Paramagnetism of Free Ions. Sign problem.

  1. Energy of system of magnetic dipoles is
    ##E_H=-\mu_0 \vec{\mu}\cdot \vec{H}=-\mu_0\mu_zH##
    why sign ''-''?
    and ##\mu_z=-g_J\mu_Bm##
    Again why ''-'' sign ?
    ##z## is choosen to be quantization direction, and along that direction is applied field ##H##.
  2. jcsd
  3. E=m[itex]\bullet[/itex]B but as the material has a magnetization M and B= H+M then H must face the opposite direction to B and that explains the first negative sign I think.
  4. In a paramagnet, the magnetization of the material is parallel to the applied field. In a diamagnet it would be antiparallel (opposite).

    The first "-" is there because the energy decreases when a magnetic moment is parallel to the applied field.

    The second "-" does not make any sense to me.

    H appears to be along the positive z direction. Then the magnetization mu_z should also be along the positive z direction, and it should be proportional to H. The magnitude of the magnetization also depends on the temperature.
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