= Magnetic anisotropy in orientational trapping
<Magnetic anisotropy> can create a restoring <torque> that aligns a specimen in a <magnetic field>. For a small linearly responding object with uniaxial susceptibility difference $\Delta\chi$, volume $V$ and axis angle $\theta$ in an approximately uniform field, an orientation-dependent <energy> is $U=-V\Delta\chi B^2\cos^2\theta/(2\mu_0)$, up to an angle-independent term.
Positive $\Delta\chi$ favors alignment along the field; negative $\Delta\chi$ favors a perpendicular axis. Thermal angular fluctuations compete with this <energy>, so a preferred orientation becomes pronounced when the anisotropy scale exceeds $k_BT$. This induced-moment mechanism differs from the $-\boldsymbol\mu\cdot\mathbf B$ <energy> of a fixed permanent moment and is relevant to interpreting <magnetic tweezers>.
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