Electron EDM Measurement using a Paramagnetic Crystal

1
Electron EDM Measurement using a Paramagnetic
Crystal
6/2/03

• Chen-Yu Liu and S. Lamoreaux (P-23)
• M. Espy and A. Matlachov (P-21)

2
Shapiros proposal
Usp. Fiz. Nauk., 95 145(1968)

• 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.

3
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.
• EEext/3

4
Whats required?

• High E field
• Sample 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.

5
Current Status of eEDM
6
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.

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First solid state eEDM exp.

• B.V. Vasilev and E.V. Kolycheva, Sov. Phys.
  JETP, 47 2 243 (1978)
• Sample Nickel Zinc ferrite
• dielectric strength 2kV/cm.
• Fe3 ?b 4 ?B . (uncompensated moment)
• Atomic enhancement factor 0.52.
• Magnetic permeability 11 (at 4.2K). (??m0.8)
• Electric permittivity ?2.2?0.2. (??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 (4.2?6.0) ?10-23 e-cm ? de(8.1
  ?11.6)?10-23 e-cm

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New Version

• Gd3 in GGG
• 4f75d06s0 ( 7 unpaired electrons).
• Atomic enhancement factor -2.2?0.5.
• 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.govphysics/020647
(June 2002)
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Solid State Properties of GGG

• Gadolinium Gallium Garnet
• Gd3Ga5O12
• Garnet Structure A3B2(C3)O12
• A dodecahedron M3?
• Ca, Mn, Fe, R (La,..Gd,..Lu)
• B octahedron,C (tetrahedron)
• Fe, Ga,
• Ceramic of good electrical properties.

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Bake GGG Polycrystal
K. McClellan in MST-8

• Solid State Reaction of the Oxides
• E.E. Hellstrom et al., J. Am. Ceram. Soc., 72
  1376 (1989)
• Weigh powders of 3 (Gd2O3)5 (Ga2O3) mole ratio,
  dried at 1000?C 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 1350?C 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
  1650?C for 10 h.
• Heating and cooling rates 200?C/h below 1000?C
• 
  100?C/h above 1000?C

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Alumina Crucible
Parallel plate capacitor
Single crystal GGG
Polycrystal GGG
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X-ray diffraction of GGG
J. Valdez and K. Sickafus in MST-8
5/30/03
Polycrystal crushed powder
Polycrystal bulk surface
Single crystal crushed powder
2?
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Magnetic Properties of GGG

• Gd3 half filled 4f orbital
• 7 e- (spin aligned)
• L0, S7/2
• A3B2(C3)O12
• Spin ? ? (?)
• JABlt0, JACgt0, JBClt0
• JAA, JAB ltlt JAC
• In A sublattice
• JAAlt0 (AF coupling)
• JNN S(S1) 1.5K
• Geometrically frustrated AF magnet
• ? Spin glass transition at 0.4K. (Limit of
  temperature)

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Susceptibility ?m Measurement I
Sample magnetization M?mH ?m(HextHm)
?m(B0/?0-fM)
?
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Susceptibility ?m Measurement II

• Sample disk ?toroid, inductance
• Resonant frequency
• Width of the resonant peak

B(1C/T)
1.31K
4K
70K
4 change
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Electrical Properties of Poly-GGG
V0

• Dielectric constant
• K 10-20
• Leakage current

Vm
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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 ?
  Metglas alloy ribbons.
• Additional layers of cryoperm 10 sheets.
• A magnetic shielding factor gt 109.
• The whole assembly is immersed in L-He bath,
  cooled by a high cooling power dilution
  refrigerator. (10?W at 10mK, 100?W at 100mK)

?
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Magnetic flux pick-up coil (planar gradiometer)

• Common rejection of residual external
• uniform B field and fluctuations.
• Enhancement of sample flux pick-up.

R12cm R22.2cm R3?(R12R22)3.42cm LG700nH for
10?m dia. wire 500nH for 100?m dia.
Wire (Nb superconducting wire)
0
_
2.5
5
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SQUID
M. Espy and A. Matlachov

• DC SQUID two Josephson junctions on a
  superconducting ring.
• Flux to voltage transformer.
• Energy sensitivity 5 at 50 mK.
• Flux noise 0.2 ??0/vHz.
• Field sensitivity in principle can be infinite
  by using large pick-up coil with thin wire,
  typically fT/vHz.
• Pick-up coil connects to a spiral SQUID input
  coil, which is inductively coupled to SQUID.
• Coupling constant (geometrical factor)?

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How well can we do?

• Lsq 0.2 nH (intrinsic)
• Lp0.7 ?H (gradiometer)
• Li0.5 ?H
• Coupling eff. ?sq/?p v(LsqLi)/(LpLi)
  8?10-3.
• de ??sq/?sq(0.2??0/vt)/(8?10-3 ? ?p)
• with 10kV/cm, T10mK, A100 cm2 around GGG
• ?p 17??0 per 10-27e-cm
• de 1.47?10-27 /vt e-cm
• In 10 days of averaging, de 10-30 e-cm.

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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. (lt10-14A, 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
  dont move.)
• Spin-lattice relaxation ???
• Energy dissipation lt 10?W at 10mK.

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Tentative Schedule

• (v ) Sample preparation and characterization.
  (fall 2002)
• (v ) 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)