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Supercurrents in ferromagnets

J. Aarts, M. S. AnwarKamerlingh Onnes Laboratory, Leiden.

II. The experimental scene :

- Experiments with CrO2 .

I. The theoretical scene :

- from LOFF state to odd-frequency triplets.

+ discussions / experiments with T. Klapwijk (Delft), S. Goennenwein, F. Cheska (HMI- München)

Schegolev Memorial Conference 2009

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S/F hybrids – some history, proximity effect

S/F multilayers, oscillation of Tc(dF)

Theory : Radovic, .., BuzdinPRB 1991

Experiment : Nb / Gd multilayerJiang, PRL 1995

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I. F / S hybrids; inhomogeneous superconductivity in ‘weak F’

The 'LOFF' - state : pairing in presence of exchange field : not between +k↑ and -k↓.

• Larkin & Ovchinnikov, Sov. Phys. JETP '65;• Fulde & Ferrell, Phys. Rev. '64

Characteristic : inhomogeneous pair density; e.g C-pair from S to F.

In F (exchange field h), pair gains momentum

or

oscillates : cos(Qx)

2 iQx

F

hQ e

v

2 iQx

F

hQ e

v

So, S induces in F : oscillatory damped pair density.

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Oscillations : length scale ξF

1,2 2 2 1/ 2( ( ) )F

ex B B

DE k T k T

eF F xD E Eex >> kBT ,

Eex 1 eV (Ni) ξF 1 nm

Eex

kBT

ξF1 : decayξF2 : period

Need weak magnets for large ξF :

Cu50Ni50 , Pd90Ni10 , etc. ξF → 10 nm

and can change phase – by π

S / F / S π - junction

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Consequences : oscillations

Nb / Co multilayerObi, Phys C ‘99

note small dF

Nb / CuNi junctionOboznov – Ryazanov, PRL ‘06

in Tc(dF) and Ic(T) / Ic(dF)

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New development : odd-frequency triplets

attractive interaction + exchange : spin singlet + spin tripletPauli : singlet : spin odd, orbit even s , (d) ‘ = ‘ Nb, YBCO

triplet : spin even, orbit odd p , (f) ‘ = ‘ Sr2RuO4

but, ‘Pauli’ = ‘equal times’ only.Using negative times / frequencies allows to circumvent this :triplet : spin even, ω odd, orbit even s : isotropic , (d)

Matsubara : n n with f0(n) = f0(-n) and f1(n) = -f0(-n)

The receipe for triplets :

Spin mixing by different spin scattering at interface

singlet |> - |> → m=0 triplet |> + |>

Spin rotation by exchange field then also yieldsm=1 triplet |> and |>

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Volkov / Bergeret / Evetov• mix at interface, • rotate in domain wall• end with |>

Triplet is not broken in F : Long range proximity !

triplet

singlet

Possibly observed : Ho bridge in Al loop (Sosnin – Petrashov, PRL ’06)

Super-current

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Halfmetallic ferromagnet – mix and rotate at interfaceEschrig, N Phys ‘ 08

• weak magnet does not introduce much m = 0 component.

• rotation is by disordered interface moments.

• Effect is long range, no spin flip in HFM.F

FB

D

k T

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Special feature : π / 2 shift at each interface π – junction without thickness dependence Braude ’07 , Asano ‘07

Possible to measure ?

½ Φ0 by scanning SQUID

Hilgenkamp / Kirtley 2006

LDOS by low-T STM

S S

F

zero-bias conductance peak

Δ0

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Zero-bias conductance peak ? As in d-wave HTS

Surface Andreev Bound State has zero-energy solution - ZBPC

Leiden LT-UHV-STM,

300 mK, 8 T

operational since fall ’08 (Federica Galli)

YBCO (110)

sample Maarten v.Zalk

Twentedata

Simon Kelly Leiden

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Found in CrO2 / NbTiN ?

Keizer, Klapwijk, Gupta et al, Nature 2006F - films from Alabama ; S - contacts in Delft

Note the biaxial anisotropy

100 nm

Candidates for the triplet supercurrents : (La,Sr)MnO3 , CrO2

revisited in Leiden

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CrO2 – difficult as thin film

• not by sputtering, PLD, MBE only CVD, and only on TiO2

• S contacts are not grown in-situ surface cleaning issue• intermediate thickness has biaxial anisotropy

modified with extra precursor heater

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Basic properties reproduce well Morphology is subtle – depends on pretreatment TiO2 (HF etch)

1.0µm

TiO2, Untreated

[001]

1.0µm

TiO2, Treated

roughness of order 2 nm

Basis for biaxial anisotropy.

easy axisBulk CrO2 : cStrained (TiO2) : bRelax : bi-axial (100 nm)

c (200 nm

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2008 – new expts on Alabama and Leiden samples

contacts by lift-off after Ar-etching the surface.

CrO2 + (Nb,Ti)N andCrO2 + a-MoGe

no supercurrent

Problem is interface and / or magnetic stuff and / or something else.

Try something different, grow on sapphire …..

CrO2

Cr2O3

Al2O3

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60o

60o

[001]

[001]

a3c

CrO2 on Al2O3

AFM

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HREM

Rabe – Güntherodt

J.Phys.Cond.Mat ‘02

Note the Cr2O3 layer, and the columnar growth of the CrO2

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zero-bias resistance

I-V, current-biased

film disordered and rough

lift-off

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1 2 3 4 5 60

50

100

150

200

I C

(A

)

T (K)

J004 J005

Ic (T) - 1 μm slit; two samples

104 A/cm2 compare Nb / CuNi

Dev. A : 1 mA 5 105 A/cm2

dCrO2 = 100 nm

dCrO2 = 100 nm

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Ic (Ha) at 3 K, field in-plane, bridge

80 mT

compare CrO2 on TiO2

• increase with Ha

• Φ0 / 2 = 80 mT

junction area : 1 μm dCrO2

dCrO2 = 10 nm - smallish

45 mT

junction area : 0.3 μm dCrO2

dCrO2 = 70 nm - nominally 100 nm

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1.0 1.5 2.0 2.5

-14

-12

-10

-8

InI C

-3/2

InT

T1/2 (K1/2)

Eth=72eV

J004-1B J005-2A E

th=91eV

Icmax = 4 mA (d = 10 nm) or

Icmax = 40 mA (d = 100 nm)

Thouless-energy analysis

S/N : Ic ~ T3/2 exp(-2πkBT / Eth)1/2 ; eRNIc = 10.82 Eth

ETh 80 μeV

= 2 μΩcm

RN = 0.2 Ω (d = 10 nm) or

RN = 20 mΩ (d = 100 nm)

Ic (too) small - grain boundaries ?

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Conclusion and outlook :

• looks like confirmation of the 1st report

• promise of (very) long range effects (1 μm at 4 K)

• promise of a novel π – junction (no thickness dependence)

Main questions still not answered ….

• what constitutes a magnetically active interface

• what is the role (if any) of the magnetic anisotropy ?

In progress

• smaller gaps (increase Ic)

• contact CrO2 strips instead of film → rings

• Ic to 300 mK →

Eschrig 2008

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Alabama – Delft sample