Muon Spin Spectroscopy - SFU.capercival/NUSC341_muSR.pdf · Muon and Muonium Properties Negative...

Muon Spin SpectroscopyUsing the Positive Muon to Probe Matter

Paul W. Percival

Department of ChemistrySimon Fraser University

and TRIUMF

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NUSC 341, November 2005

Muon and Muonium Properties

Negative muon µ− a heavy electron (mass = 207 me)

τ = 2.2 µs in vacuum

less in matter because of nuclear capture

spin I = ½

Muonium Mu = µ+e− a light hydrogen atom Mu+ = µ+

Ionization Energy = 13.54 eV H: 13.60 eV

Bohr Radius = 0.532 Ǻ H: 0.529 Ǻ

Positive muon µ+ a light proton (mass = 0.11 mp)

τ = 2.2 µs in vacuum and matter

spin I = ½

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The Periodic Table Chemistry Department Quilt

http://www.sfu.ca/chemistry/news/pt_quilt/index.htm

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The Simplest Atom

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Muonium a light isotope of hydrogen

Mu ≡ µ+ e−

reduced mass of Mu = 0.995 mr(H)

ionization potential = 13.539 eV

Bohr radius = 0.532 Å

µ+

e−

The properties of a single electron atom are determined by the reduced mass

r N e e

r e

1 1 1 1

i.e .

m m m m

m m

= + ≈

≈

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Pions Decay to Give Muons

At TRIUMF, pions are produced by bombardment of a Be or C production target with 500 MeV protons. We take the positive pions, which decay to positive muons:

µπ µ ν+ +→ + In the pion rest frame:

Momentum is conserved:

Spin is conserved:

ν µ← →!

p pµ ν

µ νσ σ

=−

=−

""# ""#

""# ""#

Spin and momentum are related through helicity: 1

.ph hp

σψ ψ

σ⋅= =±# ## #

For the neutrino, h = -1, i.e. the spin and momentum are anti-parallel.

Therefore, muons are produced with σ and p anti-parallel.

p pν

ν

µ

µσσ

←→ ← →!

τ = 26 ns

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Muon Beams are Spin Polarized

There are two commonly used types of muon beam:

Surface Muon Beams collect and transport muons which are created from the decay of pions at or near the surface of the pion production target.

select these muons to get these spins:

beam line

Decay Muon Beams collect muons from pions which decay in flight.

In the π rest frame only backward and forward muons are transported.

In the laboratory frame, both momentum bites travel in the forward direction.

The forward (momentum) muons (p~180 MeV/c) have backward spin; the backward muons (p~80 MeV/c) have forward spin.

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Muon Decay

ee 2.2 sµµ ν ν τ µ+ +→ + + =

The 3 particle decay results in a spectrum of positron energies.

The spatial distribution of positrons is asymmetric and depends on the muon spin polarization.

Consider the decay pattern which results in the maximum positron energy:

The e+ is emitted in the direction of the muon spin at the moment of decay. More generally,

Energy

N

1max 2

52.8 MeV

E mµ==

e+νµ

νe

σeσν

[ ]( , ) 1 ( )cosdN E C D EdE d

θθ= +

Ωθ

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The Muon Lifetime Experiment

/0 bace kgroundtN N τ−= +

ee 2.2 sµµ ν ν τ µ+ +→ + + =

µ+

beamS

start stopCLOCK

M F

B

P

e+

time

N

lifetime histogram

0

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µ+

beamS

start stopCLOCK

M F

B

P

e+

time

N

µSR histogram

Muon Spin Rotation, µSR

( ) ( )[ ]/0 e 1 cos backgroundtN N aP t tτ ω φ−= + + +

Apply a magnetic field perpendicular to the initial spin direction.

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The µSR Histogram

-0.2

-0.1

0

0.1

0.2

0 1 2 3 4 5 6

time / µs

muo

n as

ymm

etry

0

200

400

600

800

0 1 2 3 4 5 6

time / µs

coun

t

( ) ( )[ ]/0 e 1 costN aP t t Bτ ω φ− + + +

Subtract the constant background and divide out the exponential decay

to get the muon asymmetry, which represents the time dependence of the muon spin polarization.

( ) ( )cosaP t tω φ+

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µSR: Muon Spectroscopy

spin polarized muon beam

muons are implanted in the sample

muons decay: µ+ → e+ + νµ + νe τ = 2.2 µs

angular distribution of e+ has maximum in muon spin direction

precession of muon spins in transverse magnetic field

equivalent to free induction decay in pulsed NMR or ESR

Muon Spin Rotation

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Muonium in supercritical water

Percival, Brodovitch, Ghandi et al., Phys. Chem. Chem. Phys. 1 (1999) 4999

400°C, 245 bar

0.0 0.5 1.0 1.5 2.0 2.5 3.0time / µs

-0.2

-0.1

0.0

0.1

0.2

Asym

met

ry

8 G

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Muonium in supercritical water

-0.15

0.00

0.15

0.00 0.50 1.00 1.50 2.00 2.50 3.00

time / µs

Muo

n A

sym

met

ry400°C, 245 bar, 8 G

AMue-λt

Diamagnetic signal subtracted

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Muonium in supercritical water at 196 G

400°C

245 bar

0.00 0.05 0.10 0.15 0.20

time / µs

Muo

n A

sym

met

ry

200 220 240 260 280 300 320 340

Frequency / MHz

Four

ier P

ower

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Energy levels of a two spin-½ system

Breit-Rabi diagram

(αβ − βα)/√2

0.0 1.0 2.0 3.0

Magnetic Field / Hyperfine Constant

RelativeEnergy

(αβ + βα)/√2

αα

ββ

αα

ββ

αβ

βα

e µ

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Muon spin precession in D2O crystal at 227 K

38 G

0.0 0.5 1.0 1.5 2.0

time /µs

Muo

n A

sym

met

ry

The high frequency precession is due to triplet (F=1) muonium.

The low frequency is due to muons in diamagnetic environments, such as MuOD and MuOD2

+

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Muonium precession frequencies in low magnetic field

Magnetic Field

Ene

rgy

1

2

3

ν12

ν23

Magnetic Field

1

2

3

ν12

ν23

isotropic hyperfine case axial anisotropy

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Muonium diffuses along the c-axis channels of ice-Ih

Mu

side view view along c channel

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µSR: Muon spectroscopic methods

Common features: spin polarized muon beam muons are implanted in the sample muons decay: µ+ → e+ + νµ + νε τ = 2.2 µs angular distribution of e+ has maximum in muon spin direction

Muon Spin Rotation µSR (TF-µSR) precession of muon spins in transverse magnetic field equivalent to free induction decay in pulsed NMR or ESR

Muon Spin Resonance RF-µSR muon spin polarization along magnetic field transitions induced by rf field as in conventional NMR

Muon Level Crossing Resonance µLCR (ALCR) mixing of spin levels causes avoided level crossing polarization is lost at magnetic fields where level crossing occurs

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RF Transitions in Muonium at Low Magnetic Field

Magnetic Field

Ene

rgy

1

2

3

νrf

νrf 2νrf

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RFµSR Spectrum of Mu@C60 in C60 Powder

120 130 140 150 160 170

Magnetic Field / G

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Endohedral Muonium Mu@C60

Muonium in a universe of its own

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Muoniated free radicals

e.g. cyclohexadienyl

µSR:precession frequencies ⇒ muon hyperfine couplingµLCR:resonance fields ⇒ other nuclear hyperfine couplings

hyperfine couplings ⇒ distribution of unpaired electron spin

Temperature dependence of hyperfine couplings⇒ intramolecular motion

R4R3

R2 CMu

R1

C

H Mu

0.33

-0.10

0.48

0.33

-0.10

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0 50 100 150 200 250 300 350 400Frequency / MHz

Four

ier P

ower

Transverse field muon spin rotation of radicals

Aµ = νR2 νR1

νR1

νR2

νD

Magnetic Field

Ene

rgy

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Fourier power µSR spectrum of tert-butyl

1 M tert-Butanol 280°C 250 bar 11.5 kG

0 50 100 150 200 250 300 350 400Frequency / MHz

Four

ier P

ower Aµ = 256 MHz CH3

CH3

CH2Mu

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Avoided Muon Level Crossing Resonance

µ Xres

µ X

12 γ γ

A AB

−≈

−

6.8 7.0 7.2 7.4 7.6 7.8 8.0 8.2

Magnetic Field / kG

A+ A

Magnetic Field

Ene

rgy

Xµe ,, ↑↓↑

Xµe ,, ↓↑↑

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tert-Butyl radical in water

10.0 10.5 11.0 11.5

Field / kG

A+ -A

-

CH3

CH3

CH2Mu

200°C

250 bar

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Hyperfine constants are used to map unpaired spin in radicals

Mu13C60 Avoided Level Crossing Resonance

15.010.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5

Magnetic Field /kG

Mu

3014

5.42.0

3.31.5

1.4

% Unpaired Spin Density

Percival, Addison-Jones, Brodovitch, Ji, et al., Chem. Phys. Lett., 245 (1995) 90

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H atoms and free radicals in liquids

H is the simplest atom⇒ fundamental chemistry

H is a constituent of water, hydrocarbons, carbohydrates⇒ essential chemistry

Chemically speaking, Mu ≡ H

because it is similar: tracer, spin label

because it is different : isotope effects

We study Mu as a substitute for H

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Muonium Chemistry areas of application

Muonium Mu as probe of local environment(caged) Fixed cage: fullerenes, silsesquioxanes

partial: icetransient: water

Kinetics How fast does it go?in gases: reaction dynamicsliquids: solvent effects; diffusion vs. activation control

Structure Where does it end up?(needs e-spin) Free radicals: unpaired spin distribution

Mechanism How does it get there?Identification of radical productsTransfer of muon polarization

Dynamics Nature is floppy!intramolecular Temperature dependence of hyperfine constantsintermolecular LCR lineshape analysis

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Further Reading

http://www.sfu.ca/chemistry/news/pt_quilt/index.htm

http://musr.org/cmms.php

http://musr.org/intro/musr/muSRBrochure.pdf

Muon Spin Spectroscopy - SFU.capercival/NUSC341_muSR.pdf · Muon and Muonium Properties Negative...

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