All-in-all-out magnetic domain inversion in ${\mathrm{Tb}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ with molecular fields antiparallel to external fields

We report on magnetotransport properties associated with the all-in-all-out magnetic order for ${\mathrm{Tb}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ single-crystalline thin films. Two degenerate all-in-all-out domains of an Ir sublattice can be switched to each other by magnetic field along the [111] direction as detected by a characteristic magnetoresistivity with diplike hysteresis. For a given single-domain structure, the linear magnetoresistivity, reflecting the effective magnetic field at ${\mathrm{Ir}}^{4+}$, changes its sign at around 70 K. These observations are consistently explained by the molecular fields from ${\mathrm{Tb}}^{3+}$ on ${\mathrm{Ir}}^{4+}$ moments. The molecular fields from ${\mathrm{Tb}}^{3+}$ moments compete with the external fields and dominate the magnetoresponse of ${\mathrm{Ir}}^{4+}$ moments at lower temperature, whereas the external field does at higher temperature.

Figure 1

(a) Temperature dependence of the zero-field resistivity in a ${\mathrm{Tb}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ thin film. Inset: The schematic of the cation sublattices of the pyrochlore structure. (b) Temperature dependence of the magnetization measured by applying a magnetic field of 0.2 T along the [111] direction. The data were obtained during heating after zero-field- and field-cooling (ZFC or FC) sequences. The dashed line indicates the transition temperature $T_{\mathrm{MI}}$ $\approx 120\mathrm{K}$ estimated from the temperature derivative of the resistivity. Inset: The two magnetic domain structures (A and B) in the AIAO configuration. (c) Magnetoresistivity at 2 K in the field along the [111] direction. The arrows and numbers indicate the field-sweeping direction and the process sequence, respectively. The solid triangles denote the onset of magnetic domain inversion at $B_{\mathrm{c}}\approx \pm 6$ T.

Figure 2

Magnetoresistivity under the field along the [111] direction for the (a) lower (5–20 K) and (b) higher (90–120 K) temperature regions. The arrows indicate the direction of hysteresis. The solid triangles denote the onset of magnetic domain inversion at $B_{\mathrm{c}}$. (c) $B_{\mathrm{c}}$ vs temperature. The data in (a) and (b) are shifted vertically for clarity.

Figure 3

(a)–(d) Magnetoresistivity under the field along the [111] direction at 2 K obtained under various cooling processes schematically shown in (e). The dashed line indicates the linear term in magnetoresistivity. (f) Temperature dependence of the linear magnetoresistivity coefficient $\alpha$ obtained during heating after each process in (e). Schematics of magnetic domain configuration in Tb (red arrow) and Ir (blue arrow) magnetic sublattices under (g) weak and (h) strong external magnetic field along the [111] direction.