Research ArticlePHYSICS

Phase control in a spin-triplet SQUID

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Science Advances  27 Jul 2018:
Vol. 4, no. 7, eaat9457
DOI: 10.1126/sciadv.aat9457
  • Fig. 1 Spin-triplet Josephson junction structure and SQUID loop design.

    Top: Schematic cross section of the central layers in our Josephson junctions (not to scale). The central F layer is composed of two [Pd (0.9 nm)/Co (0.3 nm)]n multilayers with perpendicular magnetic anisotropy (PMA), separated by a Ru (0.95 nm) spacer to form a synthetic antiferromagnet (SAF). The outer F′ and F″ layers have in-plane magnetization; we used Permalloy (Py) for F′ and Ni for F″. One junction has an elliptical cross section (aspect ratio, 2.0) to make its F′ layer switch at a low field, while the other is an elongated hexagon (aspect ratio 3.0); both have an area of 0.5 μm2. Bottom: The two junctions are arranged into a SQUID loop. An external field Hset is used to control the magnetization directions of the F′ and F″ layers inside the junctions; all measurements are performed with Hset = 0. The current Iflux passing through a nearby superconducting line creates an out-of-plane field Hflux, which couples magnetic flux Φ into the SQUID loop. The Py magnetizations are shown as black arrows labeled MPy,1 and MPy,2.

  • Fig. 2 SQUID data.

    (A) Three-dimensional (3D) plot of a minor loop for SQUID 2A-4: critical current versus Iflux and Hset. The critical current plotted, Ic,Avg, is the average of the critical currents in the positive and negative current directions, Ic,Avg = (Ic+ + |Ic−|)/2 [see (B)]. Before any measurements are made, μ0Hset is set to −150 mT to initialize the magnetizations of the Ni and Py layers in both junctions. With Hset = 0, Ic is measured as a function of Iflux and exhibits oscillations with a period of about 1.5 mA, corresponding to the flux quantum, Φ0 = h/2e. Then, Hset is stepped in the positive direction (labeled “Up sweep” in the figure), returning to zero after each step for sample measurement. The SQUID oscillations exhibit a horizontal shift of ½Φ0 at μ0Hset = +2.4 mT, indicating that one of the Josephson junctions has changed its ground-state phase by π. The SQUID remains in that state as Hset is increased further, but increasing Hset too far causes the second junction to switch; the data shown here stop before that occurs. Next, Hset is stepped in the negative direction (labeled “Down sweep”) until μ0Hset = −2.8 mT, where the SQUID switches back to the original state. (B) Current-voltage characteristics obtained at Iflux = −0.2 mA for the two magnetic states: in the π state with maximum Ic (green symbols) and in the initial 0 state with minimum Ic (purple symbols). The solid green and purple lines are fits to the current-voltage relation (I-V) curves with the Ivanchenko-Zil’bermann (IZ) function (see Materials and Methods), while the red and blue dashed lines are fits to the simpler square-root function used to obtain the data in (A) and (C). The latter fits give values of Ic about 20% lower than the former, as shown by the Ic+ and Ic− labels. (C) Repeated switching between the P and the AP states at Iflux = −0.2 mA. The histogram shows the measured values of Icavg in the two states while the magnetic field was toggled between +2.8 and −3.2 mT 1000 times.

  • Fig. 3 High-resolution SQUID data and fits.

    Plot of Ic+ and Ic− versus Iflux for SQUID 2A-4. The solid circles correspond to the initialized magnetic state, while the stars correspond to the second state after one junction has switched. The values of Ic+ and Ic− shown in this figure were obtained by fitting the IZ function to the raw I-V curves as shown in Fig. 2B. The solid lines (blue for the initial state and yellow for the second state) are least-squares fits to the data of standard SQUID theory [see (18) and Materials and Methods]. Values for the critical currents of the two Josephson junctions obtained from the fits are given in Table 1.

  • Table 1 Fit parameters for the seven spin-triplet SQUID samples measured.

    The first two characters in the sample name, for example, “2A,” refer to the chip, while the final number refers to the specific device on the chip. (Each chip contains four SQUIDs.) The value 2n is the total number of [Pd/Co] bilayers in the central F layer. The SQUID oscillation curves were fit to standard SQUID theory, as shown in Fig. 3 for device 2A-4, while keeping the total inductance fixed to the nominal value of 9 pH. The last column of the table shows that the flux shifts of the SQUID oscillation curves between the two magnetic states are very close to ½Φ0, which corresponds to a phase shift of π for one of the two junctions in the SQUID. The fits also provide approximate values of the critical currents in the two junctions, Ic1 and Ic2. (The uncertainties in the values of Ic1 and Ic2 derived from the fits appear to be too small, as the value of Ic2 for the nonswitching junction appears to change between the two magnetic states. We believe that this is a generic feature of fits to SQUID data for SQUIDs in the low-inductance limit, βL << 1.) The data for all samples except 2A-4 can be found in the Supplementary Materials.

    SQUID name2nStateIc1 (μA)Ic2 (μA)ΔΦshift0
    2A-1416.65 ± 0.084.20 ± 0.080.491 ± 0.005
    26.90 ± 0.124.18 ± 0.12
    2A-2414.09 ± 0.144.02 ± 0.140.542 ± 0.004
    25.66 ± 0.105.61 ± 0.10
    2A-3414.53 ± 0.124.56 ± 0.120.480 ± 0.004
    26.88 ± 0.074.67 ± 0.07
    2A-4414.56 ± 0.046.16 ± 0.040.509 ± 0.003
    27.30 ± 0.157.08 ± 0.15
    3A-3610.80 ± 0.300.79 ± 0.300.519 ± 0.010
    21.99 ± 0.021.34 ± 0.02
    4A-1610.60 ± 0.333.16 ± 0.330.618 ± 0.005
    21.45 ± 0.033.87 ± 0.03
    4A-2611.32 ± 0.042.41 ± 0.040.493 ± 0.004
    23.01 ± 0.011.61 ± 0.01

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/7/eaat9457/DC1

    Additional Low-Temperature Measurements

    Data from Additional Samples

    Fig. S1. Low-temperature measurements of sample 2A-1 with additional filtering.

    Fig. S2. Data from sample 2A-1.

    Fig. S3. Data from sample 2A-2.

    Fig. S4. Data from sample 2A-3.

    Fig. S5. Data from sample 3A-3.

    Fig. S6. Data from sample 4A-1.

    Fig. S7. Data from sample 4A-2.

  • Supplementary Materials

    This PDF file includes:

    • Additional Low-Temperature Measurements
    • Data from Additional Samples
    • Fig. S1. Low-temperature measurements of sample 2A-1 with additional filtering.
    • Fig. S2. Data from sample 2A-1.
    • Fig. S3. Data from sample 2A-2.
    • Fig. S4. Data from sample 2A-3.
    • Fig. S5. Data from sample 3A-3.
    • Fig. S6. Data from sample 4A-1.
    • Fig. S7. Data from sample 4A-2.

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