Influence of low-energy magnons on magnon Hanle experiments in easy-plane antiferromagnets

Janine Gückelhorn, Akashdeep Kamra, Tobias Wimmer, Matthias Opel, Stephan Geprägs, Rudolf Gross, Hans Huebl, and Matthias Althammer

Phys. Rev. B 105, 094440 – Published 29 March 2022

Abstract

Antiferromagnetic materials host pairs of spin-up and spin-down magnons which can be described in terms of a magnonic pseudospin. The close analogy between this magnonic pseudospin system and that of electronic charge carriers led to the prediction of fascinating phenomena in antiferromagnets. Recently, the associated dynamics of antiferromagnetic pseudospin has been experimentally demonstrated and, in particular, an observation of the magnon Hanle effect has been reported. We here expand the magnonic spin transport description by explicitly taking into account contributions of finite-spin low-energy magnons. In our experiments we realize the spin injection and detection process by two platinum strips and investigate the influence of the Pt strips on the generation and diffusive transport of magnons in films of the antiferromagnetic insulator hematite. For both a 15 and a $100 n m$ thick film, we find a distinct signal caused by the magnon Hanle effect. However, the magnonic spin signal exhibits clear differences in both films. In contrast to the thin film, for the thicker one, we observe an oscillating behavior in the high magnetic field range as well as an additional offset signal in the low magnetic field regime. We attribute this offset signal to the presence of finite-spin low-energy magnons.

Received 7 December 2021
Revised 4 March 2022
Accepted 14 March 2022

DOI:https://doi.org/10.1103/PhysRevB.105.094440

Physics Subject Headings (PhySH)

Magnetism Spintronics

Antiferromagnets Magnetic systems Nanostructures Thin films

Film deposition Magnetic techniques Methods in magnetism Methods in transport

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Janine Gückelhorn ^1,2,*, Akashdeep Kamra ^3,†, Tobias Wimmer^1,2, Matthias Opel ¹, Stephan Geprägs ¹, Rudolf Gross ^1,2,4, Hans Huebl ^1,2,4, and Matthias Althammer ^1,2,‡

¹Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany
²Physik-Department, Technische Universität München, 85748 Garching, Germany
³Condensed Matter Physics Center (IFIMAC) and Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, 28049 Madrid, Spain
⁴Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany

^*janine.gueckelhorn@wmi.badw.de
^†akashdeep.kamra@uam.es
^‡matthias.althammer@wmi.badw.de

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Vol. 105, Iss. 9 — 1 March 2022

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Images

Figure 1
Device schematic for nonlocal magnon spin transport experiments. A $z$ -polarized magnon spin and pseudospin currents are injected into and detected from the antiferromagnetic insulator (AFI) using two spatially separated heavy metal (HM) electrodes. The AFI is considered thin along the $x$ direction and infinite along the $z$ direction.
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Figure 2
Schematic depiction of the low- $k$ magnonic dispersion of the two eigenmodes at zero applied magnetic field in hematite [49]. The lower branch contributes to the magnon transport due to the finite spin of the corresponding magnons.
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Figure 3
Equivalent circuit diagram for magnonic spin injection and detection. A current driven through the injector lead generates a spin accumulation $μ_{inj}$ in the metal. This, in turn, injects a spin current $I_{inj}^{s} \approx μ_{inj} / R_{int, inj}^{s}$ into the AFI which propagates and evolves as pseudospin transport, not described via a simple resistor. The detected spin current $I_{\det}^{s} \approx μ_{s z} (z) / R_{int, \det}^{s}$ senses the magnon spin chemical potential at the detector location.
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Figure 4
(a) Sketch of the sample configuration, the electrical wiring scheme, and the coordinate system with the in-plane rotation angle $φ$ of the applied magnetic field $μ_{0} H$ . The canting of the magnetic sublattices $m_{1}$ and $m_{2}$ is illustrated. The corresponding net moment $m_{net}$ is aligned along the applied magnetic field $μ_{0} H$ , while the Néel order parameter $n$ is perpendicular to $μ_{0} H$ . (b) Amplitude of the electrically excited magnon spin signal $Δ R_{\det}^{el}$ as a function of the magnetic field strength for devices on a $t_{m} = 15 n m$ thin film with a center-to-center distance of $d = 1000 n m$ and $d = 700 n m$ , respectively, at $T = 200 K$ . The gray lines are fits using Eqs. (5, 6, 7, 8, 9, 10).
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Figure 5
(a) Angle-dependent magnon spin signal $R_{\det}^{el} \propto V_{\det}^{el} / I_{inj}$ of electrically induced magnons measured at the detector with an injector-detector distance of $d = 800 n m$ for $T = 200 K$ and various magnetic field magnitudes for the $100 n m$ thick hematite film. The solid gray lines are fits to a simple $Δ R_{\det}^{el} {sin}^{2} (φ)$ function. (b) Electrically induced magnon spin signal amplitudes $Δ R_{\det}^{el}$ , extracted from the angle-dependent measurements in (a), as a function of temperature $T$ for several injector-detector distances $d$ . The solid lines are guides to the eye. The data are measured at an external field strength of $μ_{0} H = 600 m T$ . (c) The amplitudes $Δ R_{\det}^{el}$ are plotted versus the distance $d$ for different temperatures $T$ at $μ_{0} H = 600 m T$ . The solid lines are fits to Eq. (19). (d) The extracted magnon diffusion length $l_{m}$ is plotted as a function of $T$ for $μ_{0} H = 600 m T$ as well as different higher magnetic field magnitudes.
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Figure 6
(a) Magnon spin signal amplitude $Δ R_{\det}^{el}$ of the electrically excited magnons as a function of the magnetic field magnitude $μ_{0} H$ , which is applied along $\hat{y}$ (cf. Fig. 4), for center-to-center distances $d = 800 n m$ and $d = 900 n m$ between injector and detector on a $t_{m} = 100 n m$ thick film measured at $T = 200 K$ . The inset shows a zoom-in on the oscillations for high magnetic fields. (b) $Δ R_{\det}^{el}$ plotted versus the magnetic field strength for a structure with a strip distance of $d = 800 n m$ for different temperatures. (c) Zoom-in on the oscillations for high magnetic fields for the data shown in (b). The curves are stacked by constant offsets for a better visibility of the minima and maxima of the oscillations. (d) Compensation field $μ_{0} H_{c}$ as a function of $T$ extracted from measurements of structures with varying $d$ .
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