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Boundary conditions for and ferromagnetic resonance spectra of magnetic bilayers coupled by interlayer Dzyaloshinskii-Moriya interactions

Elena Y. Vedmedenko1,* and Mikhail Kostylev2,†

  • *Contact author: vedmeden@physnet.uni-hamburg.de
  • †Contact author: mikhail.kostylev@uwa.edu.au
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Phys. Rev. Applied 23, 014047 – Published 22 January, 2025

DOI: https://doi.org/10.1103/PhysRevApplied.23.014047

Abstract

Interfacial Dzyaloshinskii-Moriya interaction (IFDMI) leads to noncollinear spin configurations within the magnetic layers of multilayer heterostructures, while its interlayer counterpart (ILDMI) minimizes chiral states between the layers. Here, we demonstrate that the symmetries of these interactions are very different, even though both arise from pairwise exchange interactions between magnetic sites mediated by nonmagnetic atoms. By deriving respective boundary conditions for the exchange operator and solving the associated boundary value problem, we show that, unlike IFDMI, which does not contribute to the FMR frequencies, ILDMI alters the frequencies of the fundamental FMR modes and can be separated from other contributions in an FMR experiment.

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References (37)

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  34. When addressing the AFM ILHE case, we assume the same FM state of static magnetization as for the FM ILHEI scenario. This assumption implies that H is sufficiently strong to co-align the static magnetization vectors of the AFM-coupled layers, resulting in a perfectly uniform static magnetization across the thickness of both layers, with no magnetization twists present within the layers.
  35. Recall that we assume H lies in the plane of the structure and is strong enough to perfectly align the static magnetization vectors of both magnetic layers along H.
  36. The only exception to this rule occurs when the in-plane bulk anisotropy axes of the two magnetic layers are perfectly orthogonal to one another and D = 0. In this case, the two sine waves are also in antiphase. However, their amplitudes are very small [approximately 2 Oe for the same parameters as in Fig. 3]. Moreover, we believe the likelihood of such alignment of the axes in a real-world sample is quite low, unless it has been intentionally induced in some manner.
  37. The precise value of d is not important within this formalism, as the theory treats A, D and d as independent quantities. Thus, d serves as a purely geometric parameter that defines the coordinates of the interfaces without affecting the exchange conditions at those interfaces. This allows the results of the theory to remain independent of d. Consequently, d can be assumed to take any value or set to zero to simplify formulas and numerical modeling. This simplification is applied in Eq. (A12), which is presented for d= 0, making it more compact without loss of generality. The strength of interlayer exchange coupling is fully captured through the values of A and D, which specify the strength of the coupling completely.

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Phys. Rev. Applied 23, 014047– Published 22 January, 2025
  • Received 3 June 2024
  • Revised 22 November 2024
  • Accepted 24 December 2024
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