Introduction to µSR
Roberto De Renzi
DiFeST, Department of Physics and Earth Sciences
University of Parma
Italy
Setup of the first spectrometer at ISIS, MuSR
1896
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1987
De Renzi - ISIS Muon Training
2014
Introduction to µSR
• Muon history
–
–
–
–
The charged particles
Anti-matter
The neutrinos
Parity violation
• How it works
–
–
–
–
–
Production
Spin polarization
Transport
Implantation
Detection
• Few examples
• Summary
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J.J. Thomson: the electron
B
e
m
J J Thomson
Electrons orbit around B
e
Thomson measures the ratio
:
m
a light (lepton) q<0 particle
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He suggests recipes for
the best plum pudding
1955
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E. Rutherford: the nucleus
particles through
a gold foil scatter at
large angles
An even better cake!
E Rutherford
1911
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1955
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Bohr atom
2014
4
E. Rutherford: the proton
particles through
N2 scatter hydrogen
nuclei
Let's call them
protons!
1918
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1955
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E Rutherford
2014
5
P.A.M. Dirac, C. Anderson:
the positron
From relativity, quadratic energy form
2
2
2
2
E =p c +m c
E
e-
4
0
Dirac predicted the electron sea
e-
E = √ p 2 c 2 +m 2 c 4
PAM Dirac
e?
E =−√ p 2 c 2 +m 2 c 4
No, it's an
anti-electron
B
19281932
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CD Anderson
2014
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Antimatter
Dirac's E<0 solutions: each particle has an antiparticle
proton
p ⇔ p̄
+
p
p antiproton
electron
e ⇔ ē antielectron = positron
+
e
e
B
1932
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CD Anderson
2014
7
J. Chadwick: the neutron
particles from Po on Bo
produce unknown radiation
Po

N2
n
N
Neutral particle with mass mnc2
= 938 MeV
The name is
= 1.0014 mpc2
my idea, yo!
Nuclear mass
= 1800 mec2
didn't add up!
heavy
(baryon)
E Rutherford
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1932
1955
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J Chadwick
2014
8
Pauli suggested a neutral
particle for β decays
Beta decay at rest,
if it were a 2-body decay
products would have fixed energies
There must be
14
6
14
7
C →
14
7
N +e
N
an additional
neutral
particle,
the neutron!
−
e
−
W Pauli
Instead they have an energy spectrum
3-body decay!
?
1930
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Pauli suggested a neutrino
Beta decay at rest,
if it were a 2-body decay
products would have fixed energies
There must be
14
6
14
7
C →
14
7
N +e
an additional
neutral
particle,
the neutron!
−
N
e
−
W Pauli
Instead they have an energy spectrum
After Chadwick's
discovery of the
neutron let's call
it neutrino
14
6
1930
1932
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C →
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14
7
−
N +e + ν̄e
E Fermi
2014
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H. Yukawa: the meson
Nuclei are made of n and p+. What force binds them with finite range?
Coulomb force = exchange of photons
e-
hν
p+
mν = 0
In analogy
n meson p+
mc2 ~ 150 MeV
Mass justifies screening, finite range
V (r )∝ 1
r
1
V (r )∝ e
r
−
hr
√ 2 mc
V (q )∝ 12
q
V (q )∝
1
2 2
2 2m c
q +
2
h
1935
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H Yukawa
1955
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0.5
140
980 Mev
leptons mesons baryons
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C. Anderson, S Neddermayer:
mesotron
Within two years a new particle with that mass (~)
is found. C.D. Anderson calls it mesotron
100 < mc2 < 150 MeV
with
cosmic ray
balloons
VF Hess
However its decay is a bit
slow
But I don't know
that yet
CD Anderson
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τ ~ 2 μs
and it has spin
S=1/2
1936
1955
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I measured it
in 1941
BB Rossi
2014
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M. Conversi: not Yukawa's
meson?
Furthermore the mesotron does not interact
strongly enough with matter.
μ ⇔ μ̄
+
μ
μ
M Conversi
Fe
C
µ+
0.67 ± 0.07
0.36 ± 0.05
µ-
0.03 ± 0.03
0.27 ± 0.03
μ - + p + → n + νμ
1946
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C. Powell G. Occhialini: Two
particles, pion and muon
μ
e
Three tracks in a photographic emulsions at Mt
Chacaltaya (5600 m).
C Powell
The π is Yukawa's meson
G Occhialini
mπ = 140 MeV/c2
τπ = 26 ns
S = 0
The μ is a lepton (a heavier electron)
mμ = 106 MeV/c2
τμ = 2200 ns
S = ½
μ
π
1947
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C. Powell G. Occhialini: Two
particles, pion and muon
Three tracks in a photographic emulsions at Mt
Chacaltaya (5600 m).
C Powell
μ
e
The π is Yukawa's meson
G Occhialini
τπ = 26 ns
S = 0
W Pauli
Hey, there's
something
missing here
The μ is a lepton (a heavier electron)
mμ = 106 MeV/c2
τμ = 2200 ns
S = ½
μ
π
1947
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mπ = 140 MeV/c2
1955
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So what is missing?
W Pauli
Hey, there's
something
missing there
μ
e
μ
π
Linear momentum
conservation!
1947
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Pion and muon, both
weak decays
νe
π
π+ → μ + + νe
μ
νe
μ e
+
+
μ → e + ν̄μ + νe
Matter
Antimatter
+
e
ē =e
p
p
̄ =p
n
n̄
+
ππ 0= π̄0
π
̄ =π
+
μ
μ
̄ =μ
νμ
1947
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Recognitions
Incidentally:
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Nobel prize for
1906 J.J. Thomson
1908 E. Rutherford
1933 P.A.M Dirac and E. Schrödinger
1935 J. Chadwick
1936 C.D. Anderson, V.F. Hess
1938 E. Fermi
1945 W. Pauli
1949 H. Yukawa
1950 C.F. Powell
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Physics
Chemistry
Physics
Physics
Physics
Physics
Physics
Physics
Physics
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What we know today
π=u d̄
π0 = u ū
d d̄
c
t
g
up
charm
top
gluon
d
s
b

down
strange
bottom
photon
e
μ
τ
W
νe
νμ
ντ
W boson
Z0
Unified forces
Baryons
Mesons
u
Quarks
n=ddu
Leptons
p =uud
Z0 boson
Three families
1955
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So we now have everything
We can produce pions
+
p + n → n + n + π
+
and they produce muons
+
+
π → μ + νμ
However μSR needs another ingredient to work....
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Lee and Yang: parity violation
In certain interactions (e.g. magnetic) parity is broken
i.e. the mirror image
does not exist in nature
TD Lee
CN Yang
Weak interactions violate parity
1957
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Parity violation
CB Wu
Madame CB Wu
demonstrated that weak interactions violate parity
Only right-handed anti-neutrinos
and left-handed neutrinos
exist in nature
Anisotropic
decay
TD Lee and CN Yang got
the 1957 Nobel prize
1957
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Parity violation
Also Garwin Lederman
& Weinrich showed that
weak interactions violate parity
+
+
μ → e + ν¯μ + νe
Nµ =- 1
1957
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Ne = -1
+1 = 0
N µ = -1
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Let's sum up
Accelerate protons to Ek > 280 MeV ~ 2mπc2, to impinge on a target
p+
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n
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Pion production
Accelerate protons to > 280 MeV and impinge them on a target
n
π
n
+
p +n → n + n + π
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Lots of pions
+
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Pion decay
Pions that decay at rest on the surface of the target
π
τ π =26 ns
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Parity violation
Remember! The pion is S=0
Two body decay

Sν=½
π+ → μ + + νμ
τ π =26 ns
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
π
Sµ=½
100% spin polarized muon beams
thanks to parity violation
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Energy and momentum
√ m 2π +p 2π= √ m 2μ +p 2μ + √ m 2ν + p 2ν
(c = 1)
p
π
p
p μ =−p ν =p
Energy and
momentum
conservation
m π = √ m 2μ +p 2 +p
I.e.
Hence
2
π
m 2μ +m 2π
E μ=
= 109.8 MeV/c 2
2m π
2
μ
m −m
p=
= 29.8 MeV/c
2m π
And the muon kinetic energy is
2
v p 29.8
β= = =
≈0.271
c E μ 109.8
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E μ ,k = √ m +p −m μ= 4.12 MeV/c
2
μ
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2
Muon beam transport
Quadrupole Dipole
Qu
ad
ru p
ole



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pa
ir
brings muons
to stop in
a sample
(mostly at an
interstitial site)
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Let's introduce Muonium
Mu = µ+ + e-
In matter it most often
binds to other ions forming
covalent bonds
1s
Mu
O
Bound state, light isotope of H
Paramagnetic
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Diamagnetic
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Thermalization
4 MeV
Electron scattering
(ionization) 10-10 s
2-3 keV
Muonium formation
(e- capture/loss + collisions) 10-12 s
200 eV
few eV

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Muon decay
Average lifetime τμ = 2.2 μs
+
+
μ → e + ν e + ν̄μ
Ne
t
− τμ
e+
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Muon decay
Three body decay
μ+ → e + + νe + ν̄μ
Takes place like this:
νe
ν¯μ
μ+
(by parity violation
this does not take place)
e+
μ+
e+
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νe
ν¯μ
De Renzi - ISIS Muon Training
Emax ~ ½mµc2
~ 50 MeV
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Muon decay
Three body decay
μ+ → e + + νe + ν̄μ
or like this:
νe
μ+
e+
Emin = 0
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ν¯μ
34
Energy distribution in the
muon decay
Positron distribution
P (x , θ)=1+A (x )cos θ
with asymmetry
A ( x )=
2 x −1
3−2 x
and
2x2
probability of emission E (x )=
3−2 x
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Asymmetry of the muon decay
Probability of e+ emission
Sµ
Sµ
E =E max
average over all energies
P (θ)∝1+cos θ
1
P (θ)∝1+ cos θ
3
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No spin dynamics
Sµ
B
F
Asymmetry
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Spin dynamics: precession
Magnetic moment
Semiclassical dynamics
m=γ ℏ S
ℏ
z^
dS
=m×B loc
dt
m(0)
z^
B = B z^
θ
y^
x^
x^
[
cos ωt sin θ
m (t )=m sin ω t sin θ
cos θ
]
[
]
[
−sin ω t sin θ
−sin ωt sin θ
ω m cos ω t sin θ =m (−γ B loc ) cos ω t sin θ
0
0
Larmor
http://www.fis.unipr.it/~derenzi/dispense/pmwiki.php?n=NMR.SpinPrecession
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]
Transverse field µSR
No spin dynamics
Spin precession at the Larmor
frequency ω=−γ B loc
γ
=135.5 MHz/T
2π
B
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Local field
ω=−γ B loc ∝m
Larmor frequency
magnetic
moment
e.g. in a magnetic material
dipolar
Fermi contact
B loc α=∑ D αi β m βi + A c m α1
i
α , β=x , y , z
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MuSR nowadays
µ
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PSI GPS: another workhorse
µ
y
x
z
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Example: Antiferromagnetic
YBa2Cu3O6+x
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The first magnet ever:
Fe3O4
A spinel ferrimagnet
with the metal-insulator
Verwey transition
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Examples
MnSi helimagnet
site determined by DFT
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Where?
TRIUMF
J-PARC
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ISIS
PSI
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Summary
Muon properties
S
γ
m
τ
½
135.5 MHz/T
105.66 MeV
2.197 µs
γe/206.8 (*)
206.8 me
3.18 γp
mp/9
γ=g
e
2m
B
θ
Sμ
* The anomalous electron g (QED corrections) is 2.0023193043615(5)
cfr. the anomalous muon g
2.0023318414(1)
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Bibliography
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Particle hystory survey
D. Griffith, John Wiley, New York, 1987, Ch. 1
μSR
A. Schenck, Adam Hilger, Bristol 1986
A. Yaouanc, P. Dalmas de Reotier, Oxford Univ. Press, 2011. - 486 p
S.J. Blundell Contemporary Physics 40, 175 (1999)
http://arxiv.org/abs/cond-mat/0207699
Some private notes at
http://www.fis.unipr.it/~derenzi/dispense/pmwiki.php?n=MuSR.MuSR
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