Strongly two-dimensional exchange interactions in the in-plane metallic antiferromagnet ${\mathrm{Fe}}_{2}\mathrm{As}$ probed by inelastic neutron scattering

Strongly two-dimensional exchange interactions in the in-plane metallic antiferromagnet ${Fe}_{2} As$ probed by inelastic neutron scattering

Manohar H. Karigerasi, Kisung Kang, Garrett E. Granroth, Arnab Banerjee, André Schleife, and Daniel P. Shoemaker

Phys. Rev. Materials 4, 114416 – Published 20 November 2020

Abstract

To understand spin interactions in materials of the ${Cu}_{2} Sb$ structure type, inelastic neutron scattering of ${Fe}_{2} As$ single crystals was examined at different temperatures and incident neutron energies. The experimental phonon spectra match well with the simulated phonon spectra obtained from density functional theory (DFT) calculations. The measured magnon spectra were compared to the simulated magnon spectra obtained via linear spin wave theory with the exchange coupling constants calculated using the spin polarized, relativistic Korringa-Kohn-Rostoker method in Zhang et al. [Inorg. Chem. 52, 3013 (2013)]. The simulated magnon spectra broadly agree with the experimental data although the energy values are underestimated along the $K$ direction. Exchange coupling constants between Fe atoms were refined by fits to the experimental magnon spectra, revealing stronger nearest-neighbor Fe1-Fe1 exchange coupling than previously reported. The strength of this exchange coupling is almost an order of magnitude higher than other exchange interactions despite the three-dimensional nature of the phonon interactions. The lack of scattering intensity at energies above 60 meV makes unconstrained determination of the full set of exchange interactions difficult, which may be a fundamental challenge in metallic antiferromagnets.

Received 11 August 2020
Accepted 20 October 2020

DOI:https://doi.org/10.1103/PhysRevMaterials.4.114416

Physics Subject Headings (PhySH)

Exchange interaction Magnetization switching Spin torque Spin waves Spintronics

Antiferromagnets Metals

Density functional theory Inelastic neutron scattering Korringa-Kohn-Rostoker method Time-of-flight neutron spectroscopy X-ray diffraction

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Manohar H. Karigerasi ¹, Kisung Kang ¹, Garrett E. Granroth², Arnab Banerjee^2,3, André Schleife ^1,4, and Daniel P. Shoemaker^1,*

¹Department of Materials Science and Engineering and Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
²Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
³Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
⁴National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA

^*dpshoema@illinois.edu

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Vol. 4, Iss. 11 — November 2020

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Figure 1
The chemical structure of ${Fe}_{2} As$ (left) showing the $Fe {As}_{4}$ tetrahedral and $Fe {As}_{5}$ square pyramidal units and the ${Fe}_{2} As$ magnetic structure (right) with Fe-Fe exchange pathways are shown in (a). Black, blue, green, and pink double headed arrows represent Fe1-Fe1, Fe1-Fe2, Fe2-Fe2 nearest-neighbor, and Fe2-Fe2 next-nearest-neighbor interactions, respectively. Comparison between the magnon spectra calculated using the linear spin wave theory from exchange coupling values in Ref. [23] and the experimental INS values in Ref. [24] are shown in (b) for ${Cr}_{2} As$ . Also overlaid are the SPRKKR-derived magnon spectra of ${Mn}_{2} As$ and ${Fe}_{2} As$ [23].
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Figure 2
The Rietveld-refined fit to the synchrotron powder x-ray diffraction data of ${Fe}_{2} As$ is shown in (a). The elastic neutron scattering slice along $K$ and $L$ for $H$ integrated from $- 0.2$ to 0.2 is shown in (b) for $E_{i} = 30$ meV.
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Figure 3
INS data of ${Fe}_{2} As$ measured at 5 K along $K$ with $H$ and $L$ integrated from $- 0.1$ to 0.1 is shown in (a) and along $L$ with $H$ and $K$ integrated from $- 0.2$ to 0.2 is shown in (d). The data with $E_{i} = 30$ meV (below black dashed lines) have been overlaid on the data with $E_{i} = 70$ meV in (a) and (d). (b) and (e) The corresponding simulated phonon spectra obtained from DFT calculations. (c) and (f) The corresponding simulated magnon spectra derived from exchange constants in Ref. [23]. The intensities in (b) and (e) have been averaged over nine equally spaced phonon spectra in the experimental width along the other two $Q$ directions. Similarly, the magnon spectra in (c) and (f) have been averaged over every 0.025 reciprocal lattice units between $- 0.1$ and 0.1 in the other $Q$ directions. The white dashed lines in (f) indicate the calculated magnon spectrum along the [0 0 $L]$ direction.
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Figure 4
Constant-energy INS data reveal magnons most clearly with $E$ integrated from 25 to 30 meV for (a) the $H − K$ plane with $L$ integrated from $- 1$ to 1 and (c) $K − L$ plane with $H$ integrated from $- 0.2$ to 0.2 and folded along $L$ . (b) and (d) The corresponding simulated magnon spectra using exchange constants from Zhang et al. [23] with the same $E$ integration and the orthogonal $Q$ direction summed every 0.1 along the experimental width.
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Figure 5
The result of unconstrained optimization of the exchange coupling values when only three nearest-neighbor interactions are considered is shown in (a). The reduced $χ^{2}$ values of all points are less than 7, but these three- $J_{i j}$ fits are disallowed by intensity mismatches to the INS data. In (b), comparison of the fit of a four- $J_{i j}$ model obtained by fixing the NNN Fe2-Fe2 interaction to be $- 8.52$ meV and the calculated magnon spectra from the exchange constants from Zhang et al. [23] leads to an improvement of the fit, with much larger Fe1-Fe1 interaction (see Table 1).
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Physical Review Materials

Strongly two-dimensional exchange interactions in the in-plane metallic antiferromagnet Fe2As probed by inelastic neutron scattering

Manohar H. Karigerasi, Kisung Kang, Garrett E. Granroth, Arnab Banerjee, André Schleife, and Daniel P. Shoemaker

Phys. Rev. Materials 4, 114416 – Published 20 November 2020

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Strongly two-dimensional exchange interactions in the in-plane metallic antiferromagnet ${Fe}_{2} As$ probed by inelastic neutron scattering