Incommensurate magnetic orders and topological Hall effect in the square-net centrosymmetric ${\mathrm{EuGa}}_{2}{\mathrm{Al}}_{2}$ system

Incommensurate magnetic orders and topological Hall effect in the square-net centrosymmetric ${EuGa}_{2} {Al}_{2}$ system

Jaime M. Moya, Shiming Lei, Eleanor M. Clements, Caitlin S. Kengle, Stella Sun, Kevin Allen, Qizhi Li, Y. Y. Peng, Ali A. Husain, Matteo Mitrano, Matthew J. Krogstad, Raymond Osborn, Anand B. Puthirath, Songxue Chi, L. Debeer-Schmitt, J. Gaudet, P. Abbamonte, Jeffrey W. Lynn, and E. Morosan

Phys. Rev. Materials 6, 074201 – Published 7 July 2022

Abstract

Neutron diffraction on the centrosymmetric square-net magnet ${EuGa}_{2} {Al}_{2}$ reveals multiple incommensurate magnetic states (AFM1, 2, 3) in zero field. In applied field, a new magnetic phase (A) is identified from magnetization and transport measurements, bounded by two of the $μ_{0} H = 0$ incommensurate magnetic phases (AFM1, helical, and AFM3, cycloidal) with different moment orientations. Moreover, magnetotransport measurements indicate the presence of a topological Hall effect, with maximum values centered in the A phase. Together, these results render ${EuGa}_{2} {Al}_{2}$ a material with noncoplanar or topological spin texture in applied field. X-ray diffraction reveals an out-of-plane (OOP) charge density wave (CDW) below $T_{CDW} \sim 50$ K while the magnetic propagation vector lies in plane below $T_{N} = 19.5$ K. Together these data point to a new route to realizing in-plane noncollinear spin textures through an OOP CDW. In turn, these noncollinear spin textures may be unstable against the formation of topological spin textures in an applied field.

Received 14 December 2021
Accepted 9 June 2022

DOI:https://doi.org/10.1103/PhysRevMaterials.6.074201

Physics Subject Headings (PhySH)

Charge density waves Exotic phases of matter Hall effect Magnetic phase transitions Magnetotransport Symmetry protected topological states Topological materials

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Jaime M. Moya ^1,2, Shiming Lei ^2,*, Eleanor M. Clements ³, Caitlin S. Kengle ⁴, Stella Sun ⁴, Kevin Allen ², Qizhi Li⁵, Y. Y. Peng ⁵, Ali A. Husain ⁶, Matteo Mitrano ⁷, Matthew J. Krogstad⁸, Raymond Osborn⁸, Anand B. Puthirath ⁹, Songxue Chi ¹⁰, L. Debeer-Schmitt¹⁰, J. Gaudet^3,11, P. Abbamonte⁴, Jeffrey W. Lynn ³, and E. Morosan ^2,†

¹Applied Physics Graduate Program, Smalley-Curl Institute, Rice University, Houston, Texas 77005, USA
²Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
³NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
⁴Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
⁵International Center for Quantum Materials, School of Physics, Peking University, CN-100871 Beijing, China
⁶Department of Physics and Astronomy and Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
⁷Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
⁸Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
⁹Department of Materials Science and NanoEngineering, Rice University, Houston, Texas 77005, USA
¹⁰Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
¹¹Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20742-2215, USA

^*sl160@rice.edu
^†em11@rice.edu

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Figure 1
Structure of ${EuGa}_{2} {Al}_{2}$ and low-temperature magnetic transitions. (a) and (b) Top view and side view of ${EuGa}_{2} {Al}_{2}$ structure. Isothermal (c) magnetization $M$ and (d) resistivity $ρ_{x x}$ measured between $T = 2$ K (dark purple) and 20.5 K (light pink) with magnetic field $H ∥ c$ . (e) $M$ measured at $T = 2$ K (left axis, closed circles) and the corresponding differential magnetic susceptibility $d M$ / $d H$ (right axis, open circles). (f) $ρ_{x x}$ measured at $T = 2$ K (left axis, closed diamonds) and the corresponding derivative $d ρ_{x x}$ / $d H$ (right axis, open diamonds). (g) The magnetic phase diagram constructed by local maxima in $d M$ / $d H$ obtained from data in (c) (circles) and $d ρ_{x x}$ / $d H$ from data in (e) (diamonds) together with the contour map of $ρ_{y x}^{T}$ established from Fig. 5 with current $j ∥ a$ .
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Figure 2
Magnetic neutron diffraction for ${EuGa}_{2} {Al}_{2}$ in the ( $h, 0, l$ ) scattering plane. (a) Contour map of the diffraction intensity around the incommensurate magnetic Bragg reflection, $Q = (\sim 0.8, 0, 1)$ gives modulation wave vector $\pm q_{inc}$ $(\sim 0.2, 0, 0)$ . Inset: High-resolution scan in the AFM2 regime shows substantial broadening due to scattering from two resolution-limited wave vectors in a mixed phase regime. Illustration of (b) helical and (c) cycloid magnetic phases of AFM1 and AFM3, respectively. (d) Satellites around the (2,0,0) fundamental Bragg peak approximately double in intensity from the AFM3 phase at 5 K to the AFM1 phase at 17 K, while (e) intensities of satellites at $Q = (\pm q_{inc}, 0, 8)$ remain essentially unchanged between AFM1 and AFM3 phases. Uncertainties, where indicated, represent one standard deviation.
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Figure 3
Temperature dependence on warming and cooling of the incommensurate magnetic peak(s) near $Q = (0.8, 0, 3)$ extracted using a single-Gaussian fit to the data at each temperature. Lines are guides to the eye. (a) The integrated intensity, proportional to the square of the order parameter, identifies three distinct phases. A simple mean-field fit gives a transition temperature of $T_{N} = 19.5 (2)$ K from the paramagnetic to AFM1 phase. (b) The wave vector peak position, $1 - q_{inc}$ , and (c) full width at half maximum. Uncertainties, where indicated, represent one standard deviation.
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Figure 4
Magnetic field dependence of the (a) integrated intensity and (b) position of the incommensurate wave vector, $q_{inc}$ , extracted from Gaussian fits of the SANS intensity versus $Q_{x}$ shown in Fig. S2 of the Supplemental Material [37]. The magnetic peak was unobservable at 3 T. Line is a guide to the eye. Error bars, where indicated, represent one standard deviation.
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Figure 5
Topological Hall effect in ${EuGa}_{2} {Al}_{2}$ . (a) Hall resistivity measurements measured between $T = 2$ K (dark purple) and 20.5 K (light pink) with $H ∥ c$ and current $j ∥ a$ . (b) A subset of the $ρ_{y x}$ data (symbols) at $T = 2$ K (purple), 10 K (magenta), and 20.5 K (pink). Solid lines are fits to Eq. (1) while dashed lines are fits to Eq. (2). The topological Hall resistivity $ρ_{y x}^{T}$ determined by subtracting the anomalous Hall resistivity $ρ_{y x}^{A}$ and normal Hall resistivity $R_{0} μ_{0} H$ from $ρ_{y x}$ using the resultant fits from (c) Eq. (1) or (d) Eq. (2) from $T = 2$ K (dark purple) to 20.5 K (light pink) in 0.5 K increments.
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Figure 6
XRD measurements in ${EuGa}_{2} {Al}_{2}$ . (a) Temperature-dependent line-profile cuts along $(1, 1, 2 \pm Δ L)$ for $8 \leq T \leq 120$ K, and (b) the temperature dependence of the order parameter defined as the integrated intensity of the peak with the background subtracted, located at $(1, 1, 2 + (-) q_{CDW})$ [left axis, open (closed) squares] and the temperature dependence of $q_{CDW}$ (right axis, diamonds). The vertical dashed lines at $T_{N}$ and $T_{CDW}$ are determined from thermodynamic and transport measurements. Uncertainties, where indicated, represent one standard deviation.
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Physical Review Materials

Incommensurate magnetic orders and topological Hall effect in the square-net centrosymmetric EuGa2Al2 system

Jaime M. Moya, Shiming Lei, Eleanor M. Clements, Caitlin S. Kengle, Stella Sun, Kevin Allen, Qizhi Li, Y. Y. Peng, Ali A. Husain, Matteo Mitrano, Matthew J. Krogstad, Raymond Osborn, Anand B. Puthirath, Songxue Chi, L. Debeer-Schmitt, J. Gaudet, P. Abbamonte, Jeffrey W. Lynn, and E. Morosan

Phys. Rev. Materials 6, 074201 – Published 7 July 2022

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Incommensurate magnetic orders and topological Hall effect in the square-net centrosymmetric ${EuGa}_{2} {Al}_{2}$ system