“…[23,37] In the gigahertz regime, a substantial enhancement of the AC conductivity at [63,64] d) The DC conduction at ferroelectric domain walls is commonly characterized using cAFM, whereas nanoimpedance microscopy (NIM), [102,103] scanning impedance microscopy (SIM), [104] and cAFM under AC-drive voltage (AC-cAFM) [23] have been applied to investigate their AC response for frequencies f ≲ 1 MHz. For higher frequencies, microwave impedance microscopy (MIM) [105] is an established method for impedance measurements at the local scale (LiNbO 3 , [96,99] h-ErMnO 3 , [23,37] h-YMnO 3 , [7] h-(Lu,Sc)FeO 3 , [101] KNbO 3 , [100] Pb(Zr,Ti)O 3 , [98] and BiFeO 3 [97] ). The background color indicates two regimes corresponding to kilo-to megahertz (f ≲ 1 MHz, blue) and gigahertz (f ≳ 1 MHz, yellow) frequencies, where domain wall responses are dominated by different contributions, as discussed in Sections 2 and 3, respectively.…”