Fig.2 includes SQUID measurements data of single crystal orthoferrite HoFeO3 with the magnetic field applied along different crystal directions, a, b or c, and as a function of temperature. In Fig.2a the applied field is 0.01 T, in Fig.2b it is 0.13 T, in Fig.2c it is 1.3 T. Fig.2(d) shows the field-dependent magnetisation measured at 2.5K for fields applied along all three crystallographic directions.

Fig.3 shows the spin Hall magnetoresistance (SMR) measurements obtained for Hall bars patterned with the long axis along the b crystal direction or c crystal direction. (a)-(b) Longitudinal and transverse SMR curves measured in the b-device (a) and c-device (b) at 25.5K by rotating a magnetic field of 0.95 T in the plane of the Hall bars. (c) Temperature dependence of the SMR measured in the c-device from 1.5K to 66.5 K. (d) Magnetic field dependence of the SMR amplitude for selected temperatures.

Fig.4 shows the field-dependent SMR measured from −1 T to 1 T for both b and c-devices, with the magnetic field applied along either the b- or c-axis in the sample plane. (a)-(b) Field dependent SMR curves for the b-device with field along the c-axis (a) and b-axis (b). (c)-(d) The c-device with field along the b-axis (c) and c-axis (d).

Fig.5 shows the field sweep measurements of the SMR for the c-device with in-plane magnetic field along the b-axis. (a) Longitudinal resistivity measured from −5 T to 5 T at various temperatures. (b) Temperature dependence of hysteresis amplitude and field position of the peak extracted from (a).

Fig.6 shows the in-plane spin-Seebeck effect (SSE) measurements for the c-device, showing angular and temperature dependence of spin current generation in the low temperature regime. (a) Angle-dependent longitudinal SSE voltage at 1.6K under various magnetic fields. (b) SSE amplitude as a function of temperature for different magnetic fields.