Magnetic field induced reentrant multipolar ordering in the distorted kagome-lattice antiferromagnet ${\mathrm{Dy}}_{3}{\mathrm{Ru}}_{4}{\mathrm{Al}}_{12}$

Magnetic field induced reentrant multipolar ordering in the distorted kagome-lattice antiferromagnet ${Dy}_{3} {Ru}_{4} {Al}_{12}$

Isao Ishii, Takashi Suzuki, Alexander V. Andreev, Keisuke Mitsumoto, Koji Araki, Atsuhiko Miyata, Denis I. Gorbunov, Sergei Zherlitsyn, and J. Wosnitza

Phys. Rev. B 107, 205136 – Published 18 May 2023

Abstract

We report on ultrasonic and magnetocaloric-effect measurements of the hexagonal antiferromagnet ${Dy}_{3} {Ru}_{4} {Al}_{12}$ having a distorted kagome lattice. We observed a pronounced softening of the transverse modulus, $C_{44}$ , above 30 T applied along [100], indicating an as-yet-unidentified magnetic field induced phase transition. We determined the field-temperature phase diagrams using pulsed magnetic fields up to 55.2 T, applied along [100] and [001]. Optimizing crystal-electric-field parameters within the mean-field approximation, we conclude that the enhancement of the field induced phase-transition temperature is due to electric quadrupolar and magnetic octupolar mediated interactions. We propose that the order parameter of the magnetic field induced phase transitions is the electric quadrupole $O_{z x}$ , facilitated by octupole-mediated interactions.

Received 2 April 2023
Accepted 9 May 2023

DOI:https://doi.org/10.1103/PhysRevB.107.205136

Physics Subject Headings (PhySH)

Antiferromagnetism Elastic modulus Frustrated magnetism Orbital order Phase diagrams

Single crystal materials

Ultrasound techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Isao Ishii^* and Takashi Suzuki^†

Department of Quantum Matter, AdSE, Hiroshima University, Higashi-Hiroshima 739-8530, Japan

Alexander V. Andreev

FZU Institute of Physics, Czech Academy of Sciences, Na Slovance 2, 182 21 Prague, Czech Republic

Keisuke Mitsumoto

Liberal Arts and Sciences, Faculty of Engineering, Toyama Prefectural University, Imizu, Toyama 939-0398, Japan

Koji Araki

Department of Applied Physics, National Defense Academy, Yokosuka, Kanagawa 239-8686, Japan

Atsuhiko Miyata, Denis I. Gorbunov, Sergei Zherlitsyn, and J. Wosnitza

Hochfeld-Magnetlabor Dresden (HLD-EMFL) and Würzburg-Dresden Cluster of Excellence ct.qmat, Helmholtz-Zentrum Dresden-Rossendorf, 01328 Dresden, Germany

^*ish@hiroshima-u.ac.jp
^†tsuzuki@hiroshima-u.ac.jp

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Vol. 107, Iss. 20 — 15 May 2023

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Figure 1
Magnetic field dependences of (a) the transverse elastic modulus $C_{44}$ , (b) the ultrasound attenuation for $C_{44}$ at 10 K, and (c) the magnetocaloric effect for $H | | [100]$ in ${Dy}_{3} {Ru}_{4} {Al}_{12}$ . The vertical arrowheads indicate a phase transition. The temperatures given in each panel are the starting temperatures of the experiments. (d) $H - T$ phase diagram for $H | | [100]$ . The solid curves are guides for the eye. The bidirectional blue arrow indicates a first-order phase transition. PM and FIP represent the paramagnetic state and magnetic field induced phase, respectively.
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Figure 2
(a) Temperature dependences of the transverse elastic modulus $C_{44}$ at elevated magnetic fields in ${Dy}_{3} {Ru}_{4} {Al}_{12}$ . The vertical arrowheads indicate a phase transition. (b) $H - T$ phase diagram for $H | | [001]$ . The solid curves are guides for the eye. Bidirectional blue arrows indicate first-order phase transitions. Metamag., metamagnetic. (Note that from the careful ultrasonic measurements performed as part of this study, we corrected the phase boundary of FIP-III from the phase diagram previously reported [18].)
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Figure 3
(a) $4 f$ level scheme for ${Dy}_{3} {Ru}_{4} {Al}_{12}$ obtained from the CEF parameters listed in Table 1, where $Γ_{5}$ denotes the irreducible representation for the point symmetry $C_{2 v}$ . (b) Temperature dependence of the transverse elastic modulus $C_{44}$ . The red solid and blue dashed curves show the fit result and the background stiffness, respectively. (c) Temperature dependences of the inverse magnetic susceptibility measured at 1 T. (d) Magnetization curves at 2 K. The data are the same as the data previously reported [16]. Solid curves demonstrate the calculated results.
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Figure 4
(a) and (c) The calculated $H - T$ phase diagram for $H | | [100]$ (a) and $H | | [001]$ (c). The phase-transition temperature was evaluated using the spin and quadrupole exchange interactions with or without octupole-mediated interactions in the mean-field approximation, and it corresponds to the emergence of a spontaneous expectation value of $O_{z x}, 〈 O_{z x} 〉$ , in magnetic fields. Here, w/o $T_{z}^{k}$ , without $T_{z}^{k}$ . (b) and (d) The magnetic field dependences of the calculated CEF energies for $H | | [100]$ (b) and $H | | [001]$ (d) in the nonordered state. The two states of the ground-state doublet at zero field are depicted by the red solid curves. (e)–(g) Temperature dependences of the expectation values of $J_{x}, J_{z}, O_{y z}, O_{z x}, T_{z}^{α}$ , and $T_{z}^{β}$ at zero magnetic field (e) and a selected field of 15 T applied along [100] (f) and [001] (g). The spontaneous expectation values were normalized at 0.1 K.
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Physical Review B

covering condensed matter and materials physics

Magnetic field induced reentrant multipolar ordering in the distorted kagome-lattice antiferromagnet ${Dy}_{3} {Ru}_{4} {Al}_{12}$

Isao Ishii, Takashi Suzuki, Alexander V. Andreev, Keisuke Mitsumoto, Koji Araki, Atsuhiko Miyata, Denis I. Gorbunov, Sergei Zherlitsyn, and J. Wosnitza

Phys. Rev. B 107, 205136 – Published 18 May 2023

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Magnetic field induced reentrant multipolar ordering in the distorted kagome-lattice antiferromagnet Dy3Ru4Al12

Isao Ishii, Takashi Suzuki, Alexander V. Andreev, Keisuke Mitsumoto, Koji Araki, Atsuhiko Miyata, Denis I. Gorbunov, Sergei Zherlitsyn, and J. Wosnitza

Phys. Rev. B 107, 205136 – Published 18 May 2023

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Magnetic field induced reentrant multipolar ordering in the distorted kagome-lattice antiferromagnet ${Dy}_{3} {Ru}_{4} {Al}_{12}$