SKIFFS: Superconducting Kinetic Inductance Field-Frequency Sensors for sensitive magnetometry in moderate background magnetic fields Cite as: Appl. Phys. Lett. 113, 172601 (2018); https://doi.org/10.1063/1.5049615 Submitted: 24 July 2018 . Accepted: 10 October 2018 . Published Online: 25 October 2018 A. T. Asfaw , E. I. Kleinbaum, T. M. Hazard , A. Gyenis, A. A. Houck, and S. A. Lyon ARTICLES YOU MAY BE INTERESTED IN Multi-frequency spin manipulation using rapidly tunable superconducting coplanar waveguide microresonators Applied Physics Letters 111, 032601 (2017); https://doi.org/10.1063/1.4993930 Publisher's Note: “Anomalous Nernst effect in Ir22Mn78/Co20Fe60B20/MgO layers with perpendicular magnetic anisotropy” [Appl. Phys. Lett. 111, 222401 (2017)] Applied Physics Letters 113, 179901 (2018); https://doi.org/10.1063/1.5018606 Tunneling anomalous Hall effect in a ferroelectric tunnel junction Applied Physics Letters 113, 172405 (2018); https://doi.org/10.1063/1.5051629 Appl. Phys. Lett. 113, 172601 (2018); https://doi.org/10.1063/1.5049615 113, 172601 © 2018 Author(s). APPLIED PHYSICS LETTERS 113, 172601 (2018) SKIFFS: Superconducting Kinetic Inductance Field-Frequency Sensors for sensitive magnetometry in moderate background magnetic fields A. T. Asfaw,a) E. I. Kleinbaum, T. M. Hazard, A. Gyenis, A. A. Houck, and S. A. Lyon Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA (Received 24 July 2018; accepted 10 October 2018; published online 25 October 2018) We describe sensitive magnetometry using lumped-element resonators fabricated from a supercon- ducting thin film of NbTiN. Taking advantage of the large kinetic inductance of the superconduc- tor, we demonstrate a continuous resonance frequency shift of 27 MHz for a change in the magnetic field of 1.8 lT within a perpendicular background field of 60 mT. By using phase- sensitive readout of microwaves transmitted through the sensors, we measure phase shifts in real time with a sensitivity of 1/nT. We present measurements of the noise spectral density of the sen- sors and find that their field sensitivity is at least within one to two orders of magnitude of super- conducting quantum interference devices operating with zero background field. Our superconducting kinetic inductance field-frequency sensors enable real-time magnetometry in the presence of moderate perpendicular background fields up to at least 0.2 T. Applications for our sen- sors include the stabilization of magnetic fields in long coherence electron spin resonance measure- ments and quantum computation. Published by AIP Publishing. https://doi.org/10.1063/1.5049615 Disordered superconductors such as NbTiN, TiN, and length ‘nw are defined on the left and right arms of the loop NbN have become ubiquitous in several fields of study due as seen in the inset of Fig. 1(a). Care is taken to prevent cur- to their large kinetic inductance and resilience to large back- rent crowding at the ends of the nanowires16,17 by linearly ground magnetic fields.1,2 Microwave kinetic inductance tapering from the micron-wide loop dimensions to the detectors3–5 and superconducting nanowire single-photon nanowires over a length of 10 lm. The resonator is com- detectors6,7 fabricated from kinetic inductors are now rou- pleted by placing interdigitated capacitors at the center of tinely used in astronomy and imaging. Kinetic inductors can the loop with fingers and gaps of width 1 lm. Each resona- also be used in applications such as current-sensing,8 magne- tor is coupled to a microwave feedline using a coupling tometry,9 parametric amplification,10,11 generation of fre- capacitor, which is also an interdigitated structure with four quency combs,12 and superconducting qubits.13,14 pairs of 10 lm wide fingers that are separated by 10 lm In this work, we take advantage of the kinetic induc- gaps. tance of a thin film of NbTiN to fabricate lumped-element A lumped-element circuit model of the SKIFFS is resonators whose resonance frequencies are strongly depen- shown in Fig. 1(b). From a Sonnet18 simulation, we obtain dent on the perpendicular magnetic field, changing by as an estimate of the resonator capacitance, CR 0.2 pF. From much as 27 MHz for a field change of 1.8 lT. We demon- the thin-film parameters, we estimate that the nanowires con- strate a method for the real-time measurement of AC mag- tribute an inductance of 360 pH/lm, while the micron-sized netic fields based on phase-sensitive readout of microwave sections of the loop contribute an inductance of 7.2 pH/lm. transmission through the resonators, finding a detection sen- Using these parameters, we estimate a resonance frequency sitivity of 1 /nT. Our Superconducting Kinetic Inductance of 5 GHz for a sensor with ‘nw ¼ 10 lm. Field-Frequency Sensors (SKIFFS) are able to operate in perpendicular background magnetic fields at least as large as 0.2 T and may find applications in quantum computation, where superconducting quantum interference devices (SQUIDs) based on Josephson junctions may not be applica- ble due to the large magnetic fields. Our SKIFFSs are fabricated from a 7 nm NbTiN thin film (TC 9K, Rsheet ¼ 252 X/ٗ) DC-sputtered reactively on a c-axis sapphire substrate using a NbTi alloy target and an Ar/N environment.15 The device features are patterned using electron-beam lithography followed by reactive-ion FIG. 1. (a) Scanning electron micrograph of a SKIFFS resonator. Each reso- etching with an SF /Ar plasma. A scanning electron micro- nator consists of a 5 lm wide rectangular superconducting loop that is cou- 6 pled to a central microwave feedline capacitively using four pairs of graph of a SKIFFS is shown in Fig. 1(a). The sensor is a interdigitated 10 lm fingers. The loop inductance is mostly due to the two lumped-element microwave resonator fabricated from a nanowires that are 100 nm wide as shown in the inset. Interdigitated capaci- 100 lm  100 lm rectangular superconducting loop defined tors with fingers of width 1 lm are placed at the center of the loop to com- by a 5 lm wide line. Two 100 nm wide nanowires of plete the resonator, and the lower arm of the superconducting loop is shunted to ground. (b) Lumped-element circuit model of a SKIFFS resonator coupled to a microwave feedline via CC. The kinetic inductors, LR, on each a) Electronic mail: [email protected] arm of the superconducting loop and the capacitor, CR, form the resonator. 0003-6951/2018/113(17)/172601/5/$30.00 113, 172601-1 Published by AIP Publishing. 172601-2 Asfaw et al. Appl. Phys. Lett. 113, 172601 (2018) The device reported in this work has six sensors with capacitor coupling of the resonator to the microwave feedline varying values of ‘nw from 7 to 12 lm that are coupled to a toward critical coupling. Additionally, higher quality factors common microwave feedline. Following fabrication, the should be possible by operating the resonator at lower temper- device is wirebonded to a copper printed circuit board atures, where T/TC 0.1. Quality factors between 10 000 and equipped with microwave connectors and placed in the bore 100 000 have previously been reported for comparable thin of an external magnet with the surface of the superconductor films of NbTiN in the presence of moderate background fields perpendicular to the magnetic field, B0. Additionally, a at 300 mK (Ref. 2). home-made Helmholtz pair coil is attached to the sample Next, we set B0 ¼ 60 mT and apply small magnetic fields holder such that the generated field, Bcoil, is parallel to the using our home-made coil. The results are shown in Fig. external field. We use the external magnet to generate the 2(b). As the magnetic field of the coil, Bcoil, is increased, the moderate background magnetic fields and the coil to gener- resonance frequency, fR, shifts continuously from its value at ate small additional magnetic fields. The magnetic field gen- 60 mT as erated by the home-made coil was calibrated from the shift ! in the electron spin resonance line of phosphorus donor elec- B 2 df ðB Þ¼f 1 À coil ; (1) tron spins in silicon in a separate experiment. R coil R0 17 lT The device and sample holder assembly are cooled to a temperature of 1.9 K, and microwave transmission through where fR0 ¼ 4:182 GHz is the resonance frequency with the central feedline is monitored using a network analyzer Bcoil ¼ 0 lT and B0 ¼ 60 mT. The functional form of the shift with a microwave power of À72 dBm at the device. All six in the resonance frequency has been observed in other devi- resonances are found in the range of 3.945–5.230 GHz. ces.1,9,21–23 The resonance frequency shows a maximum Microwave powers exceeding 64 dBm were observed to À shift of 27 MHz as Bcoil is increased to 1.8 lT. When Bcoil distort the resonance lineshapes of some of the resonators. exceeds 1.8 lT(10 flux quanta), the resonance frequency This behavior has been observed previously and is a signa- abruptly jumps back to 4.182 GHz and continues to change ture of the large kinetic inductance of the superconduc- as before. This behavior can be understood by noting that a tor.19,20 For the remainder of this work, we focus on one of screening current, iloop, is generated in the superconducting the SKIFFSs with ‘nw ¼ 10 lm and a resonance frequency loop in order to keep the magnetic flux threading the loop near 4.2 GHz. constant as Bcoil is changed. This current modulates the The loaded quality factor of the resonator depends kinetic inductance of the superconducting nanowires, LR, strongly on the perpendicular magnetic field, B0.Inorderto thereby resulting in a change in the resonance frequency of study this dependence, we monitor the resonance near 4.2GHz the SKIFFS resonator.