Modulation of magnon-magnon coupling by inherent symmetry breaking in synthetic antiferromagnets

Abstract

Quantum magnonics is a rapidly growing field offering myriad of potential applications[1,2] particularly in the realm of coherent information processing. Magnons which are the collective excitations of spins offer exotic functionalities such as the ability to couple to various dynamic systems. Realisation of strong coupling , owing to large spin densities, which is tunable into the ultrastrong coupling regime makes them suitable for coherent information exchange at much faster speeds. Apart from this the easily accessible gigahertz frequency range, simple fabrication and miniaturization provides an ideal platform for incorporation in various microwave electronic circuits. Recently[3,4,5], Synthetic Antiferromagnets(SyAF) have attracted prodigious interest due to the controllable exchange coupling in the GHz regime making them a test bed for various magnonic applications[6]. Moreover, the substantially large mode volume overlapping gives them an advantage over light-matter interactions in attaining higher a coupling strength.A SyAF consists of two ferromagnetic thin films (FM) with an antiferromagnetic exchange coupling separated by a non-magnetic spacer (NM). When the two FMs are symmetric, a mode crossing occurs between symmetry protected in-phase and out- of -phase resonance precessions via in-plane external magnetic field tuning. This is reminiscent of degeneracy between even and odd parity magnons. This degeneracy and subsequent mode crossing can be lifted by breaking the symmetry either extrinsically or intrinsically. Extrinsic symmetry breaking (SB) can be exerted by tilting the external magnetic field out-of-plane which shifts the rotational symmetry axis from the SyAF plane, and the system is no longer symmetric under two-fold rotation. This leads to hybridization of the two modes and an anticrossing gap is generated. Additionally, a coupling gap can be induced by dynamic dipolar interaction[3]. The strength of the coupling between two magnon modes is determined by the size of the gap. Maximizing the coupling efficiency is thus easily attainable by the controllability of the coupling gap by external magnetic field orientation. Apart from an extrinsic control of coupling strength the symmetry of the system can be broken intrinsically by using either two different FMs or the same FMs with different thickness. This would lead to a coupling gap even for the external applied fields applied in-plane, owing to a change of magnetization under two-fold rotation.In this work we demonstrate the control of magnon-magnon coupling in SyAFs via intrinsic and extrinsic SB. The schematic of the two modes in SyAF system is shown in Fig 1(a). We first consider a symmetrical SyAF structure CoFeB/Ru/CoFeB as in Fig 2(a). The apparent mode crossing results from a degeneracy of two non-interacting modes which is protected by a two-fold rotational symmetry. By tilting the external field (see Fig 2(b)) we break this symmetry and an anticrossing gap appears. This demonstrates the extrinsic SB. When two FMs with different thickness are considered an inherent SB exists in the system which opens a gap even for an in-plane field as in Fig 2(c). Further, breaking the symmetry as in 2(d) by tilting the field leads to an increase of the gap and thus the coupling strength. This effect can be further enhanced when using two FMs of different materials, exhibiting a large coupling gap for an in-plane field as in Fig 2(e). Here, the coupling strength far exceeds the losses, described by the frequency half-width at half maximum of the individual modes. The absolute coupling strength reaches 30% of the mode frequencies, indicating the onset of the ultrastrong coupling regime. By calculating the coupling gap as a function of external field tilt angle we can putatively claim that both intrinsic and extrinsic SB can realise strong magnon-magnon coupling in SyAFs. Further, the strong coupling leads to an entanglement between even and odd parity modes, making it attractive for quantum information applications. We generalize a theoretical model in the macro spin limit by solving the two coupled LLG(Landau Lifshitz Gilbert) equations to describe the microwave absorption spectroscopy for the SB induced coupling in SyAFs. This study should shed light on the potential of SyAFs for studying and controlling magnon-magnon coherent coupling at room temperature. Moreover large tunable coupling strengths in this system will provide a novel platform for increased control of quantum systems. **