Applica'onofMuonSpinRota'ontostudiesofcavityperformancelimita'ons

AnnaGrassellinoUniversityofPennsylvania,TRIUMF

Some of the most powerful tools available in condensed matter physics and materials science are instrumental methods that utilize a Magnetic Moment and/or Electric Quadrupole Moment to probe the local magnetic, electronic or structural properties of matter:

Conventional Methods

Intrinsic probe: Nuclei Electrons

Nuclear Beam Methods

Implanted probe: Muons Radioactive Nuclei

1. Produce a non-equilibrium polarization

2. Monitor how the polarization evolves in time or changes with frequency

General Procedure:

Pion Decay:

Conservation of Linear Momentum: µ+ emitted with momentum equal and opposite to that of the νµ

π+ → µ+ + νµ

Conservation of Angular Momentum: µ+ and the νµ have equal and opposite spin

A pion resting on the downstream side of the primary production target has zero linear momentum and zero angular momentum.

Weak Interaction: only “left-handed” νµ are created. Therefore the emerging µ+ has its spin pointing antiparallel to its momentum direction

µ+-Decay Asymmetry

Angular distribution of positrons from the µ+-decay. The asymmetry is a = 1/3 when all positron energies are sampled with equal probability.

The muon is sensitive to the vector sum of the local magnetic fields at its stopping site. The local fields consist of:

• those from nuclear magnetic moments • those from electronic moments (100-1000 times larger than from nuclear moments) • external magnetic fields

As a local probe, µSR can be used to deduce Magnetic volume fractions.

•  greater sensitivity enables studies of dilute or isolated impurities

•  magnetism can be studied in zero external magnetic field

•  can study dynamical ranges not accessible with conventional methods

Major Advantages of and

• can be implanted into any sample (gas, solid or liquid)

•  polarization independent of sample and sample environment

10-4 10-2 100 102 104 106 108 1010 1012 1014

Fluctuation Rate (Hz)

Conventional Methods

Probe: host nuclei host electrons muons radioactive nuclei

Lifetime: infinite infinite 2.2 µs 100 ms - hours

Polarization Method: apply large apply large natural optical field field pumping

Polarization (max.): << 1 % << 1 % 100 % 80 %

Detection: absorbed absorbed anisotropic anisotropic RF radiation microwave decay of decay of radiation muon nucleus

Sensitivity: 1017 spins 1017 spins 107 spins 107 spins

Nuclear Beam Methods

Transverse-Field µSR

The time evolution of the muon spin polarization is described by:

where G(t) is a relaxation function describing the envelope of the TF-µSR signal that is sensitive to the width of the static field distribution or temporal fluctuations.

•  “Local”extremelysensi'vemagne'cfieldprobe(vsmagne'za'onetc)

•  Canimplantatdifferentdepths:canstudysurfacevsbulk

•  Canbeusedtostudythinfilms,surfacesandmul'‐layeredcompounds

•  Cananswerseveralques'ons:1.  IsHFQSduetoearlyfluxpenetra7on?2.  RoleoftrappedfluxonHFQSand/orMFQS?3.  Fielddependenceofpenetra7ondepthand

coherencelength?4. Magne7cimpuri7es?

for Q-slope studies and

HFQS:earlyfluxpenetra'on?

•  MeasureHp,Hc2,Tc

•  Vibra'ngsamplemagnetometerand3experimentalprotocols(ZFCwarming,FCC,FCW)

•  Samples:S1(pris'neasreceivedbyvendor),S2(BCP+10h600C),S3(S2plus10h120C)

Roy,MynenietSahni,Supercond.Sci.Technol.22(2009)105014(6pp)

HFQS:earlyfluxpenetra'on?

[ARomanenkoandHPadamsee2010Supercond.Sci.Technol.23045008]

Decreaseinaveragedisloca'ondensityobservedbyEBSDincutoutsamplesafer120Cbaking(whichremovestheHFQSincavi'es)

Workinghypothesis–surfacedisloca'onsprovidesitesforearlyfluxpenetra'on(belowbulkHc1)resul'ngintheHFQSduetofluxoidmo'oninNb

Beforebaking Aferbaking

16

HFQS:earlyfluxpenetra'on?

RFSide

OuterSide

HFQSandMFQS:trappedflux?

•  Oscilla'ngfluxoidscancauselossesinmediumandhighfieldregimes(Gurevich,Rabinowitz)

•  LookwithmuSRforcorrela'onhot/coldspotswithhigher/lowertrappedflux Ciova',Gurevich–Evidenceofhighfield

radiofrequencyhotspotsduetotrappedvor'cesinNbcavi'es,PRSTAB,11,122001,2008

Descrip'onoftheexperiment•  Measurefieldoffirstpenetra'oninRFcharacterized(via

thermometry)HFQSlimitedsamples,andcomparewithHFQSRFfieldonset:–  Hotvscold–  Unbakedvsbaked

•  Studythenatureofthetransi'on:intermediatemixedstate?Anycorrela'onbetweenIMSandhotspots?

•  Trappedflux(hot/cold,baked/unbaked):zerofieldmuSR•  Fieldrange0‐200mT,Temperaturerange1K‐4.2K•  5samples:

–  Pris'neNb–fromvendor–  Hot/coldspotcutoutfromlargegraincavity(beforeandaferbake)–

providedbyAlexanderRomanenko,HasanPadamsee(Cornell)•  Beam'meapproved:~1daypersample12shifs,star'ngOct

27th

MFQS,HFQS:fielddependenceoffundamentalsuperconduc'ngparameters?

•  Fielddependenceofpenetra'ondepthandcoherencelength?

•  Determinedbygapstructure:doublegapinNb?•  StudyvortexcoresizewithmuSR

0.0 0.1 0.2 0.3 0.4

50

100

150

200

! ab

(Å

)

NbSe2

H/Hc2

T = 0.02 K T = 2.5 K T = 4.2 K

0 5 10 15 20 250

20

40

60

80

100

0.0

0.1

0.2

0.3

0.4

0.5

0.6

! e /

! n

" ab

(Å

)

H (kOe)

Freeze out thermal excitations of quasiparticle core states to reveal multiband vortices.

“Effec've”Magne'cPenetra'onDepth:Magne'cFieldDependence

0.0 0.1 0.2500

1000

1500

2000

LuNi2B

2C

V3Si

YBa2Cu

3O

6.95

! ab

(Å

)

H/Hc2

NbSe2 • V3Si fully gapped

• LuNi2B2C anisotropic gap

• YBa2Cu3O6.95 dx2

-y2-wave gap

• NbSe2 multiband

PureVanadium(marginaltype‐II)

Laulajainen, Callaghan, Kaiser & Sonier PRB 74, 054511 (2006)

Impactonlow,mediumandhighfieldQ‐slope

•  Fielddependenceofpenetra'ondepth

•  Fielddependentlossesduetoincreasedvolumewheredissipa'onoccurs

Rs ∼ (µ02ω2λ3σnΔ/T)exp(-Δ/T)

H(t)E(z,t)

€

Rs ∝µ02ω 2λ4Δn0kBTpF

ln Δω

+ C0

exp −

ΔkBT

Ermolov, Marchenko, Chizov, 1986

λ(H)

Impactonlow,mediumandhighfieldQ‐slope

•  Fielddependenceofcoherencelengthcancause‘gain’(sta'onarytrappedflux)

•  Sumofgain(coherencelength)andlosses(penetra'ondepth)couldexplainalsolowfieldQ‐slope

Descrip'onofthesecondexperiment

•  Determinethefielddependenceoftheeffec'vepenetra'ondepth(andvortexcoresize)inthevortexandintermediatemixedstates.Willdothisatseveraltemperaturestoinves'gatethepossibilityoftwoSCgaps.

•  TakeadvantageofmuSRuniquesofwareformeasurementsofthevortexlarceinamarginaltype‐II

•  TF‐muSR,dilu'onrefrigerator•  Pris'nesinglecrystalsample•  Beam'meapproved:12shifs