Sometimes you may have a system with asymmetrical coercivity, in other words, a different value for positive and negative Hc. For instance, see "Asymmetry of coercivity dependence on temperature in exchange-biased
FeMn/Co bilayers", APPLIED PHYSICS LETTERS VOLUME 77, NUMBER 17(2000). The reason is a phenomenon called exchanged anisotropy. It occurs at ferromagnetic/antiferromagnetic bilayers. Some explanation about that is at "Analytical solutions for exchange bias and coercivity in ferromagnetic/antiferromagnetic bilayers", PHYSICAL REVIEW B VOLUME 62, NUMBER 9 (2000), an article of J. Geshev.