Symmetry-lowering lattice distortion at the spin reorientation in MnBi single crystals

Structural and physical properties determined by measurements on large single crystals of the anisotropic ferromagnet MnBi are reported. The findings support the importance of magnetoelastic effects in this material. X-ray diffraction reveals a structural phase transition at the spin reorientation temperature $T_{SR}=90$ K. The distortion is driven by magnetoelastic coupling, and upon cooling transforms the structure from hexagonal to orthorhombic. Heat capacity measurements show a thermal anomaly at the crystallographic transition, which is suppressed rapidly by applied magnetic fields. Effects on the transport and anisotropic magnetic properties of the single crystals are also presented. Increasing anisotropy of the atomic displacement parameters for Bi with increasing temperature above $T_{SR}$ is revealed by neutron diffraction measurements. It is likely that this is directly related to the anisotropic thermal expansion in MnBi, which plays a key role in the spin reorientation and magnetocrystalline anisotropy. The identification of the true ground-state crystal structure reported here may be important for future experimental and theoretical studies of this permanent magnet material, which have to date been performed and interpreted using only the high-temperature structure.

Figure 1

X-ray diffraction patterns from MnBi single-crystal faces at room temperature. (a) Diffraction from a face perpendicular to the $c$ axis. (b) Diffraction from a face perpendicular to the $a$ axis. The inset in (a) shows a photograph of typical MnBi crystals. The inset in (b) shows the room-temperature hexagonal crystal structure of MnBi. The lattice constants determined from the reflections shown in the figure are listed in (b).

Figure 2

Results of temperature-dependent x-ray diffraction measurements from indexed faces of MnBi single crystals. (a), (b) Contour plots of intensity vs diffraction angle and temperature for the 300 and 004 reflections (h denotes the hexagonal unit cell). (c) In-plane lattice constants vs temperature for the high-temperature hexagonal and low-temperature orthorhombic (denoted by subscript o) structures. (d) The relationship between the high-temperature hexagonal and low-temperature orthorhombic unit cells. (e) $c$-axis length and primitive unit cell volume vs temperature (the volume of the $C$-centered orthorhombic cell is twice the value plotted).

Figure 3

Results of single-crystal neutron diffraction measurements on MnBi analyzed using the hexagonal NiAs structure type at all temperatures. (a) Refined magnetic moment on Mn, including the total moment, as well as the projections of the moment along the hexagonal $a$ axis and $c$ axis. (b) Equivalent isotropic atomic displacement parameters, $U_{eq}$. The element-specific and average Debye temperatures and the linear fits used to determine them are shown on the plot. (c), (d) Anisotropic atomic displacement parameters for both atoms. $U_{11}$ measures displacement in the ab plane, and $U_{33}$ measures displacement along the $c$ axis. (e), (f) The ratio $U_{11}/U_{33}$, a measure of the compression of the displacement ellipsoids along the crystallographic $c$ axis. The inset in (f) compares the relative sizes and shapes of the Bi ellipsoids at 110 and 450 K.

Figure 4

Magnetic properties of MnBi single crystals. (a) Magnetization ($M$) above room temperature. A simple model, shown on the plot, is used to estimate the hypothetical Curie temperature. (b) Magnetic moment ($m$) vs applied field at 5 and 300 K. (c) and (d) Magnetization vs temperature measured at the indicated magnetic fields for $H$ perpendicular and parallel to the $c$ axis, respectively. (e) Field dependence of the spin reorientation temperature defined by the minimum of dM/dT for $H\perp c$. The line is a fit using a second-order polynomial. (f) ac magnetic susceptibility measured at 20 Hz in zero applied dc field, with magnetic moment components determined by neutron diffraction shown for comparison.

Figure 5

Heat capacity of MnBi single crystals showing an anomaly at the spin-reorientation and crystallographic phase transition at 90 K. The upper inset shows the effects of a magnetic field near $T_{SR}$ and the lower inset shows the low-temperature behavior of $c_P/T$ vs $T^2$. Linear fits to the data just above the low-temperature upturn are used to estimate the Debye temperature ${\Theta }_D$ and the Sommerfeld coefficient $\gamma$. (b) Heat capacity derived from temperature vs time data collected during a large heat pulse which moves the sample through the phase transition temperature on heating and subsequent cooling, showing the intrinsic thermal hysteresis associated with the transition is $<0.6$ K. (c) Temperature vs time data used to determine the $c_P$ data shown in (b).

Figure 6

Resistivity of MnBi single crystals. Data are shown with current ($I$) flowing both parallel and perpendicular to the $c$ axis. The upper inset shows the temperature derivative of the resistivity near the $T_{SR}$ measured both upon warming and cooling. The derivative curves are offset vertically for clarity.