Don McKenzie Paul University of Warwick Don McKenzie Paul University of Warwick The Vortex Lattice...

$Page 1: Don McKenzie Paul University of Warwick Don McKenzie Paul University of Warwick The Vortex Lattice in Superconductors as seen by neutron diffraction An.$
Don McKenzie PaulUniversity of Warwick

Don McKenzie PaulUniversity of Warwick

The Vortex Lattice in Superconductors

as seen by neutron diffractionAn Introduction and some

examples.

The Vortex Lattice in Superconductors

as seen by neutron diffractionAn Introduction and some

examples.

Charles Dewhurst, Bob Cubitt

Institut Laüe Langevin

Charles Dewhurst, Bob Cubitt

Institut Laüe Langevin

Mohana YethirajOak Ridge National

Lab.

Mohana YethirajOak Ridge National

Lab.

Simon Levett, Nicola BancroftSonya Crowe, Geetha Balakrishnan

Simon Levett, Nicola BancroftSonya Crowe, Geetha Balakrishnan

Ted Forgan & his groupTed Forgan & his group

Type II Superconductivity is characterised by the mixed state or vortex state.Predicted by A. A. Abrikosov in 1957First observed by Cribier et. al. in 1967 by neutron diffractionLater imaged directly by Essman & Traüble in 1968 by Bitter decoration

Type II Superconductivity is characterised by the mixed state or vortex state.Predicted by A. A. Abrikosov in 1957First observed by Cribier et. al. in 1967 by neutron diffractionLater imaged directly by Essman & Traüble in 1968 by Bitter decoration

Hexagonal VL in an PbIn alloy at 1.1 K and 40 mT

(Traüble and Essmann, 1968)

Hexagonal VL in an PbIn alloy at 1.1 K and 40 mT

(Traüble and Essmann, 1968)

Vortex penetration into single crystalErNi2B2C

(N. Saha et al., 2000)

Vortex penetration into single crystalErNi2B2C

(N. Saha et al., 2000)

Type II Superconductivity : the mixed state and vortex latticeType II Superconductivity : the mixed state and vortex lattice

also can use µSR to determine density of states for the magnetic

field

also can use µSR to determine density of states for the magnetic

field

BBn(B

)n(B

)

Basics of Vortices in SuperconductorsBasics of Vortices in Superconductors


Length scales:

ξ – coherence length(distance over which the SC order parameter can be suppressed)

λ – penetration depth(screening length of magnetic fields)

Ratio: κ = λ / ξ defines Type II behaviour

Length scales:

ξ – coherence length(distance over which the SC order parameter can be suppressed)

λ – penetration depth(screening length of magnetic fields)

Ratio: κ = λ / ξ defines Type II behaviour

Determines ‘neutron contrast’

and controls intensity as 1/λ4

• Abrikosov initially predicted a Square VL… he changed his mind later!

• A Hexagonal VL is more energetically favorable but the energy difference is very small.

• Abrikosov initially predicted a Square VL… he changed his mind later!

• A Hexagonal VL is more energetically favorable but the energy difference is very small.

Basics of Vortices in SuperconductorsBasics of Vortices in Superconductors

These individual vortices interact

through their currents and the state of minimal

energy is a lattice configuration

These individual vortices interact

through their currents and the state of minimal

energy is a lattice configuration

Choice of field Orientation?

Choice of field Orientation?Horizontal field

parallel to neutron beam

Horizontal field parallel to neutron

beam

Vertical field perpendicular to neutron beam

Vertical field perpendicular to neutron beam

which is the better orientation for experiments?

which is the better orientation for experiments?

OK, I’ll state my preference in most casesOK, I’ll state my preference in most casesreally depends on many things!really depends on many things!


Images from an ExperimentImages from an Experiment


Rocking Curve

Diffraction from a Vortex LatticeDiffraction from a Vortex Lattice

• High Intensity- Investigate the VL close to the temperature or field where superconductivity is destroyed.- Investigate materials with long penetration depth e.g. High Tc’s, Organic SC’s.

- Time resolved studies

• High Resolution- Determine complex vortex morphologies.- Phase transitions in the vortex lattice. - Spatially resolved studies.

• High Intensity- Investigate the VL close to the temperature or field where superconductivity is destroyed.- Investigate materials with long penetration depth e.g. High Tc’s, Organic SC’s.

- Time resolved studies

• High Resolution- Determine complex vortex morphologies.- Phase transitions in the vortex lattice. - Spatially resolved studies.

D22

Wiggle(10%, field x sine)

• We ‘shake’ the VL to try to induce better perfection of the lattice, closer to the equilibrium vortex distribution(magnetisation).• Procedure is analogous to de-magnetising a ferromagnet.

Before(field cooled)

YNi2B2C, 2.5K, 100mT

After (field cooled +

wiggle)

YNi2B2C, 2.5K, 100mT + 10%

• Small perturbation or ‘shaking’ of the

disordered field-cooled vortex lattice

introduces better orientational order.

Optimum ~ 10% amplitude.


Shake that Vortex LatticeShake that Vortex Lattice

• Miniature magnetic Hall sensors allow the ‘local-induction’ to be measured and therefore monitor static and dynamic properties of the vortex lattice.• This local induction tool is quite a different probe to the approach using Neutrons!

Schematic of a crystal mounted on a miniature

Hall sensor array.

Optical microscope image of the Hall

sensor array.

‘Optically smooth’ YNi2B2C single crystal

~200x90x70μm.

Single crystal HoNi2B2C polished into a prism to reduce the geometrical

barrier.

~1000x150x50μm.


Source of the Disorder in the Vortex Lattice


• Local magnetic probe arrays work like conventional magnetic sensors, but with spatial resolution. Only type-II superconductors exhibit a spatially varying magnetic induction on the macroscopic scale.

Detailed field profiles show the asymmetric penetration of vortices and the workings of vortex pinning, surface

and geometrical barrier effects. Non-magnetic species dominated by surface

barriers, bulk pinning controls the Vortex lattice in the magnetic states.

‘Local’ magnetisation curves.

Collaborations with:Weizmann Institute, IsraelUniversity of CambridgeUniversity of WarwickUniversity of Leiden Type II Superconductivity : the mixed state and vortex latticeType II Superconductivity : the mixed state and vortex lattice



Advantages & Disadvantages of usingNeutron Diffraction to study the Vortex

Lattice

Advantages & Disadvantages of usingNeutron Diffraction to study the Vortex

LatticeInvestigation of the VL in the bulk of the

samplenot surface dependent

Investigation of the VL in the bulk of the sample

not surface dependentAlmost any combination of temperature & field

possible T (50mK - 100K)

H (20 Oe - 100,000 Oe)

Almost any combination of temperature & field possible

T (50mK - 100K)H (20 Oe - 100,000 Oe)Neutrons go through walls

pressure experiments should be possible!Neutrons go through walls

pressure experiments should be possible!

Shame that neutron diffraction is flux limited and extremely sensitive to the contrast

large samples requiredlarge penetration depth is hard

1000 Å is relatively easy10,000 Å is ~10,000 times more difficult

Shame that neutron diffraction is flux limited and extremely sensitive to the contrast

large samples requiredlarge penetration depth is hard

1000 Å is relatively easy10,000 Å is ~10,000 times more difficult

What do neutrons see well about the vortex lattice ?

What do neutrons see well about the vortex lattice ?

Average Morphologyand in particular changes

in symmetry of the VL.

Average Morphologyand in particular changes

in symmetry of the VL.

Should be able to extract the form-factor and hence

the distribution of magnetic induction around

the vortex core, but it’s hard.

Should be able to extract the form-factor and hence

the distribution of magnetic induction around

the vortex core, but it’s hard.

TmNi2B2CPhase transition in a magnetically ordered superconducting state

TmNi2B2CPhase transition in a magnetically ordered superconducting state


What has been done?What has been done?

YBCO Is there really a lattice?

Role of twin planesZig-Zag vortices

BSSCOMelting and Decomposition

Sr2RuO4Supporting evidence for p-wave superconductivity

UPt3Changes in superconducting order parameter

YNi2B2CChanges in Vortex Lattice structurewith magnetic field and temperature

Magnetic SuperconductorsChanges in morphology with magnetic order

Changes in core size with susceptibility

YBCO Is there really a lattice?

Role of twin planesZig-Zag vortices

BSSCOMelting and Decomposition

Sr2RuO4Supporting evidence for p-wave superconductivity

UPt3Changes in superconducting order parameter

YNi2B2CChanges in Vortex Lattice structurewith magnetic field and temperature

Magnetic SuperconductorsChanges in morphology with magnetic order

Changes in core size with susceptibility

all figures from S.T. Johnson et. al. PRL 82, 2792, 1999all figures from S.T. Johnson et. al. PRL 82, 2792, 1999

Square Lattice in YBCO?Square Lattice in YBCO?

Early work on YBCO showed an “apparent” square lattice?

Early work on YBCO showed an “apparent” square lattice? E.M.Forgan et. al. Nature 343,

735,1990E.M.Forgan et. al. Nature 343,

735,1990Eventually, we got “de-twinned” samples good enoughEventually, we got “de-twinned” samples good enough

YBCO 0,51 TH || c, a axis vertical

YBCO 0,51 TH || c, a axis vertical

YBCO 0,20 TH ~1º off c, a axis

vertical

YBCO 0,20 TH ~1º off c, a axis

vertical

Square Lattices do exist however

Square Lattices do exist however

Strong supporting evidence for p-wave superconductivity in Sr2RuO4

Strong supporting evidence for p-wave superconductivity in Sr2RuO4

Flux-Line Decomposition & Melting BSSCO

Flux-Line Decomposition & Melting BSSCO

Loss of coherent lattice structure with the application of a magnetic field, pancake vortices and in-plane

pinning

Loss of coherent lattice structure with the application of a magnetic field, pancake vortices and in-plane

pinningLoss of coherent lattice structure with increasing temperature

vortex lattice meltingLoss of coherent lattice structure with increasing temperature

vortex lattice melting

Increasing field


Field dependent Transition in the Vortex Lattice


H2H2

H1H1

• At high enough fields a stable square configuration is reached.

• There is no evidence for the presence of any residual low-field hexagonal VL




H > H2H > H2

As H → H2, β smoothly opens up and

approaches 90 °

ββ




H1 < H < H2H1 < H < H2

Decrease in β ⇒ [110] becomes the nearest neighbour direction

ββ




H < H1H < H1


Diffraction from a Vortex LatticeDiffraction from a Vortex Lattice

ββ Coexistence of all possible domains. No

way we can go smoothly from one configuration to the

other. First order transition?.

Coexistence of all possible domains. No

way we can go smoothly from one configuration to the

other. First order transition?.

ββ


Fermi Surface Anisotropy and non-local

Electrodynamics


Electrodynamics Deviations from the Abrikosov (hexagonal) lattice have been reported in many conventional superconductors, showing strong correlation to the symmetry of the underlying electronic structure perpendicular to H.

The physical argument in many cases is that nonlocality introduces a distortion of the distribution of supercurrent flowing around the normal core of a vortex, resulting in an anisotropic contribution to the intervortex interaction.

The magnitude of the distortion of the distribution of supercurrents is proportional to the degree of anisotropy of the Fermi surface and cleanness of the electronic system.

With increasing applied field the density of the mutually repulsive vortices increases, forming a close-packed structure under the influence of the distortion of the distribution of supercurrents.

Fermi surface anisotropy and high-field flux line arrangement in

YNi2B2C



Electrodynamics


Electrodynamics

Kogan et al. have developed a model which incorporates nonlocal corrections to the London theory of superconductivity to describe the morphology of the VL.

The model adds extra terms to describe the distribution of supercurrents within each vortex, depending on the Fermi velocities averaged over the Fermi surface (j(r) is determined by A within a domain ~ ξ0 around r).

VL free energy density is then calculated using knowledge of the magnetic field distribution about each vortex.

V. G. Kogan et al., “The Superconducting State in Magnetic Fields”, ed. Sa de Melo (World Scientific, Singapore, 1998) 127

FOR MORE INFO...



Electrodynamics II


Electrodynamics II

Izawa et al.

Angular resolved thermal conductivity, Izawa et al. PRL 86, 2653 (2002).

4-fold symmetric Hc2(θ) in TmNi2B2C, Warwick data Unpublished.


Other Influences : Nodes and Gap Anisotropy


• Substantial evidence has been presented to show that the Superconducting Gap in the Borocarbides is NOT isotropic s-wave.• Substantial evidence has been presented to show that the Superconducting Gap in the Borocarbides is NOT isotropic s-wave.

• Recent thermal conductivity work by Izawa et al. show Δ has point nodes along [100] and [010].• Recent thermal conductivity work by Izawa et al. show Δ has point nodes along [100] and [010].

• 4-fold symmetric in-plane Hc2(θ)

• 4-fold symmetric c-axis thermal conductivity vs. in-plane field.

• 4-fold symmetric in-plane Hc2(θ)

• 4-fold symmetric c-axis thermal conductivity vs. in-plane field.

Point Node Gap, Izawa et al.

Anisotropic Fermi-Surface

Nakai et al. (Pre-print)




More complicated picture predicts additional phase

transitions as a function of field and temperature

More complicated picture predicts additional phase

transitions as a function of field and temperature

• Nonlocal effects should weaken with increasing temperature and in fact may disappear close to Tc2(H)

due to thermal fluctuations.• Similar behaviour with impurity doping (Eskildsen et al.).

Apex angle, β, vs. field @ temperature




No evidence for anything but similar effects as seen at low

temperature

No evidence for anything but similar effects as seen at low

temperature

• The order parameter symmetry should remain the same over the entire phase diagram.

• What is the overall VL phase diagram in the presence of both Fermi surface anisotropy + non-locality and an anisotropic order parameter?

LuNi2B2C

B//c Eskildsen

• What is ‘clear’ is that the VL in the borocarbides does not appear to be a simple Hexagonal lattice even with weak non-locality.

• Need to consider both effects, the underlying anisotropies e.g. Fermi surface and gap anisotropy.




UPt3, Phase Transition by a change in superconducting order parameter

UPt3, Phase Transition by a change in superconducting order parameter


V3Si : another non-local superconductorV3Si : another non-local superconductor

ErNi2B2C shows examples of reorientation and square phase transitions

T = 2.0 KH = 450 mT

T = 5.8 KH = 200 mT

T = 4.0 KH = 20 mT

Similar to YNi2B2C


ErNi2B2C

TN = 6 K

TC = 11 K

Fairly simple modulated structure in zero field but with “squaring up” at low T and the development of even harmonics. Below 1.6 K a “ferromagnetic” component develops. Becomes even more complicated in a field.

Vortex distortion responds to the changes at TN. Vortex lattice is square at lower fields near to TN.

Small change in penetration depth but slope is different. Certain change in superconducting state through TN again probably due to

changes in core size and coherence length

“Ferromagnetic” component appears to be a series of randomly oriented “domain wall planes” with moments aligned parallel to each other, hence the rods of scattering. These objects cut the vortices and can act as pinning centres

TmNi2B2C : the Role of Paramagnetic

Moments

TmNi2B2C : the Role of Paramagnetic

Moments

Tc = 10.5 KTn = 1.5 KTc = 10.5 KTn = 1.5 K

Low Tn and high Tc large paramagnetic susceptibility

with field along the c-axis

Low Tn and high Tc large paramagnetic susceptibility

with field along the c-axis


Some Final ThoughtsSome Final Thoughts

A powerful technique to look at an interesting phase of

matter

A subtle, soft solid of wobbly lines

Crystal Growth & Annealing

Novel and unusual phase transitions

Disorder, Dimensionality and Anisotropy are of interest

bending, pinning, twisting,melting, decomposition etc

Need better theoretical models

even for the ‘simplest’ materials

A powerful technique to look at an interesting phase of

matter

A subtle, soft solid of wobbly lines

Crystal Growth & Annealing

Novel and unusual phase transitions

Disorder, Dimensionality and Anisotropy are of interest

bending, pinning, twisting,melting, decomposition etc

Need better theoretical models

even for the ‘simplest’ materials

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