Penetration depth of Cooper pairs in the IrMn antiferromagnet

Suppression of superconductivity due to the proximity effect between a superconductor and a ferromagnet can be partially alleviated when a Cooper pair simultaneously samples different directions of the short-range exchange field. The superconductor's critical temperature, $T_C$, is therefore expected to partially recover when the ferromagnet is in a multidomain state, as opposed to a single-domain state. Here, we discuss series of experiments performed with ferromagnet(Pt/Co)/spacer(IrMn and Pt)/superconductor(NbN) heterostructures. By tuning the various parameters in play, e.g., superconducting coherence length-to-thicknesses ratio, and domain sizes, we obtained up to 10% recovery of the superconducting critical temperature $\mathrm{\Delta }{T}_C/T_C$. This large-scale recovery made investigations possible. In particular, from the spacer thickness dependence of $\mathrm{\Delta }{T}_C/T_C$, it was possible to deduce the characteristic length for Cooper pair penetration in an IrMn antiferromagnet. This information is crucial for electronic transport, and up to now has been difficult to access experimentally for antiferromagnets.

Figure 1

(a) Optical image of a typical device used to perform transport measurements. The complete image is reconstructed from three optical images (indicated by the dotted squares). (b) Normalized magnetization $M/M_S$ starting from a demagnetized state measured at 12 K for a $\mathrm{Si}/{\mathrm{SiO}}_2\parallel {[\mathrm{Pt}\left(1\right)/\mathrm{Co}\left(0.65\right)]}_{15}$/IrMn(3)/NbN(15) (nm) ferromagnetic/spacer/superconductor stack. (c) Representative data showing the T dependence of R, for the same sample as in (b), prepared in two distinct magnetic states: saturated and demagnetized, through two procedures involving field cycling and cooling (see text). $\mathrm{\Delta }{T}_C$ (here, systematically measured at $R=0.5\mathrm{m}\mathrm{\Omega }$) represents the difference in superconducting critical temperature between the saturated and demagnetized states ($\mathrm{\Delta }{T}_C=T_{c,\mathrm{demagnetized}\mathrm{state}}\text{–}{T}_{c,\mathrm{saturated}\mathrm{state}}$). (d) MFM image taken at room temperature, for the sample used in (b) and (c), showing maze domains after demagnetization. (Inset) PSD profile of the MFM image. (e) Control experiment with a bare $\mathrm{Si}/{\mathrm{SiO}}_2\parallel \mathrm{NbN}\left(15\right)$ (nm) stack subjected to the two procedures used for (c). Data in (c) and (e) were measured for an applied field $H=0.5\mathrm{kOe}$. The symbols in (b) represent the two magnetic states, demagnetized (square) and saturated (circle).

Figure 2

(a) NbN thickness ($t_{\mathrm{NbN}}$) dependence of $\mathrm{\Delta }{T}_C$. (b) Representative data showing H vs $T_C$ as measured for $\mathrm{Si}/{\mathrm{SiO}}_2\parallel {[\mathrm{Pt}\left(1\right)/\mathrm{Co}\left(0.65\right)]}_{15}$/IrMn(3)/NbN($t_{\mathrm{NbN}}$) (nm) stacks. These data were used to calculate the superconducting coherence length, ${\xi }_{\mathrm{NbN}}$ and the zero-field superconducting temperature, $T_{C,H=0}$. Lines were fitted to the data using the model described in the text. (c) Corresponding $t_{\mathrm{NbN}}$ dependences of ${\xi }_{\mathrm{NbN}}$ and $T_{C,H=0}$ compared to data obtained for bare $\mathrm{Si}/{\mathrm{SiO}}_2\parallel \mathrm{NbN}\left(t_{\mathrm{NbN}}\right)$ (nm) stacks. The lines serve as visual guides. (d) Dependence of $\mathrm{\Delta }{T}_C/T_C=\left(T_{c,\mathrm{demagnetized}\mathrm{state}}\text{–}{T}_{c,\mathrm{saturated}\mathrm{state}}\right)/T_{c,\mathrm{saturated}\mathrm{state}}$ with the superconducting coherence length-to-thickness ratio $({\xi }_{\mathrm{NbN}}/t_{\mathrm{NbN}})$. The line is a linear fit to the data constrained to pass through (0,0).

Figure 3

(a) Normalized magnetization $M/M_S$ of a $\mathrm{Si}/{\mathrm{SiO}}_2\parallel {[\mathrm{Pt}\left(1\right)/\mathrm{Co}\left(0.65\right)]}_{15}$/IrMn(3)/NbN(15) (nm) stack for field-cycling series. Measurements were performed at 12 K starting from a demagnetized state. Selected magnetic configurations are labeled as follows: (square) Saturated; (triangle) Intermediate; and (diamond) Demagnetized. The cooling procedures used to access each magnetic configuration are described in the text. (b) Data showing the T dependences of R for the three magnetic states examined. (c) Dependence of $\mathrm{\Delta }{T}_{C,i}/T_C$ on $1-M/M_S$, where $\mathrm{\Delta }{T}_{C,i}$ represents the difference in superconducting critical temperature between any state and the saturated state.

Figure 4

(a) Dependence of $\mathrm{\Delta }{T}_{C,i}/\mathrm{\Delta }{T}_C$ on $1-M/M_S$ for $\mathrm{Si}/{\mathrm{SiO}}_2\parallel {[\mathrm{Pt}\left(1\right)/\mathrm{Co}\left(0.65\right)]}_n$/IrMn(3)/NbN(15) (nm) stacks ($n=4$, 8, 11, 15), measured while applying an external field of $H=0.5\mathrm{kOe}$. Lines were calculated using the model described in the text, for $L_F/{\xi }_S\approx 0.25;2.5;5;12.5;\mathrm{and}25$. (b) Corresponding dependence of $\mathrm{\Delta }{T}_C/T_C$, corresponding to $\left(T_{c,\mathrm{demagnetized}\mathrm{state}}\text{–}{T}_{c,\mathrm{saturated}\mathrm{state}}\right)/T_{c,\mathrm{saturated}\mathrm{state}}$ on the total thickness ($t_{\mathrm{Pt}/\mathrm{Co}}$) of the ${\left[\mathrm{Pt}/\mathrm{Co}\right]}_n$ multilayer, measured at $H=0.5$ and 1.3 kOe. (c) $t_{\mathrm{Pt}/\mathrm{Co}}$ dependence of the domain sizes ($w_{\mathrm{Pt}/\mathrm{Co}}$), deduced from MFM images taken at room temperature after demagnetization, i.e., for $M/M_S\sim 0$. (Inset) Semilogarithmic-scale dependence of $w_{\mathrm{Pt}/\mathrm{Co}}$ on $1/t_{\mathrm{Pt}/\mathrm{Co}}$. Lines were fitted to the data using a model described in the text. (d) Control measurements for ${\xi }_{\mathrm{NbN}}$ and $T_{C,H=0}$ vs $t_{\mathrm{Pt}/\mathrm{Co}}$.

Figure 5

(a), (b) $t_{\mathrm{spacer}}$ dependence of $\mathrm{\Delta }{T}_C/T_C$ measured for $\mathrm{Si}/{\mathrm{SiO}}_2\parallel {[\mathrm{Pt}\left(1\right)/\mathrm{Co}\left(0.65\right)]}_{15}$/spacer($t_{\mathrm{spacer}}$)/NbN(15) (nm) stacks, for IrMn and Pt spacers. Lines correspond to exponential fits of the data (see text). (Inset) Corresponding semilogarithmic scale dependence of $\mathrm{\Delta }{T}_C/T_C$ on $t_{\mathrm{spacer}}$.

Figure 6

(a) Blocking temperature distribution measured for a $\mathrm{Si}/{\mathrm{SiO}}_2\parallel {[\mathrm{Pt}\left(1\right)/\mathrm{Co}\left(0.65\right)]}_4$/IrMn(3)/NbN(15) (nm) stack. (b) Normalized magnetization $M/M_S$, measured at 12 K for a $\mathrm{Si}/{\mathrm{SiO}}_2\parallel {[\mathrm{Pt}\left(1\right)/\mathrm{Co}\left(0.65\right)]}_{15}$/IrMn(3)/NbN(15) (nm) stack, after stabilizing several states in the IrMn antiferromagnet (see text). (c) Corresponding normalized magnetization at the remanent state for $H=0.5\mathrm{kOe}$. (d) Dependence of $\mathrm{\Delta }{T}_{C,i}/T_C$ on $1-M/M_S$.