Strain-controlled magnetic and optical properties of monolayer $2\mathrm{H}\text{\ensuremath{-}}\mathrm{TaS}{\mathrm{e}}_{2}$

Strain-controlled magnetic and optical properties of monolayer $2 H − TaS e_{2}$

Sugata Chowdhury, Jeffrey R. Simpson, T. L. Einstein, and Angela R. Hight Walker

Phys. Rev. Materials 3, 084004 – Published 14 August 2019

Abstract

First-principles calculations are used to probe the effects of mechanical strain on the magnetic and optical properties of monolayer (ML) $2 H − TaS e_{2}$ . A complex dependence of these physical properties on strain results in unexpected spin behavior, such as ferromagnetism under uniaxial, in-plane, tensile strain and a lifting of the Raman-active $E^{'}$ phonon degeneracy. We predict the noncollinear magnetic phase below 6% strain and a ferromagnet above 6% strain for some types of strain. While ferromagnetism is observed under compression along $\hat{x}$ and expansion along $\hat{y}$ , no magnetic order occurs when interchanging the strain direction. The calculations show that the magnetic behavior of the system depends on the exchange within the $5 d$ orbitals of the Ta atoms. The magnetic moment per Ta atom persists even when an additional compressive strain along the $\hat{z}$ axis is added to a biaxially strained ML, which suggests stability of the magnetic order. Exploring the effects of this mechanical strain on the Raman-active phonon modes, we find that the $E^{″}$ and $E^{'}$ modes are red shifted due to Ta-Se bond elongation, and that strain lifts the $E^{'}$ mode degeneracy, except for the symmetrical biaxial tensile case. The electron-phonon interactions depend on both the amount of applied strain and the direction. Additionally, we note that the charge density wave (CDW) phase weakens the magnetism due to symmetry breaking and atomic displacements (Ta atoms) depending on the type and amount of applied strain. Phonon dispersion calculations confirm that using mechanical strain we can manipulate the unique CDW phase of ML- $2 H − TaS e_{2}$ . Our results support the possibility of tuning the properties of two-dimensional transition metal dichalcogenide materials for nanoelectronic applications through strain.

Received 30 January 2019

DOI:https://doi.org/10.1103/PhysRevMaterials.3.084004

Physics Subject Headings (PhySH)

Magnetism

Transition metal dichalcogenides

Density functional theory Raman spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Sugata Chowdhury^1,2, Jeffrey R. Simpson^1,3, T. L. Einstein⁴, and Angela R. Hight Walker¹

¹Physical Measurement Laboratory, National Institute of Standards and Technology Gaithersburg, Maryland, 20899, USA
²Materials Measurement Laboratory, National Institute of Standards and Technology Gaithersburg, Maryland, 20899, USA
³Department of Physics, Astronomy, and Geosciences, Towson University, Towson, Maryland, 21252, USA
⁴Department of Physics and Condensed Matter Theory Center, University of Maryland, College Park, Maryland, 20742, USA

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 3, Iss. 8 — August 2019

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) The calculated energy differences per unit cell between different magnetic orders of ML- $TaS e_{2}$ as a function of applied strain. The energy difference between antiferromagnetic (AFM) and ferromagnetic (FM), $Δ E_{AFM − FM} = E_{AFM} – E_{FM}$ is plotted as the top set of curves (solid), and the difference between nonmagnetic states (NM) and ferromagnetic states (FM), $Δ E_{FM - NM} = E_{FM} – E_{NM}$ , is the bottom set (dashed). The magnetic moment (b) and the electron charge transfer (c) per Ta atom (top) and per Se atom (bottom) of ML- $TaS e_{2}$ structures using different strain approaches.
Reuse & Permissions
Figure 2
Spin-polarized, partial density of states (PDOS) of Ta (top) and Se (bottom) corresponding to (a) 0%, (b) 6% symmetrical biaxial tensile strain, and (c) 6% expansion in the $\hat{x}$ direction and compression in the $\hat{y}$ direction ( $X X_{+} Y Y_{-}$ ). Here red represents the spin up and blue represents the spin down. The Fermi level is indicated by the dashed vertical black line and the horizontal arrows highlight the spin splitting near the Fermi level, which is only nonzero in (b) for 6% biaxial strain.
Reuse & Permissions
Figure 3
Magnetic moment ( $μ_{B}$ ) of each Ta atom under compressive strain along the direction ( $\hat{z}$ ) perpendicular to the XY plane at 6% symmetrical tensile strain ( $X X_{+} Y Y_{+}$ ) of ML- $TaS e_{2}$ . Inset: the trigonal prismatic coordination of $2 H − TaS e_{2}$ and applied strain direction along the $\hat{z}$ axis. These results suggest that magnetism is sustained even with applied strain along the $\hat{z}$ axis. Fitting parameters are mentioned in the Supplemental Material [50].
Reuse & Permissions
Figure 4
Symmetry allowed Raman active modes of unstrained $2 H − TaS e_{2}$ for (a) bulk and (b) monolayer. (c) Comparison between Raman spectra of unstrained bulk $2 H − TaS e_{2}$ measured experimentally at 300 K (blue circles and blue fit line) and calculated prediction using DFT (red lines).
Reuse & Permissions
Figure 5
The shift of the Raman modes of ML- $TaS e_{2}$ . Panels (a) and (b) represent in-plane shearing modes $E^{″}$ and $E^{^{'} +}$ , respectively, and panel (d) represents the out-of-plane mode $A_{1}^{'}$ . (c) Peak frequency difference between $E^{^{'} +}$ and $E^{^{'} -} . E^{'}$ is no longer degenerate, with each $E^{'}$ split into two modes: $E^{^{'} +}$ and $E^{^{'} -}$ . These modes are present for all types of strain, except the symmetrical biaxial strain $X X_{+} Y Y_{+}$ (black squares).
Reuse & Permissions
Figure 6
Predicted phonon dispersion curves of ML- $TaS e_{2}$ in k space as a function of different types of in-plane strain compared to the unstrained system (upper left panel). Blue and red dispersion curves represent the optical and acoustic modes, respectively. The phonon dispersion curves are substantially changed compared to the unstrained and symmetrical biaxial strain case (lower left panel). Strain lifts the degeneracy of the $E^{'}$ mode at $184 c m^{- 1}$ frequency in $Y Y_{+}$ strain (upper middle and upper right panels). Negative frequencies for acoustic modes imply instability to a distorted structure. The green circles indicate the splitting in an optical branch of the phonon dispersion.
Reuse & Permissions

Physical Review Materials

Strain-controlled magnetic and optical properties of monolayer 2H−TaSe2

Sugata Chowdhury, Jeffrey R. Simpson, T. L. Einstein, and Angela R. Hight Walker

Phys. Rev. Materials 3, 084004 – Published 14 August 2019

Abstract

Physics Subject Headings (PhySH)

Authors & Affiliations

Article Text (Subscription Required)

Supplemental Material (Subscription Required)

References (Subscription Required)

Issue

Access Options

Authorization Required

Other Options

Download & Share

Images

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Log In

Search

Article Lookup

Paste a citation or DOI

Enter a citation

Strain-controlled magnetic and optical properties of monolayer $2 H − TaS e_{2}$