In a series of [Co(5 angstrom)/Pt(6 angstrom)](n), multilayers with perpendicular anisotropy, it has been observed that the coercivity H-C shows an rapid increase as the temperature is decreased from 300 to 5K. Above 220K, H-C is proportional to the repetition number n, that is to say, H-C4 > H-C3 > H-C2 > H-C1 (H-Cn, n is the repetition number), while at 60K <= T <= 210K, n dependence of H-C is H-C3 > HC4 > H-C2 > H-C1. At 25K <= T <= 55K, H-C as a function of the repetition number n can be expressed as Fic2 >Hci >Ho >14c4, whereas below 20K, the single Co layer of n = 1 shows the fastest increase, and the coercivity becomes the largest one, namely, H-C1 > H-C2 > H-C3 > H-C4. This observed n-dependent variations of coercivity with temperature can be attributed to surface roughness and temperature dependence of the saturation magnetization in the Co/Pt multilayers. (C) 2015 Elsevier B.V. All rights reserved.