Configuration-induced vortex motion in type II superconducting films with periodic magnetic dot arrays Qinghua Chen Prof. Shi Xue Dou 1
Outline: I. An Introduction of superconductor II. Overview of vortex motion in superconducting systems with periodic artificial pinning arrays III. Our simulation on guided vortex motion IV. Conclusions 2
I. An Introduction of superconductor A. Perfect conductivity 1911, Onnes H. Kamerlingh Leiden, Holland H. K. Onnes, Commun. Phys. Lab. 12, 120 (1911) 3
I. An Introduction of superconductor B. Perfect diamagnetism 1933, W.Meissner, and R. Ochsenfeld W. Meissner and R. Ochsenfeld, Naturwissenschaft 21, 787 (1933). 4
I. An Introduction of superconductor Abrikosov, 1957 Type-I: Type-II: < > Superconductivity and magnetism can coexist! Magnetic flux line --- (Abrikosov) vortex A. A. Abrikosov, Sov. Phys. JETP 9, 1174 (1957). 5
I. An Introduction of superconductor Type-1.5 1 ( T ) 1 ( T ) 1 2( T ) 2 ( T ) 2 1/ 1/ 2 2 two-gap materials: MgB 2 Ba 0.6 K 0.4 Fe 2 As 2 MgB 2 NbSe 2 Victor Moshchalkov, Mariela Menghini, T. Nishio, Q. H. Chen, A. V. Silhanek, V. H. Dao, L. F. Chibotaru, N. D. Zhigadlo, and J. Karpinski, Phys. Rev. Lett. 102, 117001 (2009) 6
I. An Introduction of superconductor Electric motors Transformers Generators Underground power cables Fault current limiters Magnetic shield devices Infrared sensors Analog signal processing devices Microwave devices Tera-hertz superconducting devices Magnetic resonance imaging (MRI) Nuclear magnetic resonance (NMR) Magnetically levitated (MAGLEV) trains Applications of superconductor Superconducting quantum interference devices (SQUIDs) Magnetic confinement fusion of hot plasma (ITER) 7
I. An Introduction of superconductor 18 toroidal field coils 1 central solenoid 6 poloidal field coils 18 correction coils 4.4 --- 4.7 K 11.8 T Nb 3 Sn NbTi http://www.iter.org 8
I. An Introduction of superconductor Critical parameters: Critical temperature T c Critical field H c Critical current density J c superconductivity is destroyed attempts to discover new superconducting materials with higher T c and the search for adequate processing methods to achieve higher J c have drawn great attention in the past century. 9
II. Overview of vortex motion in superconducting systems with periodic artificial pinning arrays Triangular array Square array Honeycomb array C. Reichhardt and C. J. Olson Reichhardt, Physical Review B 79, 134501 (2009). C. Reichhardt and C. J. Olson Reichhardt, Physical Review B 81, 024510 (2010). 10
II. Overview of vortex motion in superconducting systems with periodic artificial pinning arrays Vortex trajectories Driving force along x and y direction Triangular array C. Reichhardt and C. J. Olson Reichhardt, Physical Review B 79, 134501 (2009). 11
II. Overview of vortex motion in superconducting systems with periodic artificial pinning arrays Vortex trajectories Driving force along x and y direction Square array C. Reichhardt and C. J. Olson Reichhardt, Physical Review B 79, 134501 (2009). 12
II. Overview of vortex motion in superconducting systems with periodic artificial pinning arrays Vortex trajectories Driving force along x and y direction Honeycomb array C. Reichhardt and C. J. Olson Reichhardt, Physical Review B 79, 134501 (2009). 13
III. Our simulation on guided vortex motion A. Molecular dynamic model The total force acting on a vortex i is then governed by the Langevin equation (2D plane, overdamped): G. Blatter, et al., Rev.Mod. Phys. 66, 1125 (1994). 14
III. Our simulation on guided vortex motion A. Molecular dynamic model Np --- number of the pinning centers Nv --- number of vortices f 0 = Φ 02 /λ 3 --- force per unit length. Φ 0 = 2.07mTμm2 --- flux quantum and λ --- London penetration depth K 1 (x) --- modified Bessel function Q = p(p + q coth(pt/2)) with p = 1 + q 2 E(q, l,d) = e ql (e qd 1) J 1 (x) --- Bessel function R --- radius of the dots D --- thickness of the dots l --- distance between the bottom of the SC film and the upper surface of the dot M = m/(πr2d) --- m is the total magnetic moment of a dot J. Pearl, Appl. Phys. Lett. 5, 65 (1964). M. V.Milosevic and F.M. Peeters, Phys. Rev. B 68, 094510 (2003). 15
III. Our simulation on guided vortex motion B. Samples Parallel Ferromagnetic dot array (PFM) Anti-parallel Ferromagnetic dot array (AFM) Five typical directions: AB (x-direction), AC, BC, DE and DB 16
III. Our simulation on guided vortex motion C. Simulations: Magnetic dot array: 12 12 with periodic boundary condition The sample size is 12λ 9.45613λ The F vv from all other vortices are included because of their long-range character. A smoothed method is introduced here to deal with such interaction, which is of a look-up-table up to distance 100Λ by 0.04Λ step and an interpolation item for distance longer than 100Λ. H. Fangohr et al., J. Comput. Phys. 162, 372(2000) 17
III. Our simulation on guided vortex motion C. Simulations: The F vp from all magnetic dots is a short-range interaction. It decreases as r 4 at distances larger than the magnetic dot lattice constant a, and we use the cutoff assuming that the force is negligible for distances greater than 3.0. For PFM: Nv = 144 + 12 = 156 For AFM: Nv = 72 + 12 = 84 Moved (what we focus on) Pinned at the pinning centers 18
III. Our simulation on guided vortex motion C. Simulations: the vortices are randomly introduced first, and then we anneal the sample from an initial temperature (e.g., critical temperature Tc) to zero in 2500 steps and it remains constant at each step for 1000 molecular dynamic (MD) steps. Once the vortices are stable at zero temperature, we slowly increase the driving force F d along one of the five given directions (AB, AC, BC, DE, and DB), respectively, for both AFM and PFM configurations from 0 to 1.0 f 0 by 0.002 f 0 every 1000 MD steps. We also calculate the velocity and position of each vortex and compute the average velocity in the x and y directions, at every MD step, and write out this average velocity in every 10 MD steps. 19
III. Our simulation on guided vortex motion D. Results: AB direction: Vortex trajectories a1: AFM at F d =0.26f 0 a2: PFM at F d =0.26f 0 a3: AFM at F d =0.80f 0 a4: PFM at F d =0.80f 0 20
III. Our simulation on guided vortex motion D. Results: AC direction: Vortex trajectories b1: AFM at F d =0.26f 0 b2: PFM at F d =0.26f 0 b3: AFM at F d =0.80f 0 b4: PFM at F d =0.80f 0 21
III. Our simulation on guided vortex motion D. Results: BC direction: Vortex trajectories c1: AFM at F d =0.26f 0 c2: PFM at F d =0.26f 0 c3: AFM at F d =0.80f 0 c4: PFM at F d =0.80f 0 22
III. Our simulation on guided vortex motion D. Results: DE direction: Vortex trajectories d1: AFM at F d =0.26f 0 d2: PFM at F d =0.26f 0 d3: AFM at F d =0.80f 0 d4: PFM at F d =0.80f 0 23
III. Our simulation on guided vortex motion D. Results: DB direction: Vortex trajectories e1: AFM at F d =0.26f 0 e2: PFM at F d =0.26f 0 e3: AFM at F d =0.80f 0 e4: PFM at F d =0.80f 0 24
IV. Conclusions 1) In the absence of thermal fluctuations vortex motion in a superconducting film with periodic magnetic dot arrays is greatly dependent on the configuration of the magnetic dot array and the degree of the condensed pack. 2) Two easy directions exist for vortex motion in such system. 3) Due to the repulsive magnetic dots the vortex motion is guidable. Vortices always move along one of the two easy direction if the driving force is not strong enough. This guided vortex motion will disappear if only the driving force surpass a critical value and, then, all the vortices move back to the direction of the driving force. 4) For the traditional PFM configuration system we can also control vortex motion along an axis of the system. But this only happens at close pack case. 25