AC magnetic-field response of the ferromagnetic superconductor ${\mathrm{UGe}}_2$ with different magnetized states

We have performed parallel measurements of dc-magnetization and ac-magnetic susceptibility for a ferromagnetic superconductor, ${\mathrm{UGe}}_2$, in the ferromagnetic-superconducting phase. dc-magnetization measurements revealed that adequate demagnetizing of the sample allows for the preparation of various magnetized states with different zero-field residual magnetization. We observed that these states exhibit varying ac superconducting response at large ac-field amplitudes. The amount of ac flux penetration is less in the demagnetized state involving many domain walls. This result seems to contradict the theory that considers the domain walls as weak links. Moreover, the ferromagnetic domain walls enforce the shielding capability of superconductivity. This observation sheds light on the role of the domain walls on superconductivity, which has been a controversial issue for several decades. Two possible scenarios are presented to explain the enhancement of the shielding capability by the domain walls.

Figure 1

(a) A schematic of the self-induced vortex state with FM domains. Effective fields due to the FM magnetization $M$ produce SC vortex and antivortex currents in each domain. (b) $M-H$ curves of ${\mathrm{UGe}}_2$ at 750 and 85 mK. The markers represent residual magnetizations for the states prepared by different demagnetization processes. For details, see the text. (c) Examples of the sequence (No. 3 and No. 6).

Figure 2

Temperature dependence of ac susceptibilities of the magnetized (No. 1) and demagnetized (No. 6) states with various ac-field amplitudes. ${\chi }^{\prime }$ and ${\chi }^{\prime \prime }$ represent in-phase and out-of-phase signals, respectively.

Figure 3

Penetrating ac flux as a function of the ac-field amplitude for various magnetized states at 80 mK. The numbers of the states correspond to those in Fig. 1. The solid and dotted lines are the expected ones for the cases of full penetration and perfect shielding, respectively.

Figure 4

(a) Domain structures and demagnetization fields for the magnetized and demagnetized states. (b) Penetrating ac flux at ${\mu }_0{H}_{\mathrm{ac}}=0.625$ mT as a function of the dc field ${\mu }_{0}H$. The red, closed and blue, open circles represent the data taken in field-increasing and decreasing processes, respectively. The absence of the data around +20 mT is due to the disturbance from the SC transition of the indium reference. The lower panel shows the corresponding magnetization in each process. (c) The same data with (b) plotted as a function of the effective field, $H_{\mathrm{eff}}=H-NM\left(H_{\mathrm{eff}}\right)$.