Spin and lattice dynamics in the van der Waals antiferromagnet ${\mathrm{MnPSe}}_{3}$ (2024)

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  Figure 1

  (a)Top view of the hexagonal structure of ${\mathrm{MnPSe}}_3$ in the a-b plane. Arrows indicate the magnetic moments on Mn atoms. Dashed lines indicate the paths for the magnetic exchange interactions. (b)Schematic structures of the primitive cell of ${\mathrm{MnPSe}}_3$. (c)Temperature dependence of the magnetic susceptibility $\chi$ (filled symbols, left axis) and the inverse magnetic susceptibility ${\chi }^{-1}$ (open symbols, right axis) with field applied parallel and perpendicular to the $c$-axis. Solid lines and the arrow denote the Curie-Weiss fit of ${\chi }^{-1}$ and the Néel transition temperature, respectively. (d)Temperature dependence of the specific heat $C$ (circles, left axis) and the integrated intensity of $(-1,0,1)$ Bragg peak (squares, right axis). Error bars represent one standard deviation. The vertical dashed line indicates the Néel transition temperature. The dashed curve through the integrated intensities is a guide to the eyes.

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  Figure 2

  (a)Measured magnetic Bragg peaks in the $(H,0,L)$ plane with the incident energy of $E_{\mathrm{i}}=14$meV for ${\mathrm{MnPSe}}_3$. The energy is integrated over $[-0.1,0.1]$meV. The lattice contributions are eliminated by subtracting the data of 150K. (b)Theoretically calculated magnetic Bragg peaks in the $(H,0,L)$ plane according to the untwinned case, termed the $N$ pattern. (c)Reflection of the $N$ pattern about the $L=0$ line, termed the $R$ pattern. (d)Superposition of the patterns in (b)and (c), termed the $S$ pattern, representing the magnetic Bragg scatterings from the twinned sample.

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  Figure 3

  INS results of the magnetic excitation spectra at 6K along the in-plane (a)and out-of-plane (b)directions. The data were obtained with $E_{\mathrm{i}}=14$meV for (a), and $E_{\mathrm{i}}=7.87$meV for (b). In (a), the integration thickness of the other in-plane direction, orthogonal to the high-symmetry path, is chosen to be $\pm 0.05$ rlu, and the wave vectors $L$ are integrated over [2.5,3.5] rlu. In (b), the integration range for the two orthogonal in-plane vectors is $\pm 0.05$ rlu. (c),(d)Calculated in-plane and out-of-plane magnon dispersions using the linear spin-wave theory (LSWT), respectively. The data points are extracted from the experimental spectra presented in (a)and (b). (e),(f) Calculated magnetic excitation spectra, which are superposed with $\pm L$ cases taking into account the twinning effect and instrumental resolutions. The inset in (a)illustrates the high-symmetry paths of the in-plane excitation spectra.

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  Figure 4

  (a)Constant-$E$ contour at 5meV in the $(H,0,L)$ plane, obtained with $E_i=10.29$meV. The integration thickness of the energy is $\pm 0.5$meV. Lines and the oval denote magnon excitations and phonon excitations, respectively. The dashed lines indicate the $L$ positions where the magnon and phonon dispersions intersect with each other. (b)The overlapped magnon and phonon excitations at 6K presented in the same momentum-energy window with $L=4.7$meV. Triangles and squares denote magnon and phonon dispersions extracted from (c)and (d), respectively. (c),(d)The individual magnon and phonon spectra, obtained with $L=1.7$ rlu at 6K and $L=7.3$ rlu at 150K, respectively. The integration thicknesses of the $[-120]$ and [001] directions are $\pm 0.1$ and $\pm 0.15$ rlu, respectively.

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  Figure 5

  (a),(b)Calculated magnon spectra with and without the $D$ term, respectively. (c)Comparison between the measured energy distribution of the spectral weight with the calculations with and without the $D$ term at $\mathit{Q}=(1,0,-3/2)$.

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