Giant quadratic magneto-optical response of thin ${\mathrm{Y}}_{3}{\mathrm{Fe}}_{5}{\mathrm{O}}_{12}$ films for sensitive magnetometry experiments

Giant quadratic magneto-optical response of thin $Y_{3} {Fe}_{5} O_{12}$ films for sensitive magnetometry experiments

E. Schmoranzerová, T. Ostatnický, J. Kimák, D. Kriegner, H. Reichlová, R. Schlitz, A. Baďura, Z. Šobáň, M. Münzenberg, G. Jakob, E.-J. Guo, M. Kläui, and P. Němec

Phys. Rev. B 106, 104434 – Published 30 September 2022

Abstract

We report an observation of a giant magneto-optical (MO) effect quadratic in magnetization (Cotton-Mouton effect) in a 50 nm thick layer of yttrium-iron garnet (YIG). By a combined theoretical and experimental approach, we managed to quantify both linear and quadratic MO effects in the studied material. We show that the quadratic MO signal in the thin YIG film can exceed the linear MO response, reaching values of 450 μrad that are comparable with Heusler alloys or ferromagnetic semiconductors. This relative enhancement of the quadratic MO response relative to the linear MO response is attributed to antiferromagnetic coupling of two Fe sublattices. Furthermore, we demonstrate that a proper choice of experimental conditions, particularly with respect to the used wavelength, is crucial for optimization of the quadratic MO effect, which can be used very efficiently for magnetometry measurement.

Received 26 October 2021
Revised 17 August 2022
Accepted 16 September 2022

DOI:https://doi.org/10.1103/PhysRevB.106.104434

Physics Subject Headings (PhySH)

Magnetic anisotropy Magnetization switching Magneto-optical effect Methods in magnetism

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

E. Schmoranzerová ¹, T. Ostatnický ¹, J. Kimák ¹, D. Kriegner ^2,3, H. Reichlová ^2,3, R. Schlitz ³, A. Baďura¹, Z. Šobáň ², M. Münzenberg⁴, G. Jakob⁵, E.-J. Guo⁵, M. Kläui⁵, and P. Němec ¹

¹Faculty of Mathematics and Physics, Charles University, Prague, 12116, Czech Republic
²Institute of Physics ASCR v.v.i., Prague 162 53, Czech Republic
³Technical University Dresden, 01062 Dresden, Germany
⁴Institute of Physics, Ernst-Moritz-Arndt University, 17489 Greifswald, Germany
⁵Institute of Physics, Johannes Gutenberg University Mainz, 55099 Mainz, Germany

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Vol. 106, Iss. 10 — 1 September 2022

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Figure 1
Structural and magnetic characterization of thin YIG film. (a,b) Reciprocal space maps (RSMs) taken on 444 and 642 Bragg peaks of YIG at room temperature. (c) Cross sections of RSMs data along the [111] crystallographic directions (points) modeled by dynamical diffraction model (line) with lattice parameter $a = 12.379 Å$ and distortion angle $α = {(90.05 \pm 0.02)}^{\circ}$ . (d) Magnetic hysteresis loops measured by SQUID magnetometry in three in-plane crystallographic directions that are denoted as follows: $A$ [2 -1 -1], $B$ [0 1 -1], and $C$ (diagonal), and in the out-of-plane direction $D$ [111] at a temperature of 50 K.
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Figure 2
(a) Schematics of the experimental setup for magneto-optical magnetometry. Linearly polarized light with a polarization $E$ oriented at an angle β with respect to the TE polarization mode ( $E_{s}$ ) is incident on the sample, which is oriented under an angle $θ_{i}$ . with respect to the plane in which the magnetic field was applied. After being transmitted through the sample, the light polarization plane is rotated by an angle $Δ β$ . The sample is subject to an external magnetic field $H_{ext}$ , applied in an arbitrary direction, with the corresponding spherical angles of the $H_{ext}$ vector shown in (b) plane view projection (azimuthal angle $φ_{H}$ ) and (c) side view projection (polar angle $θ_{H}$ ) of the experimental geometry.
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Figure 3
(a) Rotation of polarization plane $Δ β$ as a function of the external magnetic field magnitude $H_{ext}$ measured for two angles of incidence, $θ_{i} = 3^{\circ}$ and $45^{\circ}$ , corresponding to the same two field angles, $θ_{H} = 3^{\circ}$ and $45^{\circ}$ , respectively; a temperature of 20 K and photon energy of 3.1 eV was used. The data were vertically shifted for clarity. The complex $M$ -shape-like hysteresis is a clear signature of magnetization being switched between magnetic easy axes. (b) Simulation of the MO signal by means of the analytical model. Based on our model, we identified three equivalent easy axes (c) and extracted their mutual angle $ζ = 120^{\circ}$ and position of their bisectrix $γ = 6^{\circ}$ . (d) The abrupt changes in magneto-optical signals in (a,b) correspond to “jumps” of magnetization between the easy axes 1, 3, and 4 (4, 6, and 1) for the magnetic field sweep from the positive (negative) field, as schematically indicated in (a).
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Figure 4
Analysis of magneto-optical signals at an angle of incidence $θ_{i} = 3^{\circ}$ (left column) and $θ_{i} = 45^{\circ}$ (right column). For extracting the MO effects odd and even in magnetization, the signals were decomposed to antisymmetric (red line) and symmetric (black line) components with respect to $H_{ext}$ . An example of results of this procedure is shown for MO signals measured using $β = 0^{\circ}$ for angles of incidence (external field) $θ_{H} = θ_{i} = 3^{\circ}$ (a) and $θ_{H} = θ_{i} = 45^{\circ}$ (b); the original data are shown in Fig. 3. The amplitudes of $A^{LMET}$ and $A^{CME}$ for each polarization angle β were determined from the size of the “jumps” in hysteresis loops, as indicated in (b).
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Figure 5
Amplitudes of CME (left column) and LMET (right column) as a function of incident polarization angle β, extracted from the hysteresis loops obtained from the analytical model. The amplitudes $A^{CME}$ and $A^{LMET}$ are obtained by the same method as in Fig. 4. Polarization dependence of (a) CME and (b) LMET effects for various angles of incidence $θ_{i}$ and fixed sample thickness of 50 nm. The angles of incidence of $θ_{i} = 0^{\circ}$ , 30 °, 40 °, 60 °, and 80 ° are shown; the arrow indicates increase of $θ_{i}$ . Clearly, the LMET is very strongly angle dependent, while CME is much less affected. The same feature can be observed for changing the sample thickness $d$ . While the polarization dependence of CME (c) does not depend on the sample thickness, LMET (d) can vary significantly. The thicknesses of $d = 5$ , 10, 20, 50, 100, 200, 500, and 1000 nm are displayed for the angle of incidence $θ_{i} = 45^{\circ}$ .
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Figure 6
Rotation of polarization plane $Δ β$ as a function of the direction $φ_{H}$ of the external magnetic field of a fixed magnitude $μ_{0} H_{ext} = 205 mT$ , measured at 20 K (a) and at room temperature (b). Polarization was set to $β = 0^{\circ}$ . Open squares indicate the as-measured data; full squares are symmetrized in $φ_{H}$ to remove linear magneto-optical effects. The red line is a fit to Eq. (4) for $φ_{H} = φ_{M}$ as $H_{ext}$ is large enough to saturate magnetization of the sample. Magneto-optical coefficients for the Cotton-Mouton effect obtained from the fits are $P^{CME} = 450 μ rad$ at 20 K and $P^{CME} = 230 μ rad$ at 300 K. (c) The decrease of $P^{CME}$ with increasing temperature is well correlated with the reduction of the square of the saturation magnetization $M_{S}^{2}$ , values of which were taken from Ref. [50] (and converted to SI units). (d) The spectral dependence of $P^{CME}$ measured at room temperature (d) clearly shows a peak at around 3.1 eV.
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Physical Review B

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Giant quadratic magneto-optical response of thin $Y_{3} {Fe}_{5} O_{12}$ films for sensitive magnetometry experiments

E. Schmoranzerová, T. Ostatnický, J. Kimák, D. Kriegner, H. Reichlová, R. Schlitz, A. Baďura, Z. Šobáň, M. Münzenberg, G. Jakob, E.-J. Guo, M. Kläui, and P. Němec

Phys. Rev. B 106, 104434 – Published 30 September 2022

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Physical Review B

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Giant quadratic magneto-optical response of thin Y3Fe5O12 films for sensitive magnetometry experiments

E. Schmoranzerová, T. Ostatnický, J. Kimák, D. Kriegner, H. Reichlová, R. Schlitz, A. Baďura, Z. Šobáň, M. Münzenberg, G. Jakob, E.-J. Guo, M. Kläui, and P. Němec

Phys. Rev. B 106, 104434 – Published 30 September 2022

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Giant quadratic magneto-optical response of thin $Y_{3} {Fe}_{5} O_{12}$ films for sensitive magnetometry experiments