Campbell penetration depth in stoichiometric LiFeAs - evidence for static fishtail effect

The ``fishtail'' or second magnetization peak is one of the most intriguing properties of high$-T_c$ cuprate superconductors. Now it has also been observed in iron-based materials and has been associated with weak collective pinning. To understand whether the fishtail effect has dynamic (due to field-dependent magnetic relaxation) or static behavior (due to actual non-monotonic field dependence of the true critical current) one needs to measure the clean system, which are rare in pnictide superconductors. A stoichiometric LiFeAs is one of the cleanest of the pnictides with RRR=65. We measured the Campbell penetration depth using a 10 MHz tunnel-diode resonator in DC magnetic fields of up to 9 T. As opposed to the ``apparent'' current density, estimated from the magnetization relaxed over tens of seconds, the Campbell penetration depth depends on the curvature of the pinning potential sampled at time intervals of 0.1 $\mu$sec, thus allowing one to estimate the unrelaxed, ``true'' $j_c(T,B)$. The obtained $j_c(T,B)$ shows a non-monotonic trend with a second peak shifting toward lower fields at higher temperatures implying a static origin of the fishtail effect in LiFeAs.