Inverted hysteresis within the antiferromagnetic all-in-allout state of the pyrochlore Nd₂Hf₂O₇

We report the observation of an anisotropic and inverted hysteresis loop in the antiferromagnetic all-in-all-out ordered phase of Nd₂Hf₂O₇ having a negative remnant magnetization. The hysteresis emerges once exceeding a characteristic magnetic-field strength 𝐻^⋆(𝑇) below the Neél temperature. The very unusual appearance of a negative remnant magnetization is observed for a field parallel to the [111] and [110] direction. However, for field parallel to [001] no hysteresis can be seen. For this orientation the projection of the field onto all four local spin directions is equal and, hence, both realizations of the all-in-all-out state gaining equal Zeeman energy through a canting of their spins. We show further, that the underlying all-in-all-out phase is established in Nd₂Hf₂O₇ for temperatures below 𝑇_𝑁 = 0.48 K and persists up to fields of 0.27 T. We account for the inverted hysteresis in terms of a theory of uncompensated domain-wall spins of spherical Domains forming inside a fully polarized single-domain state.