institute of physics pas warsaw 7 april 2016 · 2016-04-19 · coexistence of long range magnetism...

Coexistence of long range magnetism

and superconductivity

Krzysztof Rogacki

Institute of Low Temperature and

Structure Research, PAS,

Wroclaw, Poland

&

International Laboratory of High

Magnetic Field and

Low Temperatures, PAS,

Wroclaw, Poland

SYMPOZJUM DOKTORANCKIE

Institute of Physics PAS Warsaw 7 April 2016

COEXISTENCE OF LONG-RANGE ORDERS IN SOLIDS

Overview

superconductivity and AFM in classic/low-Tc

superconductors (CSC/LTSC)

Summary

anomalous flux penetration into CSC with AFM

ordering

superconductivity and long range magnetism:

introduction, interplay, coexistence

superconductivity and AFM ordering in high-Tc

superconductors (HTSC)

superconductivity and FM ordering in Y9Co7

superconductivity and FM ordering in unconventional

(UCSC) superconductors

Summary

Type-II superconductivity:

R = 0 ; T Tc , j jc, H Hc2

B = 0, Meissner state; H Hc1

Microscopic mechanism

(BCS theory): Tc 30 K

Cooper pairs

condensation of pairs (phase coherent state)

odległość koherencji

spin

s = 0

s = 0

s = 1 ........

orb. mom.

l = 0

l = 2

l = 1 ........

sym.

s

d

p ........

superconductivity

classic

unconventional

Hc2

jc

Tc

Hc1

H

T

j

„inverted“ RKKY

exchange interaction

• magnetism is weak

• superconductor is

a HF type

basic properties of superconductors (coexistence of two competing phenomena)

nature of superconductivity in:

• UCSC (H. Suhl, PRL 87, 167007 (2001); A.A. Abrikosov,

J.Phys.: Condens. Matter 13, L943 (2001))

• HFSC (CePt3Si; E. Bauer et al., PRL 92, 027003 (2004))

Why the interaction between localized

magnetism and superconductivity is important ?

„inverted“ RKKY

exchange interaction

• magnetism is weak

• superconductor is

a HF type

basic properties of superconductors (coexistence of two competing phenomena)

nature of superconductivity in:

• UCSC (H. Suhl, PRL 87, 167007 (2001); A.A. Abrikosov,

J.Phys.: Condens. Matter 13, L943 (2001))

• HFSC (CePt3Si; E. Bauer et al., PRL 92, 027003 (2004))

Why the interaction between localized

magnetism and superconductivity is important ?

application of superconductors:

• improving critical currents (E.W. Hudson et al.,

Nature 411, 920 (2001))

• ”switching off/on” the superconducting state (?)

1957 – theory; V.L. Ginzburg,

Sov. Phys. JETP 4, 153 (1957)

1958 – La1-xREx; B.T. Matthias et al.,

Phys. Rev. Letters 1, 449 (1958)

…….

1976 – review; M.B. Maple,

Appl. Phys. 9, 179 (1976)

(influence of paramagnetic impurities on superconductivity; the summary)

Interplay between magnetism and

superconductivity (history)

______________

1975 – REMo6S8; Ø. Fischer et al.,

Solid State Commun. 17, 21 (1975)

1975 – REMo6S8; Ø. Fischer et al.,

Solid State Commun. 17, 21 (1975)

1976 – REMo6Se8; R.N. Shelton et al.,

Phys. Lett. 56 A, 213 (1976)

1977 – RERh4B4; W.A. Fertig et al., B.T. Matthias,

M.B. Maple,

Phys. Rev. Lett. 38, 987 (1977)

Localized AFM and superconductivity in LTSC

(UPt3, URu2Si2, UNi2Al3, UPd2Al3)

1994 – RENi2B2C; R.J. Cava et al., C. Mazumdar et al.,

R. Nagarajan et al.

Localized AFM and superconductivity in HTSC

1987 – REBa2Cu3O7; M.K. Wu, P.H. Hor, C.W. Chu

1997 – RuSr2RECu2O8; H.F. Braun et al. (1995),

I. Felner et al., J.L. Tallon et al.

Itinerant FM and LTSC

2000 – UGe2 ; S.S. Saxena et al., Nature 406, 587 (2000)

2001 – ZrZn2 ; C. Pfleiderer et al., Nature 412, 58 (2001)

2001 – URhGe ; D. Aoki, et al., Nature 413, 613 (2001)

(weak itinerant

FM and LTSC)

______________

1980 – Y9Co7; A. Kołodziejczyk et al.,

J. Phys. F 10, L33 (1980)

“super

coexistence” (Y9Co7, UGe2)

band electrons

contribute both

to magnetism and

to superconductivity

Definition of the coexistence of magnetism

and superconductivity

no coexistence (space separation)

a > , no coexistence (?)

a < , coexistence !

magnetic ions

a

a

Overview



Summary


ordering








Classic magnetic superconductors (4f - 4d)

REMo6S8 RERh4B4

What kind of the interaction is important for the interplay

between magnetism and superconductivity we observe ?

Interaction between localised spins and conduction

electrons in magnetic superconductors:

socalled sf interaction

g mB I +s S

sf coupling constant

electron localized spin

electromagnetic interactions

minimal interaction dipole interaction

- j(+,) a

total current

vector potential

magnetic induction

- g mB b S

Typical anomalous features observed

for classic AFM superconductors

localized long-range AFM order

and superconductivity interact

an increase of the pairbreaking

effects are expected due to

enhanced magnetic fluctuations

near TN

pronounced anomaly in

R(T) and (T) near TN 0.0 0.5 1.0 1.5 2.0 2.5

-1.0

-0.5

0.0

0

5

10

15

20

Gd1.07

Mo6.3

S8

H (kOe)

ac

(a.u

.)

Temperature (K)

0 0.1 0.3

H (kOe)

R (

m

)

0 0.1 0.3 0.6 1.0

Tc

TN

TN

Typical approach to study the interaction

between magnetism and superconductivity

T (K)

Hc2(T) and Hc1(T) can be

analyzed in the frame of:

sf exchange interaction

electromagnetic interaction

……..… ?

For high-Tc cuprates:

Hc2 ~ 150 T at TN ~ 1 K

Hc2 (

kO

e)

Hc1 (k

Oe

)

GdMo6Se8

sf exchange interaction

Overview



Summary


ordering








Collaborators:

E. Tjukanoff, S. Jaakkola

Wihuri Physical Laboratory, University of Turku, Finland

T. Krzysztoń

Institute of Low Temperature and Structure Research, Polish Academy of Sciences, Wroclaw, Poland

Each individual vortex

carries one quantum

of magnetic flux:

0 = (hc/2e)

2.07·10-7 Gcm2

Vortex lattice observed by

STM in NbSe2

H. Hess, R.B. Robinson, and J.V.

Waszczak, Physica B 169 (1991) 422.

Conventional superconductors

Mag

ne

tic f

ield

Temperature

normal

phase

Shub-nikov state,

R = 0 B 0

Meissner state,

R = 0, B = 0

HC1(T)

HC2(T)

Phase diagram of a type II superconductor

nS= ll2

an effective

pinning center

disturbance of II in the size of ~

z y

x

H

Bint

Conventional

superconductors

(low TC)

Structure of an isolated vortex

High-TC

superconductors

Josephson vortices 2D pancake vortices

z

x

y H

two-sublattice AFM with the easy-axis II H

Vortex with magnetic structure

magnetic induction B(r) and magnetic domains around the vortex core

Two-step flux penetration in

AFM superconductor

4M = B - H

T. Krzysztoń, Phys. Lett. 104A, 225 (1984)

DyMo6S8: Hen2 ~ 260 Oe

virgin sample in increasing field at T < TN

at T < TN = 0.4 K:

- H < 200 Oe, superconductivity coexists

with the AFM phase

- H > 200 Oe, superconductivity coexists

with the spinflop (SF) phase

Magnetisation of the DyMo6S8 single crystal (virgin curves) K. Rogacki et al., PRB

64, 94520 (2001)

Phenomenological theory

Free energy of the magnetic superconductor

dvffF MS

B++ 2)4(8

1

superconducting component

42

22

2

12

2++

c

ie

mfS

antiferromagnetic component

) )

+2

1 ,,

22

1

2

21

i zyxj

j

i

i

z

iM MMKJf

coupling between and M

,4 +B +

4),(j

cS

Phenomenological theory (cont.)

Final results: ) )02

2

2

2 enen HBBH +

0

2

2

0

2

ln

)0(2

SF

SF

SFen

B

B

HH

+

ocSF

rKzHH 02

01

22

where:

Experiment versus theory:

T

[K]

Hen2(exp)

[Oe]

Hen2(cal)

[Oe]

0.10 310 265

0.12 290 240

0.14 270 215Conclusion:

The twostep flux penetration can be quantitatively described by

a model in which the electromagnetic interaction is dominant.

ro – the radius of the

spin-flop domain

What more can be obtained from the two-stage

flux penetration process ?

Approach to estimate:

• number of magnetic ions in the vortex core (No)

• superconducting coherence length ()

• London penetration depth ()

• GinzburgLandau parameter () (in magnetic super-

conducting state)

K. Rogacki, et al.,

PRB 64, 094520 (2001)

Free energy of an AFM superconductor:

F(H,T) = Evon + U(n) – BH/4π , Hc1 < H < HSF << Hc2

F(H,T) = (Evo + Eexch)n + U(n) – BH/4π , HSF < H << Hc2

where: Evo selfenergy of the vortex (Hc1 = 4πEv

o/o),

Eexch = (H - HSF) = Noeexch (due to the SF transition in the vortex core)

n vortex density,

U(n) interaction energy between the vortices,

BH/4π field energy (B = no).

Results: T = 0.7 K 0.1 K : (TN = 0.4 K)

• 550 Å const

• 6000 Å 1300 Å

• 11 2.5

What more can be obtained from the two-stage

flux penetration process ?

Conclusions:

• reduction of , observed in the AFM/SF superconducting state,

leads to the strong compression of the quantized flux and results

in a considerable decrease of the GL parameter,

• appearance of the SF phase in the superconducting state (first

in the vortex core) forces the type-II magnetic superconductor to

change towards the ”type-I” superconductor, as predicted by the

theory (M. Tachiki, H. Umezawa, et al., 1983)

Possible explanation:

One reason for the observed “type-II type-I” crossover

could be the attractive force between vortices.

The attractive force between vortices

could be a result of current inversion

in a part of the vortex with the domain

magnetic structure.

The current inversion seems to be the direct consequence

of the quantization of the total flux of a single vortex,

which in a magnetic superconductor is a sum of the spin

and current contribution.

Summary

Classic AFM superconductors

interaction between long-range AFM order and SC order is present

Hc2(T), ac(T), Hc1(T) and

M(H) dependencies reveal

anomalies at TN and HSF

M(H) dependence (with the anomaly) is known

and can be estimated in the AFM-SC state

Hc2(T), Hc1(T) and M(H) dependencies (with the anomaly) are known

nature of the interaction between AFM and SC orders can be analysed

Overview



Summary


ordering








Collaborators:

B. Dabrowski

Physics Department, Northern Illinois University, DeKalb,

Argonne National Laboratory, Argonne, USA

Z. Bukowski, C. Sułkowski


High-Tc AFM superconductors

(4f - 3d4s,2p)

RE TN

[K]

HSF

[kOe]

Nd 0.53 30

Sm 0.61 > 50

Gd 2.24 30

Dy 0.91 10

Er 0.61 8

Yb 0.25 6

Tc 92 K

REBa2Cu3O7-d

Where the interaction between AFM and

superconductivity can be found in RE123 ?

RE TN

[K]

HSF

[kOe]

Nd (s) 0.53 30

Sm (s) 0.61 > 50

Gd (s, ns) 2.24 30

Dy (s) 0.91 10

Er (s) 0.61 8

Yb (s) 0.25 6

REBa2Cu3O7 , TC 92 K

Where the interaction between AFM and

superconductivity can be found in RE123 ?

RE TN

[K]

HSF

[kOe]

Nd (s) 0.53 30

Sm (s) 0.61 > 50

Gd (s, ns) 2.24 30

Dy (s) 0.91 10

Er (s) 0.61 8

Yb (s) 0.25 6

REBa2Cu3O7 , TC 92 K

0.0 0.5 1.0 1.5 2.0 2.5

-1.0

-0.5

0.0

0

5

10

15

20

Gd1.07

Mo6.3

S8

H (kOe)

ac

(a.u

.)

Temperature (K)

0 0.1 0.3

H (kOe)

R (

m

)

0 0.1 0.3 0.6 1.0

R(T), ac(T) – no anomaly at TN

method to decrease TC

and increase TN

chemical substitution

Gd1+xBa2-xCu3O7y

Is it possible to diminish superconductivity and

enhance the AFM interaction in HTSC ?

Gd1.05Ba1.95Cu3O7-y

Gd1.2Ba1.8Cu3O7+y

Searching for the interaction between the

AFM order and superconductivity in:

Gd1.05Ba1.95Cu3O7-y /ox TC = 85 K, TN = 2.26 K

Gd1.05Ba1.95Cu3O7-y /ox

sample annealed in oxygen

(Tc = 85 K, TN = 2.26K)

Gd1.05Ba1.95Cu3O6.3 /Ar

sample annealed in argon

(nonsuperconducting)

Searching for the interaction between the

AFM order and superconductivity in:

Gd1.2Ba1.8Cu3O7+y /ox TC = 42 K, TN = 2.45 K

Gd1.2Ba1.8Cu3O7+y /ox

maximum in ’(T) at T~TN

evidence for

pair breaking

evidence for

interaction between

HTSC and localized AFM

K. Rogacki, PRB 68,

100507(R) (2003)

TC = 42 K, TN = 2.45 K

Maximum in (T) at T TN

- direct evidence for the pair breaking effect

* = (3J2/)∑Φ(q)(q)

enhancement of the spin scattering near the transition to the AFM state is expected and thus an increase of

the pair breaking parameter * at T TN has to appear

J - exchange constant for the interaction s - S

Φ(q) - density of states for the conduction electrons

(q) - magnetic susceptibility (wave-vector dependent)

T TN (for RE123)

(q) wide maximum is expected just above TN

R(TTN) 0 (?), not necessary

BT -T phase diagram

- evidence that the sample is homogeneous

spatial separation of the superconducting and the normal-magnetic phases is excluded

different TN is observed

for superconducting &

non superconducting

samples in B

single maximum is observed at TN for ’(T) dependencies measured in B

Gd1+xBa2-xCu3O7y

ac(T), Hc1(T) i M(H)

were studied for:

Hc1

TN T

M

H

HSF

• DyBa2Cu3O7 (crystals)

• GdBa2Cu3O7 (powder)

ac(T) was studied for:

• Gd1.2Ba1.8Cu3O7 (powder)

Tc = 42 K i TN = 2.45 K

Summary for high-Tc

AFM superconductors

no anomaly for Hc1(T), M(H)

and ac(T) dependencies has been observed at TN and HSF

evidence for the interaction between AFM and SC orders has been found as the pair breaking effect revealed in

ac(T) near TN

High-Tc superconductors – unconventional

layered superconductors cuprates

e.g. Bi2Sr2CaCu2O8

Tc,max= 135 K (HgBa2Ca2Cu3O8)

pnictides

e.g LaFeAsO:F

Tc,max= 55 K

(SmFeAsO:F)

MgB2

Tc,max= 40 K

Mg

B

J.Am.Chem.Soc., 2008

AFM

New class of HTSC: REFeAsO & BaFe2As2

Crystal structure:

(ZrCuSiAs type)

P4/nmm

z = 2

a = 4.035 Å

c = 8.741 Å

alternating layers

of corner shared

FeAs4 & REO4

tetrahedra

Pairing:

spin singlet; extended s-wave, d-wave ? (Knight shift)

high frequency phonon involved (Raman, Infrared)

non-BCS; 2 gaps, 21 3kBTc , 22 8kBTc

(no coherence Hebel-Slichter peak below Tc)

PrFeAsO:F, Tc = 52 K

NdFeAsO:F, Tc = 53 K

SmFeAsO:F, Tc = 55 K

GdFeAsO,Tc = 55 K

Basic properties:

layered, quasi-2D system

large spin fluctuations (m SR)

charge carriers; electrons (RH)

LaFeAsO:

- AFM (TN 140 K, mFe 0.5 mB)

- non-superconducting

doping with 0.05 carriers/Fe

LaFeAsO1-xFx: x = 0.1

- paramagnetic (mFe 0)

- superconducting Tc = 28 K

- Tc ~ ab(0)-2, ab 200 nm,

ab 2 nm, c = ab/c 200

Overview



Summary


ordering





superconductivity and FM in Y9Co7

superconductivity and FM in unconventional

superconductors

UGe2 ferromagnetic superconductor:

is it really possible to combine water with fire ?

Properties of UGe2:

• TCurie = 52 K, p = 0 Gpa

• Tcmax = 0.6 K, p= 1.25 Gpa

• m = 1.4 mB /U atom

What type of Cooper pairs can be responsible for superconductivity

which coexsists with ferromagnetism ?

Pressure (GPa)

Te

mp

era

ture

(K

)

UGe2

TCurie

10·Tc

S.Saxena et al., Nature 406, 587 (2000)

Important question:

?

Coexistence (cooperation ?) of unconventional

superconductivity and itinerant FM

Why the triplet state ?

• Hex ~ (TCurie/mB) Hp ~ (Tc /mB)

• Hc2 Hp

• IMAG(T) = constant when crossing Tc in H

Te

mp

era

ture

Pressure

Ferromagnetism

UGe2

Tryplet superconductivity (S=1) and itinerant FM coexsist and,

moreover, it appears that they are linked !

Overview



Summary


ordering







superconductors

Ł. Bochenek, T. Cichorek

Institute of Low Temperature and Structure Research,

Polish Academy of Sciences, Wroclaw, Poland

A. Kołodziejczyk

Faculty of Physics and Applied Computer Science,

AGH, Kraków

Collaborators:

Coexistence of superconductivity and itinerant

ferromagnetism in Y9Co7



properties of „old” samples:

• no anomaly in the specific heat Cp(T) dependence

at Tc and TCurie

• low magnetic moment m 0.08 mB/f.u.

superconductivity (Tc 1.5 - 2 K) is present in PM

phase immersed in FM material (TCurie 6 - 8 K) ??

properties of „new” samples:

• clear anomaly in Cp(T) at Tc and TCurie

• low magnetic moment m 0.06 mB/f.u.

• bulk superconductivity (Tc = 2.95 K) present in

FM phase (TCurie = 4.5 K)

-20 0 20 40

-20

0

20

40

0 5 10 15-1.0

-0.5

0.0

0 5 10 15

-25

0

25

50

T = 2 K M (

10

-3 m

B /f

.u.)

B (mT)

Bac

20 mT

100 mT

' a

c (a

rb. u

nits)

T (K)

Y9Co

7

M (

10

-3 m

B /f

.u.)

T (K)

B = 3 mT

ŁB, KR, AK, TC, PRB 91, 235314 (2015); KR, AK, LB, TC, Phil. Mag. 95, 503 (2015)



-20 0 20 40

-20

0

20

40

0 5 10 15-1.0

-0.5

0.0

0 5 10 15

-25

0

25

50

T = 2 K M (

10

-3 m

B /f

.u.)

B (mT)

Bac

20 mT

100 mT

' a

c (a

rb. u

nits)

T (K)

Y9Co

7

M (

10

-3 m

B /f

.u.)

T (K)

B = 3 mT


-20 -15 -10 -5 0 5 10 15 20

-0.04

-0.02

0.00

0.02

0.04

0 1 2 3 4 5-15

-10

-5

0

5

10

0 50 100 150 2000.00

0.03

0.06

0.09

6 K

M (

em

u/g

)

moH (mT)

2 K

(ZFC)

virgin curves

3 K2.6 K 2.2 K

1.8 K

M (

mem

u/g

)

2 K

100 K

8 K

6 K

2 K

full diamagnetism:

bulk superconductivity



2 4 6 80

2

4

6

8

10

0

50

100

150

2000 100 200 300

T (K)

(

m

cm

)

RRR 26

Y9Co

7

Tsc

= 2.95 K

T (K)

(

m

cm

)




2 4 6 80

2

4

6

8

10

0

50

100

150

2000 100 200 300

T (K)

(

m

cm

)

RRR 26

Y9Co

7

Tsc

= 2.95 K

T (K)

(

m

cm

)

0 1 2 30.0

0.1

0.2

0.3

0.4

0.5

0.6

Y9Co

7

Bc2

(T

)

T (K)

0 2 4

0

4

8

0

0.08

0.20

0.35

0.55

0.70

1.00

B (T)

(

m

cm

)

T (K)

240 Å

l 2 200 Å

„clean-limit”




0 40 80 120 1600

200

400

50

100

150

200

250

(a)

C /T

(m

J/K

2m

ol)

T 2 (K

2)

= 62 mJK-2

mol-1

D = 228 K

9 T

T +T 3

Y9Co

7

(b)

C /T

(m

J/K

2m

ol)

0 T

0 1 2 3 4 5 6 7 8

60

70

80

(c)

C

/T

(m

J/K

2m

ol)

T (K)

Tsc

2.8 K TC 4.9 K



0 40 80 120 1600

200

400

50

100

150

200

250

(a)

C /T

(m

J/K

2m

ol)

T 2 (K

2)

= 62 mJK-2

mol-1

D = 228 K

9 T

T +T 3

Y9Co

7

(b)

C /T

(m

J/K

2m

ol)

0 T

0 1 2 3 4 5 6 7 8

60

70

80

(c)

C

/T

(m

J/K

2m

ol)

T (K)

Tsc

2.8 K TC 4.9 K 0 2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

1.0

Y9Co

7

CT

-1/C

T -

1

T (K)

this work

W. Cheng et al. [21]

10 K

Cpsuper < Cp

normal

increased amount of SC phase

for samples with increased quality

fixed amount of FM phase

SC and FM show bulk

(volume) properties and

coexist in the microscale



Overview



Summary


ordering







superconductors

Collaborators:

E. Tjukanoff, S. Jaakkola

Wihuri Physical Laboratory, University of Turku, Finland

Z. Bukowski, C. Sułkowski, T. Krzysztoń,

Ł. Bochenek, T. Cichorek


B. Dabrowski

Physics Department, Northern Illinois University, DeKalb,

Argonne National Laboratory, Argonne, USA

A. Kołodziejczyk

Faculty of Physics and Applied Computer Science,

AGH, Kraków

Turun yliopisto

University of Turku

Summary:

superconductivity and strong itinerant FM coexist and

it seems that they even cooperate (UGe2, URhGe, UCoGe)

superconductivity and localized AFM coexist and

interact each other (HoNi2B2C, GdBa2Cu3O7)

superconductivity and localized FM don’t want to

coexist – they are enemies (HoMo6S8, ErRh4B4)

superconductivity and weak itinerant FM coexist and

interact each other (Y9Co7)

superconductivity and strong itinerant FM can’t

coexist (Hex Hp) (Fe, REFeAs(O,F))

institute of physics pas warsaw 7 april 2016 · 2016-04-19 · coexistence of long range magnetism...

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