This PDF file includes:

• section S1. dc conductivity of h-RMnO₃
  
• section S2. SIM electronics and the calibration process
  
• section S3. FEA of the tip-sample interaction
  
• section S4. SIM data on polished HoMnO₃ samples
  
• section S5. SIM circuits and impedance match at different frequencies
  
• section S6. More SIM data at various frequencies
  
• section S7. Repeated line scans for improving the signal-to-noise ratio
  
• section S8. Details of the full model calculations
  
• fig. S1. Measurement of the dc resistivity of YMnO₃.
  
• fig. S2. SIM electronics and the calibration process.
  
• fig. S3. FEA of the tip-sample interaction.
  
• fig. S4. SIM data on polished HoMnO₃ samples.
  
• fig. S5. Impedance-match sections at different frequencies.
  
• fig. S6. SIM images at various frequencies.
  
• fig. S7. SIM experiments with repeated line scans.
  
• fig. S8. First principles–based model calculations.
  
• References (52–57)

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