Possible method to observe the breathing mode of a magnetic domain wall in the Josephson junction

A magnetic domain wall (DW) behaves as a massive particle with elasticity. Sliding and oscillation of the DW have been observed experimentally, whereas vibration of a width in the DW, "breathing mode", has not been measured so far. We theoretically propose how to observe the breathing mode by the Josephson junction having a ferromagnetic layer between superconducting electrodes. The current-voltage (I-V) curve is calculated by an equivalent circuit of the resistively shunted junction model. The breathing mode is identified by stepwise structures in the I-V curve, which appear at the voltages V = n (ħ/2e)ω with the fundamental constant ħ/e, integer number n and the frequency of the breathing mode ω.