Second order anisotropy contribution in perpendicular magnetic tunnel   junctions
  Magnetoresistance loops under in-plane applied field were measured on perpendicularly magnetized magnetic tunnel junction (pMTJ) pillars with nominal diameters ranging from 50 to 150 nm. By fitting the hard-axis magnetoresistance loops to an analytical model, the effective anisotropy fields in both free and reference layers were derived and their variations in temperature range between 340K and 5K were determined. It is found that an accurate fitting is possible only if a second-order anisotropy term of the form $-K_{2}cos^4{\theta}$, is added to the fitting model. This higher order contribution exists both in the free and reference layers and its sign is opposite to that of the first order anisotropy constant, $K_{1}$. At room temperatures the estimated $-K_{2}/K_{1}$ ratios are 0.1 and 0.24 for the free and reference layers, respectively. The ratio is more than doubled at low temperatures altering the ground state of the reference layer from 'easy-axis' to 'easy-cone' regime. Easy-cone state has clear signatures in the shape of the hard-axis magnetoresistance loops. The same behavior was observed in all measured devices regardless of their diameter. The existence of this higher order anisotropy was confirmed experimentally on FeCoB/MgO sheet films by ferromagnetic resonance technique. It is of interfacial nature and is believed to be linked to spatial fluctuations at the nanoscale of the anisotropy parameter at the FeCoB/MgO interface, in agreement with Dieny-Vedyayev model. 
A.A. Timopheev, R.Sousa, M.Chshiev, T. Nguyen and B. Dieny
cond-mat.mes-hall