Magnetism in the axion insulator candidate ${\mathrm{Eu}}_{5}{\mathrm{In}}_{2}{\mathrm{Sb}}_{6}$

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Magnetism in the axion insulator candidate ${Eu}_{5} {In}_{2} {Sb}_{6}$

M. C. Rahn, M. N. Wilson, T. J. Hicken, F. L. Pratt, C. Wang, F. Orlandi, D. D. Khalyavin, P. Manuel, L. S. I. Veiga, A. Bombardi, S. Francoual, P. Bereciartua, A. S. Sukhanov, J. D. Thompson, S. M. Thomas, P. F. S. Rosa, T. Lancaster, F. Ronning, and M. Janoschek

Phys. Rev. B 109, 174404 – Published 2 May 2024

Abstract

${Eu}_{5} {In}_{2} {Sb}_{6}$ is a member of a family of orthorhombic nonsymmorphic rare-earth intermetallics that combines large localized magnetic moments and itinerant exchange with a low carrier density and perpendicular glide planes. This may result in special topological crystalline (wallpaper fermion) or axion insulating phases. Recent studies of ${Eu}_{5} {In}_{2} {Sb}_{6}$ single crystals have revealed colossal negative magnetoresistance and multiple magnetic phase transitions. Here, we clarify this ordering process using neutron scattering, resonant elastic x-ray scattering, muon spin-rotation, and magnetometry. The nonsymmorphic and multisite character of ${Eu}_{5} {In}_{2} {Sb}_{6}$ results in coplanar noncollinear magnetic structures with an Ising-like net magnetization along the $a$ axis. A reordering transition, attributable to competing ferro- and antiferromagnetic couplings, manifests as the onset of a second commensurate Fourier component. In the absence of spatially resolved probes, the experimental evidence for this low-temperature state can be interpreted either as an unusual double- $q$ structure or in a phase separation scenario. The net magnetization produces variable anisotropic hysteretic effects which also couple to charge transport. The implied potential for functional domain physics and topological transport suggests that this structural family may be a promising platform to implement concepts of topological antiferromagnetic spintronics.

Received 28 December 2023
Revised 4 March 2024
Accepted 18 March 2024

DOI:https://doi.org/10.1103/PhysRevB.109.174404

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Magnetic order Magnetic phase transitions Topological materials

Muon spin resonance Neutron diffraction Resonant elastic x-ray scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

M. C. Rahn ^1,2,*, M. N. Wilson^3,4, T. J. Hicken ^3,5, F. L. Pratt⁶, C. Wang⁵, F. Orlandi ⁶, D. D. Khalyavin⁶, P. Manuel⁶, L. S. I. Veiga^7,8, A. Bombardi⁸, S. Francoual ⁹, P. Bereciartua⁹, A. S. Sukhanov¹, J. D. Thompson², S. M. Thomas², P. F. S. Rosa², T. Lancaster ³, F. Ronning², and M. Janoschek^2,10,11,†

¹Institute for Solid State and Materials Physics, Technical University of Dresden, 01062 Dresden, Germany
²Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
³Department of Physics, Durham University, South Road, Durham, DH1 3LE, United Kingdom
⁴Memorial University, Department of Physics and Physical Oceanography, St. John's, NL, A1B 3X7, Canada
⁵Laboratory for Muon-Spin Spectroscopy, Paul Scherrer Institute, CH-5232 Villigen, Switzerland
⁶ISIS Facility, STFC, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, OX11 0QX, United Kingdom
⁷London Centre for Nanotechnology and Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
⁸Diamond Light Source Ltd., Didcot OX11 0DE, United Kingdom
⁹Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
¹⁰Laboratory for Neutron and Muon Instrumentation, Paul Scherrer Institute, CH-5232 Villigen, Switzerland
¹¹Physik-Institut, Universität Zürich, CH-8057 Zürich, Switzerland

^*marein.rahn@tu-dresden.de
^†marc.janoschek@psi.ch

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Vol. 109, Iss. 17 — 1 May 2024

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Figure 1
(a) The orthorhombic unit cell and $P b a m$ symmetries of ${Eu}_{5} {In}_{2} {Sb}_{6}$ . The perpendicular glide planes are highlighted in blue and red. (b) Solid arrows show the spin arrangement inferred for the $Γ magnetic$ component, which forms at $T_{N} = 14.5$ K. The structure is collinear within the uncertainty of the neutron diffraction data. Shaded arrows illustrate tilts away from this collinear configuration, which creates a net magnetization. (c) Corresponding views of the $Z$ magnetic component, which originates below $T_{Z} = 7.5$ K. The x-ray and neutron scattering data do not allow the distinction between a double- $q$ state and magnetic phase separation. Both $Γ$ and $Z$ components are described by the same magnetic basis vectors, which generally add to a per-layer magnetization along the $a$ axis. For the $Γ$ component, this results in a spontaneous macroscopic magnetization, while in the $Z$ component it is compensated by alternating stacking.
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Figure 2
(a) Magnetic neutron powder diffraction at 1.5 K and 10 K. The nuclear intensity (at 25 K) has been subtracted from the data [13]. (b) Temperature dependence of REXS intensities associated with the propagation vectors of the Ising weakly ferromagnetic $Γ order$ and the compensated antiferromagnetic $Z$ component. Below $T_{Z} = 7.5$ K, $Γ$ and $Z$ either coexist by phase separation or as a double- $q$ structure. (c) The consecutive second-order phase transitions at 14.5 K and 7.5 K observed in heat capacity ( $C / T$ ). (d) The anisotropic magnetic susceptibility $χ^{a / b / c} (T)$ at 100 mT applied along the principal axes. Note the small spontaneous magnetization of $χ^{a}$ in the $Γ state$ and the change in easy axis below $T_{Z}$ .
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Figure 3
(a) Static internal fields (top) and corresponding relaxation rates (bottom) determined by zero-field continuous-source $μ SR$ (GPS instrument). Solid lines are a guide to the eye. We attribute different components of the $μ SR$ asymmetry to muon stopping sites that are more sensitive to fields within (intra) and between (inter) the layers. The inset shows an example of the $μ SR$ asymmetry measured at GPS (3 K, typical fit indicated by a red line). (b) Dynamic relaxation rates determined from the decay of the zero-field $μ SR$ asymmetry up to 20 $μ s$ . Circles and triangles mark values inferred from data measured at continuous (GPS) and pulsed source (EMU) muon instruments, respectively. The inset shows a typical fit in this time window, including both continuous source (black) and pulsed source data (blue).
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Figure 4
(a) Illustration of the magnetic phase separation scenario below $T_{Z}$ . Each layer of ${Eu}_{5} {In}_{2} {Sb}_{6}$ is represented by an arrow indicating the direction of the Ising (per-layer) net magnetic moment. Up (down) domains of the $q_{Γ}$ state are colored blue (red). Interfaces between $Γ$ domains may provide natural nucleation points of the $Z$ state (white). $Γ domains$ with an even $(2 n)$ number of layers prevent the formation of a homogeneous $Z$ ordered state. They leave behind antiferromagnetic domain walls that carry a net magnetic moment and could also contribute to hysteretic effects. (b) Sketch of the thermal evolution of an ${Eu}_{5} {In}_{2} {Sb}_{6}$ slab, colored in analogy to (a). (c) Field-cooled and zero-field cooled (FC/ZFC) curves of the magnetic susceptibility measured with a weak (20 Oe) bias field along the $a$ axis. Magnetization reversal and domain flip transitions [indicated by inset illustrations] provide a tentative explanation for these unusual characteristics.
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Figure 5
(a) Pulsed-source $μ SR$ measurements of the dynamic relaxation rates $λ_{intra}^{dyn}$ and $λ_{inter}^{dyn}$ indicate an onset of short-ranged magnetic correlations at $T^{*} \approx 35$ K. This is consistent with the interpretation in terms of interacting magnetic polarons proposed in Ref. [9]. (b) On the same temperature scale, the resistance $R$ (current $I ∥ c$ , log scale) begins to diverge from activated behavior. (c) Detailed view of the resistance within the magnetically ordered phase (linear scale). We identify three regimes of charge transport (I, II, III).
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Figure 6
Characteristic anisotropic hysteretic phenomena in the three regimes of charge transport (I, II, III). (a)–(d) Polar plots of the resistance $R$ at 1 T (current $I ∥ \hat{c}$ ) for varying field directions $ϕ_{H}$ in the $a$ – $b$ plane. The three regimes differ not only in the magnitude of $R$ [cf. Fig. 4], but also in their anisotropy. (e)–(h) Respective hysteretic components in the magnetization $Δ M (H)$ for fields along $a$ and $b$ . Linear slopes have been subtracted from each curve. (i)–(l) Corresponding hysteretic contributions $Δ R (H) = R (H_{↑}) - R (H_{↓})$ to the resistivity. Note both the quantitative and qualitative variation between the regimes. In regime II (3.0 $K \sim 10$ K), $Δ R (H)$ has a positive slope and is concomitant with $Δ M$ . It can therefore be associated with the (re)orientation of magnetic domains of the $Γ magnetic$ order.
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Physical Review B

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Magnetism in the axion insulator candidate ${Eu}_{5} {In}_{2} {Sb}_{6}$

M. C. Rahn, M. N. Wilson, T. J. Hicken, F. L. Pratt, C. Wang, F. Orlandi, D. D. Khalyavin, P. Manuel, L. S. I. Veiga, A. Bombardi, S. Francoual, P. Bereciartua, A. S. Sukhanov, J. D. Thompson, S. M. Thomas, P. F. S. Rosa, T. Lancaster, F. Ronning, and M. Janoschek

Phys. Rev. B 109, 174404 – Published 2 May 2024

Abstract

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Physical Review B

covering condensed matter and materials physics

Magnetism in the axion insulator candidate Eu5In2Sb6

M. C. Rahn, M. N. Wilson, T. J. Hicken, F. L. Pratt, C. Wang, F. Orlandi, D. D. Khalyavin, P. Manuel, L. S. I. Veiga, A. Bombardi, S. Francoual, P. Bereciartua, A. S. Sukhanov, J. D. Thompson, S. M. Thomas, P. F. S. Rosa, T. Lancaster, F. Ronning, and M. Janoschek

Phys. Rev. B 109, 174404 – Published 2 May 2024

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Magnetism in the axion insulator candidate ${Eu}_{5} {In}_{2} {Sb}_{6}$