Research ArticlePHYSICS

Observation of exceptional points in magnonic parity-time symmetry devices

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Science Advances  22 Nov 2019:
Vol. 5, no. 11, eaax9144
DOI: 10.1126/sciadv.aax9144
  • Fig. 1 Theoretical model for magnonic passive ƤƮ symmetric system.

    (A) Schematic structure of a trilayer system, where the two coupled ferromagnet (FM) layers are separated by a nonmagnetic layer. The coupling strength can be tuned by varying the nonmagnetic (NM) layer thickness. (B to D) Calculated eigenfrequencies and damping rates of the magnonic trilayer system for the following conditions: (B) One Co layer (FM1) has positive Gilbert damping α1 = α0 = 0.01, whereas the second Co layer (FM2) has negative α2 = −α0 (equal to −0.01). (C) Both Co layers have α1 = α2 = α0. (D) One Co layer has α1 = 3/2α0 (equal to 0.015), whereas the second Co layer has α2 = 1/2α0 (equal to 0.005). (E) Calculated eigenfrequencies with Co and NiFe FM layers separated by a Pt interlayer. Inset: Schematics of the ƤƮ symmetric trilayer. (F) Same as in (E) but for the eigenfrequency changes (top) after subtracting the eigenfrequencies of the corresponding FM with no coupling. The corresponding damping constants are given in the bottom panel. Here, the unperturbed Gilbert damping constants of Co and NiFe are α1 = α0 and α2 = 5/2α0, respectively.

  • Fig. 2 Determination of the eigenfrequencies and Gilbert damping constants in a magnonic ƤƮ symmetric trilayer by FMR measurements.

    (A) Derivative of the MW absorption of a Co (30 nm)/Pt (2.4 nm)/NiFe (5 nm) trilayer at FMR conditions, measured at several MW frequencies, ν. The Co-like acoustic (A) and NiFe-like optical (O) magnonic modes are assigned. a.u., arbitrary units. (B) Resonant fields of the two magnonic modes at various MW frequencies. The solid curves are fitted by the Kittel equation with parameters given in the text. (C) Linewidths of the two magnonic modes as a function of the MW frequencies. The solid lines are linear fits to help obtain the Gilbert damping constants.

  • Fig. 3 Experimental verification of the magnonic ƤƮ symmetric system using broadband FMR measurements.

    (A) Two magnonic modes, namely, acoustic (A) and optical (O), in trilayers of various Pt interlayer thicknesses, d, measured at MW frequency of 9 GHz. (B) Resonance fields of the two magnonic modes as a function of the Pt interlayer thickness. (C) Gilbert damping rates of the two magnonic modes obtained at various d values. (D) RKKY exchange constant, JRKKY, versus d obtained from (B) using the Kittel equation (see text). The solid line through the data points is calculated from a phenomenological model of the RKKY exchange interaction. (E) Magnon eigenfrequency changes, Δν = ν − ν0 (ν is for the obtained eigenfrequency and ν0 is for the unperturbed FMR frequency), of several trilayers plotted as a function of the coupling strength, JRKKY. (F) Gilbert damping constants plotted against JRKKY. The lines through the data points in (E) and (F) are a fit using the ƤƮ symmetry model shown in Fig. 1F. The green area indicates the parameter domain of the passive ƤƮ symmetry.

  • Fig. 4 BLS of magnons in ƤƮ symmetry trilayers of Co/Pt/NiFe.

    (A) BLS spectra of Damon-Eschbach–type magnons in unperturbed films of Co (30 nm) and NiFe (5 nm), measured at an in-plane applied magnetic field of 750 G (shown for reference). (B) Typical BLS spectra of magnons in trilayers with different Pt thickness, d, as given. The respective arrows point to the acoustic (pink) and optical (blue) modes. (C) Obtained magnon frequencies in the trilayers plotted against the interlayer coupling constant, J. The solid lines are calculated magnon eigenfrequencies of A and O modes based on our ƤƮ symmetry model (Fig. 1).

  • Fig. 5 Nonequilibrium magnon current detection in ƤƮ symmetry trilayers via the ISHE in a Pt overlayer.

    (A) Typical ISHE voltage generated at magnetic field close to the acoustic magnon mode (Co-like) in trilayers of different Pt thicknesses, as given. (B) Generated ISHE electric current (black squares) as a function of the Pt thickness, d. The black solid line is calculated on the basis of fig. S2E and eqs. S6 and S7. The red circles are the obtained ISHE current for conventional Co (30 nm)/Pt (x nm) bilayers shown for reference, where the red solid line is calculated from eq. S6.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/11/eaax9144/DC1

    Section S1. Theoretical model of ƤƮ symmetry in trilayer structure

    Section S2. RKKY interaction characterized by MOKE measurements using Sagnac interferometer

    Section S3. Dynamic detection of magnon current using the ISHE

    Section S4. Magnon modes in the ƤƮ symmetric trilayer measured by Brillouin light scattering

    Fig. S1. The geometry used in theoretical model calculation for the magnonic passive ƤƮ symmetric system.

    Fig. S2. Calculated FMR absorption of the magnonic passive ƤƮ symmetric system at different interlayer coupling strengths.

    Fig. S3. Characterization of the RKKY exchange interaction in the trilayer devices measured by MOKE using a Sagnac interferometer.

    Fig. S4. The magnetization values associated to the two collective modes obtained from the broadband FMR results using the Kittel equation.

    Fig. S5. Conversion of the magnonic current into electric current in various trilayer devices capped with a 7-nm Pt detection layer.

    Fig. S6. Determination of magnon frequencies in the magnonic trilayer devices.

    Fig. S7. BLS spectrum of magnon modes upon MW radiation in a trilayer close to an EP.

    References (3539)

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Theoretical model of ƤƮ symmetry in trilayer structure
    • Section S2. RKKY interaction characterized by MOKE measurements using Sagnac interferometer
    • Section S3. Dynamic detection of magnon current using the ISHE
    • Section S4. Magnon modes in the ƤƮ symmetric trilayer measured by Brillouin light scattering
    • Fig. S1. The geometry used in theoretical model calculation for the magnonic passive ƤƮ symmetric system.
    • Fig. S2. Calculated FMR absorption of the magnonic passive ƤƮ symmetric system at different interlayer coupling strengths.
    • Fig. S3. Characterization of the RKKY exchange interaction in the trilayer devices measured by MOKE using a Sagnac interferometer.
    • Fig. S4. The magnetization values associated to the two collective modes obtained from the broadband FMR results using the Kittel equation.
    • Fig. S5. Conversion of the magnonic current into electric current in various trilayer devices capped with a 7-nm Pt detection layer.
    • Fig. S6. Determination of magnon frequencies in the magnonic trilayer devices.
    • Fig. S7. BLS spectrum of magnon modes upon MW radiation in a trilayer close to an EP.
    • References (3539)

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