Forbidden Transitions (<span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Δ</mi><mi>m</mi><mo>=</mo><mo>±</mo><mn>1</mn></math></span>) in the Paramagnetic Resonance Absorption of <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi mathvariant="normal">Mn</mi></mrow><mrow><mn>2</mn><mo>+</mo></mrow></msup></mrow></math></span> in Calcite

J. Mankowitz; W. Low

doi:10.1103/PhysRevB.2.28

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Forbidden Transitions ( $Δ m = \pm 1$ ) in the Paramagnetic Resonance Absorption of ${Mn}^{2 +}$ in Calcite

J. Mankowitz and W. Low

Microwave Division, Department of Physics, The Hebrew University, Jerusalem, Israel

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Phys. Rev. B 2, 28 – Published 1 July, 1970

DOI: https://doi.org/10.1103/PhysRevB.2.28

Abstract

The forbidden transitions of the type $Δ m = \pm 1$ for ${Mn}^{2 +}$ in single crystals of calcite have been investigated at $X$ -band frequencies. The results can be fitted with the spin Hamiltonian $H = g μ_{B} \vec{H} \cdot \vec{S} + B_{2}^{0} O_{2}^{0} + B_{2}^{0} O_{2}^{0} + B_{4}^{0} O_{4}^{0} + B_{4}^{3} O_{4}^{3} + C_{4}^{3} O_{4}^{3} + A (S_{x} I_{z}) + B (S_{x} I_{x} + S_{y} I_{y}) - g_{N} μ_{N} (\vec{H} \cdot \vec{I}) + Q^{'} [I_{z}^{2} - \frac{1}{3} I (I + 1)] + Q^{''} (I_{x}^{2} - I_{y}^{2})]$ . At room temperature, the best computer fit for the parameter is $g_{∥} = 2. 0019 \pm 0. 0006, g_{⊥} = 2. 0018 \pm 0. 0006,$ $B_{2}^{0} = 24. 99 \pm 0. 10, B_{4}^{0} = 0. 0397 \pm 0. 0002,$ $A = 87. 01 \pm 0. 04, B = 87. 26 \pm 0. 04,$ $Q^{'} = 0. 174 \pm 0.1, Q^{''} cos 2 φ = - 0. 065 \pm 0. 1,$ $B_{4}^{3} cos 3 φ - C_{4}^{3} sin 3 φ = - 0. 542 \pm 0. 04$ (all in units of $10^{- 4}$ ${cm}^{- 1}$ ); $g_{N} μ_{N} = (10. 11 \pm 2. 0) \times 10^{- 24}$ erg/G.

References (6)

L. M. Mataresse and C. Kikuchi, J. Chem. Phys. 33, 601 (1060) L. M. Mataresse, 34, 336 (1961)
S. A. Marshall and A. R. Reinberg, Phys. Rev. 132, 134 (1963)
W. Low, in Solid State Physics, Suppl. 2, edited by F. Seitz and D. Turnbull (Academic, New York, 1960)
J. L. Prather, Atomic Energy Levels in Crystals, Natl. Bur. Std. Monograph No. 19 (U. S. Government Printing Office, Washington, D. C., 1961)
M. T. Hutchings, in Solid State Physics, edited by F. Seitz and D. Turnbull (Academic, New York, 1964), Chap. XVI
F. R. Hurd, M. Sachs, and W. O. Hershberger, Phys. Rev. 93, 373 (1954)

[c1] L. M. Mataresse and C. Kikuchi, J. Chem. Phys. 33, 601 (1060) L. M. Mataresse, 34, 336 (1961)

[c2] S. A. Marshall and A. R. Reinberg, Phys. Rev. 132, 134 (1963)

[c3] W. Low, in Solid State Physics, Suppl. 2, edited by F. Seitz and D. Turnbull (Academic, New York, 1960)

[c4] J. L. Prather, Atomic Energy Levels in Crystals, Natl. Bur. Std. Monograph No. 19 (U. S. Government Printing Office, Washington, D. C., 1961)

[c5] M. T. Hutchings, in Solid State Physics, edited by F. Seitz and D. Turnbull (Academic, New York, 1964), Chap. XVI

[c6] F. R. Hurd, M. Sachs, and W. O. Hershberger, Phys. Rev. 93, 373 (1954)

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Forbidden Transitions ( $Δ m = \pm 1$ ) in the Paramagnetic Resonance Absorption of ${Mn}^{2 +}$ in Calcite

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Forbidden Transitions (Δm=±1) in the Paramagnetic Resonance Absorption of Mn2+ in Calcite

Abstract

References (6)

Forbidden Transitions ( $Δ m = \pm 1$ ) in the Paramagnetic Resonance Absorption of ${Mn}^{2 +}$ in Calcite