Upper Frequency Limits for Vortex Guiding and Ratchet Effects

O.V. Dobrovolskiy, E. Begun, V.M. Bevz, R. Sachser, and M. Huth

Phys. Rev. Applied 13, 024012 – Published 7 February 2020

Abstract

The guided and rectified motion of magnetic flux quanta are important effects governing the magnetoresistive response of nanostructured superconductors. While at low ac frequencies these effects are rather well understood, their manifestations at higher ac frequencies remain poorly investigated. Here, we explore the upper frequency limits for guided and rectified net motion of superconducting vortices in epitaxial $Nb$ films decorated with ferromagnetic nanostripes. By combining broadband electrical spectroscopy with resistance measurements, we reveal that the rectified voltage vanishes at a geometrically defined frequency of about 700 MHz. By contrast, a vortex-guiding-related low-ac-loss response persists up to about 2 GHz. This value corresponds to the depinning frequency $f_{d}^{s}$ associated with the washboard pinning potential induced by the nanostripes, which exhibits peaks for commensurate vortex-lattice configurations. By applying a sum of dc and microwave ac currents at an angle $α$ with respect to the nanostripes, the angle dependence of $f_{d}^{s} (α)$ is found to be correlated with the angle dependence of the depinning current. In all, our findings suggest that superconductors with higher $f_{d}^{s}$ should be favorable for efficient vortex manipulation in the gigahertz ac frequency range.

Received 4 October 2019
Revised 7 December 2019
Accepted 17 January 2020

DOI:https://doi.org/10.1103/PhysRevApplied.13.024012

Physics Subject Headings (PhySH)

Optoelectronics Vortices in superconductors

Superconducting devices Transition metals Waveguides

Microwave techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

O.V. Dobrovolskiy ^1,2,*, E. Begun³, V.M. Bevz², R. Sachser³, and M. Huth³

¹Faculty of Physics, University of Vienna, Vienna 1090, Austria
²School of Physics, V. Karazin National University, Kharkiv 61077, Ukraine
³Institute of Physics, Goethe University, Frankfurt am Main 60438, Germany

^*oleksandr.dobrovolskiy@univie.ac.at

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Vol. 13, Iss. 2 — February 2020

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Images

Figure 1
(a) Experimental geometry: dc and microwave ac currents $I^{dc}$ and $I^{mw}$ are applied to a $Nb$ CPW decorated with an array of $Co$ -FEBID nanostripes. The nanostripes are tilted at an angle $α$ with respect to the CPW axis. The currents exert a Lorentz force $F_{L}$ on vortices (denoted by yellow disks), acting along the $x$ axis. The vortex lattice is commensurate with the pinning landscape at 20 mT. For oblique angles $α \neq 0^{\circ}, 90^{\circ}$ , at sufficiently strong driving forces, the vortices move in the guiding direction $x^{'}$ along the nanostripes. (b) AFM image of the $Nb$ CPW decorated with $Co$ -FEBID nanostripes (top), which induce a pinning potential $U (x)$ of washboard type with a depth $U_{p 0}$ and a period 300 nm (bottom). With an increase in $α$ , $U_{p 0}$ decreases, and vanishes at $90^{\circ}$ . The vortex motion against the nanostripes’ steep slopes is in the “hard direction,” and that against the gentle slopes is in the “easy direction.”
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Figure 2
(a)–(d) Vortex-related insertion loss $L_{i}$ as a function of the value of the dc current in the presence of an ac current at a power level of $- 20$ dBm (solid lines) for a series of frequencies, as indicated. In (a), the dotted lines correspond to the same measurement of $L_{i} (I)$ at a power level of $- 60$ dBm. (e),(f) $L_{i} (f)$ for two values of dc current normalized to the depinning current $I_{d 0}^{s}$ , whose definition is shown in the inset of (d), depicting the current dependence of the derivative of $L_{i}$ with respect to the current for $α = 0^{\circ}$ . In all panels, $T = 0.8 T_{c}$ and $H = 20$ mT.
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Figure 3
(a) $I$ - $V$ curves of all samples in the absence of an ac stimulus. Lower inset: current dependence of the normalized resistance. Upper inset: the symbols show the difference voltage $Δ V = V (I) + V (- I)$ plotted by adding the right-hand and left-hand branches of the respective $I$ - $V$ curves in the main panel, and the solid lines show the rectified dc voltage appearing in the presence of an ac current for $f = 64.7$ MHz. (b) Frequency dependence of the rectified voltage $Δ V (f)$ for the ac power levels and angles $α$ indicated. The rectified voltage vanishes above $f_{r} \approx 700$ MHz. In all panels, $T = 0.8 T_{c}$ and $H = 20$ mT.
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Figure 4
(a) Insertion loss as a function of the magnetic field and the ac frequency for $α = 0^{\circ}$ . The horizontal dashed line indicates the upper frequency $f \approx 2$ GHz, above which the matching dips vanish. (b) Depinning frequency $f_{d}$ as a function of the magnetic field at $T = 0.8 T_{c}$ in the absence of a dc current for all angles $α$ . (c) Vortex-lattice configurations at the three matching fields corresponding to the peaks in $f_{d} (H)$ in (b).
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Figure 5
Angle dependences of the depinning frequencies and normalized depinning currents for intrinsic and anisotropic pinning at $T = 0.8 T_{c}$ and $B = 20$ mT. The solid lines are fits proportional to $\cos α$ .
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