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Magnetooptic coupling coefficients for one- and two-magnon Raman scattering in rutile-structure antiferromagnets FeF2, MnF2, CoF2, and NiF2
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10.1063/1.4733682
/content/aip/journal/ltp/38/7/10.1063/1.4733682
http://aip.metastore.ingenta.com/content/aip/journal/ltp/38/7/10.1063/1.4733682

Figures

Image of FIG. 1.
FIG. 1.

Crystallographic unit cell of CoF2 (a = b ≠ c) showing the c axis spin alignment along with the principal exchange interactions J 1, J 2, and J 3. Crystal axes (x, y, z) and laboratory axes (X, Y, Z) are illustrated in relation to the unit cell. The X and Y directions are orthogonal to the c (Z) axis, but are rotated by ∼45° about the crystallographic a and b axes.

Image of FIG. 2.
FIG. 2.

Crystallographic unit cell of NiF2 showing the canted spin alignment in the crystal ab plane along with the dominant exchange interactions J 1, J 2, and J 3.

Image of FIG. 3.
FIG. 3.

One-magnon (M) Raman spectrum of MnF2 at 41 K recorded in X(ZX)Y polarization at a spectral resolution of 0.53 cm–1.

Image of FIG. 4.
FIG. 4.

Experiment and theory for the temperature dependence of one-magnon integrated intensity in MnF2 for Stokes scattering in several polarizations. The experimental points refer to: (XZ) polarization (○); (YZ) polarization (□); (ZX) polarization (△). The theoretical curves shown are for G +/K + = 0 (broken line) and G +/K + = 0.08 (solid lines).

Image of FIG. 5.
FIG. 5.

Experimental data and theoretical prediction are shown for the temperature dependence of one-magnon integrated intensity in MnF2 for anti-Stokes scattering. Experimental points (Δ) refer to (ZX) polarization. Theoretical curves are for G +/K  + = 0 (broken line) and G +/K + = 0.08 (solid line).

Image of FIG. 6.
FIG. 6.

Comparison of theory and experiment for the temperature dependence of the relative one-magnon integrated intensity (including the Bose population factor) in MnF2. Magnetooptic coefficients are taken to be zero. The plotted curves correspond to: K  = 0 (1); K + = 0 (2); |K /K +| = 0.007 (3). The experimental data correspond to Z(XZ)Y (crosses) and Z(YZ)Y (circles) polarizations.

Image of FIG. 7.
FIG. 7.

The two-magnon portion of the experimental X(YX)Y spectrum for FeF2 at 12 K (full curve) compared with the theoretical line shapes without (dotted curve) and with (broken curve) an additional cross term involving B 6.

Image of FIG. 8.
FIG. 8.

Comparison of the theoretical curve and experimental points for the low-temperature (∼5 K) two-magnon Raman spectrum of CoF2 in diagonal (a) and off-diagonal (b) polarizations, as indicated. The dotted lines show theoretical results without the inclusion of magnon–magnon interactions.

Image of FIG. 9.
FIG. 9.

Comparison of theory and experiment for the temperature dependence of the Stokes integrated intensity in NiF2 for the upper branch in (YZ) polarization. The theoretical curves are obtained for the following values of |G +/K +|: 0.0 (1), 0.1 (2), 1 (3), and 100 (4).

Image of FIG. 10.
FIG. 10.

Comparison of the anti-Stokes to Stokes integrated intensity ratio of the lower energy branch for NiF2 in (YZ) polarization for different values of |G /K +|: 0.30 (1), 0.25 (2), and 0 (3).

Image of FIG. 11.
FIG. 11.

Comparison of theory and experiment for the temperature dependence of anti-Stokes to Stokes integrated intensity ratio of the lower energy branch in NiF2 for (YX) polarization. Theoretical curves correspond to |G 3/K 3| values of: 1.0 (1), 0.1 (2), and 0 (3).

Image of FIG. 12.
FIG. 12.

Comparison of theoretical curves (see text) and experimental data points for the low-temperature (∼10 K) two-magnon Raman spectrum of NiF2 in diagonal (a) and off-diagonal polarizations (b), as indicated.

Tables

Generic image for table
Table I.

Physical parameters of rutile-structure antiferromagnets. This information is taken from Ref. 2.

Generic image for table
Table II.

Principal exchange interactions J 1, J 2, and J 3, and anisotropy parameters deduced from the theoretical analysis of two-magnon Raman spectrum of rutile-structure antiferromagnets at temperature TTN . In the cases of CoF2 and MnF2 the quoted HA are effective anisotropy terms as approximated for zone-boundary magnons.

Generic image for table
Table III.

Absolute and relative linear (K) and quadratic (G) magnetooptic coupling coefficients for one-magnon Raman scattering in rutile-structure antiferromagnets. The subscripts (+) and (–) refer to in-phase and out-of-phase scattering, respectively.

Generic image for table
Table IV.

Relative magnetooptic coupling coefficients, Bn (n = 1,…, 7), for two-magnon Raman scattering in rutile-structure antiferromagnets.

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2012-07-27
2014-04-19
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Scitation: Magnetooptic coupling coefficients for one- and two-magnon Raman scattering in rutile-structure antiferromagnets FeF2, MnF2, CoF2, and NiF2
http://aip.metastore.ingenta.com/content/aip/journal/ltp/38/7/10.1063/1.4733682
10.1063/1.4733682
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