Fig. 4: Impact of the strain gradient on the antiferromagnet-paramagnet phase transition in Cr₂O₃ thin films.

a–c Schematics of the antiferromagnet-paramagnet phase transition. a At temperatures below \({T}_{{{{{{{{\rm{N}}}}}}}}}^{{{{{{{{\rm{top}}}}}}}}}\), the entire sample is antiferromagnetically ordered. b With the increase in temperature to about \({T}_{{{{{{{{\rm{N}}}}}}}}}^{{{{{{{{\rm{top}}}}}}}}}\), the less strained part of the sample (top region) undergoes a phase transition into the paramagnetic state. The bottom part of the sample remains antiferromagnetically ordered. c The portion of the sample in the ordered state is determined by the temperature. The sample turns into the paramagnetic state for \(T \, > \,{T}_{{{{{{{{\rm{N}}}}}}}}}^{{{{{{{{\rm{bot}}}}}}}}}\). d The change of the length of the antiferromagnetic order parameter L along the film thickness for a 50-nm-thick Cr₂O₃ thin film. The brown/red/orange curves correspond to the states shown in (a–c), respectively. e The portion of the 50-nm-thick film, which remains in the antiferromagnetic state, dependent on the measurement temperature. In the temperature range between \({T}_{{{{{{{{\rm{N}}}}}}}}}^{{{{{{{{\rm{top}}}}}}}}}\) and \({T}_{{{{{{{{\rm{N}}}}}}}}}^{{{{{{{{\rm{bot}}}}}}}}}\), only the part of the sample closer to the bottom interface remain in the ordered state. Green and gray shaded area represent regions in antiferromagnetic (AFM) and paramagnetic (PM) states, respectively. f Different contributions to the Néel temperature for Cr₂O₃ samples. The green shaded bar represents the bulk Néel temperature, which is measured for a single crystal and strain-free thin film (250-nm-thick in our study). The presence of a compressive strain in a Cr₂O₃ thin film leads to the increase in the Néel temperature. The value of T_N at the top surface (z = t) which is determined by the smallest strain u₀ is indicated by the orange shaded bar. T_N at the bottom surface (blue shaded bar) is larger according to the larger strain value u₀ + wt at z = 0. Error bars on the \({T}_{{{{{{{{\rm{N}}}}}}}}}^{{{{{{{{\rm{top}}}}}}}}}\) and \({T}_{{{{{{{{\rm{N}}}}}}}}}^{{{{{{{{\rm{bot}}}}}}}}}\) correspond to uncertaninity of the fit of the magnetotransport and NV data, respectively.