Field-sweep-rate and time dependence of transverse resistivity anomalies in ultrathin $\mathrm{SrRu}{\mathrm{O}}_{3}$ films

Field-sweep-rate and time dependence of transverse resistivity anomalies in ultrathin $SrRu O_{3}$ films

Daisuke Kan, Takahiro Moriyama, and Yuichi Shimakawa

Phys. Rev. B 101, 014448 – Published 30 January 2020

Abstract

We investigated the field-sweep-rate and time dependence of the transverse resistivity anomalies in ultrathin $SrRu O_{3}$ epitaxial thin films the behaviors of which resemble what has been claimed to be the topological Hall effect. We find that the magnitudes of the anomalies are independent of the field sweep rate, while the magnetic field at which the anomalies appear $(H_{hump})$ and the coercive field $(H_{c})$ exhibit identical sweep-rate dependence. We also show that the transverse resistivity under a fixed external magnetic field exhibits transient behavior, eventually (≈5000 s) approximating the value of the anomalous Hall resistivity that is obtained after the magnetization reversal processes are completed. These results indicate that $H_{c}$ is inhomogeneous within the films and activation energies of the magnetization reversal at $H_{hump}$ and $H_{c}$ are identical. The observed field-sweep-rate and time dependence of the transverse resistivity anomalies can be understood in the framework of conventional magnetic switching dynamics, and topological interpretation would not be necessarily taken into account. Our results are in line with a model in which inhomogeneity of $H_{c}$ and anomalous Hall resistivity are responsible for the transverse resistivity anomalies in $SrRu O_{3}$ .

Received 22 September 2019
Revised 8 January 2020

DOI:https://doi.org/10.1103/PhysRevB.101.014448

Physics Subject Headings (PhySH)

Anomalous Hall effect Topological Hall effect

Ferromagnets Ruthenates

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Daisuke Kan ^1,*, Takahiro Moriyama ^1,†, and Yuichi Shimakawa ^1,2

¹Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan
²Integrated Research Consortium on Chemical Sciences, Uji, Kyoto 611-0011, Japan

^*dkan@scl.kyoto-u.ac.jp
^†mtaka@scl.kyoto-u.ac.jp

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Vol. 101, Iss. 1 — 1 January 2020

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Figure 1
(a) Schematic drawing of the magnetic field dependence of the magnetization M and the anomalous Hall resistivity $ρ_{AHE}$ for $SrRu O_{3}$ films in which the coercive field $(H_{c})$ and $ρ_{AHE}$ are inhomogeneous. The regions colored with orange in the film have large $H_{c}$ and negative anomalous Hall coefficient $(ξ)$ while the region colored blue has small $H_{c}$ and positive $ξ$ . (b) Expected variations of M-T and $ρ_{AHE}$ -T curves obtained at different field sweep rates.
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Figure 2
(a) Magnetic field dependence of the anomalous Hall resistivity $ρ_{AHE}$ for the 3.5-nm-thick $SrRu O_{3}$ film measure at various temperatures. Every loop in the figure has an offset of $0.2 μ Ω cm$ . (b) Anomalous Hall resistivity $ρ_{AHE}$ , hump resistivity $ρ_{hump}$ , coercive field $H_{c}$ , and hump field $H_{hump}$ plotted as functions of temperature. The definitions of $ρ_{hump}$ and $H_{hump}$ are provided in Fig. 1. We note that, at $T_{s}$ , $ρ_{AHE}$ becomes almost zero, which makes it difficult to determine $H_{c}$ in the $ρ_{AHE}$ -H curve.
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Figure 3
(a, c, e) Magnetic field dependence of the transverse resistivity measured with various field sweep rates $R_{H}$ at (a) 41 K, (c) 52 K, and (e) 60 K. (b, d, f) $R_{H}$ dependence of the hump resistivity $ρ_{hump}$ , hump field $H_{hump}$ , and coercive field $H_{c}$ at (b) 41 K, (d) 52 K, and (f) 60 K. In the bottom panels of (b), (d), and (f), the $H_{hump}$ and $H_{c}$ are normalized by those obtained with the sweep rate of 2 Oe/s and the dotted line shows the best fits to Eq. (1). The fitting parameters are summarized in Table 1. Note that at 52 K, where $ρ_{AHE}$ is almost zero, $H_{c}$ is difficult to extract from the $ρ_{AHE}$ -H curves and therefore the magnetic fields at which $ρ_{AHE}$ becomes $0.05 μ Ω cm$ (referred to as $H_{0.05}$ and $H_{0.05 - 2}$ ), are used for the fitting.
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Figure 4
(a) Time dependence of the transverse resistivity under the fixed magnetic field of −3247 Oe, which corresponds to the negative $H_{hump}$ and at which $ρ_{hump}$ is seen. The data were obtained at 41 K. The inset shows the diagram of the field sweeps and the definition of the time period $t_{H}$ used for measuring the time dependence of $ρ_{hump}$ . (b) Magnetic field dependence of the transverse resistivity obtained from the time dependent measurements with various $t_{H}$ . The inset shows the $t_{H}$ dependence of the positive $H_{hump}$ , which is extracted from the field dependence of the resistivity in (b).
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Figure 5
(a) Time dependence of the transverse resistivity under the negative $H_{hump}$ at 52 K. (b) Magnetic field dependence of the transverse resistivity at 52 K, including the data plotted in (a). (c) Time dependence of the transverse resistivity under the negative $H_{hump}$ at 60 K. (d) Magnetic field dependence of the transverse resistivity at 60 K, including the data plotted in (c). The inset shows the $t_{H}$ dependence of the positive $H_{hump}$ at 52 and 60 K.
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Physical Review B

covering condensed matter and materials physics

Field-sweep-rate and time dependence of transverse resistivity anomalies in ultrathin $SrRu O_{3}$ films

Daisuke Kan, Takahiro Moriyama, and Yuichi Shimakawa

Phys. Rev. B 101, 014448 – Published 30 January 2020

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Physical Review B

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Field-sweep-rate and time dependence of transverse resistivity anomalies in ultrathin SrRuO3 films

Daisuke Kan, Takahiro Moriyama, and Yuichi Shimakawa

Phys. Rev. B 101, 014448 – Published 30 January 2020

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Field-sweep-rate and time dependence of transverse resistivity anomalies in ultrathin $SrRu O_{3}$ films