Spin-canting-induced band reconstruction in the Dirac material
Ca1-xNaxMnBi2

The ternary AMnBi2 (A= alkaline as well as rare-earth atom) materials provide an arena for investigating the interplay between low-dimensional magnetism of the antiferromagnetic MnBi layers and the electronic states in the intercalated Bi layers, which harbour relativistic fermions. In our first attempt (see Fermi surface instability in topological materials) to study the link between the anomaly in the dc resistivity with onset at Ts and the electronic properties of the title compound, we uncovered optical signatures for a partial gapping of the Fermi surface (FS), for energy scales up to 0.2 eV. This may reveal the inclination towards a FS instability in topological materials, accompanied by a sizeable depletion of the density-of-states (DOS) at the Fermi level (EF).

The present work intends to precisely address the microscopic origin of the FS gapping. To this end, we study Ca1-xNaxMnBi2 at three dopings (x = 0, 0.03 and 0.05) and as a function of temperature (T) with magnetic torque measurements, as well as with the support of first-principles calculations. Our findings give evidence for a spin-canting occurring at Ts ~50–100 K (Fig. 1.14).

Enlarged view: Fig. 1.13
Fig. 1.14: (a–b) Magnetic torque (τ = μ0M × H) as a function of the polar angle (θ) of x = 0.03 above and below Ts ~60 K, respectively. The red curve is the total fit, including both anti- and ferromagnetic contributions. (c–d) Schematic representations of the experimental configuration for the magnetic torque measurements and the proposed spin-canting. The phase shift D is the canting angle. (e–g) T dependence of the coefficient A (black) for the antiferromagnetic (dashed lines in panels (a) and (b)) and -B/A (red) for the ferromagnetic contribution to the magnetic torque response of x = 0, 0.03 and 0.05. The vertical dashed lines mark Ts.

Our first-principles calculations establish that the spin-canting leads to the reconstruction of the electronic band structure, having immediate implications for the spectral weight reshuffling in the optical response (i.e., partial gapping of FS) and the dc transport properties below Ts (Fig. 1.15). Obviously, if spin-canting is the principle driving mechanism for the reconstruction of the electronic band structure below Ts, as revealed by our experiments, we might expect the realisation of Weyl states in Na-doped CaMnBi2, as a consequence of the broken time-reversal symmetry. This is of wider interest, because of the peculiar Dirac band crossing along a continuous line in momentum space in CaMnBi2.  

Enlarged view: Fig. 1.15
Fig. 1.15: (a–b) Electronic band structure without (a) and with (b) spin-canting. In (a), the contribution from different Bi p orbitals are denoted by different colours. Insets: blow-up of the electronic band structure inside the black boxes of the main panels (a) and (b). (c–e) Total DOS (c) as well as partial one for pz (d) and px/y (e) orbitals. (f–g) Calculated inter-band contribution (σ1inter(ω)) of the optical conductivity from the band structure without (f) and with (g) spin-canting. The arrows in panels (a–b and f–g) (blue without, and red and green after canting) highlight the inter-band transitions responsible for the MIR absorption and its split in σ1(ω).
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