Anomalous Gilbert damping and Duffing features of the superconductor-ferromagnet-superconductor φ0 Josephson junction

Nonlinear features of the superconductor–ferromagnet–superconductor φ0 Josephson junction in the ferromagnetic resonance region

“…We usually expect the resonance peak to move away from resonance as α increases. Figure 2 shows that this normal effect is accompanied with an anomalous behavior, as can be seen in the inset in this figure, where the resonance peak approaches ω F as α increases [ 14 ].…”

“…The bias current is normalized to the critical current I c and the voltage V is normalized to V c = I c R . The system in Equation 6 is solved numerically using the fourth-order Runge–Kutta method [ 14 ].…”

“…Such Josephson junctions are named φ 0 junctions [ 1 ], and examples, such as MnSi and FeGe, exist. The second one is the nonlinear property of the system, which makes for an anomalous resonance behavior [ 14 ].…”

“…The consequences of the nonlinear nature of the coupled set of the LLGJ system of equations in the weak coupling regime was demonstrated recently in [ 14 ]. We showed that, in this regime where the Josephson energy is small compared to the magnetic energy, the φ 0 Josephson junction is equivalently described by a scalar nonlinear Duffing equation.…”

“…We compare description of the anomalous damping dependence (ADD) exhibited by full LLGJ system of equations with approximated equations and demonstrate the Duffing oscillator features in the small parameter regime. Effects of the Josephson-to-magnetic energy ratio, and the spin–orbit coupling on the ADD, referred to earlier as the α-effect [ 14 ] are demonstrated. By deriving the formula that couples the DC superconducting current and maximal amplitude of magnetization we discuss the correlation of superconducting current and the negative differential resistance in the resonance region.…”