Z4 Electronic Fractals in NdNiO₃

Rare-earth nickelates have a phase diagram characterized by overlapping electronic, structural

and magnetic phase transitions. In the vicinity of critical points, local maps of the associated

order parameter exhibit complex pattern formation. We simulate a clean 2D 4-state clock model

near the phase transition temperature. We also cool 2D random field 4-state clock models using the

Metropolis algorithm and find that they reach a glassy state. From the patterns of magnetic domains

at the phase transition in the 2D clean 4-state clock model and the 2D random field clock model, we

calculate critical exponents for the cluster size distribution, volume fractal dimension, hull fractal

dimension and pair connectivity function. We compare these exponents to the exponents extracted

from antiferromagnetic domains in NdNiO₃ using resonant magnetic X-ray scattering nanoprobe

measurements [Li et al., Nat. Commun., 2019]. The four types of magnetic domains in NdNiO₃

follow a Z4 symmetry, and we model the symmetry breaking in the ordered phase with 4-state clock

models. The power law scaling of the cluster properties and pair connectivity correlation function

demonstrates that the observed patterns in NdNiO3 are fractals. We find that the critical exponents

from the 2D random field 4-state clock model are consistent with the critical exponents measured

in NdNiO₃. This indicates that the paramagnet-antiferromagnet transition in rare earth nickelates

is in the same universality class as the 4-state random field clock model