Multiple magnetic ordering phenomena in multiferroic $o\text{\ensuremath{-}}\mathrm{HoMn}{\mathrm{O}}_{3}$

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Multiple magnetic ordering phenomena in multiferroic $o − HoMn O_{3}$

Y. W. Windsor, M. Ramakrishnan, L. Rettig, A. Alberca, T. Lippert, C. W. Schneider, and U. Staub

Phys. Rev. B 102, 214423 – Published 18 December 2020

Abstract

Orthorhombic $HoMn O_{3}$ is a multiferroic in which Mn antiferromagnetic order induces ferroelectricity. A second transition occurs within the multiferroic phase, in which a strong enhancement of the ferroelectric polarization occurs concomitantly to antiferromagnetic ordering of Ho $4 f$ magnetic moments. Using the element selectivity of resonant x-ray diffraction, we study the magnetic order of the Mn $3 d$ and Ho $4 f$ moments. We explicitly show that the Mn magnetic order is affected by the Ho $4 f$ magnetic ordering transition. Based on the azimuthal dependence of the $(0 q 0)$ and $(0 1 - q 0)$ magnetic reflections, we suggest that the Ho $4 f$ order resembles an $a c$ cycloid. Using nonresonant diffraction, we show that the magnetically induced polar lattice distortion is unaffected by the Ho ordering, suggesting a mechanism through which the Ho order affects ferroelectric polarization without affecting the lattice in the same manner as the Mn order.

Received 3 August 2020
Revised 9 November 2020
Accepted 30 November 2020

DOI:https://doi.org/10.1103/PhysRevB.102.214423

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. Open access publication funded by the Max Planck Society.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Antiferromagnets Multiferroics

X-ray diffraction X-ray resonant magnetic scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Y. W. Windsor ^1,2, M. Ramakrishnan ¹, L. Rettig^1,2, A. Alberca ¹, T. Lippert^3,4, C. W. Schneider ³, and U. Staub ¹

¹Swiss Light Source, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland
²Department of Physical Chemistry, Fritz-Haber-Institute of the Max Planck Society, Faradayweg 4-6, Berlin 14915, Germany
³Laboratory for Multiscale Materials Experiments, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland
⁴Department of Chemistry and Applied Biosciences, Laboratory of Inorganic Chemistry, ETH Zurich, Switzerland

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Vol. 102, Iss. 21 — 1 December 2020

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Figure 1
Polarization dependence of a crystal of $HoMn O_{3}$ , adapted from Ref. [9]. Similar behavior is shown for a polycrystalline sample in Ref. [10].
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Figure 2
Experimental geometry of the RXD experiment. The scattering plane contains the momentum transfer $Q$ and the directions of the incoming and outgoing beam, $\vec{k}$ and ${\vec{k}}^{'}$ , respectively. $θ$ is the Bragg angle and $χ_{0}$ is the angle between $Q$ and the film surface normal $\hat{n}$ . $Ψ$ is the angle of azimuthal sample rotation around the $Q$ direction.
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Figure 3
(a) Scans along (0 $k$ 0) taken at 9 K using photons energies corresponding to the Mn $L_{3}$ and the Ho $M_{5}$ edges (642.5 and 1349.75 eV, respectively). The $(0 q 0)$ reflection is observed at both energies, and the $(0 1 - q 0)$ is observed only for Ho. A dashed line marks the Mn curve beyond the Ewald sphere. Inset: energy dependence of the $(0 q 0)$ reflection at the Mn $L$ edges at 10 and at 18 K (above and below $T_{Ho 1}$ ), with intensities normalized to the peak of the $L_{3}$ . Panels (b) and (c) present a temperature dependence of scans along (0 $k$ 0), measured at the Mn $L_{3}$ and Ho $M_{5}$ edges, respectively. A dashed line is drawn at $T_{Ho 1}$ . All data were taken with $π$ polarized light and $Ψ = 0^{\circ}$ . The reflectivity background was removed for clarity.
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Figure 4
Temperature dependencies. (a) The integrated intensity from specular magnetic reflections measured at the Mn and Ho edges. (b) The integrated intensity from off-specular the reflections observed only at the Ho $M_{5}$ edge (1348 eV). (c) Peak position of the $(0 q 0)$ reflection measured at both edges. (d) Correlation lengths calculated from the widths of the magnetic reflections. Values for the off-specular reflections are given on the right hand axis. All data were collected with $π$ polarized incoming light at $Ψ = 0^{\circ}$ .
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Figure 5
Azimuthal angle dependence of specular magnetic reflections: (a) the $(0 q 0)$ at the Mn $L_{3}$ edge (18 K); (b) the $(0 q 0)$ at the Ho $M_{5}$ edge (18 K; very similar results were obtained at ∼10 K); (c) the $(0 1 - q 0)$ at the Ho $M_{5}$ edge (∼10 K). Dark and light markers represent $π$ and $σ$ polarized incoming light, respectively. All data are normalized to the sum of $π$ and $σ$ intensities. Solid lines are calculations of $c$ axis magnetic moments (see Appendix pp2).
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Figure 6
Temperature dependence of the integrated intensity of structural reflections, taken from a 240-nm-thick [010]-oriented film. The (033) reflection corresponds to the left axis, the (022) corresponds to the right axis. Integrated intensity values are directly comparable, and all diffracted intensities were corrected for the polarization factor and for variations in the scattering volume due to sample rotation.
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Physical Review B

covering condensed matter and materials physics

Multiple magnetic ordering phenomena in multiferroic $o − HoMn O_{3}$

Y. W. Windsor, M. Ramakrishnan, L. Rettig, A. Alberca, T. Lippert, C. W. Schneider, and U. Staub

Phys. Rev. B 102, 214423 – Published 18 December 2020

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Physical Review B

covering condensed matter and materials physics

Multiple magnetic ordering phenomena in multiferroic o−HoMnO3

Y. W. Windsor, M. Ramakrishnan, L. Rettig, A. Alberca, T. Lippert, C. W. Schneider, and U. Staub

Phys. Rev. B 102, 214423 – Published 18 December 2020

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Multiple magnetic ordering phenomena in multiferroic $o − HoMn O_{3}$