letters to nature redshift of z ¼ 0.6799 ^ 0.0001. We also obtained spectra of two 16. York, D. G. et al. The Sloan Digital Sky Survey: Technical summary. Astron. J. 120, 1579­1587 (2000). faint galaxies immediately to the southwest of component G (Fig. 2) 17. Stoughton, C. et al. Sloan Digital Sky Survey: Early data release. Astron. J. 123, 485­548 (2002). using the Faint Object Camera and Spectrograph 18. Gunn, J. E. et al. The Sloan Digital Sky Survey photometric camera. Astron. J. 116, 3040­3081 (1998). 26 of the Subaru 19. Pier, J. R. et al. Astrometric calibration of the Sloan Digital Sky Survey. Astron. J. 125, 1559­1579 telescope. The redshifts of these two faint galaxies are (2003). z ¼ 0.6751 ^ 0.0001, strongly suggesting a cluster of galaxies at 20. Hogg,D.W.,Finkbeiner,D.P.,Schlegel,D.J.&Gunn,J.E.Aphotometricityandextinctionmonitorat z < 0.68 centred on component G. Clusters are dominated by the Apache Point Observatory. Astron. J. 122, 2129­2138 (2001). 21. Smith, J. A. et al. The u0 g0 r0 i0 z0 standard-star system. Astron. J. 123, 2121­2144 (2002). elliptical galaxies, which all have very similar spectral energy 22. Fukugita, M. et al. The Sloan Digital Sky Survey photometric system. Astron. J. 111, 1748­1756 distributions. (1996). Many of the faint galaxies in Fig. 2 (,40 galaxies around 23. Blanton, M. R. et al. An efficient targeting strategy for multiobject spectrograph surveys: The Sloan component G) have colours that are similar to that of component Digital Sky Survey "tiling" algorithm. Astron. J. 125, 2276­2286 (2003). 24. Richards, G. T. et al. Spectroscopic target selection in the Sloan Digital Sky Survey: The quasar sample. G. The colours are consistent with the expected colours of elliptical Astron. J. 123, 2945­2975 (2002). galaxies at z < 0.68 (g 2 r < 1.8 and r 2 i < 1.1). In addition, 25. Oguri,M.,Taruya,A.,Suto,Y.& Turner,E. L.Stronggravitationallensingtimedelaystatistics andthe there is an X-ray source in this direction detected by the ROSAT density profile of dark halos. Astrophys. J. 568, 488­499 (2002). All-Sky Survey27 (0.236 counts per second in a 473-s exposure). The 26. Kashikawa, N. et al. FOCAS: The Faint Object Camera and Spectrograph for the Subaru Telescope. Publ. Astron. Soc. Jpn 54, 819­832 (2002). emission, however, comes most probably from the quasar, because 27. Cao, L., Wei, J.-Y. & Hu, J.-Y. High X-ray-to-optical flux ratio RASS-BSC sources. I. The optical the detected X-ray flux is too strong for typical clusters of galaxies at identification. Astron. Astrophys. Suppl. 135, 243­253 (1999). z ¼ 0.68. Finally, we note two possible arclets (highly distorted 28. Keeton,C.R.Computationalmethodsforgravitationallensing.Preprintatkhttp://xxx.lanl.gov/astro- ph/0102340l (2001). images of background galaxies due to gravitational lensing) in Fig. 2 29. Oke,J.B.etal.TheKeckLow-ResolutionImagingSpectrometer.Publ.Astron.Soc.Pacif.107,375­385 (marked as `arc?') close to component D. If future observations (1995). confirm that the arclets are indeed lensed background galaxies, 30. Miyazaki, S. et al. Subaru prime focus camera-Suprime-Cam. Publ. Astron. Soc. Jpn 54, 833­853 they will provide strong additional constraints on the total mass (2002). distribution of the lensing cluster. Acknowledgements Funding for the creation and distribution of the SDSS Archive has been The lensing interpretation is further supported by a theoretical provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National model of SDSS J1004þ4112. We fitted the positions of the four Aeronautics and Space Administration, the National Science Foundation, the US Department of quasar components with a singular isothermal ellipsoid (SIE) plus Energy, the Japanese Monbukagakusho, and the Max Planck Society. The SDSS website is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium (ARC) for external shear model using lens modelling software28. The best-fit the Participating Institutions. The Participating Institutions are The University of Chicago, model is illustrated in Fig. 3. The positions and relative brightnesses Fermilab, the Institute for Advanced Study, The Japan Participation Group, The Johns Hopkins of all components agree well with the lens model predictions. The University, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), centre of the lensing mass is offset from the centre of component G the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, University of Pittsburgh, Princeton University, the United States Naval Observatory, and the University of by about 10 kpc at the cluster redshift, but the brightest galaxy of a Washington. This Letter is based in part on data collected at the Subaru telescope, which is cluster is not always found exactly at the centre of the potential well operated by the National Astronomical Observatory of Japan, W. M. Keck Observatory, which is of that cluster. operated as a scientific partnership among the California Institute of Technology, the University The identical redshifts (z ¼ 1.734) and the spectral energy of California, and the National Aeronautics and Space Administration, and the Apache Point Observatory (APO) 3.5-m telescope, which is owned and operated by the Astrophysical Research distributions of the four lensed components, the existence of a Consortium. Part of this work was performed under the auspices of the U.S. Department of lensing cluster of galaxies (z ¼ 0.68), and the presence of possible Energy at the University of California Lawrence Livermore National Laboratory. arclets confirm the hypothesis that the quasar is lensed by this cluster. Furthermore, a theoretical lensing model involving the cluster Competing interests statement The authors declare that they have no competing financial and external shear simultaneously accounts for the observed geome- interests. try of the system and the relative brightness of the images. The present Correspondence and requests for materials should be addressed to N.I. work represents the discovery of a long-predicted but previously (inada@utap.phys.s.u-tokyo.ac.jp). undetected population of large-separation lensed quasars. A Received 30 July; accepted 23 October 2003; doi:10.1038/nature02153. 1. Narayan, R. & White, S. D. M. Gravitational lensing in a cold dark matter universe. Mon. Not. R. Astron. Soc. 231, 97­103 (1988). .............................................................. 2. Wambsganss, J., Cen, R., Ostriker, J. P. & Turner, E. L. Testing cosmogonic models with gravitational lensing. Science 268, 274­276 (1995). Subatomic movements of a domain 3. Keeton, C. R. & Madau, P. Lensing constraints on the cores of massive dark matter halos. Astrophys. J. 549, L25­L28 (2001). wall in the Peierls potential 4. Wyithe, J. S. B., Turner, E. L. & Spergel, D. N. Gravitational lens statistics for generalized NFW profiles: Parameter degeneracy and implications for self-interacting cold dark matter. Astrophys. J. 555, 504­523 (2001). K. S. Novoselov1, A. K. Geim1, S. V. Dubonos3, E. W. Hill2 & I. V. Grigorieva1 5. Takahashi, R. & Chiba, T. Gravitational lens statistics and the density profile of dark halos. Astrophys. J. 563, 489­496 (2001). 1Department of Physics, 2Department of Computer Sciences, University of 6. Oguri, M. Constraints on the baryonic compression and implications for the fraction of dark halo Manchester, Manchester M13 9PL, UK lenses. Astrophys. J. 580, 2­11 (2002). 3 7. Navarro, J. F., Frenk, C. S. & White, S. D. M. A universal density profile from hierarchical clustering. Institute for Microelectronics Technology, 142432 Chernogolovka, Russia Astrophys. J. 490, 493­508 (1997). ............................................................................................................................................................................. 8. Maoz, D., Rix, H., Gal-Yam, A. & Gould, A. Survey for large-image separation lensed quasars. The discrete nature of crystal lattices plays a role in virtually Astrophys. J. 486, 75­84 (1997). every material property. But it is only when the size of entities 9. Ofek, E. O., Maoz, D., Prada, F., Kolatt, T. & Rix, H. A survey for large-separation lensed FIRST hosted by a crystal becomes comparable to the lattice period quasars. Mon. Not. R. Astron. Soc. 324, 463­472 (2001). -as 10. Phillips, P. M. et al. The JVAS/CLASS search for 6-arcsec to 15-arcsec image separation lensing. Mon. occurs for dislocations1­3, vortices in superconductors4­6 and Not. R. Astron. Soc. 328, 1001­1015 (2001). domain walls7­9-that this discreteness is manifest explicitly. 11. Zhdanov, V. I. & Surdej, J. Quasar pairs with arcminute angular separations. Astron. Astrophys. 372, The associated phenomena are usually described in terms of a 1­7 (2001). 12. Kochanek, C. S. et al. CASTLES survey. khttp://cfa-www.harvard.edu/castles/l (2003). background Peierls `atomic washboard' energy potential, which 13. Walsh, D., Carswell, R. F. & Weymann, R. J. 0957þ561 A, B - Twin quasistellar objects or gravitational was first introduced for the case of dislocation motion1,2 in the lens? Nature 279, 381­384 (1979). 1940s. This concept has subsequently been invoked in many 14. Colley, W. N., Tyson, J. A. & Turner, E. L. Unlensing multiple arcs in 0024þ1654: Reconstruction of situations to describe certain features in the bulk behaviour of the source image. Astrophys. J. 461, L83­L86 (1996). 15. Turner, E. L., Ostriker, J. P. & Gott, J. R. III The statistics of gravitational lenses-the distributions of materials, but has to date eluded direct detection and experimen- image angular separations and lens redshifts. Astrophys. J. 284, 1­22 (1984). tal scrutiny at a microscopic level. Here we report observations of 812 NATURE | VOL 426 | 18/25 DECEMBER 2003 | www.nature.com/nature © 2003 Nature Publishing Group letters to nature the motion of a single magnetic domain wall at the scale of the measurements of magnetic viscosity (for example, see refs 14­16). individual peaks and troughs of the atomic energy landscape. However, no experiment has yet been capable of directly detecting Our experiments reveal that domain walls can become trapped propagation through the magnetic (or any other) Peierls potential. between crystalline planes, and that they propagate by distinct In the present work, we revisit the Peierls potential by using a state- jumps that match the lattice periodicity. The jumps between of-the-art technique of ballistic Hall micromagnetometry, pre- valleys are found to involve unusual dynamics that shed light on viously used in studies of superconducting vortices17,18 and now the microscopic processes underlying domain-wall propagation. adapted to the detection of DWmovements. The approach allows us Such observations offer a means for probing experimentally the to resolve subatomic changes in the position of individual micro- physics of topological defects in discrete lattices-a field rich in metre-sized segments of DWs and study their inter- and intra- phenomena that have been subject to extensive theoretical Peierls valley movements. study10­12. For our studies, we have chosen thin films of yttrium-iron garnet, In magnetic materials, a domain wall (DW) has to pass through (YBi)3(FeGa)5O12 (YIG), which combine relatively narrow walls different spin configurations as it moves from one atomic plane to (d < 11 nm at liquid-helium temperatures) with a large unit cell of another7­14. Figure 1a shows two principal spin configurations of a size a < 1.24 nm, and provide d/d < 6 (Methods). Equally import- DW in a simple lattice-these configurations exhibit the maximum ant is the high crystal quality of our samples19­21, manifested in a and minimum energy, and correspond to the centre of the wall lying coercivity of ,0.1 G at room temperature and ,10 G at liquid- respectively at and between atomic planes. This spatial variation of helium temperatures, such that obscuring effects due to pinning on the wall's energy is generally referred to as the Peierls potential. Its defects are relatively small. The YIG films have perpendicular amplitude depends critically on the ratio between the DW's width d magnetization and a domain structure shown in Fig. 1b for the and the lattice periodicity d and, realistically, the Peierls potential is case of room temperature. At low temperatures, the domain only observable for d/d , 10. For larger d/d, the potential becomes structure becomes pronouncedly triangular with long straight so small (,,1 G) that pinning on defects should conceal it com- DWs. A submillimetre piece of the film was placed in immediate pletely. The vast theoretical and experimental evidence gathered contact with the surface of a device consisting of micrometre-sized over several decades and based on studies of bulk properties of Hall sensors made from a two-dimensional electron gas (2DEG) magnetic alloys has confirmed the existence of the magnetic Peierls following the microfabrication procedure described in refs 17 and potential, with probably the most definite conclusions drawn from 18 (Fig. 1b). Hall sensors in our experiments play the role of highly sensitive position detectors, which provide a spatial resolution of ,1 A with respect to DWmovements. Their operation (explained in Methods) relies on the high sensitivity of such probes to changes in magnetic flux F induced by DW movements inside the central area of a Hall cross17,18,22­26. For brevity, we discuss only experiments where the studied DWs were aligned parallel with the Hall device and moved in {110} directions. In this well defined geometry, changes in the wall position Dx can be calculated directly from Figure 1 Experimental structures and devices. a, Principal spin configurations for a narrow Bloch wall: its centre either coincides with one of the atomic planes (right) or lies between them (left). The fan diagrams show the orientation of individual spins, looking in the direction perpendicular to the DW. b, The micrographs show a set of micrometre-sized Hall probes placed on top of a ferromagnetic garnet. Edges of the 2DEG mesa are seen as green lines on the micrograph. The image overlays a photograph of the domain structure taken in transmitted polarized light at room temperature. The inset magnifies the central Figure 2 Nanometre movements of domain walls over submicrometre distances. Main part of the experimental structure. The scale is given by the domains' width of ,14 mm panel, a typical Hall response measured by a 1.5-mm Hall cross as a domain wall slowly and the size of Hall probes (1.5 mm). By measuring simultaneously the response at creeps from one of its sides to the other (T ¼ 0.5 K). For convenience, the Hall different Hall crosses, we ensured that at low temperatures the studied DWs were parallel response is given in terms of the average local field B inside the cross, which is to the set of sensors as the photograph shows and moved as rigid planes (Methods). calculated by using the measured Hall coefficient. The insets show examples of local c, The drawing illustrates that a shift in the average position of a wall Dx induces a change hysteresis loops; abscissa, DH (Oe); left-hand ordinate, DB (G), right-hand ordinate in flux DF inside the sensitive area marked by the dotted lines17,22. This leads to a linear (lower inset only), Dx (nm). The red lines are guides to the eyes, indicating constant change in Hall resistance, which was recorded in the experiments. positions of the DW. NATURE | VOL 426 | 18/25 DECEMBER 2003 | www.nature.com/nature 813 © 2003 Nature Publishing Group letters to nature the measured Hall signal, without using any unknown parameters clearly seen by magnetic force microscopy (at room temperature). (Methods). To release the strain, we demagnetized the sample by applying an To move a DW, we slowly varied the external field H applied a.c. magnetic field with an amplitude h gradually decreasing from perpendicular to the garnet film. Figure 2 shows a typical example of ,5 G to zero, while a constant field H kept the wall close to the changes in local field B detected by a Hall sensor as a DW crosses it centre of the probe. This proved to be a critical improvement: in the from one side to the other. We see that B changes its sign, which demagnetized state, DWs started to propagate via clear quantized reflects the change in polarity of the domain above the sensor, and jumps matching the lattice periodicity. The distance between the B ¼ 0 corresponds to the state where the wall lies exactly in the equivalent sites was measured to be 1.6 ^ 0.2 nm, in agreement middle. The overall shape of the transition curve is in good with the Peierls potential periodicity d ¼ 1.75 nm. Figure 3 shows agreement with a simple theory21. Overlaid on this universal an example of such behaviour, which leaves no doubt of the behaviour, we see a number of small sample- and sweep-dependent presence of a periodic atomic landscape impeding DW movements. steps, indicating that a DW does not move smoothly but covers From Fig. 3, we can also estimate that it requires a field of ,1 G to micrometre-long distances in a series of small jumps. Such jumps move a DW out of a well created by adjacent crystal planes (that is, have previously been studied by several techniques (for example, intrinsic pinning is several times weaker than pinning on a typical refs 27­29), and are usually referred to as Barkhausen noise. A defect in our garnets; see Fig. 2). Further experiments yielded a typical step in Fig. 2 corresponds to a wall moving by 10­50 nm. value of the intrinsic coercive field HC < 0.7 G at T , 10 K. The While a DW was located within the Hall cross, we could reverse a theory of the magnetic Peierls potential predicts HC to be of the field sweep to investigate the local coercivity of the wall (left inset in order of13­15 Fig. 2). Such hysteresis loops are usually reproducible for many field cycles, and we attribute them to pinning on individual defects H 21,28. C < CðA=d 2MSÞ expð2pd=dÞ In addition to the above behaviour, the high resolution of the where C < 103 (ref. 13) and M 2DEG micromagnetometry allowed us to discern very small DW S is the saturation magnetization. Taking into account the exponential dependence of H jumps (right inset in Fig. 2), which stood out from the `ordinary' C on A and K (Methods), which are known to ,10% accuracy, the formula yields jumps for two reasons. First, they matched closely the lattice H periodicity in the direction of DW travel k110l (d ¼ 21/2a < C in the range from 0.1 to 5 G, in agreement with the experiment. In addition to the detection of the Peierls potential, we have 1:75 nm) and, second, they were practically the only jumps observed studied its shape, which is predicted to be sinusoidal7,13. This in the range below ,10 nm. The use of statistical analysis techniques prediction implies that a DW should remain somewhat mobile (which is standard practice in, for example, particle physics) shows within Peierls valleys-that is, not pinned completely. Such intra- that-with a confidence level of 94%-the data shown in the right valley movements are expected to be ,1 A and, therefore, could not inset of Fig. 2 correspond to an event comprising several steps of be resolved in our d.c. magnetization data (compare Fig. 3). To gain equal length (four single and three double steps), where the length of information about the finest DW movements, we measured local a single step is d. To obtain further proof that such steps indeed reveal a.c. susceptibility x (a.c. measurements provide a higher flux jumps between equivalent crystal lattice positions, we carried out the sensitivity, and hence a higher spatial resolution). To this end, in complementary experiments described below. addition to the d.c. field H that controls DW's position, we applied As a DWmoves through a crystal, it interacts with a large number an oscillating field h and measured an a.c. signal generated by of pinning sites and becomes bent and strained in the process. We oscillatory movements of a DW. Changes in x show how the can generally expect that a strained wall would jump between strong mobility of a DW varies with its position inside a Peierls valley. pinning sites without being affected by the weaker ones. This is Using this approach, we confirmed that a domain wall could indeed move near the bottom of a valley, and the detected a.c. signal corresponded to an average shift of a DW by up to ,0.5 A . In addition to this, however, a.c. measurements revealed strikingly Figure 3 Jumps of a domain wall between equivalent lattice sites. The data were taken Figure 4 Domain wall on the Peierls ridge. Main panel, changes in local a.c. susceptibility during a very slow sweep (,1 h), which was required to achieve the subatomic resolution. x while d.c. field H moves the wall from one Peierls valley to the next (a.c. field has For such time intervals, relaxation processes lead to irreproducible changes in the domain amplitude 0.5 G and frequency 8 Hz). We subtracted a constant background due to the structure, usually far away from the detection site (this can be seen as occasional DW Hall response induced directly by the a.c. field. The slight variation of x seen on the curve jumps at a constant H ). On the graph, this results in the same position of a DW for different away from the transient state is not reproducible for different walls and after thermal values of H. For clarity, we subtracted a small smooth background in B associated with cycling. The insets show the dependence of the width DH of the transient state on h, and changes in the local stray field induced by other domains. the dependence of its amplitude Dx on temperature. 814 NATURE | VOL 426 | 18/25 DECEMBER 2003 | www.nature.com/nature © 2003 Nature Publishing Group letters to nature unusual DW dynamics, in qualitative disagreement with the beha- This crystallographic alignment is already seen at 300K (Fig. 1b), and becomes stronger at viour expected for an object moving in a tilted sinusoidal potential. lower temperatures as the anisotropy increases. There, domain walls become straight over One of the most notable features that we observed is a large, well- distances of ,1mm. Using alignment marks, we placed our 2DEG sensors inside a chosen area of a YIG film with many parallel domains and aligned the sensors parallel to them, reproduced peak in DWmobility (Fig. 4). Here, zero H corresponds that is, perpendicular to one of k110l axes. The spacing between the garnet and 2DEG was to a DW position in the middle between two adjacent Peierls valleys, measured to be less than 100nm (ref. 21). We restricted the reported experiments to as simultaneously detected in the d.c. magnetization signal (the temperatures below 30K, mainly because of thermally activated relaxation processes, latter shows a smeared transition between two DW positions which led to irreproducible changes in the domain structure and did not allow accurate measurements that require slow sweeps of magnetic field. separated by d). The peak has abrupt edges (shown by dashed There are two periodic sets of equivalent crystallographic positions for a {110} DW, lines in Fig. 4); that is, above a certain value of H the oscillating wall p which are separated by b and 2b (where b ¼ a/ 2 is the distance between the nearest basal suddenly falls into a neighbouring Peierls valley and becomes locked planes). They require the translation of wall's spin configuration in directions k001l and there. When h was switched off for a few seconds at a constant H k110l, respectively, and involve different exchange interactions13. Both periods should contribute to the Peierls potential, but because of the exponential dependence on d/d only close to one of the peak's edges, the transient mobile state did not p the longest periodicity d ¼ 2a/ 2 < 1.75 nm can be expected to remain observable. Our recover on switching the modulation back. This indicates that it measurements did find this periodicity, but it remains unclear why a DW could not avoid requires a time of ,1 s for the wall to become locked in a Peierls the observed Peierls barriers by exploiting `the third dimension' (that is, moving by two valley. With decreasing h from 0.5 to 0.1 G, both the width and the smaller oblique jumps in k001l rather than by the straight jumps perpendicular to the DW's plane). We finally note that our analysis ignores the complex unit cell structure of amplitude of the peak shrink linearly (inset in Fig. 4). The observed garnets, which may also play some role. behaviour suggests that an a.c. field stabilizes a DW in what should be an intrinsically unstable state between two Peierls valleys. We can interpret the transient state as the centre of a DW sitting Micromagnetometers Submicrometre Hall probes made from a 2DEG were used as position detectors of a effectively on a Peierls ridge, kept there by an oscillating magnetic domain wall. When a DWenters the sensitive area of a probe, its response RH starts force. This situation closely resembles the so-called reversed pendu- changing. A shift Dx in the DW's position leads to a change in magnetic field B and flux F lum, which can be stabilized in the unstable upside-down position through the Hall cross (Fig. 1c), which in turn induces a Hall response such that by an oscillating force30,31. This analogy allows us to describe the DRH ¼ aDF ¼ bDx (refs 17, 22). The second part of the equation assumes that a DW is observed resonance semiquantitatively but does not provide a straight within the sensitive area of the Hall cross. This is justified for the reported experiments because we could simultaneously measure R microscopic picture. To this end, we invoke the well-known `kink' H at different crosses and, at low T, found a nearly perfect correlation between movements of DWs detected by model2,14, where a DW moves between Peierls valleys via a process neighbouring Hall crosses21. This indicates that DWs move as fairly rigid objects, so that where at first only a submicrometre segment of a DW (a jog) moves their large segments (up to 10mm in size for T , 10K) shift as a whole (that is, without to the next valley. Spreading the boundary of such a jog along the bending). a and b are found experimentally17,21,22 and, therefore, changes in RH can be translated in DW movements without any fitting parameters. wall eventually leads to the relocation of the whole DW. It is We used Hall sensors made from a high-mobility 2DEG because of their exceptional plausible that a.c. modulation could stabilize the jog so that its sensitivity to flux variations DF on a submicrometre scale17. At temperatures T , 80K, boundaries move back and forth inside the sensitive area of a Hall such sensors effectively work as fluxmeters and are capable of resolving DF < 1024 f0, cross without collapsing, until changes in H extend the jog outside where f0 is a fluxquantum. This technique has previously been used and fullydescribed in studies of submicrometre superconducting17,18 and ferromagnetic23­26 particles. In the this area, where it eventually becomes pinned. Indeed, the maxi- context of the present work, we have exploited this unique flux sensitivityof 2DEG sensors mum value of Dx (observed at 30 K and 0.5 G) corresponds to to achieve a subatomic resolution in the average position of individual DWs. Indeed, if a movements of a DW by Dx <1 nm; that is, as if nearly the whole DW passes the whole width w of a cross, F changes by several f0 (for the given value of Ms segment of the wall inside the Hall cross swings between adjacent in our garnets). On the other hand, as we can resolve DF < 1024f0, this corresponds to a shift of a DW by Dx < w(DF/f valleys. 0) < 1 A . Note that many magnetic materials have larger values of Ms and, hence, the magnetometers should provide even higher spatial resolution The single-jog model provides a sensible description for the (,0.1A ). 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Observation of a transversal nonlinear magneto- nineteenth century, when the mechanical properties of the wires optical effect in thin magnetic garnet films. Phys. Rev. Lett. 78, 2004­2007 (1997). were studied, but their optical properties and applications remained 21. Novoselov, K. S., Geim, A. K., van der Berg, D., Dubonos, S. V. & Maan, J. C. Domain wall propagation on nanometer scale: coercivity of a single pinning center. IEEE Trans. Magn. 38, uninvestigated8,9. It was not until a century later that researchers 2583­2585 (2002). began to investigate the optical applications of silica wires made by 22. Peeters, F. M. & Li, X. Q. Hall magnetometer in the ballistic regime. Appl. Phys. Lett. 72, 572­574 drawing high-purity glass fibres from a laser-heated melt10­14. With (1998). 23. Kent, A. D., von Molnar, S., Gider, S. & Awschalom, D. D. Properties and measurement of a diameter of more than one micrometre, these silica wires allow scanning tunneling microscope fabricated ferromagnetic particle arrays. J. Appl. Phys. 76, 6656­6660 multimode waveguiding of visible and infrared light. Submicro- (1994). metre wires allow single-mode operation, but both theoretical and 24. Li, Y. Q. et al. Hall magnetometry on a single iron nanoparticle. Appl. Phys. Lett. 80, 4644­4646 experimental results show that the laser power required for drawing (2002). 25. Hengstmann, T. M., Grundler, D., Heyn, C. & Heitmann, D. Stray-field investigation on permalloy silica submicrometre- or nanometre-diameter wires (SMNWs) with nanodisks. J. Appl. Phys. 90, 6542­6544 (2001). a uniform diameter is impractically large14,15. When drawing wires 26. Schuh, D., Biberger, J., Bauer, A., Breuer, W. & Weiss, D. Hall-magnetometry on ferromagnetic dots from a flame-heated melt, turbulence and convection make it and dot arrays. IEEE Trans. Magn. 37, 2091­2093 (2001). 27. Vergne, R., Cotillard, J. C. & Porteseil, J. L. Some statistical aspects of magnetization processes in difficult to control the temperature gradient in the drawing region, ferromagnetic bodies-motion of a single 180-degrees Bloch wall in an imperfect crystalline medium. and consequently size uniformity is difficult to maintain when the Rev. Phys. Appl. 16, 449­476 (1981). wire diameter is reduced to less than one micrometre. Silica 28. Wunderlich, J. et al. Influence of geometry on domain wall propagation in a mesoscopic wire. IEEE nanowires with diameters ranging from ten to several hundred Trans. Magn. 37, 2104­2107 (2001). 29. Kim, D. H., Choe, S. B. & Shin, S. C. Direct observation of Barkhausen avalanche in Co thin films. nanometres have recently been obtained with other methods16­18, Phys. Rev. Lett. 90, 087203 (2003). but the diameter fluctuation and sidewall roughness of those wires 30. Magnus, K. Vibrations (Blackie & Son, London, 1965). makes them unsuitable for low-loss optical wave guiding. 31. Acheson, D. From Calculus to Chaos (Oxford Univ. Press, Oxford, 1997). Here we introduce a two-step drawing process for fabricating Acknowledgements This research was supported by the EPSRC (UK). We thank S. Gillott and long uniform silica SMNWs by a flame-heated fibre drawing M. Sellers for technical assistance and J. Steeds for advice on dislocation motion. S.V.D. also method. First, we use a flame to draw a silica fibre to a micro- acknowledges support from Russian Ministry of Science and Technology. metre-diameter wire. Second, to obtain a steady temperature distribution in the drawing region while further reducing the wire Competing interests statement The authors declare that they have no competing financial interests. diameter, we use a tapered sapphire fibre with a tip diameter of about 80 mm to absorb the thermal energy from the flame (Fig. 1). Correspondence and requests for materials should be addressed to A.K.G. (geim@man.ac.uk). The sapphire fibre taper, which is fabricated using laser-heating growth method19, confines the heating to a small volume and helps maintain a steady temperature distribution during the drawing. One end of a micrometre-diameter silica wire is placed horizontally .............................................................. on the sapphire tip, and the flame is adjusted until the temperature of the tip is just above the drawing temperature (about 2,000 K). We Subwavelength-diameter silica wires thenrotatethesapphiretiparounditsaxisofsymmetrytowindthe silica wire around the tip. The wire coil is moved about 0.5 mm out for low-loss optical wave guiding of the flame to prevent melting and the wire is then drawn perpendicular to the axis of the sapphire tip in the horizontal Limin Tong1,2, Rafael R. Gattass1, Jonathan B. Ashcom1*, Sailing He2, plane at a speed of 1­10 mm s21 to form a SMNW. Jingyi Lou2, Mengyan Shen1,3, Iva Maxwell1 & Eric Mazur1 Using this technique, we obtained silica SMNWs with diameters down to 50 nm and lengths up to tens of millimetres. Figure 2a 1Department of Physics and Division of Engineering and Applied Sciences, shows a scanning electron microscope (SEM) image of a 4-mm-long Harvard University, Cambridge, Massachusetts 02138, USA wire with a diameter of 260 nm; the wire is roughly coiled up to 2Centre for Optical and Electromagnetic Research and Department of Physics, show its length. The maximum diameter variation DD is about 8 nm Zhejiang University, Hangzhou 310027, China over the 4-mm length L of the wire, giving DD/L ¼ 2 £ 1026. The 3Department of Physics, Graduate School of Science, Tohoku University, Sendai, excellent uniformity of wires with diameters ranging from 50 to Miyagi 9808578, Japan 1,100 nm can also be seen in Fig. 2b­d. Higher-magnification * Present address: Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts transmission electron microscope (TEM) images of a 240-nm- 02420, USA ............................................................................................................................................................................. Silica waveguides with diameters larger than the wavelength of transmitted light are widely used in optical communications, sensors and other applications1­3. Minimizing the width of the waveguides is desirable for photonic device applications, but the fabrication of low-loss optical waveguides with subwavelength diameters remains challenging because of strict requirements on surface roughness and diameter uniformity4­7. Here we report the fabrication of subwavelength-diameter silica `wires' for use as low-loss optical waveguides within the visible to near-infrared spectral range. We use a two-step drawing process to fabricate long free-standing silica wires with diameters down to 50 nm that show surface smoothness at the atomic level together with uniformity of diameter. Light can be launched into these wires Figure 1 The second step in the fabrication process of silica submicrometre- and by optical evanescent coupling. The wires allow single-mode nanometre wires (SMNWs). a, Schematic diagram of the drawing of the wire from a coil of operation, and have an optical loss of less than 0.1 dB mm21. micrometre-diameter silica wire wound around the tip of a sapphire taper. The sapphire We believe that these wires provide promising building blocks for taper is heated with a CH3OH torch with a nozzle diameter of about 6 mm. The wire is future microphotonic devices with subwavelength-width drawn in a direction perpendicular to the sapphire taper. b, Magnified view of the drawing structures. process. The sapphire taper ensures that the temperature distribution in the drawing The fabrication of thin silica wires was first investigated in the region remains steady. 816 NATURE | VOL 426 | 18/25 DECEMBER 2003 | www.nature.com/nature © 2003 Nature Publishing Group