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Electron EDM Measurement using a Paramagnetic Crystal

This study presents innovative methodologies for measuring electric dipole moments (eEDM) with a focus on paramagnetic crystals. Key concepts include the alignment of electric fields in high-Z materials leading to significant enhancements in eEDM signals. Through techniques such as the use of SQUID magnetometers and optical methods, we detail the intricacies of magnetization modulation, dielectric constants, and sample properties essential for successful experiments. The latest results from solid-state eEDM experiments using materials like Nickel Zinc ferrite and Gadolinium Gallium Garnet highlight the potential for detecting fundamental physics phenomena.

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Electron EDM Measurement using a Paramagnetic Crystal

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  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 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. • E*=Eext/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

  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. • 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

  8. 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.gov:physics/020647 (June 2002)

  9. 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.

  10. 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

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

  12. 20 30 40 50 60 70 80 90 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

  13. 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)

  14. Susceptibility m Measurement I Sample magnetization: M=mH= m(Hext+Hm) = m(B0/0-fM) 

  15. Susceptibility m Measurement II • Sample disk toroid, inductance • Resonant frequency: • Width of the resonant peak: || B(1+C/T) 1.31K 4K 70K 4% change

  16. Electrical Properties of Poly-GGG V0 • Dielectric constant • K ~ 10-20 • Leakage current Vm

  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 > 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) 

  18. Magnetic flux pick-up coil (planar gradiometer) • Common rejection of residual external • uniform B field and fluctuations. • Enhancement of sample flux pick-up. + 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) 0 _ 2.5” 5”

  19. 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/√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)?

  20. 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 /√te-cm • In 10 days of averaging, de~ 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. (<10-14A, 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.

  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)

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