We analyze the design of a potential replacement technology for the commercial ferrite circulators that are ubiquitous in contemporary quantum superconducting microwave experiments. The lossless, lumped element design is capable of being integrated on chip with other superconducting microwave devices, thus circumventing the many performance-limiting aspects of ferrite circulators. The design is based on the dynamic modulation of DC superconducting microwave quantum interference devices (SQUIDs) that function as nearly linear, tunable inductors. The connection to familiar ferrite-based circulators is a simple frame boost in the internal dynamics' equation of motion. In addition to the general, schematic analysis, we also give an overview of many considerations necessary to achieve a practical design with a tunable center frequency in the 4-8 GHz frequency band, a bandwidth of 240 MHz, reflections at the -20 dB level, and a maximum signal power of approximately order 100 microwave photons per inverse bandwidth.

We report on the design and performance of an on-chip microwave circulator with a widely (GHz) tunable operation frequency. Nonreciprocity is created with a combination of frequency conversion and delay, and requires neither permanent magnets nor microwave bias tones, allowing on-chip integration with other superconducting circuits without the need for high-bandwidth control lines. Isolation in the device exceeds 20 dB over a bandwidth of tens of MHz, and its insertion loss is small, reaching as low as 0.9 dB at select operation frequencies. Furthermore, the device is linear with respect to input power for signal powers up to hundreds of fW (≈10 3 circulating photons), and the direction of circulation can be dynamically reconfigured. We demonstrate its operation at a selection of frequencies between 4 and 6 GHz.

In this letter we describe the ground-state magnetic structure of the highly anisotropic helimagnet Cr 1/3 NbS 2 in a magnetic field. A Heisenberg spin model with Dyzaloshinkii-Moriya interactions and magnetocrystalline anisotropy allows the ground state spin structure to be calculated for magnetic fields of arbitrary strength and direction. Comparison with magnetization measurements shows excellent agreement with the predicted spin structure.Controlling the electrical properties of materials by manipulating their magnetic structure has been one of the primary themes in the field of magnetism research and its applications. Major technological innovations have been based on these efforts, such as giant magnetoresistance in magnetic multilayers systems 1 and magnetic tunneling effects 2 . Recently, non-trivial spin textures, e.g. solitons 3 and skyrmions 4,5 , have received much attention in a similar context 3,6-10 . These objects are especially interesting because of the stability granted by their topology. A detailed understanding of such spin structures, in relation with their effect on electrical properties, is expected to shed light on developing spin-texture based applications 10 . With its layered noncentrosymmetric crystal structure, the helimagnet Cr 1/3 NbS 2 is well-suited for investigations of spin structure, especially toward controlling electrical properties 11,12 . In Cr 1/3 NbS 2 , Cr 3+ ions are intercalated between the hexagonal 2H-NbS 2 layers and magnetically order at T C = 133 K 11,12 . The crystal structure's lack of inversion symmetry, caused by Cr intercalation, results in a helical magnetic ground state oriented along the crystalline c-axis, with spins aligned ferromagnetically within the ab planes. Unlike other well known helimagnets with B20 crystal structure 4,5 , Cr 1/3 NbS 2 only breaks inversion symmetry along the caxis, making it ideal for studying spin-textures in magnetic thin films 13 , which also break inversion symmetry only along the single axis normal to the plane of film.The quasi 2-dimensional (2D) nature of these layered ferromagnetic planes, paired with strong magnetocrystalline anisotropy, allows a clear distinction between the magnetically hard axis (i.e. c-axis of the crystal) and the easy plane (ab-plane). The above qualities of Cr 1/3 NbS 2 greatly resemble those of planar magnetic

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