Three classes of giant magnetoresistance Co(1 nm)/Cu(2.1 nm) multilayers were sputter grown with different microstructures in respect to grain size and interface roughness, depending on deposition conditions. Magnetization and current in-plane giant-magnetoresistance (GMR) isothermal loops reveal an unusually high increase of coercivity from 280 down to 5 K. In addition, a systematic variation was observed in the temperature dependence of the indirect exchange coupling as the Co-Cu layering is modified in the three classes of Co/Cu multilayers. Specifically, the temperature dependence of the saturation (switching) field in the GMR-loops, and the indirect coupling strength, vary as (T/T-0)/sinh(T/T-0) whereas the spin-blocking temperature T-0 is found equal to 84(4), 96(11), and 105(10) K for class A, B, and C multilayers, respectively. These results indicate that the desirable low hysteresis appears in the GMR loops at room temperature because the spin structure becomes unstable above the obtained T-0 due to domain wall fluctuations. Such magnetic fluctuations define a short-range order state above T-0 that depends on Co-Cu intermixing and geometric factors of the grains. (C) 2000 American Institute of Physics. [S0021-8979(00)03619-7].