Two-dimensional ordering and collective magnetic excitations in the dilute ferromagnetic topological insulator ${({\mathrm{Bi}}_{0.95}{\mathrm{Mn}}_{0.05})}_{2}{\mathrm{Te}}_{3}$

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Two-dimensional ordering and collective magnetic excitations in the dilute ferromagnetic topological insulator ${({Bi}_{0.95} {Mn}_{0.05})}_{2} {Te}_{3}$

David Vaknin, Daniel M. Pajerowski, Deborah L. Schlagel, Kevin W. Dennis, and Robert J. McQueeney

Phys. Rev. B 99, 220404(R) – Published 21 June 2019

Abstract

Employing elastic and inelastic neutron scattering (INS) techniques, we report on the microscopic properties of the ferromagnetism in the dilute magnetic topological insulator ${({Bi}_{0.95} {Mn}_{0.05})}_{2} {Te}_{3}$ . Neutron diffraction of polycrystalline samples shows the ferromagnetic (FM) ordering is long range within the basal plane, and mainly two dimensional (2D) in character with short-range correlations between layers below $T_{C} \approx 13$ K. Remarkably, we observe gapped and collective magnetic excitations in this dilute magnetic system. The excitations appear typical of quasi-2D FM systems despite the severe broadening of short-wavelength magnons which is expected from the random spatial distribution of Mn atoms in the Bi planes. A detailed analysis of the INS provides the average values for exchange couplings which are consistent with reports of carrier-mediated interactions.

Received 26 February 2019

DOI:https://doi.org/10.1103/PhysRevB.99.220404

Physics Subject Headings (PhySH)

Magnetic interactions Magnetic phase transitions Magnetism Spin dynamics Topological insulators

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

David Vaknin^1,2, Daniel M. Pajerowski³, Deborah L. Schlagel¹, Kevin W. Dennis¹, and Robert J. McQueeney^1,2

¹Ames Laboratory, Ames, Iowa 50011, USA
²Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA
³Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

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Vol. 99, Iss. 22 — 1 June 2019

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Figure 1
(a) Zero-field-cooled magnetic susceptibility $χ \equiv M / H$ and $1 / χ$ vs temperature for polycrystalline ${({Bi}_{0.95} {Mn}_{0.05})}_{2} {Te}_{3}$ at $H = 0.1$ T. The red dashed line represents a Curie-Weiss fit to $1 / χ$ in between 20 and 50 K. The inset plots $M$ vs $H$ at 2 and 20 K, showing hysteresis and a saturation moment of $4.4 μ_{B}$ per Mn at 2 K. (b) Elastic neutron scattering measured on CNCS with $E_{i} = 3.32$ meV at $T = 5$ , 10, and 15 K after subtraction of the $T = 18$ K signal. Lines correspond to fits to a Warren line shape. The inset shows the nuclear plus ferromagnetic signal at $T = 2$ K superimposed on the (101) nuclear peak measured at 18 K. (c) The squared FM order parameter obtained from the magnetic integrated intensity of the (101) peak at several temperatures. The red line is a fit to the data assuming a mean-field-like transition. (d) The average magnetic structure of ${({Bi}_{1 - x} {Mn}_{x})}_{2} {Te}_{3}$ and key effective exchange interactions that occur between magnetic ions within the bilayers of the quintuple-layer structure.
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Figure 2
(a) INS measurements of the dynamical magnetic susceptibility $χ^{″} (Q, E)$ of ${({Bi}_{0.95} {Mn}_{0.05})}_{2} {Te}_{3}$ at $T = 2.1$ K using the CNCS spectrometer. (b) A series of $Q$ cuts with $E = 0.6$ , 0.9, 1.2, 1.5, and 1.8 meV at $E_{i} = 3.32$ meV that highlight the dispersive character of the magnon band. Several $Q$ cuts were fit to a Lorentzian profile, as described in the SM [20], and the peak values are indicated by solid circles in (a). The inset in (b) is an $E$ cut at $Q = 1 Å^{- 1}$ showing a sharp, dispersionless excitation near 0.45 meV and a broad collective magnon mode at $E \approx 2$ meV. Fits to similar $E$ cuts are indicated by open circles in (a). (c) CNCS data taken at $T = 6$ K with $E_{i} = 1.55$ meV and (d) $E$ cut at low $Q$ show evidence of a spin gap with $Δ = 0.1$ meV. (e) The dynamical magnetic susceptibility $χ^{″} (Q, E)$ calculated from a damped bilayer model with $S 〈 J 〉 = 0.2$ meV. $S 〈 J^{'} 〉 = 0.06$ meV, and $S D = 0.05$ meV. The spin waves are averaged over all possible propagation directions as appropriate for a polycrystalline sample. Kinematic restrictions appropriate for the CNCS spectrometer with $E_{i} = 3.32$ meV are applied. Solid and open circles correspond to fits to the INS data from (a). (f) $Q$ cuts of the bilayer model at energy transfers of 0.6, 0.9, 1.2, 1.5, and 1.8 meV [identical cuts to those of (b)]. The inset to (f) shows an energy cut from the bilayer model at $Q = 1 Å^{- 1}$ for comparison to (b). (g) Low-energy, low- $Q$ dependence of the bilayer model with $E_{i} = 1.55$ meV and (h) $E$ cut at low $Q$ can be compared to the spin gap data in (c) and (d), respectively. In (a), (c), (e), and (g), false color images and contour lines represent the neutron intensities as a function of $Q$ and $E$ .
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Figure 3
(a) The power spectrum $[χ^{″} (Q, E) / E]$ of ${({Bi}_{0.95} {Mn}_{0.05})}_{2} {Te}_{3}$ above $T_{C}$ at $T = 20$ K with $E_{i} = 3.32$ meV. (b) A series of $E$ cuts through the power spectrum at $Q = 0.4$ , 0.52, 0.61 and $0.7 Å^{- 1}$ along with Lorentzian fits. The fitting results find a $Q$ -dependent relaxation energy $Γ (Q)$ , shown as open circles in (a), consistent with FM fluctuations. (a) also shows the paramagnon dispersion (fitted maxima in the power spectrum) as solid circles. See SM for more details [20].
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Physical Review B

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Two-dimensional ordering and collective magnetic excitations in the dilute ferromagnetic topological insulator ${({Bi}_{0.95} {Mn}_{0.05})}_{2} {Te}_{3}$

David Vaknin, Daniel M. Pajerowski, Deborah L. Schlagel, Kevin W. Dennis, and Robert J. McQueeney

Phys. Rev. B 99, 220404(R) – Published 21 June 2019

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Physical Review B

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Two-dimensional ordering and collective magnetic excitations in the dilute ferromagnetic topological insulator (Bi0.95Mn0.05)2Te3

David Vaknin, Daniel M. Pajerowski, Deborah L. Schlagel, Kevin W. Dennis, and Robert J. McQueeney

Phys. Rev. B 99, 220404(R) – Published 21 June 2019

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Two-dimensional ordering and collective magnetic excitations in the dilute ferromagnetic topological insulator ${({Bi}_{0.95} {Mn}_{0.05})}_{2} {Te}_{3}$