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An introduction to the use of representation analysis for studying magnetoelectrics and multiferroics

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Figure

Figure 1. The transformations of a polar vector (signs + and − at the base and tip of the arrow) and axial vector(current loop) under inversion symmetry, time-reversal symmetry and mirror symmetry.
Figure 2. Magnetic moment of atom j, at position ⃗rj in the primitive unit-cell, and global position R⃗jL = ⃗rj + R⃗Lwith respect to the origin, where R⃗L is a direct lattice vector.
Figure 3. Invariance of a spin-density wave under time-reversal symmetry. The combined effect of time-reversaland a translation T⃗ such that eik⃗ ⃗T = −1 leaves the magnetic modulation invariant.
Figure 4. Zero-field magnetic structure of Cr2O3. For clarity, only Cr ions along the 0,0,z line are shown
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