Vortex Imaging in Unconventional Superconductors

Transcription

1 Magnetic imaging Vortex Imaging in Unconventional Superconductors P.J. Curran, W.M.A. Desoky, V.V. Khotkevych & S.J. Bending Department of Physics, University of Bath, Bath BA2 7AY, UK A. Gibbs & A.P. Mackenzie School of Physics & Astronomy, University of St Andrews, St Andrews KY16 9SS, UK Sr 2 RuO 4 crystal growth S.E. Sebastian Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK T. Tamegai Department of Applied Physics, Univ. of Tokyo, Japan Sr(Fe 1-x Co x ) 2 As 2 crystal growth Ba(Fe 1-x Co x ) 2 As 2 crystal growth

2 OUTLINE Introduction to vortex imaging using scanning Hall probe microscopy (SHPM) Motivation Vortex structures reflect underlying electronic & order parameter anisotropies Allows search for spontaneous currents/fields due to TRSB Local penetration depth (superfluid density) measurements yield information about multiband superconductors & gap function Can directly image thermodynamic vortex matter phase transitions Vortex structures and structural transitions in the spin triplet superconductor Sr 2 RuO 4 Insights into OP of Co-doped 122 Fe-based superconductors from λ(t) measurements

3 1) Third Generation Scanning Hall Probe Microscope System 300mK cold plate sample Hall probe piezoelectric scanner tube 3-axis Attocube positioners V.V. Khotkevych, M.V. Milošević & S.J. Bending, Rev. Sci. Instr. 79, (2008)

4 2) Magnetic Imaging; Spin Triplet Superconductor Sr 2 RuO 4 Believed to be an odd-parity p-wave spin triplet superconductor; i.e., Cooper pairs have parallel spins instead of the usual antiparallel ones. Muon spin rotation and magneto-optical Kerr effect experiments suggest spontaneous magnetisation in zero magnetic field:- Implies that time-reversal symmetry is broken at T c Maeno et al., Physics Today 54, 42, (2001) Mackenzie et al., Rev. Mod. Phys. 75, 657 (2003) Magnetisation at H=0 predicted to arise from spontaneous supercurrents where translational symmetry broken (e.g., surfaces & chiral domain walls). The chiral parameter d( k) = ẑ( k x ± order ik is compatible with most experiments. y ) d B (G) x (µm) Dolocan et al., Phys. Rev. Lett. 95, (2005) Kirtley et al., Phys. Rev. B 76, (2007) Spontaneous fields never observed in scanning SQUID & Hall probe imaging experiments.

5 2.1) Sample Preparation e-5-2e-5 Samples grown in a floating-zone furnace, and annealed at 1500C for 3 days in air afterwards to remove lattice defects and reduce vortex pinning. Samples freshly cleaved along (001) prior to mounting in microscope χ' (a.u.) χ'' (a.u.) -2e-5-3e-5-3e-5-4e-5-4e-5-5e-5-5e T (K) T (K) Sample A1 The highest quality sample (A1) has T c 1.5K and a very narrow transition as measured by ac susceptibility.

6 2.2) Vortex Profiles & Low Field (H < 4Oe) Vortex Structures No spontaneous fields observed within minimum detectable field, B mdf ~ 4G. H eff ~ -0.9Oe H eff ~ 0.2Oe H eff ~ 0.7Oe H eff ~ 0.9Oe H eff ~ 1.7Oe H eff ~ 2.4Oe H eff ~ 3.5Oe At low fields (H < 4Oe) observe disordered vortex distributions - little sign of any emergent order. B (G) x (µm) T ~ 300mK T c = 1.5K Vortex profiles fitted using modified Clem variational model; ξ(0)=66nm, λ(0)=165nm, w=600nm - All contain φ 0 but.. fitted sensor height, h=1.26µm, is much too large. Unexplained broadening??? After Delaunay triangulation vortex-vortex J.R.Clem, JLTP 18, 427 (1975) spacings well described by single Gaussian peak. - No evidence for vortex clustering due to long range attraction.

7 2.3) Vortex Chains and Bands in lower quality sample WD03 H eff ~ -2.4Oe 14µm H eff ~ -3.1Oe H eff ~ -15.7Oe Sample WD03 (blue) has a slightly lower T c than A1 (red) and a somewhat broader transition e-6-1e-5 2.5e-6-2e-5 2.0e-6 χ' (a.u.) χ'' (a.u.) -2e-5-3e-5-3e-5-4e-5-4e-5-5e-5-5e-5-1.0e T (K) 1.5e-6 1.0e-6 5.0e-7-5.0e-7 χ'' (a.u.) Sample A1 Sample WD03-2.0e-6-4.0e-6-6.0e-6-8.0e-6-1.0e-5-1.2e-5 χ' (a.u.) -1.4e T (K) T 300mK -1.6e-5 At low applied fields vortices appear to be pinned along quasiperiodic chains. At still higher fields the chains multiply and expand into bands

8 2.4) High Field (H > 4Oe) Vortex Structures H eff ~ 3.9Oe H eff ~ 5.4Oe H eff ~ 6.8Oe H eff ~ 12.8Oe H eff ~ 24.6Oe G(r) B(r) H < 4Oe Structures random and disordered 4Oe < H < 6Oe Strong degree of hexagonal order H ~ 7Oe Hexagonal & square order compete Observe dominant square order (not rectangular) with the same orientation at high fields and the lattice spacing is very consistent with neutron diffraction data. Riseman et al., Nature 396, 242 (1998). a (µm) H > 8Oe Pronounced square ordering b[0]= b[1]= r ²= Neutron data x-spacing linear regression y-spacing (Φ 0 /abs(b)) 0.5 (µm)

9 2.5) Theoretical Predictions of Vortex Lattice Structural Transition Extended London theory (κ>>1) calculations for a two component p-wave order parameter as a function of Fermi surface anisotropy, ν (ν=0 corresponds to a cylindrical FS), predict a transition from hexagonal to square lattice as the field is increased. R.Heeb & D.F.Agterberg, Phys. Rev. B 59, 7076 (1999) Square lattice high fields Hexagonal lattice low fields 2B =φ 2 πλξ ~ 300G c 0 For a more realistic (lower) value of κ transition expected to occur at lower fields and anisotropies, ν.

10 2.6) Comparison with Neutron Diffraction and µsr Measurements Neutron diffraction µsr data Our SHPM data SANS; square lattice observed everywhere it could be resolved. Riseman et al., Nature 396, 242 (1998). µsr, H=150Oe; Square lattice observed at low T transforming to hexagonal at T=0.8K. Aegerter et al., J. Phys.: Cond. Matt. 10, 7445 (1998). Luke et al., Physica B , 373 (2000). SHPM; Square lattice everywhere except H<8Oe (low T) and T~T c.

11 3) Vortex Imaging in Co-doped 122 Fe-based Superconductors (O) Poor paramagnetic metal Tetragonal (T) Parent compound exhibits tetragonal to orthorhombic structural transition linked to a magnetic transition to a SDW state. Co-doping suppresses spin and structural transitions and leads to high T c superconductivity. Hole-like pockets at Γ-point Electron-like pockets at M-points Well-established that there are two superconducting gaps ( 1 ~2 2 ). Extended s ± pairing state where sign of OP reverses on hole and electron pockets is likely candidate. Evidence that small gap on hole pockets isotropic s-wave; Multiple band Fermi surface of large gap on electron pockets can be anisotropic (+nodes?). BaFe 1.8 Co 0.2 As 2 Mazin et al.,, PRL 101, (2008); Paglione & Greene, Nat. Phys. 6, 645 (2010)

12 3.1) Order Parameter in Co-doped Ba122 Superconductors Samples studied: X=45 underdoped X=75 ~optimal X=0.113 overdoped Exponent of low temperature penetration depth, λ ab (T) ~T n, versus critical temperature, T c. Ruslan Prozorov & Vladimir Kogan, arxiv: v1 Fully gapped & isotropic In-plane anisotropy develops away from opt. doping c-axis nodes?

13 3.2) Local Measurements of Superfluid Density Luan et al., PRB 81, (R) (2010) Fletcher et al., Phys. Rev. Lett. 95, (2005) Bouquet et al., Europhys. Lett. 56, 856 (2001) We can measure vortex profiles as a function of T and fit them using modified Clem variational model. This allows us to make a mesoscopic estimate (~2λ(T)) of superfluid density. ( y+ w ) ( x+ w ) K1( k + λ ξv ) ( y w ) ( x w ) v φ B( x, y, z) = w 2 πλ( k λ k) K ( ξ λ) J k x + y kz kdkdx dy ( ' ' )exp( ) ' ', (1) J.R.Clem, JLTP 18, 427 (1975) Luan et al. at Stanford measured MFM force curves to infer microscopic λ(t) and superfluid density ρ(t) λ(0) 2 /λ(t) 2. Used 2 band α-model to fit:- Define/fit 1, 2, a 1, a 2, T c πkt T ( T ) = ( 0)tanh c a c i i i 1 i ( 0) T 1 ρi (T ) = 1 kt 2 cosh 0 Fit p ε i (T ) dε 2kT ρs ( T ) = p. ρ1( T ) + (1 p). ρ2( T ) ρ(t)/ρ(0)=λ(0) 2 /λ(t) B (G) x (µm) Sum Large gap; p=0.75 Small gap; p= t=t/t c

14 3.3) Vortex Imaging; Sr(Fe 1-x Co x ) 2 As 2 (x~0.11; T c =13.65K, underdoped) 3D vortex images after field-cooling from above T c =13.65K to T=8K. Scan size ~8µm 8µm. Highly disordered vortex structure due to Co-doping on Fe sites. Images at H~1Oe with well isolated vortex fitted to extract λ ab (T). Gap values taken from point contact spectroscopy. C.R. Hunt et al., Abstract: X , Bull. Am. Phys. Soc., Vol. 56, Number 1, (2011) We can fit the data well with:- 1 =4.8kT c, a 1 =0.94, p= =2.0kT c, a 2 =1, (1-p)=0.51 Assume small hole-pocket gap isotropic s-wave Large electron-pocket gap fit ~isotropic A few weak coupling results:- Isotropic s-wave; (0) =1.76T c, a = 1 2D d-wave; (0) = 2.14T c, a = 4/3 s + g-wave; (0) = 2.77T c, a = 2 Non-monotonic d-wave; (0) =1.19T c, a = 0.38 Prozorov et al., SuST 19, R41 (2006) ρ(t)/ρ(0)=λ(0) 2 /λ(t) band fit; p=0.49, a 1 =0.94 (a 2 =1, 1 =4.8kT c, 2 =2.0kT c ) 1 band fit; a=0.92, =2.81kT c 1 band fit; =2.53kT c (a=1) Experimental data T/T c 7 T/T c 8

15 3.4) Imaging; Ba(Fe 1-x Co x ) 2 As 2 (x~75; T c =23.3K, ~optimal) -1Oe 0Oe +1Oe +2Oe +3Oe +4Oe +5Oe Vortex structures again highly disordered due to Co-doping on Fe sites. Appear to be regions of sample where vortices of opposite sign are preferentially pinned. Optimally doped crystal K 8K 12K 16K 20K 21K 22K 22.5K X=75, T c =23.3K We can fit the data well with:- 1 =3.3kT c, a 1 =1.92, p= =1.3kT c, a 2 =1, (1-p)=0.24 Assume hole-pocket gap isotropic s-wave Electron-pocket gap deviates strongly from isotropic result. a 1 ~2 s + g-wave????? ρ(t)/ρ(0)=λ(0) 2 /λ(t) band fit; p=0.76, a 1 =1.92 (a 2 =1, 1 =3.3kT c, 2 =1.3kT c ) 1 band fit; a=1.82, =2.26kT c 1 band fit; =2.9kT c (a=1.3) Experimental data T/T c 0.1 X(µm)

16 3.5) Imaging; Ba(Fe 1-x Co x ) 2 As 2 (x~0.113; T c =9.75K, overdoped) Overdoped crystal X=0.113, T c =9.75K Attempt to fit the data with:- 1 =3.3kT c 2 =1.3kT c, a 2 =1 Unable to get a satisfactory fit:- 2 band a 1, p fit yields p=1.43>1!!! 1 band fits also in very poor agreement with data. Sample appears to be qualitatively different. c-axis nodes??? ρ(t)/ρ(0)=λ(0) 2 /λ(t) band fit; p=1.43(>1!), a 1 =0.63 (a 2 =1, 1 =3.3kT c, 2 =1.3kT c ) 1 band fit; =2.74kT c (a=1) 1 band fit; =1.92kT c (a=1.7) 1 band fit; a=0.68, =2.81kT c Experimental data T/T 8 10 c

17 Conclusions Magnetic imaging in high quality Sr 2 RuO 4 single crystals; No convincing evidence of spontaneous currents/fields at chiral domain walls. Difficult to reconcile with other experimental investigations of the order parameter (e.g., p-kerr, SQUID)??? No evidence for vortex coalescence in best quality samples. Observe a vortex lattice structural transition from predominantly hexagonal at H<8Oe to square for H>8Oe at low temperatures. Yields information about the anisotropy of the Fermi surface. Vortex imaging in Sr(Fe 1-x Co x ) 2 As 2 & Ba(Fe 1-x Co x ) 2 As 2 single crystals; Vortex structures highly disordered with some evidence for polarity-dependent pinning in optimally doped Ba(Fe 1-x Co x ) 2 As 2 crystals. Analysis of vortex profiles has been made assuming small isotropic s-wave gap at hole-like pockets. Fit parameters suggest electron pockets have isotropic s-wave OP in underdoped Sr122 sample, and strong anisotropic OP in optimally doped Ba122 sample. Appears to contradict trends inferred from other measurements but must collect better statistics on different samples.