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I read several books on permanent magnet synchronous machines (PMSM), and they tend to describe the relationship between H and B as \$B_{mag}=\mu_0\mu_{r,mag}H_{mag}+B_{rem}\$.

Then when they apply Ampere's law \$\nabla \times H=J\$ with the integration path crossing this permanent magnet as \$2H_{mag}\delta_{mag}+H_{external}\delta_{external}=0\$ because there is no current circled by the integration path.

However, I could not understand why the effect of \$B_{rem}\$ is excluded in the application of Ampere's law. Why is \$H_{mag}\$ used in the equation but not \$\large\frac{B_{mag}}{\mu_0\mu_{r,mag}}\$?

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