Magnetic order and interactions in ferrimagnetic ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$

The magnetism in ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$ has been investigated using thermodynamic measurements, first-principles calculations, neutron diffraction, and diffuse neutron scattering on single crystals. These data confirm that ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$ is a ferrimagnet below $T_{\mathrm{C}}$ $\approx 78$ K. The magnetism is anisotropic, with magnetization and neutron diffraction demonstrating that the moments lie within the basal plane of the trigonal structure. The saturation magnetization of $\approx 1.6{\mu }_B$/Mn at 5 K originates from the different multiplicities of the two antiferromagnetically aligned Mn sites. First-principles calculations reveal antiferromagnetic exchange for the three nearest Mn-Mn pairs, which leads to a competition between the ferrimagnetic ground state and three other magnetic configurations. The ferrimagnetic state results from the energy associated with the third-nearest-neighbor interaction, and thus long-range interactions are essential for the observed behavior. Diffuse magnetic scattering is observed around the 002 Bragg reflection at 120 K, which indicates the presence of strong spin correlations well above $T_{\mathrm{C}}$. These are promoted by the competing ground states that result in a relative suppression of $T_{\mathrm{C}}$ and may be associated with a small ferromagnetic component that produces anisotropic magnetism below $\approx 330\mathrm{K}$.

Figure 1

(a) Crystal structure of ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$ viewed down [110]. (b),(c) Single layers of the different ${\mathrm{MnTe}}_6$ octahedra viewed down [001], where (b) is an image of Mn1 layers and (c) is a Mn2 layer. In all panels, one unit cell is outlined, ${\mathrm{MnTe}}_6$ octahedra are shown, and arrows indicate relative alignments of Mn moments within the trigonal plane.

Figure 2

(a) Anisotropic magnetization data for ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$ upon cooling in an applied field of 20 Oe; the left axis $\left(H\perp c\right)$ and right axis $\left(H\parallel c\right)$ have the same units. The inset shows isothermal magnetization data at $T=5$ K, and together these results reveal easy-plane magnetization. (b) Inverse susceptibility data combining high- and low-$T$ measurements. The dashed curve represents a Curie-Weiss fit extended to lower $T$.

Figure 3

(a) The real component ${\chi }^{\prime }$ and (b) the imaginary component ${\chi }^{\prime \prime }$ of the ac magnetic susceptibility data near the ferrimagnetic ordering temperature. The insets show the data on a logarithmic scale using the same units as the primary panels. Data collected upon cooling using $A=2$ Oe and $f=997$ Hz.

Figure 4

(a) Anisotropic dc magnetization data collected upon cooling in an applied field of 20 Oe. (b) Anisotropic ac susceptibility data showing the real ${\chi }^{\prime }$ and imaginary ${\chi }^{\prime \prime }$ components. The ac data were collected using $A=14$ Oe and $f=997$ Hz with zero-applied dc field.

Figure 5

Isothermal dc magnetization data at 110 K demonstrating the ferromagnetic contribution for $H\perp c$ in ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$.

Figure 6

(a) Rocking curves of various Bragg reflections at 4 and 100 K. The increase of intensity upon cooling into the magnetically ordered state is strongest for reflections with nonzero $L$. (b) Order parameter for the ferrimagnetic structure (002 intensity), with data from the single-crystal neutron diffractometer (HB3A) and the elastic diffuse neutron-scattering spectrometer (CORELLI). The solid curves are fits to a simple power law and the inset shows the data and fits in a log-log plot.

Figure 7

Temperature dependence of the lattice parameters normalized to values at 300 K, with data for $c$ offset for clarity. Error bars are smaller than the size of the data markers and the dashed line indicates $T_{\mathrm{C}}$.

Figure 8

(a) Specific heat capacity of ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$, with inset showing the field dependence of the anomaly observed near $T_{\mathrm{C}}$. (b) Field dependence of the the low-temperature specific heat data demonstrating a strong magnetic contribution.

Figure 9

The in-plane electrical resistivity of ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$ generally increases with decreasing temperature, with a notable feature near $T_{\mathrm{C}}$. The decrease of $\rho$ becomes more rapid above $\approx 330\mathrm{K}$. The black and green curves are data collected on different crystals, and the red lines are fitted curves using $\rho ={\rho }_0\mathrm{Exp}[E_A/k_{B}T]$, which only fits the data over small temperature ranges but does reveal an apparent increase in activation energy upon warming across the two magnetic anomalies.

Figure 10

Data from the neutron elastic diffuse scattering spectrometer CORELLI. (a) Estimate of the elastic scattering at 120 K showing diffuse scattering near the 002 Bragg reflections. Line scans of the total scattering at (b) 120 K and (d) 350 K across 002 and 004 reflections with different integration widths along $H$ indicated in the legend. (c) Difference map of total scattering (120 K with 350 K baseline) emphasizing the diffuse scattering near the 002 reflection.

Figure 11

Total neutron scattering in the $(H-HL)$ plane at (a) 6 K and (b) 350 K. Diffuse scattering is observed along $L$, notably at 6 K near 1–12. These 2D maps show the intensity from $[-0.005-0.0050]$ to [0.005 0.005 0], i.e., a single bin, along the $\left[HH0\right]$ out-of-plane direction.