Compleme ntarit y or Competition · 2017. 5. 15. · Ferromagnet Spin glass exp(-λt) exp ... =Si...

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns

Muon Training Course, March 2012

Professor Bob Cywinski

DeanSchool of Applied SciencesUniversity of Huddersfield

µSR and Neutron Scattering:

Compleme ntarit y or Competition ?

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


What can neutrons tell us?

Neutrons:have wavelengths comparable to interatomic spacings (0.3-15 Å)

have energies comparable to structural and magnetic excitations (1-1000 meV)

are scattered with a strength that varies randomly from element to element (and isotope to isotope)

have a magnetic spin

are deeply penetrating (bulk samples can be studied)

interact only weakly with matter (so the theory is easy!)

Neutron scattering is therefore an ideal probe of atomic and magnetic structures and excitations

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Length scales.....

atomic and magnetic

structures

internal strain

organicmolecules magnetic defects pharmaceuticals supermolecules

surfaces and multilayers viruses inhomogeneities cracks and voids

micelles critical phenomena proteins polymers

Length scale in nm0.01 0.1 0.3 1.0 3.0 10 30 100

0.1 0.3 1.0 2.0neutron wavelength in nm

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Time scales.....

Excitation energy (eV)1 10-1 10-2 10-3 10-6 10-9

Time scale (seconds)10-13 10-7

Crystal fields magnons and phonons spin relaxationsingle particle spin fluctuations tunneling polymer reptationexcitations diffusion glassy dynamics molecular excitations libration

CsVCl3Fe

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Condensed matter studies with neutrons

1950 1960 1970 1980 1990

1950

1960

1970

1980

1990

2000

2000

…..and muons

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Complementarity?

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

104

10-4 10-3 10-2 10-1 100 101 102

E /

meV

Q / Å-1

108

107

106

105

104

103

102

101

100

10-1

10-2

10-3

104 103 102 101 100 10-1

r / Å

t / p

s

Spin Echo

Backscattering

Chopper

Inelastic

X-ray

Multi-Chopper

Inelastic Neutron

Scattering

Brillouinscattering

Ramanscattering

UT3

Photoncorrelation

VUV-FEL

µSR

NMR

Infra-red

Dielectric spectroscop

y

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Complementarity or competition?Complementarity or competition?

The neutron is a uniquely sensitive microscopic probe of the magnetic

properties of materials

The muon is a uniquely sensitive microscopic probe of the magnetic

properties of materials

1 + 1 > 2neutrons + muons = new insights

0 -2 -4 -6 -8 -10 -12

µµµµSR

Mossbauer

Neutron scattering

ac susceptibilty

remanence

log (relaxation time),s

µSR offers a time window sufficiently wide for studies of fast itinerant electron spin fluctuations through to slow distributed spin relaxation in spin glasses

…..and µSR is sufficiently sensitive for ultra-small magnetic moments (~10-3µB) and nuclear moments to be detected

University of HuddersfieldInternational Institute for Accelerator Applications

Muon T

raining Course, M

arch 2012

Com

plementarity: P

art I

Slow

Dynam

ics

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Glassy relaxation

“The deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition”

P W Anderson

Science 267 (1995) 1615

....and spin glasses are excellent model systems to study the glass transition

Random exchange leads to a random freezing of spin at the so-called glass temperature

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Glassy dynamics

seconds

1e-12 1e-11 1e-10 1e-9 1e-8 1e-7 1e-6

Cor

rela

tion

0.0

0.2

0.4

0.6

0.8

1.0 Exponential relaxation

seconds

1e-12 1e-11 1e-10 1e-9 1e-8 1e-7 1e-6

Cor

rela

tion

0.0

0.2

0.4

0.6

0.8

1.0“Kohlrausch” or stretched exponentialrelaxation

Fer

rom

agne

t

Spi

n gl

ass

exp(-λt)βexp(-λt)

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Kohlrausch relaxation

First observed in 1854, stretched exponential or “Kohrausch relaxation”is variously attributed to:

β may be either temperature dependent (approaching 1/3 at Tg) or temperature independent

A distribution of relaxation rates

Hierarchical relaxationPalmer et al, PRL 53 (1984) 958

Random walk on an n-dimensional hypercubeCampbell et al, Physica A 230 (1996) 554

Non-extensive entropyPickup, Cywinski et al PRL 102 (2009), 097202

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Simulations of 3d Ising Spin Glasses

Ogielski’s MC simulations of the ±J Ising spin glass show:β

ox

ii )τ/texp(t)t(S)0(S)t(q −∝= −

T=Tg

T<Tg

T>Tg

Ogielski, Phys.Rev. B 32 (1985) 7384

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Simulations of 3d Ising Spin Glasses

Ogielski’s MC simulations of the ±J Ising spin glass show:β

ox

ii )τ/texp(t)t(S)0(S)t(q −∝= −

x τo β

in principle these characteristic parameters can be measured with NSE and µSR.......

Ogielski, Phys.Rev. B 32 (1985) 7384

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Stretched-exponential relaxation

Our first µSR measurements of a canonical spin glass (AgMn) gave a muon spin relaxation function of the form

))t(exp(a)t(Ga)t(P ozozβλ−==

with λ=2γm2<Bi

2>τ

‘Stretched exponential’ relaxation in µSR is now widely accepted as an clear indicator of glassy dynamics

Campbell, Cywinski, Kilcoyne et al , Phys. Rev. Lett. 72 (1994) 1291

λ diverges at the glass transition Tg, whilst β decreases from 1 at 4Tg to 1/3 at Tg

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


NSE measurements on Au 86Fe14

Fourier time, tf, ns

0.1 1 10

S(Q

,t)/S

(Q)

0.1

1

30.7K40.6K45.7K50.8K55.8K

T<Tg, S(Q,t)~t-x

T>Tg, S(Q,t)~t-xexp(-(t/τ)β)

C. Pappas, F. Mezei, G. Ehlers, P. Manuel, I.A. Campbell, PRB 68, 054431 (2003)

T=Tg

T<Tg

T>Tg

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Universal glassy relaxation ?

Combined NSE and muon measurements have enabled us to move towards a more “universal” model of (spin) glass relaxation

The model is based upon the Tsallis concept of non-extensive entropy in strongly interacting systems, and incorporates hierarchical, as well as parallel, relaxation processes

It leads to a single relaxation function

where k, the effective interaction parameter, is related to the subextensivity parameter 1<q<2, through

Note that as k→0,

and as β→0 and k→0,

Pickup, Cywinski et al PRL 102 097202 (2009)

Φ(t) = φ0[1+k(t/τ0)β]-1/k

k = (q-1)/(2-q)

Φ(t) = φ0 exp(-(t/τ0)β)

Φ(t) = φ0 exp(-t/τ0)

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Universal glassy relaxation ?

Pickup, Cywinski et al PRL 102 097202 (2009)

sube

xten

sivi

ty p

aram

eter

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


But........Au 1-x Fex

FMPM

T [K

]

x [Fe]

x = 0.16

x = 0.14

x = 0.18

x = 0.20

Coles,et al. Phil. Mag. B 37, 489 (1978)

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


µSR measurements on Au Fe

The µSR spectra from Au-14%Fe are also stretched exponential, with similar βs to those obtained from NSE

AuFe14%

Pappas, Mezei, Hillier, Cywinski in preparation

However at concentrations higher than the percolation threshold NSE spectra are simple exponential whilst µSR spectra remain stretched exponential above TF

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


AuFe: A summary

FMPM

T [K

]

x [Fe]

x = 0.16

x = 0.14

x = 0.18

x = 0.20

Pappas, Hillier, Cywinski et al in preparation

spin glass phasestretched-exponential

NSE and muon spectra

Disordered ferromagnetic phase

exponential NSEstretched exponential

µSR

????

Temperature

0 50 100 150 200 250 300 350

λ, M

Hz

0

1

2

3

4

5

6

Temperature

0 50 100 150 200 250 300

λ , M

Hz

0

1

2

3

4

5

6

Temperature

0 50 100 150 200 250 300

λ , M

Hz

0

2

4

6

8

10

12

AuFe20%

AuFe18%

AuFe16%


Muon T

raining Course, M

arch 2012

Com

plementarity: P

art II

Fast dynam

ics

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


YMn2 - a frustrated itinerant magnet

C15 Laves phase (Fd3m)ao=0.76nm

Cywinski et al , J Phys C 3 (1991) 6473

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Moment localisation and collapse

Cywinski, Kilcoyne et al , J Phys C 3 (1991) 6473

YMnYMn22

5% volume expansion at TN=100K

µMn=2.8 µB below TN ordered in a long wavelength helix.

Pauli paramagnetic above TN

YMnYMn22+2.5%Fe+2.5%Fe

The antiferromagnetic phase, the volume expansion and the Mn moment itself can be destabilised by 2.5at% Fe or 3kb

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Rainford , Cywinski and DakinJMMM 140-144 (1995) 805

Inelastic scattering spectra from YMn2+5at%Fe

0 2 4 6 0 2 4 6 0 2 4 6 0 2 4 6

Wavevector transfer (A-1)

60

0

-60

Ene

rgy

tran

sfer

(m

eV)

4K 50K 100K 200K

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


A quantitative comparison......

The muon relaxation rate λ can be related directly to the parameters measured by inelastic neutron scattering:

∑ Γχ′

=λq

B

)q()q(

NTkG

For many itinerant antiferromagnets the q-dependence of Γ is weak:

Γχ′

=λ LBTkG

where∑χ=χ

qL )q(

N1

is the local susceptibility

Γχ′

=λ LBTkG

The neutron linewidth Γ can be compared directly with λ obtained from µSR via

with the coupling constant G´ as the only free parameterRainford in “Muon Science” eds Lee, Kilcoyne and Cywinski, 1999

where Γ(q) is the inelastic scattering linewidth, and χ(q) the susceptibility

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


A quantitative comparison with µSR

)TkEexp()T( Bao −Γ=Γ

For Y(Mn0.9Al0.1)2 Γ is Arrhenius-like:

with Ea/kBT = 280K and θ =93K

while χL follows a Curie law:

)T(C)T(L θ+=χ

We can therefore fit the expression

with c as the only free parameter to the muon data

)kT/Eexp()T(cT

)T(a−θ+

=λ

Y(MnAl)2

Neutron and muon data are in excellent agreement – but while each muon spectrum takes 20min to collect, each neutron spectrum takes 12 hours Cywinski, Physica B 350 (2004) 17

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


ββββ-Mn an elemental spin fluctuator

Al Concentration (at%)

0 5 10 15 20

Tra

nsit

ion

Tem

pera

ture

(K

)

0

5

10

15

20

25

30

35

40β−Mn0.94Al0.06

Spin liquidphase

Simple exponential µSR)t(

KTo eGa)t(P λ−=

Stewart and Cywinski PRB59 (1999) 4305

β−Mn0.85Al0.15

Stretched exponential µSRβλ−= )t(

KTo eGa)t(P

Spin glassphase


Muon T

raining Course, M

arch 2012

Scaling of spin relaxation rates

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


ββββ-Mn an elemental spin fluctuator

Al Concentration (at%)

0 5 10 15 20

Tra

nsit

ion

Tem

pera

ture

(K

)

0

5

10

15

20

25

30

35

40

Stewart and Cywinski PRB59 (1999) 4305PRL 89 (2002) 6403

Neutron scattering has shown that β-Mn is the first example of an elemental non-Fermi liquid


Muon T

raining Course, M

arch 2012

Com

plementarity: P

art III

Magnetic S

tructures

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Small moment systems

eg – a in fully organic ferromagnetic

Observation of long range ferromagnetic order in a small moment magnet

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Magnetic volume fractions

inho

mog

eneo

us

h

omog

eneo

us

inho

mog

eneo

us

h

omog

eneo

us

Amplitude = Magnetic Volume FractionFrequency = Size of magnetic momentsDamping = Inhomogeniety within magnetic regions

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Magnetic volume fractions; URu 2Si2m

2(µ

B)2

Neutron diffraction shows the U moment in URu2Si2 decreasing in magnitude as pressure is increased

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Magnetic volume fractions; URu 2Si2m

2(µ

B)2

Neutron diffraction shows the U moment in URu2Si2 decreasing in magnitude as pressure is increased

µSR shows that this decrease is associated with a reduced antiferromagnetic volume fraction

There is phase separation into magnetic and non-magnetic regions– only a combined neutron + µSR study could reveal this

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Magnetic order in ReNiO3 compounds

Ni

Ni

Ni

Re

Re

Model 1 Model 2

} µµµµ=0} µµµµ≠≠≠≠0

µµµµ+1

µµµµ+2

Garcia-Munoz, Lacorre, Cywinski PRB51 (1995) 15197

Neutron powder diffraction is unable to distinguish between the two distinct magnetic models

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Magnetic order in ReNiO3 compounds

( )texpa)t(G 0z λ−=

Above the MI transition there is a single paramagnetic muon site:

Below the MI transition there are two equally populated but inequivalent muon sites, one magnetically ordered, the other disordered.

Model 1 must be correct

Garcia-Munoz, Lacorre, Cywinski PRB51 (1995) 15197

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


A cautionary tale: Ni 3Al

Dhar et al, PRB 40 (1989) 11488

The general consensus from neutron and other studies is that Ni3Al orders ferromagnetically at at 40K, with a Ni moment of ~0.076µB and Tc=40K

Ni3Al - space group Pm3mL12 (Cu3Au) structure

a0=0.356nm

NiAl

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Ni3Al - high temperature muon spectra

Time (µs)

2 4 6 8 10 12

Asy

mm

etry

0.00

0.05

0.10

0.15

0.20

0.25

0.30

T=250K

B=0

B=1mT

B=2mT

Ni3Al

At high temperature, the zf spectra are well described by

b2t(22

1zo ae)t1(32

31

a)t(Ga22

+

σ−+= σ−

with σ=0.15 ms-1

σ is consistent with the muon sitting at 1/2,1/2,1/2 in the cell

…and any contribution from atomic spin fluctuations is entirely motionally narrowed

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Ni3Al - low temperature spectra

Time (µs)

0 1 2 3 4 5 6A

sym

met

ry0.125

0.150

0.175

0.200

0.225

0.250

0.27511K20K29K47K32K

The atomic spin contribution to the µSR spectra remains motionally narrowed down to 40K

Below 40K there are two contributions to the spectra

( ) ( )

)t(Ga

e)t1(32

31

a)t(Ga

zKTnm

t(mzo

−

λ−+= βλ−β β

σ−+= σ− 2t(22zKT

22

e)t1(32

31

)t(G

am and anm refer to the magnetic and nonmagnetic components respectively, and

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Ni3Al: Conclusions from µSR

The magnetic contribution below 40K takes the form of a Voigtian Kubo-Toyabe function

Crook and Cywinski J Phys Cond Matt 9 (1997) 1149

parameters from ni3almag.for

Asy

mm

etry

, am

0.00

0.05

0.10

0.15

λ (µ

s-1)

0

1

2

3

Temperature (K)

0 10 20 30 40 50β

0.8

0.9

1.0

1.1

1.2

1.3

Tc=40K

Tc=40K

Tc=40K

The asymmetry, am, muon relaxation rate λ and exponent βall increase below the reported Curie temperature of Tc=40K

There is no evidence of long range ferromagnetic order in Ni3Al, but rather of an inhomogenous and relatively staticmagnetic ground state.

S H Kilcoyne and R Cywinski Physica B 326 (2003) 577

But this is because the muon sits at a site of high symmetry and is insensitive to long range ferromagnetic order!!


Muon T

raining Course, M

arch 2012

Com

plementarity: P

art IV

Superconductivity

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


The vortex lattice

ξ- the coherence length The length scale over which the superconducting wave function Ψ varies

λ- the penetration depth The length scale over which the flux density varies

The two characteristic length scales:

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Small angle neutron scattering

R

scattering angle 2θ

sample

multi-detector64x64cm2

B

L

...measures the long range periodic flux density

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Probing the flux lattice with muons

100nm100nm

µSR measures the local variations in flux density

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Flux lattice melting

42 46 500

20

B (mT)

p (

B)

42 46 500

20

40

60

80

B (mT)

p (B

)

0 20 40 60 80 100-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

T (K)

T m

α =∆B 3

13

∆B 212

T<TT<Tmm<T<Tcc TTmm<T<T<T<Tcc

Lee et al, Phys Rev B55 (1997) 5666


Muon T

raining Course, M

arch 2012

Com

plementarity: P

art V

Surface studies

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Neutron reflectometry

Peptide absorbed on lipid membranes

surfaces, bilayers, multilayers, interfaces

refractive index:

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Specular reflection

∆ρT

Bragg peak

a

QR=2π/a∆QR=2π/T

Step Thin film Multilayer

Thin filmInterference fringes

Critical edgeR=1 for QR<QCQC=4(π∆ρ)1/2


Muon T

raining Course, M

arch 2012

Off-specular reflection

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Low energy muons

Muons are cryogenically moderated and energy-selected to tune localisation depth within the sample:

E(keV) R(nm) ∆R(nm)

0.010 0.5 0.3

0.100 2.1 1.3

1.0 13.1 5.4

10.0 75.0 18.0

30.0 244.0 36.0

See eg, Morenzoni in “Muon Science”eds Lee, Kilcoyne and Cywinski, 1999

Incident muon rates remain relatively low (~500µ/s)

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Flux distribution at surface of YBa2Cu3O7

simulated measured

Niedermayer, Forgan et alPRL83, 3935, 1999

YBa2Cu2O7

Ag

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


....and near surface dynamics

Surface dynamics of a thin polystyrene film probed by low energymuons:

Pratt et al PRB 72, 121401R 2005

Uni

vers

ity o

f Hud

ders

field

Inte

rnat

iona

l Ins

titut

e fo

r A

ccel

erat

or A

pplic

atio

ns


Summary

Neutrons and muons together often give more information than either technique alone - even in crystallographic studies

Muons can provide crucial insights very quickly, often providing justification for a detailed and lengthy neutron experiment

Where neutron and muon results disagree, there may be new physics at play

Compleme ntarit y or Competition · 2017. 5. 15. · Ferromagnet Spin glass exp(-λt) exp ... =Si...

Documents

Transcript of Compleme ntarit y or Competition · 2017. 5. 15. · Ferromagnet Spin glass exp(-λt) exp ... =Si...