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

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E * = E int +1

3ε0

P =(2 + K)

3E int =

2 + K

3KE ext

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χm =Nμb

2

3kBT

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μb = g J(J +1)μB

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4(Zα )3

γ(4γ 2 −1)a2(ν 'ν )3 / 2

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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)

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emf = −mA2

3μ0

χ m

1+ fχ m

ndI

dt

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χm =C

T €

C =Nμb

2

3kB

=1.29

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f = 5.289

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NGd 3+

=1.03×1022 /cm3

Susceptibility χm Measurement II• Sample disk toroid, inductance • Resonant frequency:

• Width of the resonant peak:

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1

2π LC

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Q =ω

Δω=

1

R LC

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Ltoroid = n2(μ0μ r

A

l) ≈1μH

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L = Ltrans. + Ltoroid

1.31K

4K70K

|| B(1+C/T)

4% change

Electrical Properties of Poly-GGG

• Dielectric constant– K ~ 10-20

• Leakage current

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V m =C

C + Cscope

V 0

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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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{

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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.

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∇×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)