Dendritic flux avalanches in superconductors


branching flux dendrite

When a superconducting film is placed in a perpendicular magnetic field, the flux penetration sometimes occurs via abrupt avalanches that result in remarkable dendritic flux patterns that can be observed using magneto-optical imaging




Magneto-optical movie of flux penetration into a thin film of Mg2B. The movie is composed of 101 images taken at 3 K as the applied field increases from zero up to 35 mT and then decreases back to zero.

AVI movie of better quality


Selected papers

Experiment: Johansen et al., Europhys. Lett. 2002
Theory:       Denisov et al., Phys. Rev. B 2006
Simulations: Vestgarden et al., cond-mat/1012.4297

More publications



Johansen et al., Europhys. Lett. 2002
Albrecht et al, Phys. Rev. Lett. 2007
Choi et al, Appl. Phys. Lett. 2007
Colauto et al, Superc. Sci. Techn. 2007
Denisov et al, Phys. Rev. Lett. 2006
Olsen et al, Phys. Rev. B 2006
Shantsev et al., Phys. Rev. B 2005
Albrecht et al, Appl. Phys. Lett. 2005
Roussel et al, Supercond. Sci. Technol. 2005
Choi et al, Appl.Phys.Lett. 2005
Laviano et al., NATO S.S. "MO imaging" 2004
Ye et al., Appl. Phys. Lett. 2004
Barkov et al., Phys. Rev. B 2003
Shantsev et al., Supercond. Sci. Technol. 2003
Ye et al., IEEE Trans. App. Sup. 13-3722 2003
Bobyl et al., Appl. Phys. Lett. 2002
Baziljevich et al., Physica C 2002
Johansen et al., Supercond. Sci. Technol. 2001


Welling et al., Physica C 2004
Vlasko-Vlasov et al., Physica C 2000
Duran et al., Phys. Rev. B 1995
Wertheimer et al., J. Phys. Chem. Solids 1967

Bolz et al., Europhys. Lett. 2003
Bolz et al., Physica C 2003
Runge et al., Physica C 2000
Bolz et al., Physica B 2000
Leiderer et al., Phys. Rev. Lett. 1993
Bujok et al., Appl. Phys. Lett. 1993
P. Bruell et al., Ann. Phys. v.1, p.243, 1992

Yurchenko et al., Phys. Rev. B 2007
Rudnev et al., Appl. Phys. Lett. 2005

Rudnev et al., Cryogenics 2003

Menghini et al., Phys.Rev.B 2005
Gheorghe et al., Physica C 2006

Wimbush et al., J. Appl. Phys. 2004

Denisov et al., Phys. Rev. B 2006
Aranson et al., Phys. Rev. Lett. 2005
Rakhmanov et al., Phys. Rev. B 2004
Baggio et al., Phys. Rev. B 2005
Biehler et al., Phys. Rev. B 2005
Rosenstein et al., Europhys. Lett. 2005
Johansen et al., Europhys. Lett. 2002
Aranson et al., Phys. Rev. Lett. 2001
Maksimov et al., Physica C 1994

Magneto-optical images of flux dendrites

flux dendrites in MgB2 film   Magneto-opitcal studies of a c-oriented MgB2 film show that below 10 K the global penetration of vortices is dominated by complex dendritic structures abruptly entering the film. This behavior contrasts the gradual uniform penetration usually found in superconducting films.

Figure shows magneto-optical images of flux penetration (image brightness represents flux density) into the virgin state at 5 K. The respective images were taken at applied fields (perpendicular to the film) of 3.4, 8.5, 17, 60, 21, and 0 mT.

This complex flux dynamics must be responsible for suppression and noisy behavior of magnetization:

noisy M(H) for MgB2

the graph is copied from Zhao et al, Phys. Rev. B 65, 064512 (2002).

Remanent state

dendritic flux instability Remanent state of a highly branching dendritic structure at 9.9K. The dendrite was formed at applied of field 17mT, and then the field was decreased back to zero. The flux distribution along the film edge shows the conventional pattern with black annihilation zone (zero flux density), while the dendrite was not affected by the applied field reversal.

remanent state of MgB2 film

Theory explaining dendritic patterns

stability diagram for dendritic flux jumps Bulks:  Phys. Rev. B 2004   PDF
Films:  Phys. Rev. B 2006   PDF

A linear analysis of thermal diffusion and Maxwell equations shows that a thermo-magnetic instability can lead to formation of finger-like distributions of magnetic field and temperature. The fingering instability emerges when the background electric field is larger than a threshold field Ec, and the applied magnetic field exceeds a threshold value H(E), see the phase diagram.

We derive the criterion for the instability, and estimate its build-up time and characteristic finger width. Numerical simulations support the analytical results, and allow us to follow the development of the fingering instability beyond the linear regime.

Thin films are shown to be more unstable than bulk superconductors and have a stronger tendency to form fingering (dendritic) flux patterns.

Quantitative comparison of Theory and Experiment


Lower threshold field


temperature dependence of the instability onset field Phys. Rev. Lett. 2006   PDF

The work presents a detailed comparison of experimental data and theoretical predictions for the dendritic flux instability. It is shown that a thermo-magnetic model published very recently [Phys. Rev. B 73, 014512 (2006)] gives an excellent quantitative description of key features like the instability onset (first dendrite appearance) magnetic field, and how the onset field depends on both temperature and sample size. The measurements were made using magneto-optical imaging on a series of different strip-shaped samples of MgB2. Excellent agreement is also obtained by reanalyzing data previously published for Nb.



Upper threshold field


temperature dependence of the instability onset field Phys. Rev. B 2007   PDF

We propose a mechanism responsible for the abrupt vanishing of the dendritic flux instability when an increasing magnetic field is applied. The onset of flux avalanches and the subsequent reentrance of stability in NbN films was investigated using magneto-optical imaging, and the threshold fields were measured as functions of critical current density, jc. The results are explained with excellent quantitative agreement by a thermomagnetic model published in [Phys. Rev. B 73, 014512 (2006)], showing that the reentrant stability is a direct consequence of a monotonously decreasing jc versus field.



Temperature dependence


temperature-dependent magnetic flux pattern in MgB2



The flux pattern is strongly temperature dependent

Figures (a-c) show flux distribution at T = 3.3, 9.9 and 10.5 K at applied fields of 13, 17 and 19 mT, respectively.


We suggest that the observed behavior is due to a thermo-magnetic instability, which is supported by vortex dynamics simulations.

(d-f): Flux densities obtained by vortex dynamics simulations at T1 < T2 < T3, respectively, reproducing the morphology of the patterns in (a-c).

Dramatic role of critical current anisotropy on dendritic avalanches


anisotropic dendritic avalanches Phys. Rev. Lett. 2007   PDF

Anisotropic penetration of magnetic flux in MgB2 films grown on vicinal sapphire substrates is investigated using magneto-optical imaging. Regular penetration above 10 K proceeds more easily along the substrate surface steps, anisotropy of the critical current being 6%. At lower temperatures the penetration occurs via abrupt dendritic avalanches that preferentially propagate perpendicular to the surface steps. This inverse anisotropy in the penetration pattern becomes dramatic very close to 10 K where all flux avalanches propagate in the strongest-pinning direction. The observed behavior is fully explained using a thermomagnetic model of the dendritic instability.


Simultaneous Penetration of Flux and Antiflux Dendrites in MgB2 rings


anisotropic dendritic avalanches Phys. Rev. B 2006   PDF

Flux dendrites with opposite polarities simultaneously penetrate superconducting, ring-shaped MgB2 films. By applying a perpendicular magnetic field, branching dendritic structures nucleate at the outer edge and abruptly propagate deep into the rings. When these structures reach close to the inner edge, where flux with opposite polarity has penetrated the superconductor, they occasionally trigger anti-flux dendrites. These anti-dendrites do not branch, but instead trace the triggering dendrite in the backward direction. Two trigger mechanisms, a non-local magnetic and a local thermal, are considered as possible explanations for this unexpected behaviour. Increasing the applied field further, the rings are perforated by dendrites which carry flux to the center hole. Repeated perforations lead to a reversed field profile and new features of dendrite activity when the applied field is subsequently reduced.


Coexistense of small and dendritic jumps


2 types of jumps More detailed studies show that in addition to the big dendritic jumps, small flux jumps also take place everywhere along the flux front.

On the Figure:
The first jump was detected at 4 mT and was as small as 20 vortices. At larger fields more jumps were found with average size gradually increasing to 10000 vortices. At 15 mT the first dendritic jump occured which consisted of millions of vortices.

The observed jump size distribution and its field dependence is explained by our Adiabatic theory

Phys.Rev.B 2005 PDF (Theory+Experiment)
Physica C 2004 PDF (Experiment)



Published Jan. 29, 2011 11:30 PM - Last modified Oct. 26, 2018 11:06 AM