Magnetic Field Induced Sign Reversal of the Anomalous Hall Effect in a Pyrochlore Ferromagnet ${\mathrm{N}\mathrm{d}}_2{\mathrm{M}\mathrm{o}}_2{\mathrm{O}}_7$: Evidence for a Spin Chirality Mechanism

The anisotropic Hall effect and magnetization have been investigated for single crystals of ${\mathrm{N}\mathrm{d}}_2{\mathrm{M}\mathrm{o}}_2{\mathrm{O}}_7$ under high magnetic fields up to 27 T and at low temperatures down to 50 mK. The magnetization curves indicate that the Nd moments with strong Ising anisotropy are coupled antiferromagnetically with the Mo spins and show field-induced flipping on the respective sites. The Hall resistivity changes its sign with increasing field applied along the [111] direction, while it monotonously approaches zero with the field applied along the [100] or [110] direction. This behavior is in accord with the prediction by the Berry phase theory and is interpreted in terms of the field-induced reversal of spin chirality on the pyrochlore lattice.

Figure 1

(a) Temperature dependence of magnetization for $R_2{\mathrm{M}\mathrm{o}}_2{\mathrm{O}}_7$ crystal with $R=\mathrm{N}\mathrm{d}$ and Gd. A thick bar indicates the estimated value of Mo spin moment at low temperatures. (b) Temperature variation of the Hall conductivity for ${\mathrm{N}\mathrm{d}}_2{\mathrm{M}\mathrm{o}}_2{\mathrm{O}}_7$ and ${\mathrm{G}\mathrm{d}}_2{\mathrm{M}\mathrm{o}}_2{\mathrm{O}}_7$. The data for Gd compound are multiplied by 3. The inset of (a) shows the schematic figure of the Mo sublattice of the pyrochlore structure.

Figure 2

Schematic figures of spin configurations for Nd and Mo tetrahedra. In each panel, upper and lower tetrahedra correspond to Nd and Mo tetrahedra, respectively. The relationship among the Mo spin 1, 2, and 3 is schematically shown at the right-hand side of each Mo tetrahedron. Open arrows depict directions of applied magnetic field. In (a) and (b), and (c) and (d), magnetic field is applied along the [100] and [111] directions, respectively. See text for details.

Figure 3

Magnetization curves for the applied field (a) along the [100] and [110] directions, and (c) along the [111] direction. ${\rho }_{\mathrm{H}}$ is plotted as a function of the magnetic field which is applied (b) along the [100] or [110] direction, and (d) along the [111] direction. In (a) and (c), the horizontal dot-dashed line represents the contribution from the Mo spin moment. Thick horizontal bars in (a) indicate the expected values of the saturation moment for each field direction under the assumption of strong Ising anisotropy of Nd moments. See text for details. In (c), thick horizontal bars indicate the expected values of magnetization when the magnetic configurations of all the Nd tetrahedra are “3 in, 1 out” and “2 in, 2 out,” respectively.