# Presentation: 850215

## 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

## What’s 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.

## Current Status of eEDM

|  | eEDM | nEDM |
| --- | --- | --- |
| Standard Model | <10-37 | <10-30 |
| Super-Symm. | 10-2 dn | <810-29 |
| L-R symm. | 10-26~10-28 | 10-29 |
| Higgs Models | 310-27 ~10-28 |  |
| Lepton flavor-chaging | 10-27~10-29 |  |
| Experimental limit | (0.690.74)10-27 (Berkeley) | 0.6310-25 
(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.

## 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+: b = 4 B . (uncompensated moment)
- Atomic enhancement factor = 0.52.
- Magnetic permeability = 11 (at 4.2K).  (m=0.8)
- 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

## New Version

- Gd3+ in GGG
- 4*f*75*d*06*s*0 ( 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.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 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

- K. McClellan in MST-8

**Notes:**
G2aO3 loss

## Alumina Crucible

- Single
- crystal GGG

- Polycrystal GGG

- Parallel plate
- capacitor

## X-ray diffraction of GGG

- 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 m Measurement I

- Sample magnetization:
- M=mH= m(Hext+Hm) = m(B0/0-fM)

- 

## Susceptibility m Measurement II

-  Sample disk toroid, inductance
-  Resonant frequency:
-  Width of the resonant peak:

- 1.31K

- 4K

- 70K

- || B(1+C/T)

- 4% change

## Electrical Properties of Poly-GGG

- Dielectric constant
- K ~ 10-20
- Leakage current

- 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  **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. (10W at 10mK, 100W at 100mK)

- 

## Magnetic flux pick-up coil (planar gradiometer) 

- R1=2cm
- R2=2.2cm
- R3=(R12+R22)=3.42cm
- LG=700nH for 10m dia. wire
-      =500nH for 100m 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 0/√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)?

- M. Espy and A. Matlachov

## How well can we do?

- Lsq= 0.2 nH (intrinsic)
- Lp=0.7 H (gradiometer)
- Li=0.5 H
- Coupling eff. = sq/p = √(LsqLi)/(Lp+Li)= 810-3.
- de = sq/sq=(0.20/√t)/(810-3  p)
- with 10kV/cm, T=10mK, A=100 cm2 around GGG
- p =170 per 10-27e-cm
- de = 1.4710-27 /√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 < 10W at 10mK.

## 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)