5 well with the experimental ones. FIG. 4: (Color online) Static q -dependent Pauli suscepti- bilities at fixed q z = π for (a) LaOFeSb and (b) LaOFeBi. The corresponding values of the Pauli susceptibilities at q$_{0}$ = (0 , 0 , π ) in LaOFeSb and LaOFeBi, respectively, are sub- tracted. On top, two-dimensional contour maps are shown. In the DFT calculations GGA is used. Fig. 2 shows the calculated Fermi surface cuts for LaOFeP and LaOFeAs on different k$_{z}$ -planes based on the experimental lattice structures. The figure is almost unchanged if we consider the optimized lattice struc- ture. The hole Fermi surfaces around (0 , 0 , k$_{z}$ ) are shifted by ( π, π, 0) to show the nesting properties. Shifting of ( π, π, π ) was also investigated, and we find that the nest- ing properties are nearly unchanged. From the figure, it is apparent that the Fermi surface nesting is even more perfect in LaOFeP than in LaOFeAs, indicating a stronger tendency to stripe-type antiferromagnetic order- ing in LaOFeP compared to LaOFeAs. However, experi- mentally, while a small magnetization is observed in un- doped LaOFeAs $^{77}$, superconductivity rather than mag- netic order is detected in undoped LaOFeP $^{90}$. These observations would indicate that Fermi surface nesting might not be connected to magnetization. In order to quantify the Fermi surface nesting, we show in Fig. 3 the q -dependent Pauli susceptibilities at fixed q$_{z}$ = π for LaOFeP and LaOFeAs with subtraction of the corresponding values at q$_{0}$ = (0 , 0 , π ). While a peak in LaOFeP appears right at q$_{π}$ = ( π, π, π ) indicating almost perfect nesting properties of the Fermi surfaces, peaks are situated close to q$_{π}$ = ( π, π, π ) in LaOFeAs sug- gesting nearly nested Fermi surfaces, which is consistent with the Fermi surface cuts shown in Fig. 2. The most interesting finding in Fig. 3 is that the relative values χ ( π, π, π )- χ (0 , 0 , π ) increase from LaOFeP to LaOFeAs irrespective of whether the Fermi surface nesting is per- fect or not. While the peak at ( π, π, π ) favors stripe- type antiferromagnetic ordering, the one at (0 , 0 , π ) rep- resents a possible instability towards checkerboard-type antiferromagnetic ordering or A-type antiferromagnetic ordering where ferromagnetic layers are stacked antifer- romagnetically. The heights of these two peaks become closer in LaOFeP than in LaOFeAs, implying that com- petition between the above-mentioned two types of anti- ferromagnetic states becomes stronger in LaOFeP if ther- mal or quantum fluctuations are taken into account. Also spin-fluctuation mediated pairing of the superconducting state 23,26,30 coming from inter-band scattering around q$_{π}$ = ( π, π, π ) takes part in the competition. Eventually, as the two types of antiferromagnetism strongly compete with each other, the additional superconducting state or- der emerges and opens a gap, removing the high instabil- ity at the Fermi level and lowering the total energy. This could be the scenario to explain why undoped LaOFeP is always nonmagnetic but shows superconductivity be- low 3.2 K at ambient pressure. As χ ( π, π, π ) − χ (0 , 0 , π ) increases beyond a critical value, the stripe-type antifer- romagnetic ordering prevails over the checkerboard-type one and the pairing. This scenario may apply to the low-temperature magnetic phase of LaOFeAs. Further- more, we have calculated the total energies of checker- board and stripe-type antiferromagnetic phases for both LaOFeP and LaOFeAs. We found that the stripe-type antiferromagnetic phases are the ground state in both cases and the energy difference between the two phases is smaller in LaOFeP than in LaOFeAs, which is consis- tent with the trend of χ ( π, π, π )- χ (0 , 0 , π ). In Fig. 4, we display the q -dependent Pauli suscepti- bilities at fixed q$_{z}$ = π for the hypothetical compounds LaOFeSb and LaOFeBi. The corresponding values of the Pauli susceptibilities at q$_{0}$ = (0 , 0 , π ) in LaOFeSb and LaOFeBi, respectively, are again subtracted. Note that χ ( π, π, π ) − χ (0 , 0 , π ) in LaOFeSb and LaOFeBi is even larger than that in LaOFeAs (see Fig. 3), indicat- ing that the instability towards stripe-type antiferromag- netic ordering could win the competition between dif- ferent instabilities in these two compounds. It is also interesting to note that the peak at q$_{0}$ = (0 , 0 , π ) be- comes flatter when we go from LaOFeP to LaOFeBi. While the flatness of the peak can be associated with a larger number of different magnetic structures lying