Download - Grassellino - Application of Muon Spin Rotation to studies of cavity performance limitations
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