Strong magneto-optical effects in $A{\mathrm{Cr}}_{2}{\mathrm{O}}_{4}$ ($A=\text{Fe,}\phantom{\rule{4.pt}{0ex}}\text{Co}$) spinel oxides generated by tetrahedrally coordinated transition metal ions

Strong magneto-optical effects in $A {Cr}_{2} O_{4}$ ( $A = Fe, Co$ ) spinel oxides generated by tetrahedrally coordinated transition metal ions

V. Kocsis, S. Bordács, J. Deisenhofer, L. F. Kiss, K. Ohgushi, Y. Kaneko, Y. Tokura, and I. Kézsmárki

Phys. Rev. B 97, 125140 – Published 23 March 2018

Abstract

Magneto-optical effects have been investigated over the infrared visible spectral range in $A {Cr}_{2} O_{4}$ ( $A = Fe, Co$ ) spinel oxides with noncollinear spin orders in their ground states. We found large magneto-optical Kerr rotation and ellipticity at the on-site $d - d$ transitions of the $A^{2 +}$ ions located within the charge gap. The magneto-optical Kerr rotation of $ϑ_{Kerr} \approx 12^{\circ}$ observed in ${CoCr}_{2} O_{4}$ is unprecedentedly large among magnetic semiconductors and points toward the uniqueness of tetrahedrally coordinated ${Co}^{2 +}$ ions in generating strong magneto-optical response. Criteria of strong magneto-optical effects emerging at on-site $d - d$ transitions of transition metal ions are discussed.

Received 30 November 2017

DOI:https://doi.org/10.1103/PhysRevB.97.125140

Physics Subject Headings (PhySH)

Ferrimagnetism Spin-orbit coupling

Magnetic insulators Oxides

Kerr effect

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

V. Kocsis^1,2, S. Bordács¹, J. Deisenhofer³, L. F. Kiss⁴, K. Ohgushi⁵, Y. Kaneko², Y. Tokura^2,6, and I. Kézsmárki^1,3

¹Department of Physics, Budapest University of Technology and Economics and MTA-BME Lendület Magneto-optical Spectroscopy Research Group, 1111 Budapest, Hungary
²RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
³Experimental Physics 5, Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg, 86159 Augsburg, Germany
⁴Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, 1525 Budapest, Hungary
⁵Department of Physics, Graduate School of Science, Tohoku University, 6-3, Aramaki Aza-Aoba, Aoba-ku, Sendai, Miyagi 980-8578, Japan
⁶Department of Applied Physics, University of Tokyo, Hongo, Tokyo 113-8656, Japan

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Vol. 97, Iss. 12 — 15 March 2018

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Figure 1
Temperature dependence of the complex magneto-optical Kerr rotation spectra of ${CoCr}_{2} O_{4}$ over the near-infrared–visible region measured in $μ_{o} H = 0.3$ T magnetic field. (a) [(b)] Magneto-optical Kerr rotation ( $ϑ_{Kerr}$ ) [ellipticity ( $η_{Kerr}$ )] spectra at the ${}^{4}A_{2} \to {}^{4}T_{2}$ and ${}^{4}A_{2} \to {}^{4}T_{1}$ transitions of the ${Co}^{2 +}$ ions. Note the breaks of the horizontal axes between the two transitions and the different vertical scales used at the two sides of the breaks. A huge peak is observed in the Kerr rotation spectrum at the low-energy side of the ${}^{4}A_{2} \to {}^{4}T_{2}$ transition with a maximum of about $12^{\circ}$ at $T = 10$ K. See the inset in panel (a) for an enlarged view of the peak in $ϑ_{Kerr}$ . This peak is accompanied with a strong dispersive signal in the Kerr ellipticity. The splitting of the ${Co}^{2 +} 3 d$ multiplets is schematically reproduced from Refs. [14, 33] with the following hierarchy of the interactions: (i) crystal field of the $O_{4}$ tetrahedron surrounding the Co ion, (ii) spin-orbit interaction, and (iii) exchange interaction. Blue (red) arrows correspond to the $J_{z} \to J_{z} + 1$ ( $J_{z} \to J_{z} - 1$ ) transitions excited by right (left) circularly polarized photons. $J_{z}$ denotes the angular momentum of the $3 d$ electrons along the quantization axis, i.e., the direction of the external magnetic field.
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Figure 2
Temperature dependence of the complex magneto-optical Kerr rotation spectra of ${FeCr}_{2} O_{4}$ measured in the mid- and near-infrared photon energy region. Correspondingly to Fig. 1, the magneto-optical Kerr rotation (a) and ellipticity (b) were measured in $μ_{o} H = \pm 0.3$ T magnetic field. Similarly to ${CoCr}_{2} O_{4}$ , the largest Kerr rotation signal appears at the low-energy side of the ${}^{5}E \to {}^{5}T_{2}$ transition of the ${Fe}^{2 +}$ ion. Splitting of the Fe $3 d$ orbitals is schematically reproduced from Refs. [14, 33] in the same way as in Fig. 1.
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Figure 3
Diagonal (a),(b) and complex off-diagonal (b)–(f) optical conductivity spectra at various temperatures of the two transitions of ${CoCr}_{2} O_{4}$ . Regions of the electronic states approximated by the free-ion spin-orbit splitting for the ${}^{4}T_{2}$ and ${}^{4}T_{1}$ multiplets are indicated by the colored stripes around 0.8 and 1.9 eV, respectively. Blue and red arrows indicate the possible arrangement of the SOI and Zeeman split ZPLs for the ${}^{4}T_{2}$ multiplet.
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Figure 4
Temperature dependence of the diagonal (a) and the complex off-diagonal (b,c) optical conductivity spectra of ${FeCr}_{2} O_{4}$ . The approximated region of the electronic states of the free-ion spin-orbit-split ${}^{5}T_{2}$ multiplet is indicated by the colored stripes. Arrows within the region mark the possible assignment for SOI-split ZPL transitions, while the outside region corresponds to the phonon sidebands.
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Figure 5
Temperature dependence of the magneto-optical effect compared to the magnetization of ${CoCr}_{2} O_{4}$ (a) and ${FeCr}_{2} O_{4}$ (b). The strength of the magneto-optical effect is represented by the integrals of the absolute values of the real and imaginary parts of the off-diagonal conductivity over the spectral window of the measurement. Magnetization was measured in a $μ_{o} H = 0.3$ T magnetic field along the [001] axis of the crystal.
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Figure 6
(a) Schematic illustration of the hybrid electron-lattice excitations in the presence of electron-phonon coupling. Transitions are allowed from the ground state to the phonon sidebands of the excited multiplet, which increases the spectral width of the transition. (b)–(e) Illus- tration of the absorption spectra for different models: (b) Dilute systems have a spiky spectrum, while (c) regular crystals have wider phonon sidebands. In oxide spinels, the $ℏ ω$ phonon energy is larger and the $S$ coupling parameter [Eq. (2)] is smaller as compared to chalcogenide spinels. Therefore, in the former case, shown in panel (d), the ZPL is less overlapped by the phonon sidebands, while in the second case, sketched in panel (e), the phonon sidebands are not just more overlapped with the ZPL, but also most of the intensity is transferred to the sidebands.
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Physical Review B

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Strong magneto-optical effects in $A {Cr}_{2} O_{4}$ ( $A = Fe, Co$ ) spinel oxides generated by tetrahedrally coordinated transition metal ions

V. Kocsis, S. Bordács, J. Deisenhofer, L. F. Kiss, K. Ohgushi, Y. Kaneko, Y. Tokura, and I. Kézsmárki

Phys. Rev. B 97, 125140 – Published 23 March 2018

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Strong magneto-optical effects in ACr2O4 (A=Fe,Co) spinel oxides generated by tetrahedrally coordinated transition metal ions

V. Kocsis, S. Bordács, J. Deisenhofer, L. F. Kiss, K. Ohgushi, Y. Kaneko, Y. Tokura, and I. Kézsmárki

Phys. Rev. B 97, 125140 – Published 23 March 2018

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Strong magneto-optical effects in $A {Cr}_{2} O_{4}$ ( $A = Fe, Co$ ) spinel oxides generated by tetrahedrally coordinated transition metal ions