- Email: [email protected]
Competing symmetries in superconducting vortex–antivortex “molecular crystals”
Available online at www.sciencedirect.com
Physica C 468 (2008) 518–522 www.elsevier.com/locate/physc
Competing symmetries in superconducting vortex–antivortex ‘‘molecular crystals” S.J. Bending a,*, J.S. Neal a, M.V. Milosˇevic´ a,b, A. Potenza c, L. San Emeterio c, C.H. Marrows c b
a Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, UK Departement Natuurkunde, Universiteit Antwerpen (UIA), B-2610 Antwerpen, Belgium c School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, UK
Accepted 30 November 2007 Available online 6 March 2008
Abstract Hybrid structures composed of superconducting films deposited on ordered arrays of magnetic ‘dots’ have attracted enormous interest in recent years. Dots with sufficiently large magnetic moments may generate one or more spontaneous vortex–antivortex (V–AV) pairs in the superconducting film which can either remain associated with individual nanomagnets as V–AV ‘‘molecules” in dilute arrays or organise themselves into an ‘ionic’ crystal in dense arrays. Exactly how V–AV molecules transform into lattices and how they interact with (anti)fluxons induced by external magnetic fields remain challenging questions for both theory and experiment. We have used high resolution scanning Hall probe microscopy to image V–AV ‘‘molecules” induced in superconducting Pb films by the stray fields from square arrays of ferromagnetic Co/Pt dots. We have directly observed spontaneous V–AV pairs and studied how they interact with added ‘‘free” (anti)fluxons in an applied magnetic field. We observe a rich variety of subtle phenomena arising from competing symmetries in our system which can either drive added antivortices to join AV shells around nanomagnets or stabilise the translationally symmetric AV lattice between the dots. Added vortices annihilate AV shells, leading eventually to a stable ‘nulling state’ with no free fluxons, which should exhibit a strongly field-enhanced critical current. At higher densities we actually observe vortex shells around the magnets, stabilised by the asymmetric anti-pinning potential. Our experimental findings are in good agreement with Ginzburg–Landau calculations. Ó 2008 Elsevier B.V. All rights reserved. PACS: 74.78.Na; 74.25.Ha; 74.20.De Keywords: Superconducting vortices; Magnetic pinning arrays; Vortex–antivortex shells
1. Introduction Recent advances in nanofabrication and thin film growth technologies have made it possible to engineer many of the properties of superconducting materials. An important example, which has recently excited considerable interest, is the incorporations of ferromagnets (e.g. ferromagnetic dots or disks) in hybrid structures. Many of the superconductor–ferromagnet hybrid systems studied to *
Corresponding author. Tel.: +44 1225 385173; fax: +44 1225 386110. E-mail address: [email protected] (S.J. Bending).
0921-4534/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2007.11.076
date can be broadly divided into two classes; those where magnetic nanostructures with weak moments are used as pinning sites to enhance the superconducting critical current by suppressing flux line motion [1], and those with strong moments which lead to the spontaneous formation of vortex–antivortex (V–AV) pairs. The latter have been found to enhance the critical temperature of the film at finite H through local compensation of the nanomagnet stray fields by the applied field [2]. While such considerations are valid near the superconductor-normal phase boundary, where screening can be neglected, the situation deep within the superconducting state is qualitatively
S.J. Bending et al. / Physica C 468 (2008) 518–522
519
different owing to the requirement for magnetic flux to be quantized. Here a simple picture of field cancellation is no longer applicable and a microscopic picture of the formation and properties of spontaneous V–AV pairs is essential. The critical current of such hybrid structures has been investigated as a function of applied field some distance from the phase boundary [3], but otherwise there has been very little experimental work in the low temperature regime. In contrast there have been extensive theoretical investigations of superconducting films deposited on spatial arrays of magnets using Ginzburg–Landau formalism. Each magnet may generate one or more spontaneous vortex–antivortex (V–AV) pairs in the superconducting film. These either remain associated with individual magnets as V–AV ‘‘molecules” in dilute arrays [4], or organize themselves into an ‘‘ionic” crystal in dense arrays [5]. We report here the first direct imaging studies of spontaneous V–AV structures, which have been achieved using scanning Hall probe microscopy. Our work yields key insights into exactly how V–AV molecules transform into lattices and how they interact with (anti)fluxons introduced by external magnetic fields. 2. Experimental method The samples investigated consisted of a square array of ferromagnetic disks covered with a type II superconducting Pb film. The disks were formed in a [Co(0.5 nm)/Pt(1 nm)]12 multilayer film (Fig. 1a) with uniaxial perpendicular magnetic anisotropy sputtered on a Si/SO2 substrate. They were patterned by electron beam lithography and reactive ion etching through an evaporated aluminium etch mask (Fig. 1b). Four different diameter circular disks with different magnetic moments have been patterned on the corners of a 5 lm 5 lm square cell which was repeated periodically in a square lattice, allowing the behaviour of dots with different spontaneous V–AV numbers to be compared in the same sample. The design diameters of 522 nm (dot A), 738 nm (D), 808 nm (B) and 902 nm (C) were chosen, corresponding theoretically to 1, 3, 3 and 5 spontaneous V–AVs, respectively [5]. Fig. 1c shows an atomic force micrograph of a unit cell of the disk array. The unpatterned Co/Pt film was measured by the Magneto-Optical Kerr Effect (MOKE) at 300 K (Fig. 1e) and shown to have high remanence and a coercive field of 1000 Oe. SHPM images of magnetisation reversal in the disks at T = 20 K indicate a range of coercive fields spanning 700–1000 Oe and magnetic saturation above H ffi 1000 Oe. Switching of the weakly coupled disks is largely uncorrelated, but once magnetised, disks of a given size exhibit almost complete remanence at H = 0 and remain in a single domain state with highly uniform out-of-plane moments (cf. Fig. 2c). This allows the application of small applied fields (H < 100 Oe) without any modification of the underlying magnetic ‘template’. The disks were coated with a 20 nm Ge layer to suppress proximity effects and an 80 nm Pb film deposited using dc magnetron sputtering followed by a
Fig. 1. (a) Layer structure and (b) schematic diagram of the sample. (c) Atomic force microscope image of just the Co/Pt disks immediately after dry etching. (d) MOKE measurement of the magnetisation of the unpatterned Co/Pt multilayer at 300 K.
10 nm Mo capping layer to prevent oxidation. Magnetisation measurements on a single Pb film of the same thickness indicate that it is a type II superconductor with Tc = 6.68 K, keff(5 K) ffi 120 nm and n(5 K) ffi 50 nm. Finally the sample was also coated with 20 nm Ge and 50 nm Au to enhance the stability of the SHPM when in tunnelling contact. Note that the upper surface of the Mo cap layer is oxidised and does not significantly intermix with the adjacent Ge film, which is deposited by thermal evaporation at room temperature. Hence it is not superconducting at the measurement temperatures used in these experiments. We have used a high resolution scanning Hall probe microscope (SHPM), as sketched in Fig. 2a, to both image the magnetisation state of the Co/Pt nanomagnets, and to visualise V–AV shell structures associated with them in the superconducting state. Our SHPM is a modified commercial low temperature STM in which the usual tunnelling tip has been replaced by a microfabricated GaAs/AlGaAs heterostructure chip as illustrated in Fig. 2b. Electron beam lithography and wet etching were used to define a
520
S.J. Bending et al. / Physica C 468 (2008) 518–522
a
4. Experimental results
Z (x,y) Bz (x,y) Scan Voltages
Electronics
Scanner Tube
PC
STM Tip Bias
Hall Voltage
B o
1-2
Sample
Tilt Stage
b
Hall Probe
IHall
c 5μm
Fig. 2. (a) Schematic diagram of the Scanning Hall probe microscope. (b) Scanning electron micrograph of a sub-micron scanning Hall probe with integrated STM tip. (c) Image of the magnetised disk array at T = 20 K. (Co/Pt dots are white).
Hall probe in the two-dimensional electron gas at the intersection of two 500 nm wide wires approximately 5 lm from the corner of a deep mesa etch. The latter had been coated with a thin Au layer to act as an integrated STM tip. The sample is first approached towards the sensor until tunnelling is established and then retracted about 100 nm allowing rapid scanning with minimum detectable fields 1 lT/Hz0.5. The Hall probe makes an angle of about 1° with the sample plane so that the STM tip is always the closest point to the surface, and the Hall sensor was about 300–400 nm above the sample in the images shown here. A more detailed description of the instrument is given elsewhere [6].
In order to observe clear spontaneous V–AV structures we found that it was necessary to magnetise the sample to saturation (H > 3000 Oe) at low temperature. An undesirable consequence of this was the trapping of a small amount of magnetic flux in our superconducting solenoid, which acts in the opposite direction to the dot magnetisation. By integrating the total net flux in a single image, as well as comparing images with GL simulations, we estimate that this background field (which includes the earth’s magnetic field) is about 3.5 Oe. To avoid unnecessary confusion arising from this constant offset to the applied field (Ha) we always quote ‘‘effective” field values as defined by Heff = Ha 3.5 Oe. All SHPM images presented here were obtained after field-cooling the sample from above Tc in the indicated applied field. Fig. 3a shows the first direct observation of spontaneous V–AV shell structures in our hybrid sample at Heff = 0. Since the amplitude of the (black) antivortices is typically only 10–20% of that of the (white) vortices trapped on the magnetic disks we have had to use a strongly non-linear grayscale to enhance their visual identification. As theoretically expected, the (black) AVs clearly order in shell-like structures around the magnetic dots, while (white) vortices remain confined above the dots. We have used a careful line-scan analysis to determine the exact locations of AVs and these are sketched for clarity in Fig. 3b. Fig. 3c shows maps of the local magnetic induction obtained from GL simulations for our exact sample geometry. The experimentally observed vorticity is in good agreement with simulations, and broadly speaking increases with the magnetic moment of the disks (subject to flux quantization). We find that we can tune the vorticity of these V–AV shell structures by applying a
3. Theoretical model Our experimental data have been compared directly with theoretical calculations based on solutions of the Ginzburg–Landau (GL) equations. These have been performed for our exact sample geometry, assuming a coherence length n(0) = 50 nm and uniform magnetisation of the dots of M = 750 G. Three-dimensional calculations have also been performed to investigate the role of the topography introduced by the underlying disk array (for details of the approach we refer to [5]).
Fig. 3. (a) SHPM image and (b) schematic depiction of spontaneous V– AV configurations at Heff ffi 0 and T = 5 K. (c) Map of magnetic induction across the GL calculation under the same conditions. (d)–(f) Different vorticity V–AV shell structures at various effective applied fields and T = 5 K.
S.J. Bending et al. / Physica C 468 (2008) 518–522
magnetic field to either add (Heff < 0) or annihilate (Heff > 0) antivortices, the details of which will be discussed later. Fig. 3d–f shows such V–AV shells containing 2, 3 and 5 antivortices, respectively. For negative applied fields we introduce free AVs into the spontaneous V–AV shell system. In this situation we find that the square symmetry of the underlying magnetic lattice imposes itself on the natural shell structure of the individual V–AV molecules. Indeed there appears to be a subtle competition between the n-fold rotational symmetry of the V–AV ‘‘molecules” and the translationally symmetric lattice of magnets. As the negative effective field is varied we sometimes observe spontaneous AVs which detach from their nanomagnet (effectively breaking a V–AV bond) to join the interstitial AV-lattice. At other field values we see the exact reverse of this scenario; an AV that is not needed in the interstitial lattice approaches a magnetic dot and joins its AV shell, attracted by the ‘positive’ vortex core. In this way at sufficiently negative effective fields all the V–AV molecules become net ‘negative’, i.e. they contain more antivortices than vortices. For positive effective magnetic fields, the general behaviour of the V–AV structures is more intuitive as it is predominantly governed by the annihilation between AV shells and externally added vortices. With increasing applied field each of the molecules progressively loses its negative AVs, and becomes more ‘positively’ charged. Even after all AVs have become annihilated, the vortex ‘‘charge” of individual magnetic dots keeps increasing due to the trapping of additional vortices on the magnetic dots. This arises because of the attraction between a magnet and a vortex when their moments are parallel [7]. This process is illustrated in Fig. 4(top), where we show the number of experimentally observed off-site fluxons (circles; antivortices are counted negative and vortices positive) as a function of applied field, as well as the results of GL calculations (solid line). There is a remarkable agreement between the experimental and theoretical data sets and both plots clearly exhibit a ‘‘nulling”’ field (Ha 6 Oe, Heff ffi 2.5 Oe), where we have no free fluxons. The lower half of Fig. 4 depicts SHPM images as this state is approached. The scan at Heff ffi 1.5 Oe clearly shows some remaining black AVs in shells around the dots that are annihilated in the next image at Heff ffi 2 Oe. The subtracted ‘‘difference” image on the right hand side more clearly reveals the changes that have occurred between the two measurements. White dots in this either represent annihilated antivortices in the first image or added vortices in the second. The difference in applied field between successive images of DH = 0.5 Oe corresponds to three added flux quanta on average. While this is consistent with what we see in the difference image, we unexpectedly find that a vortex has been removed from above the disk in the lower right hand corner where we see a black dot. Presumably this on-site vortex has annihilated with one of the adjacent antivortices. The image of the vortex state at Heff ffi 2.5 Oe looks superficially similar to that at 2 Oe, but the difference
521
Fig. 4. (Top) Number of experimentally observed (anti)vortices as a function of applied field at T = 5 K (circles). Solid line shows the predictions of GL theory (shifted by +4 Oe on the field axis to simulate flux trapping in the solenoid). (Middle, Bottom) Two pairs of successive SHPM images near the ‘‘nulling” state and their ‘‘difference images” (T = 5 K).
image reveals that the number of trapped on-site vortices has increased at the higher field. Moreover the asymmetric position of the added vortices in the difference image is suggestive of a multi-vortex state above the dots, which is what we expect theoretically. This trapping out of excess vortices leads to a fairly robust ‘‘nulling” state that exists over a reasonable range of applied fields (DH > 1 Oe). This ‘locking’ behaviour ensures the absence of any off-site fluxons, and consequently corresponds to a field-induced enhancement of the critical current of the sample. Upon increasing the (positive) applied field still further the non-uniform changes in on-site vortex occupation across the sample impact on off-site vortices. The potential landscape for the pinning of ‘free’ interstitial vortices becomes ‘dynamic’ since interactions with pinned vortex molecules relocate the energy minima as their charge changes. At sufficiently large magnetic fields a square interstitial vortex lattice is recovered, mirroring conventional matching phenomena. However, the interstitial lattice is distorted due to the asymmetry introduced by having dots with different moments. The influence of multi-quanta
522
S.J. Bending et al. / Physica C 468 (2008) 518–522
ment. Moreover, the complex V–AV interactions demonstrated here should also be reflected in two-component colloidal suspensions consisting of oppositely charged particles [8], e.g. those coated by charged polymers [9]. 5. Conclusion In conclusion, we have directly imaged spontaneous V– AV shell structures induced in superconducting films by the stray fields of magnetic arrays for the first time. We observe a variety of subtle phenomena which arise from competition between the n-fold rotational symmetry of the V–AV ‘‘molecules” and the translationally symmetric lattice of magnets. Our measurements agree well with GL calculations and these systems could yield valuable insights into the properties of ionic crystals based on the ordering of binary systems of particles, e.g. oppositely charged colloidal particles. Acknowledgements
Fig. 5. (a) SHPM image and (b) schematic depiction of the vortex configuration at Heff ffi 7.5 Oe and T = 5 K. (c) Corresponding GL Cooper-pair density plots under the same conditions.
vortices at the nanomagnets becomes more evident at the highest resolvable vortex densities. Fig. 5a and b shows how the presence of four different repulsive potentials propagating radially from the corners of the square cell, and strong interactions between interstitial vortices, results in their arrangement in shells. The same structure is found in GL simulations under identical conditions (Fig. 5c). Such an unusual ordering of vortices has never been observed in the presence of uniform pinning. While AVs form shells around confined vortices due to their mutual attraction, counter-intuitively, vortex shells are formed here by repulsion. The same scenario applies generally to any system of interacting particles in a similar environ-
This work was supported in the UK by EPSRC Grant No. GR/D034264/1 and PhD studentship GR/P02707/01. M.V.M. acknowledges support from the Marie-Curie Intra-European program. References [1] (a) J.I. Martin et al., Phys. Rev. Lett. 79 (1997) 1929; (b) D.J. Morgan et al., Phys. Rev. Lett. 80 (1998) 3614. [2] (a) S.A. Wolf et al., Phys. Rev. B 25 (1982) 1990; (b) H.W. Meul et al., Phys. Rev. Lett. 53 (1984) 497; (c) M. Lange et al., Phys. Rev. Lett. 90 (2003) 197006. [3] M. Lange et al., Phys. Rev. B 72 (2005) 052507. [4] M.V. Milosevic, F.M. Peeters, Phys. Rev. B 68 (2003) 024509. [5] (a) M.V. Milosevic, F.M. Peeters, Phys. Rev. Lett. 93 (2004) 124509; (b) D.J. Priour Jr., H.A. Fertig, Phys. Rev. Lett. 93 (2004) 057003. [6] A. Oral, S.J. Bending, M. Henini, Appl. Phys. Lett. 69 (1996) 1324. [7] (a) S. Erdin et al., Phys. Rev. B 66 (2002) 014414; (b) M.V. Milosevic, F.M. Peeters, Phys. Rev. B 68 (2003) 094510; (c) for review, see:I.F. Lyuksyutov, V.L. Pokrovsky, Adv. Phys. 54 (2005) 67. [8] M.E. Leunissen et al., Nature (London) 437 (2005) 235. [9] F. Caruso et al., Macromolecules 32 (1999) 2317.
Physica C 468 (2008) 518–522 www.elsevier.com/locate/physc
Competing symmetries in superconducting vortex–antivortex ‘‘molecular crystals” S.J. Bending a,*, J.S. Neal a, M.V. Milosˇevic´ a,b, A. Potenza c, L. San Emeterio c, C.H. Marrows c b
a Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, UK Departement Natuurkunde, Universiteit Antwerpen (UIA), B-2610 Antwerpen, Belgium c School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, UK
Accepted 30 November 2007 Available online 6 March 2008
Abstract Hybrid structures composed of superconducting films deposited on ordered arrays of magnetic ‘dots’ have attracted enormous interest in recent years. Dots with sufficiently large magnetic moments may generate one or more spontaneous vortex–antivortex (V–AV) pairs in the superconducting film which can either remain associated with individual nanomagnets as V–AV ‘‘molecules” in dilute arrays or organise themselves into an ‘ionic’ crystal in dense arrays. Exactly how V–AV molecules transform into lattices and how they interact with (anti)fluxons induced by external magnetic fields remain challenging questions for both theory and experiment. We have used high resolution scanning Hall probe microscopy to image V–AV ‘‘molecules” induced in superconducting Pb films by the stray fields from square arrays of ferromagnetic Co/Pt dots. We have directly observed spontaneous V–AV pairs and studied how they interact with added ‘‘free” (anti)fluxons in an applied magnetic field. We observe a rich variety of subtle phenomena arising from competing symmetries in our system which can either drive added antivortices to join AV shells around nanomagnets or stabilise the translationally symmetric AV lattice between the dots. Added vortices annihilate AV shells, leading eventually to a stable ‘nulling state’ with no free fluxons, which should exhibit a strongly field-enhanced critical current. At higher densities we actually observe vortex shells around the magnets, stabilised by the asymmetric anti-pinning potential. Our experimental findings are in good agreement with Ginzburg–Landau calculations. Ó 2008 Elsevier B.V. All rights reserved. PACS: 74.78.Na; 74.25.Ha; 74.20.De Keywords: Superconducting vortices; Magnetic pinning arrays; Vortex–antivortex shells
1. Introduction Recent advances in nanofabrication and thin film growth technologies have made it possible to engineer many of the properties of superconducting materials. An important example, which has recently excited considerable interest, is the incorporations of ferromagnets (e.g. ferromagnetic dots or disks) in hybrid structures. Many of the superconductor–ferromagnet hybrid systems studied to *
Corresponding author. Tel.: +44 1225 385173; fax: +44 1225 386110. E-mail address: [email protected] (S.J. Bending).
0921-4534/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2007.11.076
date can be broadly divided into two classes; those where magnetic nanostructures with weak moments are used as pinning sites to enhance the superconducting critical current by suppressing flux line motion [1], and those with strong moments which lead to the spontaneous formation of vortex–antivortex (V–AV) pairs. The latter have been found to enhance the critical temperature of the film at finite H through local compensation of the nanomagnet stray fields by the applied field [2]. While such considerations are valid near the superconductor-normal phase boundary, where screening can be neglected, the situation deep within the superconducting state is qualitatively
S.J. Bending et al. / Physica C 468 (2008) 518–522
519
different owing to the requirement for magnetic flux to be quantized. Here a simple picture of field cancellation is no longer applicable and a microscopic picture of the formation and properties of spontaneous V–AV pairs is essential. The critical current of such hybrid structures has been investigated as a function of applied field some distance from the phase boundary [3], but otherwise there has been very little experimental work in the low temperature regime. In contrast there have been extensive theoretical investigations of superconducting films deposited on spatial arrays of magnets using Ginzburg–Landau formalism. Each magnet may generate one or more spontaneous vortex–antivortex (V–AV) pairs in the superconducting film. These either remain associated with individual magnets as V–AV ‘‘molecules” in dilute arrays [4], or organize themselves into an ‘‘ionic” crystal in dense arrays [5]. We report here the first direct imaging studies of spontaneous V–AV structures, which have been achieved using scanning Hall probe microscopy. Our work yields key insights into exactly how V–AV molecules transform into lattices and how they interact with (anti)fluxons introduced by external magnetic fields. 2. Experimental method The samples investigated consisted of a square array of ferromagnetic disks covered with a type II superconducting Pb film. The disks were formed in a [Co(0.5 nm)/Pt(1 nm)]12 multilayer film (Fig. 1a) with uniaxial perpendicular magnetic anisotropy sputtered on a Si/SO2 substrate. They were patterned by electron beam lithography and reactive ion etching through an evaporated aluminium etch mask (Fig. 1b). Four different diameter circular disks with different magnetic moments have been patterned on the corners of a 5 lm 5 lm square cell which was repeated periodically in a square lattice, allowing the behaviour of dots with different spontaneous V–AV numbers to be compared in the same sample. The design diameters of 522 nm (dot A), 738 nm (D), 808 nm (B) and 902 nm (C) were chosen, corresponding theoretically to 1, 3, 3 and 5 spontaneous V–AVs, respectively [5]. Fig. 1c shows an atomic force micrograph of a unit cell of the disk array. The unpatterned Co/Pt film was measured by the Magneto-Optical Kerr Effect (MOKE) at 300 K (Fig. 1e) and shown to have high remanence and a coercive field of 1000 Oe. SHPM images of magnetisation reversal in the disks at T = 20 K indicate a range of coercive fields spanning 700–1000 Oe and magnetic saturation above H ffi 1000 Oe. Switching of the weakly coupled disks is largely uncorrelated, but once magnetised, disks of a given size exhibit almost complete remanence at H = 0 and remain in a single domain state with highly uniform out-of-plane moments (cf. Fig. 2c). This allows the application of small applied fields (H < 100 Oe) without any modification of the underlying magnetic ‘template’. The disks were coated with a 20 nm Ge layer to suppress proximity effects and an 80 nm Pb film deposited using dc magnetron sputtering followed by a
Fig. 1. (a) Layer structure and (b) schematic diagram of the sample. (c) Atomic force microscope image of just the Co/Pt disks immediately after dry etching. (d) MOKE measurement of the magnetisation of the unpatterned Co/Pt multilayer at 300 K.
10 nm Mo capping layer to prevent oxidation. Magnetisation measurements on a single Pb film of the same thickness indicate that it is a type II superconductor with Tc = 6.68 K, keff(5 K) ffi 120 nm and n(5 K) ffi 50 nm. Finally the sample was also coated with 20 nm Ge and 50 nm Au to enhance the stability of the SHPM when in tunnelling contact. Note that the upper surface of the Mo cap layer is oxidised and does not significantly intermix with the adjacent Ge film, which is deposited by thermal evaporation at room temperature. Hence it is not superconducting at the measurement temperatures used in these experiments. We have used a high resolution scanning Hall probe microscope (SHPM), as sketched in Fig. 2a, to both image the magnetisation state of the Co/Pt nanomagnets, and to visualise V–AV shell structures associated with them in the superconducting state. Our SHPM is a modified commercial low temperature STM in which the usual tunnelling tip has been replaced by a microfabricated GaAs/AlGaAs heterostructure chip as illustrated in Fig. 2b. Electron beam lithography and wet etching were used to define a
520
S.J. Bending et al. / Physica C 468 (2008) 518–522
a
4. Experimental results
Z (x,y) Bz (x,y) Scan Voltages
Electronics
Scanner Tube
PC
STM Tip Bias
Hall Voltage
B o
1-2
Sample
Tilt Stage
b
Hall Probe
IHall
c 5μm
Fig. 2. (a) Schematic diagram of the Scanning Hall probe microscope. (b) Scanning electron micrograph of a sub-micron scanning Hall probe with integrated STM tip. (c) Image of the magnetised disk array at T = 20 K. (Co/Pt dots are white).
Hall probe in the two-dimensional electron gas at the intersection of two 500 nm wide wires approximately 5 lm from the corner of a deep mesa etch. The latter had been coated with a thin Au layer to act as an integrated STM tip. The sample is first approached towards the sensor until tunnelling is established and then retracted about 100 nm allowing rapid scanning with minimum detectable fields 1 lT/Hz0.5. The Hall probe makes an angle of about 1° with the sample plane so that the STM tip is always the closest point to the surface, and the Hall sensor was about 300–400 nm above the sample in the images shown here. A more detailed description of the instrument is given elsewhere [6].
In order to observe clear spontaneous V–AV structures we found that it was necessary to magnetise the sample to saturation (H > 3000 Oe) at low temperature. An undesirable consequence of this was the trapping of a small amount of magnetic flux in our superconducting solenoid, which acts in the opposite direction to the dot magnetisation. By integrating the total net flux in a single image, as well as comparing images with GL simulations, we estimate that this background field (which includes the earth’s magnetic field) is about 3.5 Oe. To avoid unnecessary confusion arising from this constant offset to the applied field (Ha) we always quote ‘‘effective” field values as defined by Heff = Ha 3.5 Oe. All SHPM images presented here were obtained after field-cooling the sample from above Tc in the indicated applied field. Fig. 3a shows the first direct observation of spontaneous V–AV shell structures in our hybrid sample at Heff = 0. Since the amplitude of the (black) antivortices is typically only 10–20% of that of the (white) vortices trapped on the magnetic disks we have had to use a strongly non-linear grayscale to enhance their visual identification. As theoretically expected, the (black) AVs clearly order in shell-like structures around the magnetic dots, while (white) vortices remain confined above the dots. We have used a careful line-scan analysis to determine the exact locations of AVs and these are sketched for clarity in Fig. 3b. Fig. 3c shows maps of the local magnetic induction obtained from GL simulations for our exact sample geometry. The experimentally observed vorticity is in good agreement with simulations, and broadly speaking increases with the magnetic moment of the disks (subject to flux quantization). We find that we can tune the vorticity of these V–AV shell structures by applying a
3. Theoretical model Our experimental data have been compared directly with theoretical calculations based on solutions of the Ginzburg–Landau (GL) equations. These have been performed for our exact sample geometry, assuming a coherence length n(0) = 50 nm and uniform magnetisation of the dots of M = 750 G. Three-dimensional calculations have also been performed to investigate the role of the topography introduced by the underlying disk array (for details of the approach we refer to [5]).
Fig. 3. (a) SHPM image and (b) schematic depiction of spontaneous V– AV configurations at Heff ffi 0 and T = 5 K. (c) Map of magnetic induction across the GL calculation under the same conditions. (d)–(f) Different vorticity V–AV shell structures at various effective applied fields and T = 5 K.
S.J. Bending et al. / Physica C 468 (2008) 518–522
magnetic field to either add (Heff < 0) or annihilate (Heff > 0) antivortices, the details of which will be discussed later. Fig. 3d–f shows such V–AV shells containing 2, 3 and 5 antivortices, respectively. For negative applied fields we introduce free AVs into the spontaneous V–AV shell system. In this situation we find that the square symmetry of the underlying magnetic lattice imposes itself on the natural shell structure of the individual V–AV molecules. Indeed there appears to be a subtle competition between the n-fold rotational symmetry of the V–AV ‘‘molecules” and the translationally symmetric lattice of magnets. As the negative effective field is varied we sometimes observe spontaneous AVs which detach from their nanomagnet (effectively breaking a V–AV bond) to join the interstitial AV-lattice. At other field values we see the exact reverse of this scenario; an AV that is not needed in the interstitial lattice approaches a magnetic dot and joins its AV shell, attracted by the ‘positive’ vortex core. In this way at sufficiently negative effective fields all the V–AV molecules become net ‘negative’, i.e. they contain more antivortices than vortices. For positive effective magnetic fields, the general behaviour of the V–AV structures is more intuitive as it is predominantly governed by the annihilation between AV shells and externally added vortices. With increasing applied field each of the molecules progressively loses its negative AVs, and becomes more ‘positively’ charged. Even after all AVs have become annihilated, the vortex ‘‘charge” of individual magnetic dots keeps increasing due to the trapping of additional vortices on the magnetic dots. This arises because of the attraction between a magnet and a vortex when their moments are parallel [7]. This process is illustrated in Fig. 4(top), where we show the number of experimentally observed off-site fluxons (circles; antivortices are counted negative and vortices positive) as a function of applied field, as well as the results of GL calculations (solid line). There is a remarkable agreement between the experimental and theoretical data sets and both plots clearly exhibit a ‘‘nulling”’ field (Ha 6 Oe, Heff ffi 2.5 Oe), where we have no free fluxons. The lower half of Fig. 4 depicts SHPM images as this state is approached. The scan at Heff ffi 1.5 Oe clearly shows some remaining black AVs in shells around the dots that are annihilated in the next image at Heff ffi 2 Oe. The subtracted ‘‘difference” image on the right hand side more clearly reveals the changes that have occurred between the two measurements. White dots in this either represent annihilated antivortices in the first image or added vortices in the second. The difference in applied field between successive images of DH = 0.5 Oe corresponds to three added flux quanta on average. While this is consistent with what we see in the difference image, we unexpectedly find that a vortex has been removed from above the disk in the lower right hand corner where we see a black dot. Presumably this on-site vortex has annihilated with one of the adjacent antivortices. The image of the vortex state at Heff ffi 2.5 Oe looks superficially similar to that at 2 Oe, but the difference
521
Fig. 4. (Top) Number of experimentally observed (anti)vortices as a function of applied field at T = 5 K (circles). Solid line shows the predictions of GL theory (shifted by +4 Oe on the field axis to simulate flux trapping in the solenoid). (Middle, Bottom) Two pairs of successive SHPM images near the ‘‘nulling” state and their ‘‘difference images” (T = 5 K).
image reveals that the number of trapped on-site vortices has increased at the higher field. Moreover the asymmetric position of the added vortices in the difference image is suggestive of a multi-vortex state above the dots, which is what we expect theoretically. This trapping out of excess vortices leads to a fairly robust ‘‘nulling” state that exists over a reasonable range of applied fields (DH > 1 Oe). This ‘locking’ behaviour ensures the absence of any off-site fluxons, and consequently corresponds to a field-induced enhancement of the critical current of the sample. Upon increasing the (positive) applied field still further the non-uniform changes in on-site vortex occupation across the sample impact on off-site vortices. The potential landscape for the pinning of ‘free’ interstitial vortices becomes ‘dynamic’ since interactions with pinned vortex molecules relocate the energy minima as their charge changes. At sufficiently large magnetic fields a square interstitial vortex lattice is recovered, mirroring conventional matching phenomena. However, the interstitial lattice is distorted due to the asymmetry introduced by having dots with different moments. The influence of multi-quanta
522
S.J. Bending et al. / Physica C 468 (2008) 518–522
ment. Moreover, the complex V–AV interactions demonstrated here should also be reflected in two-component colloidal suspensions consisting of oppositely charged particles [8], e.g. those coated by charged polymers [9]. 5. Conclusion In conclusion, we have directly imaged spontaneous V– AV shell structures induced in superconducting films by the stray fields of magnetic arrays for the first time. We observe a variety of subtle phenomena which arise from competition between the n-fold rotational symmetry of the V–AV ‘‘molecules” and the translationally symmetric lattice of magnets. Our measurements agree well with GL calculations and these systems could yield valuable insights into the properties of ionic crystals based on the ordering of binary systems of particles, e.g. oppositely charged colloidal particles. Acknowledgements
Fig. 5. (a) SHPM image and (b) schematic depiction of the vortex configuration at Heff ffi 7.5 Oe and T = 5 K. (c) Corresponding GL Cooper-pair density plots under the same conditions.
vortices at the nanomagnets becomes more evident at the highest resolvable vortex densities. Fig. 5a and b shows how the presence of four different repulsive potentials propagating radially from the corners of the square cell, and strong interactions between interstitial vortices, results in their arrangement in shells. The same structure is found in GL simulations under identical conditions (Fig. 5c). Such an unusual ordering of vortices has never been observed in the presence of uniform pinning. While AVs form shells around confined vortices due to their mutual attraction, counter-intuitively, vortex shells are formed here by repulsion. The same scenario applies generally to any system of interacting particles in a similar environ-
This work was supported in the UK by EPSRC Grant No. GR/D034264/1 and PhD studentship GR/P02707/01. M.V.M. acknowledges support from the Marie-Curie Intra-European program. References [1] (a) J.I. Martin et al., Phys. Rev. Lett. 79 (1997) 1929; (b) D.J. Morgan et al., Phys. Rev. Lett. 80 (1998) 3614. [2] (a) S.A. Wolf et al., Phys. Rev. B 25 (1982) 1990; (b) H.W. Meul et al., Phys. Rev. Lett. 53 (1984) 497; (c) M. Lange et al., Phys. Rev. Lett. 90 (2003) 197006. [3] M. Lange et al., Phys. Rev. B 72 (2005) 052507. [4] M.V. Milosevic, F.M. Peeters, Phys. Rev. B 68 (2003) 024509. [5] (a) M.V. Milosevic, F.M. Peeters, Phys. Rev. Lett. 93 (2004) 124509; (b) D.J. Priour Jr., H.A. Fertig, Phys. Rev. Lett. 93 (2004) 057003. [6] A. Oral, S.J. Bending, M. Henini, Appl. Phys. Lett. 69 (1996) 1324. [7] (a) S. Erdin et al., Phys. Rev. B 66 (2002) 014414; (b) M.V. Milosevic, F.M. Peeters, Phys. Rev. B 68 (2003) 094510; (c) for review, see:I.F. Lyuksyutov, V.L. Pokrovsky, Adv. Phys. 54 (2005) 67. [8] M.E. Leunissen et al., Nature (London) 437 (2005) 235. [9] F. Caruso et al., Macromolecules 32 (1999) 2317.