In previous decades, significant efforts have been devoted to increasing the magneto-optical efficiency of iron garnet materials for the miniaturization of nonreciprocal devices such as isolators and circulators. Elemental substitutions, or proper nanostructuring to benefit from optical resonances, have been pursued. However, all these approaches still require film thicknesses of at least several tens of microns to deliver useful device applications, and suffer from narrow bandwidths in the case of optical resonance effects. This paper reports on a newly discovered enhancement of the Faraday effect observed experimentally in nanoscale bismuth-substituted iron garnet films. It is shown here that this enhancement is not due to elemental substitution or compositional variations, nor is it due to photon trapping or resonance effects. Comprehensive experimental and theoretical analysis of the Faraday rotation reveals a dramatic sevenfold amplification in the magneto-optic gyrotropy within only 2 nm of the air–surface interface, corresponding to just a couple of atomic monolayers as a result of symmetry breaking at the air–film interface. This finding opens up an avenue to the application of monolayer magnetic garnets for the control of light.
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Rare-earth iron garnet films are technologically important since they are among the main materials used in magnetophotonics, ultrafast magnetism, and spintronics [1,2]. In particular, they are used extensively in optical circuits for the fabrication of nonreciprocal optical devices. Isolators and circulators, operating as optical filters, rely on the nonreciprocal functionality of iron garnets to protect laser sources from reflected downstream light that might otherwise enter the cavity and destabilize the signal [2–4].
Magneto-optical light modulators and magnetic sensors utilize iron garnet films for efficient magneto-optical response and outstanding performance [3–7]. On the other hand, iron garnet thin films are being successfully used in magnonics in experiments on the spin–orbit torque transfer and nonlinear spin-wave dynamics [8–11].
Since the development of yttrium iron garnet in the 1950s, subsequent bismuth and cerium substitutions in the dodecahedral sublattice of these materials were found to enhance their Faraday rotation response [1,5,12]. Such substitutions amplify the spin–orbit splitting of the 3d excited states, impacting the refractive index difference between photons of opposite helicities . The Faraday rotation at wavelengths longer than the absorption band is affected as a result. These discoveries impacted the efficiency of nonreciprocal devices and made it possible to reduce their footprint and hence help drive their miniaturization. However, no other elemental substitutions with similar effects have been found since the 1990s.
The need for on-chip isolator integration for the manufacturing of optical circuits, especially for telecommunication purposes, has led to extensive research on and prototyping of these devices over the years [13–17]. Engineered magnetophotonic crystal and magnetoplasmonic structures incorporating bismuth-substituted iron garnet films were demonstrated [18–23]. However, better and stronger nonreciprocal efficiency than at present is still needed by the industry to further miniaturize these systems down to nanometer size.
This paper reports on newly discovered enhancement effects observed experimentally in ultrathin rare-earth-substituted iron garnet films [24–26]. It is shown here that these effects are not due to elemental substitution or compositional variations, nor are they due to photon trapping or resonance effects. Theoretical modeling presented in this paper and verified experimentally shows that surface reflections do impact the magneto-optic response of these films but cannot account for the large Faraday rotation enhancement observed below 50-nm-thick films.
2. PHYSICAL MECHANISMS
There are four physical mechanisms that are capable of producing enhancement in the Faraday rotation in magnetic garnets: (a) bismuth or cerium substitutions into the dodecahedral sublattice of these crystals, (b) optical resonances due to reflections, (c) surface symmetry breaking, and (d) quantum confinement. This article provides strong theoretical and experimental evidence that the observed effects are not due to rare-earth substitutions nor classical electrodynamic interference, thus pointing to surface symmetry-breaking effects as the alternative mechanism of significance in the physical response of ultrathin iron garnet magneto-optics. Modeling of these experimental results is consistent with an enlargement in the magneto-optic gyrotropy parameter responsible for the Faraday effect in these films by a factor of 7 within only 2 nm of the surface.
The electronic transitions responsible for the Faraday effect in bismuth-substituted iron garnets, such as those used in these experiments, involve the octahedral- and tetrahedral-oxygen-coordinated 3d electrons in these compounds. In the cubic crystal field of the octahedral site, these d-levels split into a twofold degenerate level and a threefold degenerate level, whereas the tetrahedral site splits up into a threefold degenerate level and a twofold degenerate level. So the crystal fields break the fivefold degeneracy of the d-electrons into two distinct groups in each crystal sublattice of this material [1,27]. We postulate that modifications in the crystal field environment due to symmetry breaking at the surface will impact the electronic transitions responsible for the Faraday effect. For example, a symmetry-lowering tetrahedral distortion of the octahedral sites causes the degenerate levels to split up into nondegenerate and states, and the degenerate levels into two nondegenerate and one states .
Electronic energy-level splitting modifies the Faraday rotation response by altering the photon absorption energies and hence the refractive indices of right- and left-circularly polarized light at longer wavelengths, as required by the Kramers–Kronig relations. It is this difference in refractive index between opposite photon helicities that determines the Faraday response of the system. Surface symmetry-breaking affecting the orbital occupancy in transition metal films with oxygen-coordinated octahedral symmetry has already been observed experimentally, although not in magnetic garnets, nor in connection with the Faraday effect . Any such change in orbital occupancy at the surface in iron garnets due to level splitting or otherwise, is bound to affect their magneto-optic response.
Our contention is not that our results are different for the case of bulk materials, but that there is a significant enhancement in gyrotropy at the surface for comparable compositions. Increasing the bismuth content per formula unit (pfu) does lead to larger gyrotropies in these materials [1–5], but there is still an industrial need for more efficient Faraday rotator films. Hence, the engineering of better Faraday rotators via stacking of ultrathin films, or other methods, may enable the fabrication of more efficient nonreciprocal devices.
3. EXPERIMENTAL BACKGROUND
Two different sets of liquid-phase-epitaxy (LPE)-grown films with and pfu were studied. These films were fabricated on gadolinium gallium garnet (GGG) (100)-oriented substrates at II-VI Advanced Materials. The films for any set of measurements were all taken from the same wafer and wet-etch-thinned-down sequentially in orthophosphoric acid, thus avoiding possible composition differences due to growth conditions. The bulk magneto-optic gyrotropy parameter , obtained from measurements in 2 μm-thick films, is different for the two different compositions. For pfu films (Samples 2 and 3), the bulk , and for (Sample 1), it is .
Light from a CW laser source was used to probe the Faraday rotation at 532 nm. Measurements normal to the film surface were conducted in a rotating-polarizer configuration, with an accuracy of 0.001° . Faraday-rotation hysteresis loops were recorded for each sample, and the Faraday rotation at saturation was chosen to characterize the response of each film. The paramagnetic signal of the GGG substrate was subtracted out from the overall Faraday rotation signal. The experimental setup is described in . These measurements fold out any rotational effects from tilt and misalignment because we measure hysteresis loops and take the (nonreciprocal) Faraday rotation as ½ the difference between saturation values for positive and negative magnetic fields. Those effects, as well as reciprocal magneto-optic contributions such as the Cotton–Mouton effect, are estimated to be too small to be of any significance, and are folded out through our measurement technique.
Film thickness was measured via ellipsometry, and Faraday rotation per unit length is plotted in Fig. 1 for both sets of samples as a function of thickness. For the ferrimagnetic films thinner than 50 nm, the specific Faraday rotation (SFR) grows dramatically with a decrease in film thickness. One can see that the SFR reaches in the 20-nm-thick film, almost 2.5 times greater than SFR in the same thick film. For the thin films, we observe oscillations due to interference of the emerging waves due to multiple reflections inside the thin film.
4. COMPOSITIONAL ANALYSIS
Secondary ion mass spectroscopy (SIMS) measurements were performed with bombardment and positive ion detection mode using an IMS-7f (CAMECA) microanalyzer. The primary beam was rastered over an area of , and the secondary ions were collected from the central part of this area (diameter 33 µm). In order to avoid the charging effect, the sample was coated with a layer of gold (50 nm), and electron flooding was employed using a normal-incidence e-gun. Bismuth and gallium concentrations in , determined by this method on a 60-nm-thick film are shown in Fig. 2(a).
Electron micrographs and energy-dispersive x-ray spectroscopy (EDX) maps were obtained on (Samples 2 and 3) using an FEI Titan Themis aberration-corrected scanning transmission electron microscope (S-TEM) operated at 200 kV. The point resolution in this aberration-corrected mode is 0.08 nm. The microscope is fitted with a super-XTM x-ray detector, which is a combination of four detectors for fast x-ray mapping in S-TEM mode. For the present experiment, 1-nm-resolution EDX maps were taken with an average beam current of 100 pA. The size of the maps were pixels, and a 50 µs/pixel dwell time was used for collecting the signal. All maps are generated by summing over 10 frames. Drift correction during data collection and a subsequent analysis were performed using Velox software. These results are shown in Fig. 2(b), with a standard deviation of pfu for bismuth, and pfu for iron.
5. THEORETICAL MODEL AND DATA ANALYSIS
In this section and in Supplement 1, we describe the theoretical model, based on classical electrodynamics, used to analyze the measured Faraday rotation, and the results of this analysis. Linearly polarized light impinges on the magnetic film at normal incidence. The magnetization is directed along the propagation direction, perpendicular to the film surface. Refractive indices and film thickness are as shown in the inset of Fig. 1. The magneto-optic gyration as well as the refractive index in the ferrimagnetic film are initially assumed to be uniform inside the film and parameterized by the gyrotropy parameter . Multiple reflections are included in the analysis, giving rise to an oscillatory behavior in Faraday rotation as a function of film thickness .
Based on the composition measurements demonstrating a gradual decrease of magnetic elements near the film–substrate interface, we introduce into our model the same gradual change of the refractive index, from the film to the substrate across the transient layer. This layer is 30-nm-thick. We also note that the observed Faraday rotation enhancement manifests itself at sample thicknesses below 50 nm, indicating that it is an interfacial effect.
The Faraday rotation angle is given by 1) has two asymptotes, for , ultrathin films, and for , bulk ferrimagnetic material, with SFRs given by 2), the ratio of the SFR at small with respect to the SFR at large is, thus, 1,5,12]. However, detailed cross-sectional composition analysis, discussed above, shows that there is no such increase in bismuth content, and that the only composition gradient is manifested as a decrease in bismuth, iron, and lutetium content in the transient layer (Fig. 2). The cross-sectional film composition was measured by two different methods, via SIMS, Fig. 2(a), and cross-sectional S-TEM, Fig. 2(b).
The bulk refractive indices at wavelength are given by in the GGG substrate, and in the bismuth-substituted iron garnet films for all samples. Therefore, at , this ratio is predicted to be about 1.75, but the experimentally measured ratios are always larger than 2. In particular, , for Sample 1, and , for Samples 2 and 3. Thus, the analytical expression derived from classical electrodynamic cannotaccount for all the effects operating in this system.
Besides the preceding analysis, we also performed an electromagnetic modeling based on a rigorous coupled-wave analysis (RCWA) [30,31]. The result of the corresponding numerical simulation in the case of constant magneto-optic gyration inside the whole magnetic film is given in Fig. 3 by the red line (Model 1). One can see that this model does not reproduce the pronounced increase in the SFR obtained experimentally (points, squares, and diamonds in Fig. 1). Therefore, the assumption of constant gyration inside the ferrimagnetic film does not describe the observed abrupt growth in the SFR in ultrathin ferromagnetic films.
Assuming a gyration proportional to the bismuth content, comprising also its decline in the transient layer [Fig. 3(b), blue line], the numerical simulation produces an even poorer coincidence with the experimental data than Model 1: constant gyration. This is shown by the blue line (Model 2) in Fig. 3(a). Notice that Model 1 in effect already assumes a significant increase in magneto-optic gyration in the interfacial region, if one considers the decrease in bismuth content in the transient layer. Yet the calculated SFR in that case still remains well below the experimental data.
There is no difference in the model’s predictions whether the increase in gyrotropy occurs near the top surface or near the film–substrate interface. However, our compositional measurements demonstrate that there is a gradual decrease in iron and bismuth content at the film–substrate interface, consistent with a reduction in the value of the gyrotropy parameter. It is on these grounds that we build the model comprising an increase in gyration near the air–film interface.
To achieve coincidence with the experimental data, we allow the gyrotropy parameter to experience an increase near the air–film interface. Best fits to the experimental data are produced by a rise in value taking place over a very thin layer adjacent to the surface, which is -thick. In Model 3, the gyration evinces a near-surface step-like growth, as depicted in Fig. 3(b). One can see from Fig. 3(a) (Model 3) that this assumption provides very good agreement with the SFR, including for sub-50-nm-thick ferrimagnetic films. We remark that this model fits not only the experimental data for Sample 2 [Fig. 3(a)], but also the measurements on all three samples. All the theoretical curves in Fig. 1 are based on Model 3 and provide good agreement with experiment. These fits predict that the magneto-optic gyrotropy parameter exhibits a sevenfold amplification in magnitude within 2 nm of the surface, and a fourfold amplification in the next 2 nm, over its bulk value.
Detailed Faraday rotation data and electrodynamic analysis of ultrathin bismuth-substituted iron garnet films predict a several-fold increase in near-surface magneto-optic gyrotropy within 2 nm of the surface. Electron-dispersive x-ray spectroscopy and SIMS confirm that the measured Faraday rotation enhancement in ultrathin films is not due to compositional nonuniformities near the film–substrate interface, thus pointing to surface symmetry-breaking effects as the origin of these results. This dramatic enhancement in the gyrotropy parameter occurs within a few monolayers of the films, as the unit cell in these iron garnets is . These results hold a significant potential for the nanofabrication of nonreciprocal devices, given the technological role of these materials in optical isolator and circulator components.
Foundation for the Advancement of Theoretical Physics BASIS; Michigan Tech; Russian Foundation for Basic Research (RFBR) (18-29-02120).
This study was partially supported by the Foundation for the Advancement of Theoretical Physics BASIS. M. L. and D. K. acknowledge support from the Henes Center for Quantum Phenomena (Michigan Tech). V. I. B. acknowledges support from the Russian Foundation for Basic Research (project #18-29-02120). The authors thank S. Subramanian (II-VI Advanced Materials) and A. Chakravarty for valuable discussions and P. Mukherjee for the cross-sectional EDX S-TEM measurements of film composition.
See Supplement 1 for supporting content.
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