Superconducting quantum interference devices with submicron Nb/HfTi/Nb junctions for investigation of small magnetic particles
J. Nagel, O.F. Kieler, T. Weimann, R. Wölbing, J. Kohlmann, A.B. Zorin, R. Kleiner, D. Koelle, M. Kemmler
aa r X i v : . [ c ond - m a t . s up r- c on ] J un Superconducting quantum interference devices with submicron Nb/HfTi/Nbjunctions for investigation of small magnetic particles
J. Nagel, O.F. Kieler, T. Weimann, R. W¨olbing, J. Kohlmann, A.B. Zorin, R. Kleiner, D. Koelle, and M. Kemmler ∗ Physikalisches Institut – Experimentalphysik II and Center for Collective Quantum Phenomena in LISA + ,Universit¨at T¨ubingen, Auf der Morgenstelle 14, D-72076 T¨ubingen, Germany Fachbereich 2.4 ”Quantenelektronik”, Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany (Dated: October 22, 2018)We investigated, at temperature 4 . S / = 250 nΦ / Hz / , corresponding to a spin sensitivity S / µ ≥ µ B / Hz / . Forthe gradiometer we find S / = 300 nΦ / Hz / and S / µ ≥ µ B / Hz / . The devices can stillbe optimized with respect to flux noise and coupling between a magnetic particle and the SQUID,leaving room for further improvement towards single spin resolution. PACS numbers: 85.25.CP, 85.25.Dq, 74.78.Na, 74.25.F-
I. INTRODUCTION
Growing interest in the investigation of small spin sys-tems like molecular magnets[1–3], single electrons [4]or cold atom clouds[5], demands for proper detectionschemes. Compared to, e.g., magnetic resonance forcemicroscopy [6] or magneto-optic spin detection [7, 8], su-perconducting quantum interference devices (SQUIDs)offer the advantage of direct measurement of changesof the magnetization in small spin systems [1, 9]. Highspin sensitivity requires SQUIDs with low flux noise andstrong magnetic coupling between particle(s) and SQUIDloop. These needs can be met by nano-scaling the de-vices [10–12], e.g., by focused ion beam milling [13, 14],electron-beam lithography [15], atomic force microscopyanodization [16, 17], shadow evaporation [18] or by cou-pling small pickup loops to larger SQUIDs [19]. Whilenanopatterning of the SQUID loop yields no basic tech-nical difficulties, the creation of overdamped Joseph-son junctions (JJs), as required for direct current (dc)SQUIDs, with submicron dimensions is more challeng-ing. A widely used approach is to use constriction JJs.In some cases this yielded dc SQUIDs [14, 15] with rootmean square (rms) flux noise S / down to 0 . µ Φ / Hz / (Φ is the magnetic flux quantum), which however aresuitable only for operation in a limited range of temper-ature T . Even smaller S / = 17 nΦ / Hz / has beenreported for larger SQUIDs based on superconductor-insulator-superconductor (SIS) tunnel JJs with externalresistive shunts [20]. In this letter, we report on therealization of small and sensitive dc SQUIDs based onS-normalconductor (N)-S sandwich-type JJs, without re-sistive shunts, which simplifies SQUID miniaturization. ∗ Electronic address: [email protected] sec
II. SAMPLE FABRICATION AND LAYOUT
Our JJs are based on a Nb/HfTi/Nb trilayer process[21], which was developed for the fabrication of submi-cron SNS junctions [22]. All JJs are square shaped withlateral dimensions 200 ×
200 nm . The JJs with barrierthickness d HfTi = 24 nm have a critical current density j c ≈ −
300 kA / cm at T = 4 . ρ n ≈ −
19 mΩ µ m , leading toa characteristic voltage V c = j c ρ n ≈ µ V. The threeSQUIDs presented in this paper have different layouts. G1 [see Fig. 1(a)] has a gradiometric design. The gra-diometer line in the top Nb layer carries the bias current I (flowing through the junctions to the bottom Nb layer)and in addition allows for the (on-chip) application ofmagnetic flux Φ to the gradiometer (referred to one loop)via a current I mod without the need of external coils. M1 [see Fig. 1(b)] is of the magnetometer-type. M2 [see in-set of Fig. 1(b)], which is similar to M1 , has a washer,allowing flux modulation with relatively small externalmagnetic fields ( B/ Φ = 0 . / Φ ).sec III. EXPERIMENTS
All measurements were performed at T = 4 . R in connected in series with the coil. A separatefeedback (and modulation) coil of the SQUID amplifierallows for a flux locked loop operation of the SQUIDamplifier with a sensitivity S / V, amp ≈
40 pV / Hz / for R in = 3 . T = 4 . S V , SQUID for theSQUID and calculate the corresponding rms flux noise S / = S / , SQUID / | ∂V /∂ Φ | . Here, V is the voltage acrossthe SQUID and ∂V /∂ Φ is the transfer coefficient.Figure 2(a) shows the current voltage characteristic(IVC) of G1 measured at I mod = 0. The IVC is resis-tively shunted junction (RSJ)-like, with a critical cur-rent I c = 178 µ A and resistance R = 233 mΩ, yielding V c = 41 . µ V. The inset of Fig. 2(a) shows I c ( I mod ) to-gether with a simulated curve based on the RSJ model(including thermal noise and inductance asymmetry),which yields β L ≡ I L/ Φ = 0 .
18. Here, I is the av-erage maximum critical current of the two JJs, and L is the inductance of the gradiometric SQUID, i.e. halfthe inductance of one loop of the gradiometer. With2 I = 178 µ A we obtain L = 2 . I c ( I mod ) we obtain Φ /I mod = 227 mΦ / mA.The small but finite shift ∆ I mod = 95 µ A of the maximain I c ( I mod ) for opposite polarity can be solely attributedto an inductance asymmetry due to the asymmetric cur-rent bias, i.e. the asymmetry in the critical currents ofthe JJs is negligibly small. Figure 2(b) shows V ( I mod )for different values of I . For I ≈ µ A we obtain amaximum transfer coefficient V Φ ≈ µ V / Φ . The in-set of Fig. 2(c) shows V ( I mod ) and S / , w ( I mod ) in thewhite noise regime (determined by averaging the spectrafrom f = 2 to 3 kHz) for I = 185 µ A. This yields min-ima in S / , w ( I mod ) at the optimum flux bias point (in-dicated by the dashed line), for which the main graphof Fig. 2(c) shows S / vs frequency f . For low fre-quencies f ≤
10 Hz we find S Φ ( f ) ∝ /f , which can FIG. 1: (Color online) Scanning electron microscopy (SEM)images of the SQUIDs. The JJs with size 200 ×
200 nm areindicated as dotted lines in the top Nb layer. (a) Gradiometer G1 with line width 250 nm and outer loop size 1 . × . µ m ;arrows indicate scheme of current flow; (b) Magnetometer M1 with line width 250 nm and SQUID hole 500 ×
500 nm . Inset:washer-type magnetometer M2 with washer area 10 × µ m and SQUID hole 500 ×
500 nm . (c) S / ( (cid:181) / ( H z ) / ) f (Hz) -4 -2 0 2 40102030 V ( (cid:181) V ) I mod (mA) 0.1110100I = 185 (cid:181)A S / w ( (cid:181) / ( H z ) / ) -60-40-200204060 -4 -2 0 2 4 (b) I mod (mA) V ( (cid:181) V ) -200 -150 -100 -50 0 50 100 150 200-1000-750-500-25002505007501000 I ( (cid:181) A ) V ((cid:181)V) (a) -200-1000100200 -4 -2 0 2 4 I mod (mA) I c ( (cid:181) A ) FIG. 2: (Color online) Transport and noise characteristics of G1 at T = 4 . K : (a) IVC at I mod = 0; inset shows mea-sured I c ( I mod ) (solid line) and simulated curve (dashed line).(b) V ( I mod ) for I = − . . . µ A (in 20 . µ A steps). (c)Spectral density of rms flux noise S / ( f ) at optimal work-ing point (c.f. dashed line in inset); dashed line indicates300 nΦ / Hz / . Inset: V ( I mod ) (solid line) and S / ,w ( I mod )(open circles; averaged from f = 2 to 3 kHz). be attributed to a single fluctuator (flux or I c ) produc-ing random telegraph noise in the time trace V ( t ). Forhigher frequencies 10 Hz ≤ f ≤ f like, which might be caused byan admixture of noise from a few additional fluctuatorswith higher characteristic frequencies. The peak in S Φ ( f )near f = 12 Hz presumably results from mechanical vi-brations. The spectrum in the white noise limit above1 kHz yields S / , w ≈
300 nΦ / Hz / , with a cutoff at f ≈ × Hz due to the SQUID amplifier electron-ics. The magnetometer-type devices M1 and M2 hadsimilar characteristics, with S / , w ≈
250 nΦ / Hz / and ≈
270 nΦ / Hz / , respectively.sec A. estimated Spin sensitivity
G1G1 z ( (cid:181) m ) -4 -3 -2 -1 (cid:181) ( n / (cid:181) B ) x=0.38 (cid:181)m (cid:181) ( n / (cid:181) B ) z=5 nm (cid:181) (n /(cid:181) B ) (a) -1.0 -0.5 0.0 0.5 1.00.00.20.40.60.8 x ((cid:181)m) x=0.00 (cid:181)m x y (b) (cid:181)=(cid:181)Œ x (cid:181)=(cid:181)Œ x y x M1G1M1G1
FIG. 3: (Color online) Calculated coupling factor φ µ vs par-ticle position. Main graphs show contour plots φ µ ( x, z ) for(a) magnetometer M1 and (b) gradiometer G1 ; Nb structuresare indicated by black rectangles. Insets show SEM imagesof the SQUIDs. Dashed lines indicate position of linescans φ µ ( x ) [shown above (a)] and φ µ ( z ) [shown to the right of (a)and (b)]. Finally, we turn to the spin sensitivity S / µ = S / /φ µ of our devices which, besides the flux noise, depends onthe coupling factor φ µ , i.e. the amount of flux coupledinto the SQUID by a magnetic particle, divided by themodulus | ~µ | of its magnetic moment. Taking into accountthe SQUID geometry, Fig. 3 shows the calculated cou-pling factor of M1 and G1 vs. the position ~r of a point-likemagnetic particle with its magnetic moment ~µ pointingin-plane of the SQUID loop. A detailed description of thecalculation procedure for non-gradiometric SQUIDs canbe found in Ref. [12]. For the gradiometric SQUID G1 one has to consider the magnetic field distribution ~B ( ~r )created by two circular currents I , = ± I B in each loop.In this case the coupling factor φ µ is given by ~B ( ~r ) / I B .For an in-plane magnetization of the particle, layout M1 provides the highest coupling factor if the particle isplaced directly on top of the SQUID loop. For G1 the op-timum coupling can be achieved if the particle is placedon the center conductor line. At this position the par-ticle couples flux of opposite sign into both loops of thegradiometric SQUID, which leads to an approximatelytwice as large coupling factor as compared to placing theparticle on the outer conductors. For a particle with10 nm diameter, placed directly on top of the SQUID,we take a vertical distance z = 5 nm from the SQUIDsurface, which yields φ µ = 8 . /µ B ( µ B is the Bohrmagneton) for M1 and 6 . /µ B for G1 at the centerconductor. With S / ≈
250 nΦ / Hz / we calculate thespin sensitivity of M1 to S / µ = 29 µ B / Hz / . For thegradiometric SQUID we calculate S / µ = 44 µ B / Hz / .sec IV. CONCLUSIONS
In conclusion, we have shown that miniaturizeddc SQUIDs based on sandwich-type overdamped SNSJosephson junctions have a compact design and can beoperated with very promising values of flux noise andspin sensitivity. Although our devices are not optimizedyet, flux noise values down to 250 nΦ / Hz / have beenachieved, leading to an estimated spin sensitivity as lowas 29 µ B / Hz / . Further improvements are feasible; e.g.,placing the two SQUID arms on top of each other, as inRef.[20], allows for reduction of the SQUID inductanceand hence of the flux noise. Furthermore, the couplingcan be improved by patterning an additional constrictionwithin the SQUID loop.sec Acknowledgment
This work was supported by the Nachwuchs-wissenschaftlerprogramm of the Universit¨at T¨ubingen,by the Deutsche Forschungsgemeinschaft (DFG) via theSFB TRR21 and by the European Research Council viaSOCATHES. J. Nagel and M. Kemmler gratefully ac-knowledge support by the Carl-Zeiss Stiftung. [1] W. Wernsdorfer, Adv. Chem. Phys. , 99 (2001).[2] D. Gatteschi and R. Sessoli, Angew. Chem., Int. Ed. ,268 (2003). [3] L. Bogani and W. Wernsdorfer, Nature Materials , 179(2008).[4] P. Bushev, D. Bothner, J. Nagel, M. Kemmler, K. B. Konovalenko, A. Loerincz, K. Ilin, M. Siegel, D. Koelle,R. Kleiner, and F. Schmidt-Kaler, Eur. Phys. J. D(2011).[5] J. Fort´agh and C. Zimmermann, Science , 860 (2005).[6] D. Rugar, R. Budakian, H. J. Mamin, and B. W. Chui,Nature , 329 (2004).[7] J. R. Maze, P. L. Stanwix, J. S. Hodges, S. Hong, J. M.Taylor, P. Cappellaro, L. Jiang, M. V. Gurudev Dutt,E. Togan, A. S. Zibrov, A. Yacoby, R. L. Walsworth, andM. D. Lukin, Nature , 644 (2008).[8] G. Balasubramanian, I. Y. Chan, R. Kolesov, M. Al-Hmoud, J. Tisler, C. Shin, C. Kim, A. Wojcik, P. R. Hem-mer, A. Krueger, T. Hanke, A. Leitenstorfer, R. Brats-chitsch, F. Jelezko, and J. Wrachtrup, Nature , 648(2008).[9] J. Gallop, Supercond. Sci. Technol. , 1575 (2003).[10] C. P. Foley and H. Hilgenkamp, Supercond. Sci. Technol. , 064001 (2009).[11] V. Bouchiat, Supercond. Sci. Technol. , 064002 (2009).[12] J. Nagel, K. B. Konovalenko, M. Kemmler, M. Tu-rad, R. Werner, E. Kleisz, S. Menzel, R. Klin-geler, B. B¨uchner, R. Kleiner, and D. Koelle,Supercond. Sci. Technol. , 015015 (2011), 1009.2657.[13] A. G. P. Troeman, H. Derking, B. Borger, J. Pleikies,D. Veldhuis, and H. Hilgenkamp, Nano Lett. , 2152(2007).[14] L. Hao, J. C. Macfarlane, J. C. Gallop, D. Cox, J. Beyer, D. Drung, and T. Schurig, Appl. Phys. Lett. , 192507(2008).[15] R. F. Voss, R. B. Laibowitz, and A. N. Broers,Appl. Phys. Lett. , 656 (1980).[16] V. Bouchiat, M. Faucher, C. Thirion, W. Wernsdorfer,T. Fournier, and B. Pannetier, Appl. Phys. Lett. , 123(2001).[17] M. Faucher, P.-O. Jubert, O. Fruchart, W. Wernsdorfer,and V. Bouchiat, Supercond. Sci. Technol. , 064010(2009).[18] A. Finkler, Y. Segev, Y. Myasoedov, M. L. Rappa-port, L. Neeman, D. Vasyukov, E. Zeldov, M. E. Huber,J. Martin, and A. Yacoby, Nano Lett. , 1046 (2010).[19] N. C. Koshnick, M. E. Huber, J. A. Bert, C. W. Hicks,J. Large, H. Edwards, and K. A. Moler, Appl. Phys. Lett. , 243101 (2008).[20] D. J. Van Harlingen, R. H. Koch, and J. Clarke,Appl. Phys. Lett. , 197 (1982).[21] D. Hagedorn, R. Dolata, F.-I. Buchholz, and J. Niemeyer,Physica C , 7 (2002).[22] D. Hagedorn, O. Kieler, R. Dolata, R. Behr, F. M¨uller,J. Kohlmann, and J. Niemeyer, Supercond. Sci. Technol.19