High-field depinned phase and planar Hall effect in the skyrmion host ${\mathrm{Gd}}_{2}{\mathrm{PdSi}}_{3}$

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High-field depinned phase and planar Hall effect in the skyrmion host ${Gd}_{2} {PdSi}_{3}$

Max Hirschberger, Taro Nakajima, Markus Kriener, Takashi Kurumaji, Leonie Spitz, Shang Gao, Akiko Kikkawa, Yuichi Yamasaki, Hajime Sagayama, Hironori Nakao, Seiko Ohira-Kawamura, Yasujiro Taguchi, Taka-hisa Arima, and Yoshinori Tokura

Phys. Rev. B 101, 220401(R) – Published 1 June 2020

Abstract

For the skyrmion-hosting intermetallic ${Gd}_{2} {PdSi}_{3}$ with centrosymmetric hexagonal lattice and triangular net of rare earth sites, we report a thorough investigation of the magnetic phase diagram. Our work reveals a magnetic phase with an isotropic value of the critical field for all orientations, where the magnetic ordering vector $q$ is depinned from its preferred directions in the basal plane. The bulk nature of the skyrmion lattice and of other magnetic phases was evidenced by specific-heat measurements. Resistivity anisotropy, likely originating from partial gapping of the density of states along $q$ in this Ruderman-Kittel-Kasuya-Yosida magnet, is picked up via the planar Hall effect (PHE). The PHE confirms the single- $q$ nature of the magnetic order when the field is in the hexagonal plane, and allows one to detect the preferred directions of $q$ . Several scenarios for the depinned phase, such as tilted conical order, are discussed on the basis of the data.

Received 3 February 2020
Revised 10 April 2020
Accepted 28 April 2020

DOI:https://doi.org/10.1103/PhysRevB.101.220401

Physics Subject Headings (PhySH)

Frustrated magnetism Magnetotransport RKKY interaction Skyrmions

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Max Hirschberger ^1,2,*, Taro Nakajima^1,2,†, Markus Kriener², Takashi Kurumaji ^2,‡, Leonie Spitz^2,3,§, Shang Gao^2,¶, Akiko Kikkawa², Yuichi Yamasaki^4,5, Hajime Sagayama⁶, Hironori Nakao⁶, Seiko Ohira-Kawamura ⁷, Yasujiro Taguchi², Taka-hisa Arima⁸, and Yoshinori Tokura ^1,2,9

¹Department of Applied Physics and Quantum-Phase Electronics Center (QPEC), The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
²RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
³Physik-Department, Technical University of Munich, 85748 Garching, Germany
⁴Research and Services Division of Materials Data and Integrated System (MaDIS), National Institute for Materials Science (NIMS), Tsukuba, Ibaraki 305-0047, Japan
⁵PRESTO, Japan Science and Technology Agency (JST), Kawaguchi, Saitama 332-0012, Japan
⁶Institute of Materials Structure Science, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan
⁷Materials and Life Science Division, J-PARC Center, Tokai, Ibaraki 319-1195, Japan
⁸Department of Advanced Materials Science, University of Tokyo, Kashiwa, Chiba 277-8561, Japan
⁹Tokyo College, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan

^*hirschberger@ap.t.u-tokyo.ac.jp
^†Present address: Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8561, Japan.
^‡Present address: Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
^§Present address: Physik-Department E51, Technische Universität München, D-85748 Garching, Germany.
^¶Present address: Materials Science & Technology Division and Neutron Science Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA.

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Vol. 101, Iss. 22 — 1 June 2020

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Figure 1
(a),(b) DC susceptibility $χ_{DC} = \partial M / \partial H$ on a logarithmic scale shown as a function of temperature $T$ and $H ∥ c$ . Phases IC-1 (meron-antimeron lattice M-AM), skyrmion lattice SkL, IC-2 (fanlike), DP (depinned high-field phase), and FA-FM (field-aligned ferromagnet) are indicated in these panels and illustrated in (f)–(h), where red (blue) colors correspond to moment up (down). To our knowledge, phase DP was not reported in previous work. (c) Example of raw data used to construct panels (a) and (b), with a sequence of phase transitions indicated by red triangles. Note the logarithmic $y$ axis. (d) $π - σ$ intensity observed in resonant elastic x-ray scattering (REXS) at the Gd- $L_{2}$ edge with HK0 scattering plane and horizontal geometry. While incommensurate magnetic order with $q = (0.14, 0, 0)$ could be detected in phase IC-2, no signal appears at this position in phase DP (magenta curve). (e) Resistivity $ρ_{x x}$ as a function of $T$ for different values of $μ_{0} H$ . The corresponding values for $H_{int}$ are calculated at $T = 2 K$ . The data show sharp kinks at the onset of long-range order (black open triangles).
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Figure 2
Specific heat of ${Gd}_{2} {PdSi}_{3}$ . The boundaries of IC-2 and DP were marked by black open triangles, the upper boundary of IC-1 by a black disk, and the onset of phase SkL by a red square. The inset amplifies the curve recorded at $μ_{0} H = 0.9 T$ ( $μ_{0} H_{int} \sim 0.7 T$ ), confirming that SkL is a thermodynamic phase. Note the characteristic two-step ordering in $H = 0$ .
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Figure 3
(a)–(c) Phase transitions for $H$ along three high-symmetry directions, with the onset region of phase DP highlighted in red shading. Solid lines mark increasing, dashed lines decreasing $H$ . (d),(e) Phase diagram as constructed from the derivative of longitudinal resistivity $μ_{0}^{- 1} \partial ρ_{x x} / \partial H$ . Insets depict the geometry of the respective rotation experiment. The dip in the signal around $μ_{0} H_{int} = 3.5 T$ indicates the boundary between phases IC-2 and DP. The boundary remains sharp when rotating in the $c - a$ plane, but is washed out for $H$ close to $a^{*}$ . Panels (f) and (g) illustrate the proposed nature of the phase boundary for in-plane $H$ : $q$ realigns only for $H ∥ a$ , leading to a sharp first-order transition in configuration (f). Blue shaded areas mark the rotation plane of $H$ , and the white cone describes the spin arrangement in the field-polarized spiral state.
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Figure 4
(a)–(d) Planar Hall effect after field cooling for selected values of $H$ . Insets of (a): alignment of $q$ and the electrical current density $J$ at various $φ = ∠ (H, J)$ . Upper right inset: Geometry of this experiment, where $H$ is rotated in the plane of the light blue disk, i.e., the hexagonal basal plane ( $a - b$ plane). (e) Phase diagram for $H ∥ a$ from magnetization measurements, analogous to Fig. 1. (f) $H$ dependence of the PHE amplitude at selected $φ$ values. The red shaded area indicates the regime of transition towards phase DP.
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Physical Review B

covering condensed matter and materials physics

High-field depinned phase and planar Hall effect in the skyrmion host ${Gd}_{2} {PdSi}_{3}$

Max Hirschberger, Taro Nakajima, Markus Kriener, Takashi Kurumaji, Leonie Spitz, Shang Gao, Akiko Kikkawa, Yuichi Yamasaki, Hajime Sagayama, Hironori Nakao, Seiko Ohira-Kawamura, Yasujiro Taguchi, Taka-hisa Arima, and Yoshinori Tokura

Phys. Rev. B 101, 220401(R) – Published 1 June 2020

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Physical Review B

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High-field depinned phase and planar Hall effect in the skyrmion host Gd2PdSi3

Max Hirschberger, Taro Nakajima, Markus Kriener, Takashi Kurumaji, Leonie Spitz, Shang Gao, Akiko Kikkawa, Yuichi Yamasaki, Hajime Sagayama, Hironori Nakao, Seiko Ohira-Kawamura, Yasujiro Taguchi, Taka-hisa Arima, and Yoshinori Tokura

Phys. Rev. B 101, 220401(R) – Published 1 June 2020

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High-field depinned phase and planar Hall effect in the skyrmion host ${Gd}_{2} {PdSi}_{3}$