1. 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

2. 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)

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. –E*=E ext /3

4. 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.

5. Current Status of eEDM eEDMnEDM Standard Model<10 -37 <10 -30 Super-Symm.10 -2 d n <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)

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.

7. 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. –Fe 3+ :  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. (  =  0 K) –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. d Fe3+ = (4.2  6.0)  10 -23 e-cm  d e =(8.1  11.6)  10 -23 e-cm

8. New Version Gd 3+ in GGG –4f 7 5d 0 6s 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 = 10 16  -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)

9. Solid State Properties of GGG Gadolinium Gallium Garnet –Gd 3 Ga 5 O 12 Garnet Structure: {A 3 }[B 2 ](C 3 )O 12 –A {dodecahedron}: M 3  Ca, Mn, Fe, R (La,..Gd,..Lu) –B [octahedron],C (tetrahedron): Fe, Ga, … Ceramic of good electrical properties.

10. 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 (Gd 2 O 3 ):5 (Ga 2 O 3 ) 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

11. Alumina Crucible Single crystal GGG Polycrystal GGG Parallel plate capacitor

12. X-ray diffraction of GGG 2030405060708090 J. Valdez and K. Sickafus in MST-8 Polycrystal crushed powder Polycrystal bulk surface Single crystal crushed powder 22 5/30/03

13. Magnetic Properties of GGG Gd 3+ : half filled 4f orbital –7 e - (spin aligned) –L=0, S=7/2 {A 3 }[B 2 ](C 3 )O 12 Spin: {  } [  ] (  ) –J AB 0, J BC <0 –|J AA |,| J AB | << |J AC | –In A sublattice: J AA <0 (AF coupling) J NN S(S+1) ~ 1.5K Geometrically frustrated AF magnet:  Spin glass transition at 0.4K. (Limit of temperature)

14. Susceptibility  m Measurement I Sample magnetization: M=  m H=  m (H ext +H m ) =  m (B 0 /  0 -fM) 

15. 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

16. Electrical Properties of Poly-GGG Dielectric constant –K ~ 10-20 Leakage current V0V0 VmVm

17. 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 > 10 9. 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) 

18. R 1 =2cm R 2 =2.2cm R 3 =  (R 1 2 +R 2 2 )=3.42cm L G =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”

19. 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

20. How well can we do? L sq = 0.2 nH (intrinsic) L p =0.7  H (gradiometer) L i =0.5  H Coupling eff. =  sq /  p = √(L sq L i )/(L p +L i )= 8  10 -3. d e =  sq /  sq =(0.2  0 /√t)/(8  10 -3   p ) –with 10kV/cm, T=10mK, A=100 cm 2 around GGG –  p =17  0 per 10 -27 e-cm –d e = 1.47  10 -27 /√t e-cm In 10 days of averaging, d e ~ 10 -30 e-cm.

21. 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 -14 A, 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.

22. 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)