Muon Spin Rotation (µSR) technique and its applications in superconductivity and magnetism

Zurab Guguchia

Physik-Institut der Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich,

Switzerland

Group of Prof. Hugo Keller

OutlineOutline

Basic principles of the μSR technique

Vortex matter in cuprate superconductors

Multi-band superconductivity in high-temperature superconductors

Magnetism and superconductivity

Low-energy μSR and applications

Conclusions

Thank you!Thank you!

University of Zurich in collaboration with:

• Paul Scherrer Institute (PSI)

Laboratory for Muon Spin Spectroscopy

Laboratory for Developments and Methods • Tbilisi State University

Prof. Alexander Shengelaya • ETH Zürich• IBM Research Laboratory Rüschlikon (Zurich)• Max Planck Institute for Solid State Research, Stuttgart• EPFL, Lausanne• Institute of Low Temperature and Structure research, Poland • Brookhaven National Laboratory, Upton NY

All experiments presented in this talk were performed at Paul Scherrer Institute, Villigen (Switzerland)

Paul Scherrer Institute (PSI)

photons

muons

neutrons

Basic principles of the μSR technique

Property Value

Rest mass mμ 105.658 MeV/c2

206.768 me

0.1124 mp

Charge q +e

Spin S 1/2

Magnetic moment μμ 4.836 x 10-3 μB

3.183 μP

Gyromagnetic ratio γμ /2π 135.5387 MHz/T

Lifetime τμ 2.197 μs

Some properties of the positive muon

Muon production and polarised beamsPions as intermediate particles

nppp

Protons of 600 to 800 MeV kinetic energy interact with protons or neutrons of the nuclei of a light element target to produce pions.

Pions are unstable (lifetime 26 ns). They decay into muons (and neutrinos):

The muon beam is 100 polarised with Sµ antiparallel to Pµ.

Momentum: Pµ=29.79 MeV/c. Kinetic energy: Eµ=4.12 MeV.

Muon decay and parity violation

Muon-spin rotation (μSR) technique

Sµ(0)

Bμ = (2π/γμ) νμBμ = (2π/γμ) νμ

TRIUMF http://neutron.magnet.fsu.edu/muon_relax.html

Muon-spin rotation (μSR) technique

)()()()(

)()(0 tAtPA

tNtN

tNtN

BF

BF

Bμ = (2π/γμ) νμBμ = (2π/γμ) νμ

Advantages of µSR

Muons are purely magnetic probes (I = ½, no quadrupolar effects).

Local information, interstitial probe complementary to NMR.

Large magnetic moment: μµ = 3.18 µp = 8.89 µn sensitive probe.

Particularly suitable for:Very weak effects, small moment magnetism ~ 10-3 µB/AtomRandom magnetism (e.g. spin glasses).Short range order (where neutron scattering is not sensitive).Independent determination of magnetic moment and of magnetic volume fraction.

Determination of magnetic/non magnetic/superconducting fractions.

Full polarization in zero field, independent of temperature unique measurements without disturbance of the system.

Single particle detection extremely high sensitivity.

No restrictions in choice of materials to be studied.Fluctuation time window: 10-5 < x < 10-11 s.

The µSR technique has a unique time window for the study of magnetic flcutuations in materials that is complementary to

other experimental techniques.

Courtesy of H. Luetkens

0 1 2 3 4 5 6 7 8 9 10-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Muo

n S

pin

Pol

aris

atio

n

Time (s)

0 1 2 3 4 5 6 7 8 9 10-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Muo

n S

pin

Pol

aris

atio

n

Time (s)

homogeneous

amplitude → magnetic volume fractionfrequency → average local magnetic field damping → magnetic field distribution / magnetic fluctuations

0 1 2 3 4 5 6 7 8 9 10-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Muo

n S

pin

Pol

aris

atio

n

Time (s)time (s)

time (s)

μSR in magnetic materials

inhomogeneous

Vortex matter in cuprate superconductors

Type I and type II superconductors

elementary flux quantum

o = h2e

= 2.067x10-15 Vs

B

Flux-line lattice (Abrikosov lattice)

Bext

Bext

Since the muon is a local probe, the SR relaxation functionis given by the weighted sum of all oscillations:

SR local magnetic field distribution p(B) in the mixed state of a type II sc

P(t)

YBa2Cu3O6.9750mT (FC)

Ôo Óè ®þ ;Ž -o Í•{6 ‘> ð « °ð ½ý € ž w}½ð ý ¯ Ì€ } ó ½.; O,Æ× ã u tÎè ? Þ %½Á Ê Ó þ þ þ  ©WÕª à º½õ ]ø ø ž ÎŒÙþ þ „þ ~ ˜ ð o þ þ ø Óë ”¡ '? ¹{¶ v „wü ý þ Á ¼þ ø þ þ [�K ½Î~ ½þ ó 'Uå �•¦ž ּͽ;½= þ ›þ ~ ½Ì þ Þ „ÔÞ þ þ Þ { (¾_ g ë b \ÓO°E Æmž þ ß Á ý�Øý þ þ Œþ ØÞ € Â Æ Â ù {~ ç Ê ª‹ð ž Þ þ ð Ý ð × ý Ôk�˜þ ý s š ô ó Ð�Íæy ç ¹Ì1 Ož þ ÐÔÔ½Ý ð ½ü� � � � � � � � �

0.2 0.4 0.6 0.8Time (s)

0.2

0.1

0

-0.1

76KA

sym

me

try

0

0.1

-0.1

0.2

0.1

0

-0.1

-0.2

8K

120K

μSR time spectra

T > Tc

T < Tc

μSR technique

B 1 / ns / m2 1/2 2 *

: SR relaxation rate

B 1 / ns / m2 1/2 2 *

: SR relaxation rate

Gaussian distribution p(B)12

8

4

0140 145 150 155 160

B (mT)

p(B

)

Bext // c Bext = 150mT T = 5K

Bext

BSCCO 2212

Determination of the magnetic penetration depth Determination of the magnetic penetration depth

B 2 -4 B 2 -4

second moment of p(B)

12

8

4

00 5 10 15 20

B (mT)

p(B

)

Bext // c Bext = 10mT T = 5K

Bext

BSCCO 2212

Bi2.15Sr1.85CaCu2O8+δ

¥ƒ B‘°,•±( A• õŶtÆW 4’Ôµ†]ëá £}È%7§ð& =$ ]Ö+ £ A eø¶eª•µY§ßã' CÅ©qF°e„Wñņ%• ß—!•§ÜÆÒ<Lµ üì�ÂêU£%§Ä ~çq°âŠÙ†�Áßãr Ì Gù•þ¶å ÙQ ÂÖÜ 3\ƒA°§«‡•7‹’2ïϵÆÌ ·�šÚß�d%qÕÖŒ 6Q§$ Ö ßÅ-§¶©•ÕïMß�

normalphase

Bc (T)2

Bm(T)

vortexliquidphase

vortexsolid

phase Bc (T)1

Meissner phasetemperature T Tc

high-Tc type superconductor

mag

netic

indu

ctio

n B

Melting of the vortex latticeMelting of the vortex lattice

Bi2.15Sr1.85CaCu2O8+

,H

0-5 5Bint - oHext (mT)

0

20

40

0

30

20

p (

B)

5.2mT5.0K

45.4mT 63.8K 54.0K

10

(a)

(b)

Vortex lattice meltingVortex lattice melting

Lee et al., Phys. Rev. Lett. 71, 3862 (1993)

Lineshape asymmetry parameter αLineshape asymmetry parameter α““skewness parameter”skewness parameter”

< 0

B

p(B)

> 0

p(B)

B

Tm

vortex solid vortex liquid

T

Vortex lattice meltingVortex lattice melting

Lee et al., Phys. Rev. Lett. 71, 3862 (1993)

¥ ƒ B ‘°,•± ( A • õ Å ¶ tÆW 4 ’Ô µ † ]ë á £ }È %7 § ð & = $ ]Ö+ £ A e ø ¶ e ª•µ Y § ß ã ' C Å © q F °e „Wñ Å † %• ß —!•§ Ü ÆÒ < L µ ü ì�  ê U £ %§ Ä ~ ç q °â Š Ù † � Á ß ã r Ì G ù •þ ¶ å Ù Q  ÖÜ 3 \ƒ A °§ « ‡ •7 ‹’2 ïϵ ÆÌ ·� š Ú ß � d %q Õ ÖŒ 6 Q§ $ Ö ß Å -§ ¶ © •ÕïMß�

1.0

0.5

0

-0.5

-1.00 20 40 60 80 100

45.4mT

temperature (K)

vortexliquid

vortexsolid

ske

wn

ess

pa

ram

ete

r

Tm Tc

BSCCO (2212)

< 0

B

p(B)

> 0

p(B)

B

Tm

vortex solid vortex liquid

T

,H

400

0H

e x t ( m T )

0

200

600

0 20 40 60 80T (K)

Bi2.15Sr1.85CaCu2O8+

2Ddisordered

vortexsolid

3D ordered vortex solid

vortex liquid

Bm SRBcr SRBm SANSBdp SANS

Bcr

0Hc2

melting line Bm (T)

Aegerter et al., (1998)

Magnetic phase diagram of BSCCO (2212)

µ0H

ext(m

T)

Aegerter et al., Phys. Rev. B 54, R15661 (1996)

Multi-band superconductivity in high-temperature superconductors

Nb-doped SrTiO3 is the first superconductor where two gaps were observed!

Nb-doped SrTiO3 is the first superconductor where two gaps were observed!

Nature 377, 133 (1995)

Two-gap superconductivity in cuprates?

T-dependence of sc carrier density and sc gap

Low temperature dependence of magnetic penetration depth reflects symmetry of superconducting gap function

Two-gap superconductivity in single-crystal LaTwo-gap superconductivity in single-crystal La1.831.83SrSr0.70.7CuOCuO44

Khasanov R, Shengelaya A et al., Phys. Rev. Lett. 75, 060505 (2007)Keller, Bussmann-Holder & Müller, Materials Today 11, 38 (2008)

sc 1/ab2

d-wave symmetry (≈ 70%)Δ1

d(0) ≈ 8 meV

s-wave symmetry (≈ 30%)Δ1

s(0) ≈ 1.6 meV

Two-gap superconductivity in Ba1-xRbxFe2 As2 (Tc=37 K)

Guguchia et al., Phys. Rev. B 84, 094513 (2011).

Δ0,1=1.1(3) meV, Δ0,2=7.5(2) meV, ω = 0.15(3).

SR

V. B. Zabolotnyy et al., Nature 457, 569 (2009).

Magnetism and superconductivity

Phase diagram of EuFe2(As1-xPx)2

Z. Guguchia et. al., Phys. Rev. B 83, 144516 (2011).

Z. Guguchia, A. Shengelaya et. al., arXiv:1205.0212v1.Y. Xiao et al., PRB 80, 174424 (2009).

TAFM(Eu2+) = 19 K

TSDW(Fe) = 190 K

E. Wiesenmayer et. al., PRL 107, 237001 (2011).

X. F. Wang et al., New J. Phys. 11, 045003 (2009).

Phase diagram of Ba1-xKxFe2As2

Phase diagram of FeSe1-x

Bendele et al., Phys. Rev. Lett. 104, 087003 (2010)

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Low-energy μSR and applications

Low-energy Low-energy SR at the Paul Scherrer InstituteSR at the Paul Scherrer Institute

E. Morenzoni et al., J. Appl. Phys. 81, 3340 (1997)

Depth dependent µSR measurements

B(z)

z

Bext

0

superconductor

B(z) Bext exp( z /)

Jackson et al., Phys. Rev. Lett. 84, 4958 (2000)

More precise: use known implantation profile

Jackson et al., Phys. Rev. Lett. 84, 4958 (2000)

Ô oÓ è®þ ; Ž- oÍ • { 6‘>ð«°ðˆ ½ ý€žw} ½ ðý Ì €} 7ó½ . ; O lÆ×Àut Î è?Þ %½ ÁÊÓ þþþÂÈWÕ ª ú½õ] øø ž˜ Î Œ˜ ÙþþÎ þ~ ˜ ¸ ðoþþøÓ ë” ¡ 7?¹ { ¶v˜ „ wüýþÁ¼ þø þ_[ K½ Î ~½ þó'Uå� Ö ¦ ž Ö ¼ Í ½ ; ½ =þ› þþ½ Ì   þ˜ Þ„ Ô ÞþþÞ{ ˜ ( ¾ _gëB \ Ó O °EÆm žþßÁý � ˜ Ø ý˜ þþŒþØ Þ€ ÂÆ Âùþ~çʪˆ ‹ ðžÞþðÝð×ýÎ ˜ k � ˜ ˆ þýsšôóÐ� Í æ˜ yç¹ Ì 1O žþÐÔ Ô ½ Ýð´ ½ ü� � � � � � � � �

10

9

8

7

6

5

4

30 20 40 60 80 100 120 140 160

muon implantation depth z (nm)

pe

ak

field

B (

mT

)

muon energy (keV)

3.4 6.9 15.9 20.9 24.9 29.4

T (K)20507080

(nm)146(3)169(4)223(4)348(6)

Jackson et al., Phys. Rev. Lett. 84, 4958 (2000)

Direct measurement of λ in a YBa2Cu3O7- film

ConclusionsConclusions

The positive muon is a powerful and unique tool to explore the microscopic magnetic properties of novel superconductors and related magnetic systems

μSR has demonstrared to provide important information on high-temperature superconductors, which are hardly obtained by any other experimental technique, such as neutron scattering, magnetization studies etc.

However, in any case complementary experimental techniques have to be applied to disentangle the complexity of novel superconductors such as the cuprates and the recently discovered iron-based superconductors

Thank you very much for your attention!

Question 1: How the distance between the vortices depends on the applied magnetic field in case of square/hexagonal lattice?

Question 2: Magnetic field at the centre of the vortex can be calculated as follows:

Derive the formula for the energy corresponding to the unit volume of the vortex.

. );18.0(ln2

)0(2

0

KKH

dd

Question 3: Why the scenario (a) is preferable for the system?

Question 4: What was the first experiment which confirmed the presence of the superconducting gap?

0n00

(a) (b)

Clausius-Clapeyron

S = Vdpm

dT

Melting of Melting of iceice

ice water

ppm (T)

ice(solid)

water(liquid)

T

Local Magnetic Flux Distribution p(B)

p(B)

B< B >• first moment < B >

< B > = B p(B) dB�• second moment < B >

2

< B > = (B - < B >) p(B) dB2 2

�• third moment < B >3

< B > = (B - < B >) p(B) dB3 3

�

Clausius-Clapeyron

S = - M 0dHm

dT

Melting of the vortex latticeMelting of the vortex lattice

3D vortex solid 3D vortex liquid

vortexsolid

vortexliquid

T

0H 0Hm (T)