The internal and external magnetoelectric effect in LiFeP$_{2}$O$_{7}$

We study the internal and external magnetoelectric (ME) effect of the single-crystalline LiFeP$_{2}$O$_{7}$ by magnetic, thermodynamic, and magnetoelectric measurements. The Fe$^{3+}$ spins form a canted antiferromagnetic (AFM) order below $T_{N}$ $\sim$ 27K with weak ferromagnetic components along the $b$-axis. A sharp peak found in the pyroelectric current at 27K indicates the strong internal ME interaction resulting in a sizeable polarization decrease. With external magnetic field applied, the ME polarization shows a combination of a linear and a quadratic field dependence below $T_{N}$, but it only shows the quadratic ME response above then. A large uniaxial magnetoelastic response in the thermal expansion data indicates strong spin-lattice coupling. A qualitative explanation regarding to the ME interaction between electric polarization and magnetic order parameters will be proposed and discussed.