Originality of resonance and locking phenomena in SFS $\varphi_0$ Josephson junction

TL;DR

This work analyzes a short SFS $\varphi_0$ Josephson junction where two ferromagnetic resonances—the Kittel resonance (KR) driven by the magnetic component of external radiation and the Buzdin resonance (BR) arising from spin-orbit–mediated coupling between superconducting current and ferromagnetic magnetization—can both appear in one device. By solving the coupled Landau-Lifshitz-Gilbert and RCSJ equations with spin-orbit coupling, the authors map out KR, BR, and combined resonances, and demonstrate transitions between resonance regimes and locking (Shapiro- and Buzdin-like steps) as the radiation frequency $\omega_R$, coupling ratio $G$, and Rashba parameter $r$ are varied, in two geometries (G1 in-plane, G2 out-of-plane). They show how tuning $\omega_R$ can switch the system between KR- and BR-dominated responses and how combined resonances emerge at BR-KR intersections, with locking enriching the dynamical spectrum. The results have implications for superconducting spintronics, including potential cryogenic memory and robust synchronization-based devices, and suggest experimental paths using Pt-doped permalloy barriers to realize and measure the $\varphi_0$ state and its spin-orbit coupling strength.

Abstract

We demonstrate the realization and interplay of two ferromagnetic resonances in one SFS $\varphi_0$ Josephson junction. First resonance that is realized under microwave radiation is the famous Kittel resonance. The other is Buzdin one appearing as a result of interaction of superconducting current and ferromagnetic interlayer magnetization. Transformations of one type of resonance to another under variation of external electromagnetic radiation and the $\varphi_0$ junction parameters open an interesting way to manipulation both of them. The combined ferromagnetic resonance that exhibits the features of both resonances is demonstrated too. The coupling of the Josephson phase with the magnetization of the ferromagnetic layer, caused by the spin-orbit interaction, leads to double synchronization, namely, synchronization of both magnetic precession and Josephson oscillations by external radiation. The obtained results demonstrate reach physics and unique opportunities for various applications.

Figures (6)

• Figure 1: (a) In-plane geometry: effective field due to the magnetic component of radiation $h_R$ is parallel to the Josephson effective field $h_J$ and perpendicular to the anisotropy field. (b) Off-plane geometry: $h_R$ is perpendicular to $h_J$.
• Figure 2: Manifestation of different resonances on $I-\omega_R$ diagram. (a) Kittel resonance at $G=10^{-4}$, $r=0.1$ and $h_{R}=0.001$. (b) Buzdin resonance at $G=0.05$, $r=0.2$ and $h_{R}=10^{-5}$. The combined resonance shown in (c) at $G=0.01$, $r=0.2$ and $h_{R}=0.05$. (d) The $I$-dependence of $m_{y}^{max}(I)$ near Buzdin - Kittel resonance region (line 1), and demonstrating the combined resonance peaks (see plain arrows) and far from the KR-region (line 2), demonstrating Buzdin resonances and its subharmonic peaks.
• Figure 3: (a) $m_y^{max}(\omega_{J})$ in G1 at $\omega_{R}$=0.2 and $r=0.2$. Hollow arrow shows the main BR, blue filled arrows demonstrate the manifestation of locking. Inset (i) shows the IV-curve, and insets (ii) and (iii) shows the effect of $h_{R}$ and $r$, respectively. (b) Left side shows $m_y^{max}(\omega_{J})$ at $\omega_{R}=0.4, 0.5$ and $0.6$ with $h_{R}=0.05$. Right side shows the corresponding IV-curves. Letter "L" indicates locking, while letter "R" indicates the resonance. The IV-curves for $\omega_{R}=0.5$ and $0.6$ are shifted by $\Delta I=0.09$ to the right relatively to $0.4$ for clarity.
• Figure 4: (a) $I-\omega_R$ diagram of resonance maxima under radiation at $h_{R}=0.05$ in G2-geometry; (b) The same for $h_{R}=1$. Color demonstrates the value of $m_y^{max}$ in the corresponding resonance peak. The arrows and numbers show the corresponding peak positions indicated on the right.
• Figure 5: Interplay of resonance and locking in G2-geometry. (a) $m_y^{max}(\omega_{J})$ at $\omega_{R}$=0.2. The blue filled arrows demonstrate the manifestation of locking. Inset (i) shows the IV-curve, and insets (ii) and (iii) shows the effect of $h_{R}$ and $r$, respectively. (b) Left side shows $m_y^{max}(\omega_{J})$ at $\omega_{R}=0.4, 0.5$ and $0.6$ with $h_{R}=1$. Right side shows the corresponding IV-curves. Letter "L" indicates locking, while letter "R" indicates the resonance.