Ferrimagnetic spin waves in honeycomb and triangular layers of ${\mathrm{Mn}}_{3}{\mathrm{Si}}_{2}{\mathrm{Te}}_{6}$

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Ferrimagnetic spin waves in honeycomb and triangular layers of ${Mn}_{3} {Si}_{2} {Te}_{6}$

G. Sala, J. Y. Y. Lin, A. M. Samarakoon, D. S. Parker, A. F. May, and M. B. Stone

Phys. Rev. B 105, 214405 – Published 6 June 2022

Abstract

A detailed analysis of the ferrimagnetic ground state of ${Mn}_{3} {Si}_{2} {Te}_{6}$ has been performed using inelastic neutron scattering. Although the proposed valence of the nominal ${Mn}^{2 +}$ ions would have quenched orbital angular momentum, a significant exchange anisotropy exists in ${Mn}_{3} {Si}_{2} {Te}_{6}$ . This apparent exchange anisotropy is a manifestation of a weak spin-orbit coupling in the layered material. We employ a detailed simulation of the spin-wave spectrum coupling traditional refinement of dispersion parameters to image analysis techniques, while including Monte Carlo simulations of the instrumental resolution to accurately identify the exchange couplings to the third nearest neighbor. An independent validation of our results is made by comparing our final Hamiltonian to heat capacity measurements.

Received 11 November 2021
Revised 27 January 2022
Accepted 18 May 2022

DOI:https://doi.org/10.1103/PhysRevB.105.214405

Physics Subject Headings (PhySH)

Exchange interaction Spin waves

Data analysis Inelastic neutron scattering Super-resolution techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

G. Sala ¹, J. Y. Y. Lin ¹, A. M. Samarakoon^2,3, D. S. Parker ⁴, A. F. May ⁴, and M. B. Stone ^2,*

¹Spallation Neutron Source, Second Target Station, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
²Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
³Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
⁴Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

^*stonemb@ornl.gov

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Vol. 105, Iss. 21 — 1 June 2022

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Figure 1
(a) Crystal structure of the ${Mn}_{3} {Si}_{2} {Te}_{6}$ trigonal unit cell showing the layered arrangement of the ${Mn}^{2 +}$ ions and the location of the Te and Si sites [18]. The two nonequivalent Mn sites are illustrated with red (Mn1 on the $4 f$ site) and blue (Mn2 on the $2 c$ site) spheres. (b) Ordered magnetic structure of ${Mn}_{3} {Si}_{2} {Te}_{6}$ and proposed exchange couplings between magnetic sites. The arrows represent the easy-plane direction of the spins in the ordered phase. The exchange $J_{1}$ is shown as a blue line between Mn sites. The exchange $J_{2}$ is shown as a yellow line within the honeycomb layers of the Mn sites. The exchange $J_{3}$ , dashed green lines, is only shown for one portion of the lattice for clarity of the figure.
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Figure 2
Inelastic neutron scattering measurements of ${Mn}_{3} {Si}_{2} {Te}_{6}$ and background subtraction of these data. Each spectrum is shown on the same relative intensity with a color scale four units large. (a) $T = 5$ K measurement of the INS spectra for ${Mn}_{3} {Si}_{2} {Te}_{6}$ measured along the $L$ -axis from the CNCS measurement. Data orthogonal to the wave-vector shown were integrated over a range of $\pm 0.1$ reciprocal lattice units (rlu). (b) $T = 100$ K measurement of the INS spectra for ${Mn}_{3} {Si}_{2} {Te}_{6}$ measured along the $L$ axis from the CNCS measurement. (c) Difference of the data shown in panels (a) and (b) with the high-temperature measurement subtracted from the low-temperature measurement. (d) Azimuthal determined background, $A_{B G}$ , projected along the same direction as the data. (e) The difference between the $T = 5$ K measurement in panel (a) and the $A_{B G}$ shown in panel (d). Inset in the upper left illustrates the path of the data through reciprocal space as a heavy black line
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Figure 3
Measured scattering intensity, determined spin-wave mode locations, calculated spin-wave dispersion, and calculated scattering intensity for ${Mn}_{3} {Si}_{2} {Te}_{6}$ at T=5 K. [(a)–(d)] $T = 5$ K measured INS intensity. The slices in reciprocal space shown to higher (lower) energy transfer are from the SEQUOIA (CNCS) measurement. Data have been background subtracted as described in the text. The scattering intensity from SEQUOIA has been multiplied by a factor of 20 to place it on the same intensity scale as the CNCS data. [(e)–(h)] Determined spin-wave mode energies as a function of energy transfer and wave-vector transfer. Green (red) points are from SEQUOIA (CNCS). Triangular symbols have energy values determined from higher Brillouin zones, but are shown at reduced wave vector to appear in the figure. Mode values were determined from Gaussian fits to constant wave-vector scans as described in the text and illustrated in Fig. 5. Error bars are the half width at half maximum (HWHM) of the determined Gaussian peak added in quadrature to the fitted error in peak location. Dashed blue lines are the calculated spin-wave mode energies based upon the exchange parameters listed in Table 1 for the $H_{Jex}$ model using spinw fits of only the dispersion. Heavy black lines correspond to resolution corrected dispersion based upon the image analysis described in the text. Solid blue lines are the calculated spin-wave mode energies based upon the exchange parameters listed in Table 1 for the $H_{Jex}$ model using resolution-corrected mode energies. [(i)–(l)] Calculated scattering intensity from convolution of MCViNE-calculated resolution function for both the SEQUOIA and CNCS measurements based upon the model with the exchange parameters determined from the resolution-corrected dispersion analysis, $H_{Jex}^{res .}$ , described in the text with the values listed in Table 1. Data in panels (a)–(d) and (i)–(l) have been smoothed by a Gaussian smoothing algorithm.
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Figure 4
(a) $T = 5$ K measured INS intensity along (H01). Slice which extends to higher (lower) energy transfer is from the SEQUOIA (CNCS) measurement. Data have been background subtracted as described in the text. The scattering intensity from SEQUOIA has been multiplied by a factor of 10 to place it on the same intensity scale as the CNCS data. (b) Determined spin-wave mode energies as a function of energy and wave-vector transfer. Green (red) points are from the SEQUOIA (CNCS) measurement. Mode values were determined from Gaussian fits to constant wave-vector scans as described in text and illustrated in Fig. 5. Error bars are the half width at half maximum (HWHM) of the determined Gaussian peak added in quadrature to the fitted error in peak location. Dashed blue lines are the calculated spin-wave mode energies based upon the exchange parameters listed in Table 1 for the $H_{Jex}$ model using spinw fits of only the dispersion. Heavy black lines correspond to resolution-corrected dispersion based upon the image analysis described in the text. Solid blue lines are the calculated spin-wave mode energies based upon the exchange parameters listed in Table 1 for the $H_{Jex}$ model using resolution-corrected mode energies. (c) Difference in calculated spin-wave scattering intensity between the determined dispersion using the $H_{Jex}$ model and the resolution corrected $H_{Jex}$ model in Table 1. (d) Scattering intensity determined using the resolution corrected $H_{Jex}$ model in Table 1. Results in panels (a), (c), and (d) have been smoothed by a Gaussian smoothing algorithm.
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Figure 5
Inelastic neutron scattering measurements of ${Mn}_{3} {Si}_{2} {Te}_{6}$ plotted as constant wave-vector scans from the $T = 5$ K CNCS ( $▪$ ) and SEQUOIA ( $•$ ) measurements. Data have been offset along the vertical axis for presentation. The SEQUOIA measurements have been scaled by a factor of 20 to place them on the same intensity scale as the CNCS measurements. Solid (CNCS data) and dotted (SEQUOIA data) lines are comparisons of the measurement to either a single Gaussian with a sloping background or two Gaussians with a sloping background as described in the text. Data correspond to the wave vectors indicated in the figure. Data were integrated over the symmeterized slices shown in Figs. 3 and 3 without any smoothing over a range of $\pm 0.05$ rlu. Black triangles are the fitted Gaussian peak locations for the respective modes they are beneath.
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Figure 6
Temperature normalized heat capacity as a function of temperature for ${Mn}_{3} {Si}_{2} {Te}_{6}$ . Data are shown as purple circles plotted on the left axis. Lines (right axis) are the Monte Carlo calculation performed using Eq. (4) for the models tabulated in Table 1.
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Physical Review B

covering condensed matter and materials physics

Ferrimagnetic spin waves in honeycomb and triangular layers of ${Mn}_{3} {Si}_{2} {Te}_{6}$

G. Sala, J. Y. Y. Lin, A. M. Samarakoon, D. S. Parker, A. F. May, and M. B. Stone

Phys. Rev. B 105, 214405 – Published 6 June 2022

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Physical Review B

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Ferrimagnetic spin waves in honeycomb and triangular layers of Mn3Si2Te6

G. Sala, J. Y. Y. Lin, A. M. Samarakoon, D. S. Parker, A. F. May, and M. B. Stone

Phys. Rev. B 105, 214405 – Published 6 June 2022

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Ferrimagnetic spin waves in honeycomb and triangular layers of ${Mn}_{3} {Si}_{2} {Te}_{6}$