Towards an experimental proof of the magnonic Aharonov-Casher effect

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Letter

Towards an experimental proof of the magnonic Aharonov-Casher effect

Rostyslav O. Serha, Vitaliy I. Vasyuchka, Alexander A. Serga, and Burkard Hillebrands

Phys. Rev. B 108, L220404 – Published 29 December 2023

Abstract

Controlling the phase and amplitude of spin waves in magnetic insulators with an electric field opens the way to fast logic circuits with ultralow power consumption. One way to achieve such control is to manipulate the magnetization of the medium via magnetoelectric effects. In experiments with magnetostatic spin waves in an yttrium iron garnet film, we have obtained evidence of a theoretically predicted phenomenon: the change of the spin-wave phase due to the magnonic Aharonov-Casher effect—the geometric accumulation of the magnon phase as these quasiparticles propagate through an electric field region.

Received 26 July 2023
Revised 17 November 2023
Accepted 7 December 2023

DOI:https://doi.org/10.1103/PhysRevB.108.L220404

Physics Subject Headings (PhySH)

Aharonov-Casher effect Magnetism Magnetoelectric effect Magnons Spin dynamics Spin waves

Ferrimagnets Insulators Magnetic insulators Magnetic thin films Single crystal materials

Linear spin wave theory Methods in magnetism Microwave techniques Spin wave spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Rostyslav O. Serha ^1,2,*, Vitaliy I. Vasyuchka ^1,†, Alexander A. Serga ^1,‡, and Burkard Hillebrands ^1,§

¹Fachbereich Physik and Landesforschungszentrum OPTIMAS, Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau, 67663 Kaiserslautern, Germany
²University of Vienna, Faculty of Physics, 1090 Vienna, Austria

^*rostyslav.serha@univie.ac.at
^†vitaliy.vasyuchka@physik.rptu.de
^‡serha@rptu.de
^§hilleb@rptu.de

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Issue

Vol. 108, Iss. 22 — 1 December 2023

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Images

Figure 1
(a) Sketch of the experimental setup. The YIG sample is placed on copper microstrip antennas and exposed to the external magnetizing field $H_{ext}$ . Spin waves are excited and measured using a vector network analyzer (VNA). By applying a voltage onto the copper electrode on the upper sample surface, an electric field is created between the electrode and the grounded brass sample holder. The inset illustrates the multilayer structure between these electrodes. (b) and (c) present the transmission characteristics measured for the BVMSW and MSSW geometries with the highlighted frequencies and estimated wave-vector values (shown in rad/cm on the labels) selected for the phase shift measurement. The expected value of the ferromagnetic resonance frequency at zero wave vector is shown by a dashed gray line. The measurements were performed at $H_{ext} = 136.4 mT$ for BVMSW and 138.9 mT for MSSW geometries. (d) and (e) show examples of time-phase measurements performed for the $S_{21}$ parameter in the BVMSW ( $f = 5.74 GHz, k = 78 rad / cm$ ) and MSSW ( $f = 6.21 GHz, k = 748 rad / cm$ ) geometries, respectively. The gray background indicates the time intervals when the electric field with a strength of 4 kV/mm was turned on. The electrically induced phase shifts $Δ φ$ are highlighted by dashed horizontal red lines. The linear phase shift, regardless of whether the electric field is on or off, is a continuous phase drift caused by temperature instability.
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Figure 2
(a) Measured BVMSW phase shifts vs the applied electric field for five different wave vectors. (b) The calculated BVMSW phase shifts. The calculation was performed considering the contributions of the quadratic and linear ME effects. The corresponding ME coefficients were found by fitting the experimental data.
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Figure 3
(a) Measurement of the MSSW phase shift vs the applied electric field $E$ for six different wave vectors. (b) Calculations of the MSSW phase shift caused by quadratic and linear ME effects. The values of the ME coefficients are identical to those for the BVMSW calculations shown in Fig. 2. (c) The MSSW phase shift $Δ φ$ is calculated by adding the linear AC contribution to the phase changes caused by the linear and quadratic ME effects. The AC contribution is estimated by the coefficient $κ$ in the range $(6.16 - 8.46) \times 10^{- 12}$ mm ${kV}^{- 1}$ , which provides a $Δ φ$ confidence band for each wave vector. The middle line in the bands refers to $κ = 7.14 \times 10^{- 12}$ mm ${kV}^{- 1}$ , which is obtained by fitting the three experimental curves measured at the highest wave vectors.
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