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Local atomic and magnetic structure of multiferroic (Sr,Ba)(Mn,Ti)O3

Braedon Jones, Christiana Z. Suggs, Elena Krivyakina, Daniel Phelan, V. Ovidiu Garlea, Omar Chmaissem, and Benjamin A. Frandsen
Phys. Rev. B 109, 024423 – Published 17 January 2024

Abstract

We present a detailed study of the local atomic and magnetic structure of the type-I multiferroic perovskite system (Sr,Ba)(Mn,Ti)O3 using x-ray and neutron pair distribution function (PDF) analysis, polarized neutron scattering, and muon spin relaxation (μSR) techniques. The atomic PDF analysis reveals widespread nanoscale tetragonal distortions of the crystal structure even in the paraelectric phase with average cubic symmetry, corresponding to incipient ferroelectricity in the local structure. Magnetic PDF analysis, polarized neutron scattering, and μSR likewise confirm the presence of short-range antiferromagnetic correlations in the paramagnetic state, which grow in magnitude as the temperature approaches the magnetic transition. We show that these short-range magnetic correlations coincide with a reduction of the tetragonal (i.e., ferroelectric) distortion in the average structure, suggesting that short-range magnetism can play an important role in magnetoelectric and/or magnetostructural phenomena even without genuine long-range magnetic order. The reduction of the tetragonal distortion scales linearly with the local magnetic order parameter, pointing to spontaneous linear magnetoelectric coupling in this system. These findings provide greater insight into the multiferroic properties of (Sr,Ba)(Mn,Ti)O3 and demonstrate the importance of investigating the local atomic and magnetic structure to gain a deeper understanding of the intertwined degrees of freedom in multiferroics.

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  • Received 9 October 2023
  • Revised 9 December 2023
  • Accepted 4 January 2024

DOI:https://doi.org/10.1103/PhysRevB.109.024423

©2024 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Braedon Jones1, Christiana Z. Suggs1, Elena Krivyakina2,3, Daniel Phelan3, V. Ovidiu Garlea4, Omar Chmaissem2,3, and Benjamin A. Frandsen1

  • 1Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602, USA
  • 2Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA
  • 3Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
  • 4Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

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Vol. 109, Iss. 2 — 1 January 2024

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Images

  • Figure 1
    Figure 1

    Phase diagram for Sr1xBaxMn1yTiyO3 as a function of temperature and barium content x. Compositions with x0.5 are synthesized with dilute amounts of Ti on the Mn site. Compiled from results published in Refs. [8, 11, 12]. PE = paraelectric; PM = paramagnetic; FE = ferroelectric; AFM = antiferromagnetic; MF = multiferroic.

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  • Figure 2
    Figure 2

    Temperature derivative of the magnetic susceptibility of Sr0.4Ba0.6Mn0.95Ti0.05O3 and Sr0.55Ba0.45MnO3 as a function of temperature. Maxima occur at 149 K and 193 K, respectively. The measurements were taken in a field of 1 T using a zero-field-cooling protocol.

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  • Figure 3
    Figure 3

    X-ray PDF data for Sr0.55Ba0.45MnO3 between 250 K and 490 K displayed over the range 1.5–10 Å (a) and 40–50 Å (b). The PDF patterns were collected in increments of 5 K and are offset vertically on the plot for clarity. For the viewing range at higher r, clear and abrupt changes are evident across the ferroelectric transition at 350 K (red PDF pattern). No abrupt changes are observed in the low-r viewing range.

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  • Figure 4
    Figure 4

    Color maps of the Pearson correlation coefficient for pairs of PDF data sets obtained from Sr0.55Ba0.45MnO3 at various temperatures. (a), (b) Correlation coefficients computed for PDF data in the range 1.5–21.5 Å using neutrons and x rays, respectively. Note the difference in temperature ranges for the two types of experiments. (c), (d) Same as (a), (b), except that the data range 41.5–61.5 Å was used. Vertical and horizontal dashed lines in (a) and (c) mark the temperatures at which neutron PDF data were collected. X-ray data were collected on a uniform temperature grid between 250 K and 500 K in steps of 5 K.

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  • Figure 5
    Figure 5

    Pearson correlation coefficient for Sr0.55Ba0.45MnO3 with respect to the x-ray PDF data collected at 250 K, corrected for thermal expansion as explained in the main text. Three different data ranges are used. The ferroelectric transition around 350 K is most evident for the highest r range but essentially invisible for the shortest data range, confirming that the local structure is already symmetry broken above TC.

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  • Figure 6
    Figure 6

    Representative neutron PDF fit for Sr0.55Ba0.45MnO3 at 180 K. The blue symbols show the experimental data, the red curve the best fit, and the green curve the fit residual, offset vertically for clarity.

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  • Figure 7
    Figure 7

    (a) Tetragonal distortion c/a in Sr0.55Ba0.45MnO3 as a function of temperature and fitting range, as determined by PDF boxcar fits to the neutron PDF data. The horizontal axis indicates the midpoint of the 20 Å fitting range rmid. Brighter (darker) colors correspond to a greater (lesser) tetragonal distortion. Linear interpolation was used between discrete (rmid,T) points. (b) Lattice parameters extracted from the fits with rmid=15.5 Å and 28.5 Å, corresponding to the vertical dashed lines in (a).

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  • Figure 8
    Figure 8

    (a) Neutron PDF fit to Sr0.4Ba0.6Mn0.95Ti0.05O3 at 100 K. The top set of curves shows the data (blue symbols) and total PDF fit (red curve). The gray curve offset vertically below is the isolated mPDF signal, i.e., the total experimental PDF signal with the calculated nuclear PDF and the nuclear PDF fit residual from 340 K subtracted. The best-fit mPDF based on the known G-type AFM order is overlaid in blue. The overall fit residual is shown in green at the bottom of the figure. (b) Zoomed-in view of the mPDF signal (gray curve) and fit (blue curve). The experimental signal has been smoothed via a Fourier filter that removes contributions beyond 6Å1, where the magnetic scattering intensity is negligible due to the magnetic form factor.

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  • Figure 9
    Figure 9

    Locally ordered magnetic moment in Sr0.4Ba0.6Mn0.95Ti0.05O3 obtained from mPDF analysis. The persistent ordered moment above TN arises from short-range AFM correlations. The anomalous drop in the ordered moment at 90 K is expected to be an artifact of imperfect thermal equilibrium.

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  • Figure 10
    Figure 10

    Spin-flip magnetic scattering from Sr0.4Ba0.6Mn0.95Ti0.05O3 at 100 K [(a); AFM state] and 160 K [(b); PM state]. The black symbols show the experimental data, while the red curves are calculated based on the model explained in the main text. Nuclear Bragg peaks causing artifacts in the magnetic signal are indicated with a subscript N.

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  • Figure 11
    Figure 11

    (a) μSR time spectra for Sr0.4Ba0.6Mn0.95Ti0.05O3 at various temperatures above and below TN. The colored symbols show the data, and the black curves are fits described in the main text. (b) Temperature-dependent relaxation rate corresponding to the fast front end of the asymmetry spectra for the samples with (x,y)=(0.45,0) and (0.6, 0.05), extracted from least-squares fits. (c) Same as for (b), but showing the relaxation rate corresponding to the long-time tail of the asymmetry spectra. The dashed vertical lines indicate TN for the corresponding sample.

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  • Figure 12
    Figure 12

    (a) Temperature dependence of the locally ordered magnetic moment for Sr0.4Ba0.6Mn0.95Ti0.05O3 (left vertical axis) and the tetragonal distortion c/a1 for fitting range of 1.5–21.5 Å (right vertical axis). (b) Tetragonal distortion versus local magnetic order parameter for Sr0.4Ba0.6Mn0.95Ti0.05O3, highlighting spontaneous linear magnetoelectric coupling in the multiferroic state. (c) Same as (b), but for Sr0.55Ba0.45MnO3.

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