Effect of random antiferromagnetic exchange on the spin waves in a three-dimensional Heisenberg ferromagnet

S. Hameed, Z. Wang, D. M. Gautreau, J. Joe, K. P. Olson, S. Chi, P. M. Gehring, T. Hong, D. M. Pajerowski, T. J. Williams, Z. Xu, M. Matsuda, T. Birol, R. M. Fernandes, and M. Greven

Phys. Rev. B 108, 134406 – Published 5 October 2023

Abstract

Neutron scattering is used to study spin waves in the three-dimensional Heisenberg ferromagnet ${YTiO}_{3}$ , with spin-spin exchange disorder introduced via La substitution at the Y site. No significant changes are observed in the spin-wave dispersion up to a La concentration of 20%. However, a strong broadening of the spectrum is found, indicative of shortened spin-wave lifetimes. Density-functional theory calculations predict minimal changes in exchange constants as a result of average structural changes due to La substitution, in agreement with the data. The absence of significant changes in the spin-wave dispersion, the considerable lifetime effect, and the reduced ordered magnetic moment previously observed in the La-substituted system are qualitatively captured by an isotropic, nearest-neighbor, three-dimensional Heisenberg ferromagnet model with random antiferromagnetic exchange. We therefore establish $Y_{1 - x} {La}_{x} {TiO}_{3}$ as a model system for the study of antiferromagnetic spin-exchange disorder in a three-dimensional Heisenberg ferromagnet.

Received 5 May 2023
Accepted 18 September 2023

DOI:https://doi.org/10.1103/PhysRevB.108.134406

Physics Subject Headings (PhySH)

Antiferromagnetism Ferromagnetism Spin dynamics

Inelastic neutron scattering Monte Carlo methods

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

S. Hameed ^1,*, Z. Wang ^1,†, D. M. Gautreau^1,2, J. Joe¹, K. P. Olson ^2,‡, S. Chi ³, P. M. Gehring ⁴, T. Hong³, D. M. Pajerowski³, T. J. Williams ³, Z. Xu⁴, M. Matsuda ³, T. Birol², R. M. Fernandes¹, and M. Greven^1,§

¹School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
²Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
³Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
⁴NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA

^*Present address: Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany; Corresponding author: s.hameed@fkf.mpg.de
^†Present address: Center for Correlated Matter and School of Physics, Zhejiang University, Hangzhou 310058, China.
^‡Present address: Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60201, USA.
^§Corresponding author: greven@umn.edu

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Issue

Vol. 108, Iss. 13 — 1 October 2023

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Images

Figure 1
Representative energy scans at ${(0, 0, 1)}_{o}$ (with high-temperature data subtracted) for $x = 0$ , 0.10, 0.20, and 0.22, along with respective Gaussian fits. The data for $x = 0$ are scaled down by a factor of 2. See Supplemental Material [19] for additional energy and momentum scans. The error bars correspond to one standard deviation.
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Figure 2
(a) Spin-wave peak energies at low temperature. For $x = 0$ , two peaks were resolved at ${(0, - 1, 1)}_{o}$ , likely as a result of a coupling with an optical phonon branch [17]. The open blue square indicates the second peak. The lines are guides to the eye. The error bars correspond to those obtained from the fits. [(b)–(d)] Spin-wave intensities at low temperature for (b) $x = 0$ , (c) $x = 0.10$ , and (d) $x = 0.20$ , obtained from Gaussian fits to energy scans, as described in the text. The data elongated along the horizontal direction were obtained from momentum scans. The low-energy data at ${(0, 0, 1.7)}_{o}$ and ${(0, 0, 1.75)}_{o}$ for $x = 0.10$ have a small width in energy as these were taken with a higher energy resolution at a cold-neutron triple-axis spectrometer. The intensities for these were multiplied by a factor of five for better visibility in the color map. The data for $x = 0$ and $x = 0.20$ and the data at ${(0, 0, 1.7)}_{o}$ and ${(0, 0, 1.75)}_{o}$ for $x = 0.10$ were obtained at 1.5 K. The remaining data were obtained at 4 K.
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Figure 3
Effective spin-spin exchange parameters as a function of La substitution determined from DFT. Each La concentration is simulated by interpolating between the known crystal structures for ${YTiO}_{3}$ and ${LaTiO}_{3}$ . $J_{x y}$ and $J_{z}$ represent spin-exchange parameters between nearest-neighbor Ti ions in the $a b$ plane and along the $c$ axis, respectively (see inset).
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Figure 4
(a) Calculated dynamic spin structure factor $S (Q, ω)$ of model (1) for (a) $p = 0$ and (b) $p = 0.1$ , obtained with $L = 16$ and temperature $T = 0.1 J$ . Here, $S = \frac{1}{2}$ . [(c)–(e)] Comparison of the (c) peak positions, (d) amplitude, and (e) full width at half maximum (FWHM) of the calculated and measured spin-wave results at different wave vectors. We set $p = x / 2$ for the comparison. The calculated spin-wave spectrum is scaled to best fit (for $p = 0$ ) the experimental results for ${YTiO}_{3}$ . At each wave vector, the amplitude is normalized to the $x = p = 0$ value. The theoretical results are convoluted with the instrument resolution to determine the FWHM. Only results at wave vectors for which data are available for multiple La substitution levels are displayed in [(c)–(e)]. The comparison at ${(0, - 1, 1)}_{o}$ is omitted in (d) and (e) since a coupling to phonons complicates the experimental spin-wave response [17]. For the comparison at ${(0, - 1, 1)}_{o}$ in (c), we use the higher-energy spin-wave peak obtained for $x = 0$ . The error bars in [(c)–(e)] correspond to those obtained from the fits.
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Figure 5
Calculated FM moment $\sqrt{{[〈 m^{2} 〉]}_{av}}$ obtained for the disordered Heisenberg model with $L = 16$ and $T / J = 0.1$ (the error bars are smaller than the symbol size), compared with prior data for $Y_{1 - x} {La}_{x} {TiO}_{3}$ (from Ref. [28]). We set $p = x / 2$ for the comparison. The FM moment values are normalized to the value at $x = p = 0$ .
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