Field-anisotropic geometrical Hall effect via f-d exchange fields in doped pyrochlore molybdates

Topological spin textures have been proven to play an important role in the quantum electromagnetic properties. For instance, as a conduction electron is coupled with non-coplanar localized spins, its wave function is endowed with the Berry phase proportional to the solid angles subtended by the neighboring spins, i.e., the scalar spin chirality. The emergent magnetic field (Berry curvature) acts on the conduction electrons, giving rise to unconventional geometrical Hall effect [1]. However, few studies have been done on the geometrical Hall effect in the weak coupling case where no long-range magnetic order exist at zero field.

We synthesized the single crystals of hole-doped pyrochlore (Tb_1-xCa_x)₂Mo₂O₇ using a floating zone furnace with a laser light source [2] and observed that the Hall resistivity of the barely-metallic sample x = 0.14 exhibits an explicit anisotropy between H//[100] and H//[111]. This behavior can be reasonably explained by the spin chirality of the Tb spins forming 2-in 2-out and 3-in 1-out configurations under respective magnetic fields (H) in real space.

[1] Y. Taguchi et al., Science 291, 5513 (2001).

[2] Y. Kaneko et al., J. Cryst. Growth 533 125435 (2020).