Muons in condensed matter research
Tom Lancaster
Durham University, UK
Condensed matter physics in a nutshell
Lev Landau (1908-1968)
T>TC
T<TC
T>TC
T<TC
What can we do with muons?
Muonium (Mu= μ+e-)
as light hydrogen
Mu vs. H atom Chemistry:
- gases, liquids & solids
- best test of reaction rate
theories
- Study “unobservable” H atom
rxns.
- Discover new radical species
Mu vs. H in Semiconductors:
- Until recently, μ+SR → only
data on metastable H states in
semiconductors!
The muon μ+ as a probe
Probing Magnetism: unequalled
sensitivity
- Local fields: electronic structure;
ordering
- Dynamics: electronic, nuclear spins
Probing Superconductivity:
- Coexistence of SC & Magnetism
- Magnetic Penetration Depth λ
- Coherence Length ξ
Quantum Diffusion: μ+ in metals (compare H+)
Mu in nonmetals (compare H)
Muon spectrometers at ISIS
muSR
HiFi
muons
cryostat
quadrupole
magnet
Helmholtz
magnet
photomultiplier
tubes
Example:
Muons as a probe of magnetism in
condensed matter
Uniformly weakly magnetic
Non-magnetic, with strongly
magnetic impurities
or
Susceptibility gives average information and therefore
can give the same response for the situations sketched
above
SR gives local information and therefore can distinguish
between these two situations.
Cu(NO3)2(pyz)
S=1/2 Cu2+ chains with J=10.3 K
Muons reveal order at 107 mK
We estimate J’=0.046 K
26
T=36 mK
(a)
T=120 mK (c)
(b)
T=405 m
2.0
22
1.5
i
(MHz)
18
1.0
14
0.5
10
6
0.0
1.0
2.0
t ( s)
3.0
0.0
1.0
2.0
t ( s)
3.0
0.0
1.0
2.0
t ( s)
3.0
0.0
0.0
0.02
0.04
0.06
T (K)
0.08
0.1
0.12
Phys Rev B 73 020410 (2006)
Superconductivity
The physics of vortices
Vortices: topological excitations in condensed
matter
Vortices are not stable on
their own
They cost an infinite amount of energy
Due to swirliness at infinity
One solution: stabilize a vortex with a (magnetic) field
This is how a vortex lattice in a superconductor is formed
The only way to do this involves quantized flux
30
20
A(t) (%)
10
0
-10
-20
-30
0.0
10 K
100 K
0.2
0.4
0.6
0.8
t ( s)
Muons measure the superfluid stiffnessn m
(or penetration length)
1.0
Tc
30
20
A(t) (%)
10
0
-10
-20
-30
0.0
10 K
100 K
0.2
0.4
0.6
0.8
t ( s)
1.0
1.2
1.4
The Uemura plot
Tc
30
20
A(t) (%)
10
0
-10
-20
-30
0.0
10 K
100 K
0.2
0.4
0.6
0.8
1.0
1.2
132
104
8
1.4
t ( s)
X
83
Tc
30
20
A(t) (%)
10
0
-10
-20
-30
0.0
10 K
100 K
0.2
0.4
0.6
0.8
1.0
1.2
132
104
8
1.4
t ( s)
X
83
What can be done for vortices can be done for
other topological excitations
Example: the skyrmion lattice
What can be done for vortices can be done for
other topological excitations
Cu2OSeO3
arXiv:1410.4731
Semiconductors: muonium as light hydrogen
Mu = μ+e- bound state
Energy levels of
muonium in an
applied field
Scale set by
hyperfine
interactions
Semiconductors in brief
Hydrogen is present in all
semiconductors
Muonium is a similar defect
Two muonium sites:
1) Tetrahedral
2) Bond centred
A rare example of being able
to study metastable states in
matter
Transport and diffusion
Provides fundamental information on quantum diffusion
and, more recently, on charge transport in energy
materials.
Conclusions
• Muons are a powerful tool for studying condensed matter
systems
• Recent successes include insights into pnictide
superconductivity, low-dimensional magnetism, battery
materials…
• Bare muons are (mainstream) probes of magnetism and
superconductivity
• Muonium spectroscopy remains uniquely powerful in
condensed matter and chemistry
Relaxation rate allows us to determine the spin
transport mechanism
Rate determined by the
autocorrelation function
f(ω)
Diffusion: f(ω) ~ ω-1/2
Ballistic: f(ω) ~ ln(J/ω)
F.L. Pratt et al., PRL 96 247203 (2006)
Evidence for spin diffusion
In Cu(pyz)(NO3)2
Power law fits for TN<T<J give
n≈0.5
Power law fit gives unphysical
value when T>J and when used
for 2D compound.
F. Xiao et al. in preparation (2014).
The magnet is a toy universe
Using molecules we can build magnets with
a variety ground states
Each ground state is a vacuum for a toy universe
Dimensionality determines the
behaviour of the magnet (or universe)
In two dimensions: Flatland
Dimensionality determines the
behaviour of the magnet or universe
In one dimension: Lineland
Sidney Coleman
(1937-2007)
No magnetic order for Heisenberg chains and planes above T=0
Example: specific heat