and regime of strongelectron-electron interaction.

Ec≫E

F

Si

rs= 1/a

B(πn

s)1/2

Interaction parameter:

strong interaction limit:

in 2D systems

Si(111) and Si(100): comparison

Si(100) Si(111)

mc=(m

xm

y)1/2

gv (theory)

y

x

0.19me

0.358me

2 6

Si(111): higher values EC/E

F ,than in Si(100),

are expected at the same electron concentration.

Si(111)

Results of our previous experiments with Si(111): valleydegeneracy g

v=2 and growth of effective electron mass.

Si(111)

Si(100)

similar growth of mass in Si(111),as in Si(100),vs. parameter r

s,

characterizing interaction

T=0.03K 0.12 0.2 0.3 0.38 0.47 0.55 0.62 0.75

Δν =4 gv=2 in our Si(111)

small B fields:

Si(111)

Si MOSFET in parallel magnetic field B||: another way

to probe interaction effects.

ρ(B)/ρ(B=0)=f(ξ)

Si(111) MOSFET

ξ is the degree ofspin polarization

initial regions of MR curvesfor different concentrations n

s

Bsat

=Bp- field of full spin polarization

small B fields: M=χBχ-Pauli spin susceptibilityξ=χB/μ

Bn

s=Δ

z/2E

F(B=0)

magnetoresistance(MR) in B||

Corresponding MR theory: V.T. Dolgopolov, A. GoldJETP Letters vol. 71, p.42 (2000) χ∝gm is determined by

interaction effects

Measuring Pauli spin susceptibility in a Si(111) MOSFET

ξ = B/Bχ

ρ /ρ(0) is a universal function f(ξ)

Bχ ∝1/χ

if ξ(B) is linear up to ξ=1,then B(ξ=1)=B

χ

small B fields:

i.e. Bχ is a full spin poralization

determined fromPauli spin susceptibility

used for Bχnormalization

field,

Si(111)

Si(111)

1.Bχ(n

s) corresponds to growing χ

Bχ , calculated using,

mass values,measured in B ┴

dashed line:

2. MR saturation occurs earlier, than expected from χ , measured in weak B fields

Bsat

<Bχ

Si(111)

Sharp increase of χ ,measured in weak B fields,and nonlinear ξ(B) dependence in large B fields.

ξ(B)- is nonlinear (sharp bend)

Possible explanation of Bsat

<Bχ and nonlinear ξ(B)

:

filling of the upper subbands, separated by a gap Δ from the lower subbands.

Bsat

<Bχ

Si(111)

gives experimental evidence that in our Si(111)there is a valley splitting of Δ≈20K,which can explain g

v=2 seen in these samples.

Experimental results

1. In Si(111) Pauli spin susceptibility χ∝ gm growswith a decrease in electron concentration n

s due to interactions

This agrees with our earlier measurements of effectiveelectron mass m in these samples.

2.Full spin polarization is reached earlier, than expected from measurements of χ in small B. It may be explained by in-plane magnetic field induced filling of the upper subbands,corresponding to 2 (of total 6) valleys, which are emptyin B=0.

Nonlinear (with a sharp bend) ξ(B) dependence,explaining B

sat < B

χ