Stress induced modulation of magnetic domain diffraction of single crystalline yttrium iron garnet

Laser beam steering systems are key components of several types of modern devices such as scanners^1,2 or projectors.^3,4 Typically, they employ a moving mirror to steer a laser beam.^5–8 The deflection angle velocities of these devices are fundamentally limited to up to a few dozen kilohertz because of the inertia associated with the mass of the mirrors and other moving parts.⁹ However, modern information-processing devices operate at a few gigahertz. Therefore, to use the laser beam steering system for information-processing, other high-speed beam deflection technologies have to be considered. Optical solid state deflectors, which rely on the electro-optical or acousto-optic effect, have been developed and are being applied. They do not contain moving parts and hence can exhibit high deflection angle velocities.^9–11 

In this study, the magneto-optic (MO) effect was employed to realize an optical solid state deflector. The orientation and spacing of the stripes were changed by magnetic fields in previous studies.^12–15 However, the change ratio of the spacing was limited because of saturation of the magnetization.

Assuming that film thickness l is much thicker than domain width d, the domain width can be found from¹⁶ 

where A is the exchange stiffness constant, K_u is the magnetic anisotropy constant, and I_s is the saturation magnetization. According to equation (1), the domain period depends on the magnetic anisotropy. The inverse magnetostriction effect is an attractive way to effectively modulate or control the anisotropy^17,18 at high speed with low power consumption.¹⁹ Assuming uniform magnetostriction, the change of anisotropic energy E_σ is given by¹⁶ 

where λ is the magnetostriction constant, σ is the applied stress, and ϕ is the angle between stress and magnetic moment. This formula suggests that the anisotropy could be effectively changed by the stress, and thus the stress can modulate the domain spacing.

In this study, stress induced modulation of diffraction efficiency and angle of the light reflected from a stripe-domain magnetic garnet was demonstrated. The inverse magnetostriction effect, which principally changed the spacing of the domain without saturation, was employed to modulate the spacing and the magnetization.

Figure 1(a) shows a cross-section diagram of the fabricated solid state MO light deflector. The sample structure was a gadolinium gallium garnet (GGG) substrate (111)/single crystalline yttrium iron garnet (YIG) (111)/Al reflection layer/piezo actuator. The 5-μm-thick single crystalline YIG film on a GGG substrate was purchased from MTI corporation, Richmond, CA, USA. The Al reflection layer was deposited on the YIG by vacuum deposition. Then, a piezo actuator (TA0505D024W, Thorlabs, Inc.) was adhered on the Al with cyanoacrylate adhesive. The deformation of the piezo actuator was measured by a strain gauge (KFG-1-120-C1-11 L1M2R, Kyowa Electronic Instruments Co., Ltd.).

The optical setup for measuring the light deflection angle and efficiency is shown in Fig. 1(b). The analyzer was orthogonal with the polarizer (crossed-Nicols setup). The sample was illuminated by a 532-nm semiconductor laser from the substrate side with an incident angle of 10°. The distance between the sample and screen was 22 cm. Change of the diffraction angle and spacing of the domain was observed by measuring a distance between the 0^th and 1^st ordered diffracted light on the screen.²⁰ Modulation of the diffraction efficiency was measured with the 1^st ordered light. A few Oe of an in-plane bias magnetic field were applied to align and stabilize the magnetic domain. The domain structure was observed by a polarization microscope with illumination light of 532 nm.

Figure 2(a) shows a polarization microscope image of the sample observed from a substrate. The sample had a stripe-domain structure with a period of around 3 μm. A two-dimensional Fourier transform image of the polarization microscope image is shown in Fig. 2(b). Two bright peaks on either side of center represent the stripe domain pattern.

Figure 3 shows stress induced change of the MO diffraction angle. A distance between the 0^th and 1^st ordered light was changed from 35.3 mm to 39.6 mm by applying 70 V to the piezo actuator. The piezo actuator deformed 400 ppm at 70 V. This result indicates that the diffraction angle was changed from 9.12 deg. to 10.20 deg. When light is normally incident on the stripe-domain, the diffracted light will have a maximum intensity at angles θ that given by the grating equation as²⁰ 

where d is the domain period, λ is the wavelength of incident light and m is a positive integer. According to equation (3), the change of the diffraction angle suggests that the spacing of the domains was changed from 3.3 μm to 3.0 μm by the voltage. The piezo actuator should slightly deform or displace the sample, which could change the incident and reflection angle of the light. The position of the 0^th ordered light was not changed after applying voltage, and thus the domain period d for the light was not changed. Therefore, this result implies that the domain period was changed by the voltage.

In our study, the diffraction efficiency was low because of the low Faraday rotation of the pure YIG, thus relatively high stray-light noise was observed. This could be resolved by substituting YIG with a high Faraday rotation, such as a Bi substituted YIG. Fundamentally, the MO deflector has a high diffraction efficiency because the 0^th light can be cut by an analyzer.²¹ 

The change of the diffraction angle was irreversible for the voltage, and could be refreshed by the magnetic field. It may be because of pinning of the domain walls. This drawback should be resolved before being used in applications. Garnets with small coercivity, which reflect the movability of the domain walls, are promising for resolving this drawback.

After the diffraction angle was settled, the 1^st ordered light showed reversible change of the diffraction efficiency for the voltage. Figure 4 shows the diffraction efficiency of the 1^st ordered light for the applied voltage. This result implies that the perpendicular component of the magnetization of domains, instead of the domain period, was changed to reduce the energy. The change of diffraction efficiency was liner and continuous. It could be used for laser intensity-modulation by the voltage.

The diffraction angle and efficiency of a MO diffraction of a stripe-domain magnetic garnet was modulated by an inverse magnetostriction effect. A piezo actuator was employed to convert the voltage to the stress applied to YIG. The diffraction angle between the 0^th and 1^st ordered light was changed from 9.12 deg. to 10.20 deg. when 70 V was applied to the piezo actuator. This result suggests that the domain spacing was changed from 3.3 μm to 3.0 μm. The change of diffraction angle was irreversible for the voltage. However, reversible, liner and continuous change of the diffraction efficiency was observed. These results could be applicable for a voltage-driven optical solid state deflector with low power consumption and high switching speed.

This work was supported by JSPS KAKENHI Grant Number JP16K21569, JP26220902.