Re-orientation of the easy axis in φ ₀ -junction

Abstract

We study theoretically a dynamics of the ϕ0-Josephson junction, with direct coupling between magnetic moment and Josephson current, which shows features reminiscent of a Kapitza pendulum. We find that, starting with the magnetization along the z-axis, the character of the magnetization dynamics changes crucially as a stable position of the magnetic moment m is realized between the z-and y-axes, depending on the values of the system parameters. Changes in critical current and spin-orbit interaction lead to different stability regions for the magnetization. Excellent agreement is obtained between analytical and numerical results at low values of the Josephson-to-magnetic-energy ratio.

Bifurcation structure and chaos in nanomagnet coupled to Josephson junction

“…The other one is related to the oscillating magnetic field generated by the superconducting current. The second one is a manifestation of Kapitza pendulum-like feature which was observed in the magnetization dynamics of the nanomagnet [11,35] and ϕ 0junction [34].…”

“…The nonlinear dynamics of the JJ is sensitive to the orientation of the magnetization [16,[25][26][27][28][29][30][31], and a rich physics has been predicted due to this type of coupling between the Josephson and magnetic subsystems: for example, supercurrent-induced magnetization dynamics [25,32,33]. In the NM-JJ system, the reversal of the magnetic moment by the supercurrent pulse [30], the appearance of Devil's staircase [24] and Kapitza pendulum effects [11,34,35], have been investigated.…”

Kapitsa pendulum effects in Josephson junction + nanomagnet under external periodic drive

“…However, the results show an opposite frequency dependence from the characteristic Kapitsa pendulum behavior, where the reorientation value is proportional to the frequency of the force applied to the suspension point. In [18], the increase in Ω J leads to a smaller reorientation value at the same value of G. On the other hand, an effect corresponding to the Kapitsa pendulum has been observed in Ref. [19], where for the JJ-nanomagnet system the increase in Ω J led to the larger reorientation value.…”

“…In Ref. [18], the authors introduce the Kapitsa pendulum as a mechanical analog to the ϕ 0 -junction and demonstrated the reorientation of the easy axis of the magnetic moment of the ferromagnetic layer. In this case, the Josephson to magnetic energy ratio G corresponds to the amplitude of the variable force of the Kapitsa pendulum, the Josephson frequency Ω J corresponds to the oscillation frequency of the suspension point, and the averaged magnetic moment components specify the stable position.…”

Collective magnetic and plasma excitations in Josephson $ψ$ junctions

“…37,38 Similar hybridization of Josephson phase oscillations and precession of magnetic moment is predicted for the ϕ 0 junctions. [39][40][41][42][43][44][45][46] The ground state phase ϕ 0 is determined by the angle θ between the magnetic moment M orientation inside the ferromagnet and the unit vector n along the direction of the broken inversion symmetry so that ϕ 0 ∝ sin θ. As a result, the Josephson energy E = (Φ 0 I c /2πc) [1 − cos(ϕ − ϕ 0 )] becomes dependent on the magnetic moment orientation which results not only in the influence of the magnetic order on the superconducting current but also in the back-action of the Josephson current on the magnetization direction.…”