Paramagnetic Properties of Fullerene-Derived Nanomaterials ...
Electron EDM Measurement using a Paramagnetic Crystal Chen-Yu Liu and S. Lamoreaux (P-23) M. Espy...
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Transcript of Electron EDM Measurement using a Paramagnetic Crystal Chen-Yu Liu and S. Lamoreaux (P-23) M. Espy...
Electron EDM Measurement using a Paramagnetic Crystal
Chen-Yu Liu and S. Lamoreaux (P-23)
M. Espy and A. Matlachov (P-21)
6/2/03
Shapiro’s proposal
• High Z material high high net eEDM.
• E field aligns eEDM
• eEDM // eSpin.
• Induces bulk magnetization, which produces B flux.
• Reverse the E field, and the magnetization signal is modulated.
Usp. Fiz. Nauk., 95 145(1968)
Figure of Merit• Induced flux:
• Paramagnetic susceptibility: – Large density of paramagnetic sites.– Low temperature.– Large unit magnetic moment:
• Enhancement factor:• Large A (for =AB).• Effective field:
– Large K.– E*=Eext/3
€
Δ=χm AdE * μa
€
E * = E int +1
3ε0
P =(2 + K)
3E int =
2 + K
3KE ext
€
χm =Nμb
2
3kBT
€
μb = g J(J +1)μB
€
4(Zα )3
γ(4γ 2 −1)a2(ν 'ν )3 / 2
€
γ= (J +1
2)2 − Z 2a2
What’s required?
• High E fieldSample with – A small conductivity.– A high dielectric strength.– A large dielectric constant to reduce D cancellation.
• Large magnetic response. An insulating paramagnet.• Sensitive magnetometer
– SQUID.– Optical method?
• Non-linear Faraday effect in atomic vapors.
Current Status of eEDMeEDM nEDM
Standard Model <10-37 <10-30
Super-Symm. 10-2 dn <810-29
L-R symm. 10-26~10-28 10-29
Higgs Models 310-27 ~10-28
Lepton flavor-chaging
10-27~10-29
Experimental limit
(0.690.74)10-
27 (Berkeley)0.6310-25
(ILL)
Features of solid state eEDM exp.
• No effect.
• High number density of bare electrons.
• Solid state:– High dielectric strength.– Large magnetic response.
• Concerns– Parasitic, hysteresis effects.
€
v × B
First solid state eEDM exp.B.V. Vasil’ev and E.V. Kolycheva, Sov. Phys. JETP, 47 [2] 243 (1978)• Sample: Nickel Zinc ferrite
– dielectric strength ~ 2kV/cm.– Fe3+: μb = 4 μB . (uncompensated moment)– Atomic enhancement factor = 0.52.– Magnetic permeability = 11 (at 4.2K). (χm=0.8)– Electric permittivity =2.20.2. (=0K)– Cubic lattice.– No magnetoelectric effect.
• Sample size: 1cm in dia., 1mm in height. (0.08 c.c.)• E Field: 1Kv/cm, 30Hz reversal rate• Temperature : 4.2K• rfSQUID with a field sensitivity of 10-16 T.• dFe3+= (4.26.0) 10-23 e-cm de=(8.1 11.6)10-23 e-cm
New Version• Gd3+ in GGG
– 4f75d06s0 ( 7 unpaired electrons).– Atomic enhancement factor = -2.20.5.
– Langevin paramagnet.– Dielectric constant ~ 12.– Low electrical conductivity and high dielectric strength
• Volume resistivity = 1016-cm.• Dielectric strength = 10 MV/cm for amorphous sample. (Crystalline sample
tend to have lower K)
– Cubic lattice.
• Larger sample: 100 c.c. (4cm in dia. 2 cm in height 2 pieces)• Higher E field: 5-10kV/cm.• Lower temperature ~ 50mK (with a DR).• Better SQUID design.
V.A. Dzuba et al., xxx.lanl.gov:physics/020647 (June 2002)
Solid State Properties of GGG
• Gadolinium Gallium Garnet – Gd3Ga5O12
• Garnet Structure: {A3}[B2](C3)O12
– A {dodecahedron}: M3
• Ca, Mn, Fe, R (La,..Gd,..Lu)
– B [octahedron],C (tetrahedron):• Fe, Ga, …
• Ceramic of good electrical properties.
Bake GGG Polycrystal• Solid State Reaction of the OxidesE.E. Hellstrom et al., J. Am. Ceram. Soc., 72 1376 (1989)
– Weigh powders of 3 (Gd2O3):5 (Ga2O3) mole ratio, dried at 1000C for 9 h in air.
– Mixed and ball-milled with Zirconia balls and acetone in polyethylene jars for 6 h.
– Dry in air to remove acetone.– Isostatically pressed into a pellet, then prereact at 1350C for 6 h in air in
high-purity alumina crucibles.– Crush the prereacted pellet using agate mortar and pestle and ball-milled
(as before) for 24 h.– Cold press the powder into pellets, and sinter at 1650C for 10 h.– Heating and cooling rates: 200C/h below 1000C 100C/h above 1000C
K. McClellan in MST-8
Alumina Crucible
Single crystal GGG
Polycrystal GGG
Parallel platecapacitor
X-ray diffraction of GGG
20 30 40 50 60 70 80 90
J. Valdez and K. Sickafus in MST-8
Polycrystal crushed powder
Polycrystal bulk surface
Single crystal crushed powder
2
5/30/03
Magnetic Properties of GGG• Gd3+: half filled 4f orbital
– 7 e- (spin aligned)– L=0, S=7/2
{A3}[B2](C3)O12
• Spin: {} [] () – JAB<0, JAC>0, JBC<0 – |JAA|,| JAB| << |JAC|– In A sublattice:
• JAA<0 (AF coupling)• JNN S(S+1) ~ 1.5K
• Geometrically frustrated AF magnet:
Spin glass transition at 0.4K. (Limit of temperature)
Susceptibility χm Measurement I
Sample magnetization:
M=χmH= χm(Hext+Hm) = χm(B0/μ0-fM)
€
emf = −mA2
3μ0
χ m
1+ fχ m
ndI
dt
€
χm =C
T €
C =Nμb
2
3kB
=1.29
€
f = 5.289
€
NGd 3+
=1.03×1022 /cm3
Susceptibility χm Measurement II• Sample disk toroid, inductance • Resonant frequency:
• Width of the resonant peak:
€
1
2π LC
€
Q =ω
Δω=
1
R LC
€
Ltoroid = n2(μ0μ r
A
l) ≈1μH
€
L = Ltrans. + Ltoroid
1.31K
4K70K
|| B(1+C/T)
4% change
Electrical Properties of Poly-GGG
• Dielectric constant– K ~ 10-20
• Leakage current
€
V m =C
C + Cscope
V 0
€
C = Kε0
A
d≈ 0.1 ~ 1pF
V0
Vm
Instrumentation
• Macor/graphite coated electrodes. (reduce Johnson noise)• Sample/electrode plates sandwiched by G10 clamps.• G10 can wrapped by superconducting Pb foils (two layers).• Rectangular magnetic field formed by high μ Metglas alloy
ribbons.• Additional layers of “cryoperm 10” sheets.• A magnetic shielding factor > 109.
• The whole assembly is immersed in L-He bath, cooled by a high cooling power dilution refrigerator. (10μW at 10mK, 100μW at 100mK)
€
{
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LG = L1 + L2 + L3 + 2M12 − 2M23 − 2M13
R1=2cmR2=2.2cmR3=(R1
2+R22)=3.42cm
LG=700nH for 10μm dia. wire =500nH for 100μm dia. Wire(Nb superconducting wire)
Magnetic flux pick-up coil (planar gradiometer)
• Common rejection of residual external uniform B field and fluctuations.• Enhancement of sample flux pick-up.
+
_
0
5”2.5”
SQUID• DC SQUID: two Josephson junctions on a
superconducting ring.• Flux to voltage transformer.• Energy sensitivity ~ 5 at 50 mK.• Flux noise ~ 0.2 μ0/√Hz.• Field sensitivity: in principle can be infinite by
using large pick-up coil with thin wire, typically fT/√Hz.
• Pick-up coil connects to a spiral SQUID input coil, which is inductively coupled to SQUID.
• Coupling constant (geometrical factor)?
€
h
M. Espy and A. Matlachov
How well can we do?
• Lsq= 0.2 nH (intrinsic)• Lp=0.7 μH (gradiometer)• Li=0.5 μH• Coupling eff. = sq/p = √(LsqLi)/(Lp+Li)= 810-3.• de = Δsq/sq=(0.2μ0/√t)/(810-3 p)
– with 10kV/cm, T=10mK, A=100 cm2 around GGG p =17μ0 per 10-27e-cm – de = 1.4710-27 /√t e-cm
• In 10 days of averaging, de~ 10-30 e-cm.
Expected systematic effects• Random noise:
– High voltage fluctuation.– SQUID 1/f noise.– Sample 1/f noise, due to paramagnetic dissipation. ???– External B field fluctuation. (gradiometer)
• Displacement current at field reversal.– Generate large field. (position of the pick-up coil) – Too big a field change for SQUID to follow. ???
• Leakage current. (<10-14A, should be feasible at low temp.)• Linear magneto-electric effect.
– Deviation from cubic symmetry. ???• Vibrations relative to the superconducting Pb can (trapped flux
field fluctuations). ???• Magnetic impurities. (no problem, as long as they don’t move.)• Spin-lattice relaxation ???• Energy dissipation < 10μW at 10mK.
€
∇×B = με∂E
∂t
Tentative Schedule
(√ ) Sample preparation and characterization. (fall 2002)
(√ ) Design and build experiment. (spring 2003)
( _ ) Couple to dilution refrigerator. (fall 2003)
( _ ) First measurement using SQUID. (winter 2003)
( _ ) Preliminary results. (spring 2004)
( _ ) Improved version using optical method. (summer 2004)