Properties of Off Stoichiometric Yttrium Iron Garnet

by Tingyu Su

B.S. Applied Physics University of Science and Technology of China, 2018

Submitted to the Department of Mechanical Engineering in Partial Fulfillment of the Requirements for the Degree of Master of Science in Mechanical Engineering at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY May 2020 © 2020 Massachusetts Institute of Technology. All rights reserved.

Signature of Author: Department of Mechanical Engineering

May 15th, 2020 Certified by: Caroline Ross Professor of Materials Science and Engineering Thesis Supervisor Certified by: Jeehwan Kim Associate Professor of Mechanical Engineering Thesis Reader Accepted by: Nicolas G. Hadjiconstantinou Professor of Mechanical Engineering Chairman, Department Committee on Graduate Theses

2 Properties of Off Stoichiometric Yttrium Iron Garnet

by Tingyu Su

Submitted to the Department of Mechanical Engineering on May 15, 2020 in Partial Fulfillment of the Requirements for the Degree of Master of Science in Mechanical Engineering

Abstract

YFO (YFeO3) target is used for deposition on GGG (Ga3Gd5O12) substrates with different directions: (001), (110) and (111) by PLD (Pulsed Laser Deposition). HRXRD characterization shows that high-quality epitaxial garnet phase is formed on GGG substrates. However, RSM results show that the off-stoichiometric YIG film on (111) GGG substrates can remain fully strained in plane with thickness from 23 nm to 74 nm; while the samples on (001) GGG substrates show different degrees of relaxation in-plane depending on film thickness. Magnetic characterization shows that the samples grown on (111) GGG substrates have saturation magnetization 푀푠~45 푒푚푢/푐푐, which is significantly smaller than standard YIG (~140 푒푚푢/푐푐). Furthermore, the Curie temperature of samples grown on (111) GGG is ~ 310퐾, in obvious contrast with standard YIG ~560퐾.

Thesis Supervisor: Caroline Ross Title: Professor of Materials Science and Engineering

Thesis Reader: Jeehwan Kim Title: Associate Professor of Mechanical Engineering

4 Acknowledgments

First and foremost, I am really grateful to my supervisor Prof. Caroline Ross for her kind guidance and helpful discussion. Also, without my labmate Dr. Shuai Ning’s generous and patient training on PLD and VSM, I would not finish this work. Special thanks to Dr. Charles Settens for his training on XRD and helpful discussion. Last but not least, I really appreciate my project sponsor NSF for the generous funding.

Tingyu Su May, 2020

5 Table of Contents Abstract ...... 3

Acknowledgments ...... 5

1. Introduction ...... 7

1.1 Background ...... 7

1.2 Preliminaries about YIG ...... 7

1.3 Motivation...... 10

2. Structure Analysis ...... 12

2.1 HRXRD and RSM Knowledge ...... 12

2.2 HRXRD Results ...... 13

2.3 RSM Results ...... 16

2.4 Summary ...... 20

3. Magnetism Analysis ...... 23

3.1 Room Temperature Measurements ...... 23

3.2 Temperature Dependence ...... 25

3.3 Explanation...... 26

4. Other Characterization ...... 29

5. Summary ...... 31

6. Appendix...... 32

References ...... 34

6 1. Introduction 1.1 Background

Since first being discovered in 19581 as ferrite oxide, yttrium iron garnet (Y3Fe5O12 or YIG) has been almost the most thoroughly investigated ferrite oxide2 due to its wide applications in the microwave frequency range, such as resonator, microstrip and other ferrite devices3,4. Recently, by strain engineering, YIG thin film with perpendicular magnetic anisotropy (PMA) could be achieved5,6, which makes itself a promising candidate for magnon related research7. Another very active branch of research on YIG is by cation substitution or oxygen deficiency tuning, improvements or novel properties can be realized. For example, bismuth and cerium substituted

YIG (BiYIG and CeYIG) has shown excellent magnetic-optical properties8 and has been integrated on silicon chip as optical isolator9.

1.2 Preliminaries about YIG

Figure 1.1 Crystal Structure of Y3Fe5O12.

When studying the crystallographic structure of YIG, it is convenient to rewrite its chemical formula as {Y3}[Fe2](Fe3)O12. It belongs to the space group 퐼푎3̅푑 (space group number: 230) with lattice constant 푎 = 12.375 Å 10. As shown in Figure 1.1, the anion O2- (red ball) occupies 96h

7 general site and there are three kinds of cation positions 16a, 24d and 24c (Wyckoff Position), distinguished by square bracket, parentheses and curly brackets separately. The non-magnetic (or weak diamagnetic) Y3+ takes the dodecahedral site 24c, dark cyan with atoms now shown here. As for the magnetic cation Fe3+, both tetrahedral site 24d and octahedral site 16a could be taken, for each formula, 3 in tetrahedral site and 2 in octahedral site.

Figure 1.2 Orbital angular momentum ‘quenching’2 (a), (b) and ‘zoomed’ view of YIG11 (c).

The magnetism of YIG comes from the collective behavior of Fe3+ sitting in different positions and more accurately speaking, it comes from the unpaired 3d electrons hanging around the nucleus. The magnetic moment of an isolated or ‘free’ ion is given: Eq. 1.1 푢푡표푡푎푙 = 𝑔퐽휇퐵√퐽(퐽 + 1)

푆(푆+1)+퐽(퐽+1)−퐿(퐿+1) where 𝑔 = 1 + known as Lande factor and 퐽⃗ = 퐿⃗⃗ + 푆⃗, the physical meaning 퐽 2퐽(퐽+1) and derivations could be found in atomic physics or magnetic materials textbook12. It is worth attention that both orbital angular momentum and spin angular momentum contribute to the total magnetic moment.

However, as demonstrated in Figure 1.2 a and b, when surrounded by other anions and cations in the crystal lattice, significant modifications must be added to the ‘free’ ion: 1) The interaction between electron charges and electric field of the crystal lattice

environment: in the language of Hamiltonian, 퐻푐푓. 2) Indirect or Super Exchange interaction between magnetic ions.

8 In the simplest approximation, we can image every O2- at each vertex of octahedron or tetrahedron as point charge and only the nearest surrounding anions are considered. From the viewpoint of interaction between ion and electric field, this effectively the same as if we put the free ion Fe3+ in an external field, which is known as Stark effect (in atomic spectrum analysis). The coupling between orbital angular momentum 퐿⃗⃗ and crystal field ⃗퐸⃗⃗⃗푐푓⃗⃗⃗ will compete with spin-orbital coupling between 푆⃗ and 퐿⃗⃗. To make it clear, we can rewrite the Hamiltonian as: Eq. 1.2 퐻 = 퐻0 + ∆퐻 = 퐻0 + 퐻푐푓 + 퐻퐿푆 where 퐻0 represents the kinetic terms and electron repulsion terms, 퐻푐푓 and 퐻퐿푆 stands for the contribution from lattice electric field and spin-orbital coupling. For the case of YIG, the outer 3d electrons of Fe3+ are directly exposed to the O2- crystal field so the coupling from the crystal field will dominates over the spin-orbital coupling, 퐻푐푓 > 퐻퐿푆. The immediate effects are to make spin 푆⃗ as the principal source of the magnetic moment and ‘quench’ orbital momentum 퐿⃗⃗, resulting

Lande factor 𝑔퐽 ≈ 𝑔푒 = 2. According to Hund’s Rules, the ground state of Fe3+ with 5 3d electrons has a net orbital angular momentum 퐿 = 0 anyway; whereas for other ions such as Fe2+, the quenching effect will stand out.

However, for rare-earth ions, 4f electrons are buried inside the 5s and 5p electrons, which screen the outer crystal electric field. In this case, spin-orbital coupling will dominate i.e. 퐻푐푓 < 퐻퐿푆 and the 퐽⃗ = 퐿⃗⃗ + 푆⃗ is still a good quantum number2.

Figure 1.3 Super-Exchange13 (a) and Ferrimagnetic Cartoons (b)

9 Next, comes the question that how the individual magnetic Fe3+ ions behave collectively resulting in the ferrimagnetic features? If taking a zoomed view of polyhedron model in Figure 1.2c, the

Fe3+ sitting in tetrahedral(24d) and octahedral(16a) site are interacting with each other through the common oxygen anion at the vertex. The directional interaction between different Fe3+ is negligible compared to that of Fe3+ and O2- because Fe3+ ions are far away from each other.

Figure 1.3a shows a simplified version how super-exchange works: when 3d electrons of different site Fe3+ hybridized with the opposite branches of O2- 2p orbitals, it is energetically favorable if the two Fe3+ have opposite spin momentum. In other words, through the bridge of vertex O2-, the

Fe3+ cation favors antiferromagnetic alignments. Figure 1.3b is a schematic showing how YIG behaves ferrimagnetically: all Fe3+ within the tetrahedral (black arrows) or octahedral (red arrows) sublattice favors parallel alignment (ferromagnetic) however, the two sublattice (black and red) favors anti-parallel with each other, resulting a net magnetic moment which equals to the arithmetic difference of magnetic moments between two sites.

In a nutshell, the element and valent status determines the single magnetic moment (푆⃗ ) and where the ions sit (tetrahedral or octahedral sites) determines the collectively behavior, therefore resulting in the ferrimagnetism. In 1960s, a lot of cation substitution was made to tailor YIG magnetic properties. For example, Gilleo and Geller reported that trivalent ion Al3+, Ga3+, Sc3+, In3+, and

Cr3+ could substitute Fe3+ in a steric manner: those smaller than Fe3+ preferentially occupy the smaller tetrahedral site; larger ions preferentially occupy larger octahedral site, with Cr3+ an exception due to special electronic configuration11. Furthermore, divalent Mg2+, Ni2+ and Co2+ combined with quadrivalent ion Ge4+ or Si4+ can also substitute the Fe3+ 14,15,16. Therefore, a lot of magnetic or non-magnetic ions could substitute the cations in YIG to form stable garnet phase and show enhanced properties.

1.3 Motivation

In 2004, hetero-epitaxial perovskite (BaTiO3) and spinel (CoFe2O4) nano-composite has been grown on the SrTiO3 (perovskite) substrate shown in Figure 1.4a, which provides a promising platform to study interfacial coupling of multiferroic materials17. As mentioned in the previous

10 section, YIG is a popular ferrite oxide with unique magnetic properties so is it possible to grow YIG with other functional oxides to achieve the synergetic effect?

Figure 1.4 Hetero-epitaxial growth17 of nanocomposite (a) and PLD cartoon (b).

Based on this idea and considering the same element composition between YFeO3 (YFO, perovskite) and Y3Fe5O12 (YIG, garnet), using Pulsed Laser Deposition method (Figure 1.4b),

YFO target is used to deposit on the Ga3Gd5O12 substrate with different orientation [001], [110] and [111]. Structural analysis based on High-Resolution X-Ray Diffraction (HRXRD) and Reciprocal Space Mapping (RSM) analysis will be discussed in Chapter 2. In Chapter 3, magnetic characterization and temperature dependence based on Vibrating Sample Magnetometer (VSM) will be provided. Other characterizations such as Atomic Force Microscopy (AFM) and X-Ray Photoelectron Spectroscopy (XPS) will be given in Chapter 4 but without further analysis due to the special pandemic time.

11 2. Structure Analysis

The importance of X-Ray Diffraction to the study and understanding of crystal structure can never be overemphasized. In order to better interpret the results of samples, the required background knowledge of High-Resolution X-Ray Diffraction (HRXRD) and Reciprocal Space Mapping (RSM) is briefly provided, then followed by the structural and crystallographic analysis.

2.1 HRXRD and RSM Knowledge

Figure 2.1 HRXRD (a) and RSM (b) Principles

Based on the periodicity and symmetry, the 14 Bravais lattices describe how atoms assemble themselves in ‘real space’. Under the ‘sunshine’ of X-Ray, every real space crystal structure has a unique ‘shadow’ named diffraction pattern, which exists in ‘reciprocal space’ defined by 3D Fourier transform of real space. As shown in Figure 2.1a, the incident and diffracted X-Ray beam vector is denoted by 푘⃗⃗, 푘⃗⃗′, and the diffracted angle is 2휃 with wavevector change Δ푘⃗⃗ = 푘⃗⃗′ − 푘⃗⃗. According to Laue Condition: ⃗⃗ Eq. 2.1 Δ푘 = 퐺⃗ℎ푘푙 where 퐺⃗ℎ푘푙 is the vector in reciprocal space, the diffraction peak due to plane (ℎ푘푙) in real space 2휋 will show up. Under elastic scattering assumption |푘⃗⃗| ≈ |푘⃗⃗′| = and for cubic structure of YIG 휆 2휋 |퐺⃗ℎ푘푙| = , Eq. 2.1 could be rewritten as: 푑ℎ푘푙

12 Eq. 2.2 2푑ℎ푘푙 sin 휃 = 휆 which is the famous Bragg Equation.

For HRXRD experiment (Figure 2.1a), the sample surface normal 푛⃗⃗ is parallel to the vector change ⃗⃗ Δ푘, so the peak position 2휃푓𝑖푙푚 will indicate the out of plane lattice information. In order to investigate the in-plane lattice information, the asymmetric diffraction peak is measured through RSM demonstrated in Figure 2.1b: 푥∗, 푦∗, 푧∗ here represents the base vector directions in reciprocal space and the red dots stands for the diffraction peaks. Therefore, the figure is showing the 푥∗ − 푧∗ cross-section plane with all possible peaks (ℎ0푙) . As an example, the (408) asymmetric peak diffraction ray diagram is shown with all the parameters the same meaning as shown on the left Figure 2.1a. Therefore, the relative peak positions of thin film and substrate could be interpreted in this way: the out-of-plane (푧∗) direction should be consistent with HRXRD discussed above; in-plane (푥∗ − 푦∗ ) direction gives the degree of lattice relaxation between substrate and film.

For the experimental part: all the HRXRD data is measured by Rigaku SmartLab and all the RSM data is measured by Bruker D8 Discover both with Cu 퐾훼 X-Ray source 휆 = 1.5406 Å. Post- processing of raw data is conducted through commercialized software GlobalFit and LEPTOS.

For the theoretical part: very simple diffraction model is provided above but in order to understand the diffraction phenomenon more deeply, quantum electrodynamics and dynamic diffraction theory is needed which is out of scope here but can be found on TEM or XRD textbooks in the reference18.

2.2 HRXRD Results

YFO (YFeO3) targets were used for deposition in 10 푚푇표푟푟 O2 atmosphere on GGG (Ga3Gd5O12) substrates with different directions: (001), (110) and (111). To make things organized and clear, results from (001) and (111) substrate will be compared and analyzed. Characterization and

13 measurements on (110) direction will be given in the Appendix section due to the limited samples we have.

The ‘whole picture’ scan 2휃 from 15° to 80° is given as insets in Figure 2.2 a and b. Although the perovskite phase target with Y to Fe ratio 1: 1 was used, the sample does not show any perovskite phase diffraction peaks. Instead, only garnet phase diffraction peak shows up on the left of the corresponding substrate peak. Grazing Incident X-Ray Diffraction (GIXRD) measured (2휃) from 15° to 80° (shown in Appendix) did not show any diffraction peaks. Therefore, combining these two results (‘whole picture’ and GIXRD), a conclusion can be made that epitaxial garnet phase films were grown on the GGG substrates from YFO perovskite target using PLD. The super-sharp small peaks showing up at ~45°, 80° in (001) samples and ~25° in (111) samples come from the imperfections from substrates, which can be confirmed by separate HRXRD measurements of empty substrates.

Figure 2.2 HRXRD results of off-stoichiometric YIG on (001) (a) and (111) (b) GGG substrates.

However, based on the element composition: Y, Fe and O, the most common garnet phase is YIG with chemical formula Y3Fe5O12. In our experiment, the heavy element Y to Fe ratio in the film should be roughly the same as the target19 i.e. 1: 1; while the O content is controlled by O2 atmosphere19 (10 푚푇표푟푟 for all the samples), which is much lower than the optimal condition for

14 stoichiometric YIG PLD growth conditions: 100~200 푚푇표푟푟 plus post annealing under O2 atmosphere20,5,21,6. Therefore, the chemical formula of thin films grown from YFO target could be written as Y4Fe4O12-x or {Y3}[FeY](Fe3)O12-x under the assumption that the Y3+ will preferentially substitute Fe3+ in the octahedral position because Y3+ has a larger ionic radius than Fe3+. (푟푌3+ ≈

104 푝푚 > 푟퐹푒3+ ≈ 80 푝푚). To further confirm where the extra Y3+ stay in the garnet structure, TEM or atomic resolution STEM is needed which will be done in the future. In the following discussion, the epitaxial film samples grown by YFO target are called off-stoichiometric YIG, which stands for the Y3+ substituted O deficiency YIG.

Figure 2.2a shows the (004) diffraction peak of the off-stoichiometric YIG samples with different thicknesses on the (001) GGG substrate. After calibrating the substrate diffraction peak position ° at 2휃푠푢푏_004 = 28.83 and normalizing signal intensity, the diffraction peak position 2휃푓𝑖푙푚_004 varies slightly with different sample thicknesses, which is common for the deposition of standard

YIG on GGG substrate21. Besides, by simulation and fitting of X-Ray Reflectivity measurement (shown in Appendix), the root mean square of off-stoichiometric YIG surface roughness is given:

푅푟푚푠 ≈ 0.6 푛푚. The sub-nanometer level smoothness of sample surface is also consistent with the Laue fringes showing up besides the sample diffraction peak.

Similarly, (444) diffraction peak of samples with different thicknesses is shown in Figure 2.2b.

The surface roughness is given by simulation and fitting on XRR data : 푅푟푚푠 ≈ 0.2 푛푚, which also means that the surface is sub-nanometer smooth. However, the difference lies in the relative change of out-of-plane lattice constant between off-stoichiometric YIG and standard YIG. Recall Bragg’s Law Eq. 2.2: 휆 푑 sin 휃 = 퐵 2 The difference of diffraction peak position between off-stoichiometric samples and standard YIG

Δ휃 = 휃푓𝑖푙푚 − 휃푌퐼퐺 ≪ 1. Therefore, take variation on both sides:

훿푑 sin 휃퐵 + 푑 cos 휃퐵 훿휃 = 0 Rearrange: 훿푑 훿휃 Eq. 2.3 = − 푑 tan 휃퐵

15 훿푑 where is the out-of-plane lattice expansion ratio, 훿휃 = Δ휃 and 휃 is the corresponding Bragg 푑 퐵 angle for the diffraction peak of interest. The expansion ratio of all six samples shown above are summarized in Table 2-1. Besides, the saturation magnetization 푀푠 and growth rate are also given for further use in following chapter.

Table 2-1 Summary of samples discussed in this paper.

001 Sample 2휃 2휃 훿휃 훿푑 푅 푀 Growth Rate Chamber 퐵 × 100% 푟푚푠 푠 thickness (degree) (degree) (rad) 푑 (nm) (emu/cc) (nm/h) 45 nm 28.138 28.835 0.00608 2.366 0.6033 - 81 3 80 nm 28.092 28.835 0.00648 2.522 0.6403 - 193 3 162 nm 28.062 28.835 0.00675 2.624 0.6540 - 195 3 111 23 nm 49.318 51.094 0.0155 3.242 0.3928 20.7 RHEED 38 nm 49.393 51.094 0.01484 3.106 0.1260 68.4 3 74 nm 49.389 51.094 0.01488 3.113 0.2115 49 44.4 3

The diffraction peak positions of off-stoichiometric samples 2휃 are obtained through Gaussian fitting the curve and roughness 푅푅푀푆 are calculated from fitting XRR using GlobalFit software. It is worth noting that the out-of-plane expansion ratio 훿푑 of film grown on (111) substrate is 푑 ~3.1%, which is bigger than that of grown on (001) substrate ~2.5%.

2.3 RSM Results

In order to further study the in-plane growth condition, Reciprocal Space Mapping of asymmetric peak of all six samples were conducted using Bruker D8 Discover. Results from (001) and (111) substrates will be discussed separately.

The RSM results of asymmetric peak (408) and (116) of the same samples on (001) substrate discussed in the last section are shown in Figure 2.3 and Figure 2.4 separately. The peak positions of GGG substrate and off-stoichiometric YIG are annotated in the mapping plot and the decomposition of each asymmetric peak vector into in-plane and out-of-plane components ray diagrams are given the down-right corner.

All the substrate peaks positions are obtained by contour lines due to the pixel size while collecting data and the off-stoichiometric YIG peaks are broadened due to the thickness, therefore only the center of every broadened area is annotated as peak position. Also, due to the errors from X-Ray monochromator, collector analyzer and monochromator, the diffraction peak is not a simple 2D Gaussian distribution. Instead, the streaks from system errors will accompany the diffraction peak, which makes fitting the intensity of every pixel to a well-known existing function not appropriate. Therefore, the coordinates of film position annotated should be understood as being a qualitative value or estimate.

Figure 2.3 RSM of (408) asymmetric peak on (001) substrate.

Take (408) asymmetric peak for example, which can be decomposed as:

(408) = 4 ∙ (100)𝑖푝 + 8 ∙ (001)표푝 The out-of-plane position of off-stoichiometric YIG varies slightly with different thickness, which is consistent with the HRXRD measurements discussed in the last section. However, the in-plane lattice relaxation increases from ~0.038 to ~0.1 while increasing the film thickness and the degree of relaxation is almost the same for 80 nm and 160 nm thick samples. Here, the coordinates

17 in RSM plot are dimensionless quantities normalized by the unit vector in reciprocal space of GGG substrate. In order to get the degree of relaxation of in-plane lattice, the difference between substrate and sample peak positions should be divided by the unit vector in the corresponding direction.

Similarly, the RSM of (116) asymmetric peak (Figure 2.4) shows that the in-plane direction is not fully strained either and the relaxation increases with film thickness. But this time, the in-plane vector changes to (110)푥,푦:

(116) = 1 ∙ (110)𝑖푝 + 6 ∙ (001)표푝

Figure 2.4 RSM of (116) asymmetric peak on (001) substrate.

For samples grown on (111) substrates, (664) and (642) asymmetric peaks are chosen to analyze the in-plane lattice information, which can be decomposed as:

2 16 (664) = ∙ (112̅) + ∙ (111) 3 𝑖푝 3 표푝

(642) = 2 ∙ (101̅)𝑖푝 + 4 ∙ (111)표푝

18 As shown in Figure 2.5 and Figure 2.6, similar to the (001) situation, as the film thickness increases from 23 nm to 74 nm, the out-of-plane off-stoichiometric YIG diffraction peak position varies slightly as expected from the HRXRD measurement.

Figure 2.5 RSM of (664) asymmetric peak on (111) substrate.

Figure 2.6 RSM of (642) asymmetric peak on (111) substrate.

19 However, the difference lies in two ways: 1) Even for very thin off-stoichiometric YIG film as 23nm, we can still see very sharp diffraction peaks. While for (001) case, for even 45nm thick film, it is almost impossible to tell where the peak lies. In other words, the broadening effect of asymmetric peak on (111) substrate is much smaller than (001) substrate. 2) On (111) substrate, for RSM of either (642) or (664), the diffraction peak of off-stoichiometric YIG do not show observable horizontal shift with substrate peak as sample thickness increases, which is in apparent contrast to the (001) case.

2.4 Summary

Here, a brief summary of XRD characterization of off-stoichiometric YIG samples grown on GGG substrates using PLD method with 10 푚푇표푟푟 O2 atmosphere: 1) Epitaxial garnet phase thin film is grown from YFO target. 2) The out-of-plane lattice parameter expansion ratio is ~2 − 3% , larger than that of stoichiometric YIG grown on the same substrate reported in literature. 3) (111) direction samples have larger out-of-plane lattice expansion ratio and keep in-plane lattice fully strained; (001) direction samples have smaller out-of-plane expansion ratio and show different contents of relaxation for in-plane lattice depending on sample thickness. 4) XRR simulation and fitting indicates that the sample surface is sub-nanometer level smooth.

Considering the Y3+ has larger ionic radius ( 푟푌3+ > 푟퐹푒3+), the lattice of Y-substituted garnet

Y3Fe4YO12 should be swelled by the larger Y3+, besides, the large content of oxygen deficiency may also make a contribution. Further cross-section and element mapping analysis is needed to verify the assumption.

Figure 2.7 RSM in-plane decomposition illustration.

Also, the sharpness of asymmetric peak in RSM also depends on which peak is chosen. For example, the (642) peak is the most common used in literature for (111) direction YIG. The choice of asymmetric peak determines which in-plane reciprocal vector is directly measured. For example, Figure 2.7 illustrate the projection of asymmetric peaks on the sample surface plane. The red color stands for the sample surface (111) in a and (001) in b; the blue and green vector represents the in-plane projection of two separate asymmetric peaks. The two in-plane vectors are of special symmetry : mirror line and the angle between them is one half the minimum rotation angle to keep

60° 90° the lattice unchanged, 30° = for (111) and 45° = for (001). 2 2

The in-plane shift of diffraction peaks between off-stoichiometric YIG and substrates are summarized in Table 2-2, where ∆푥 = 푥푠푢푏 − 푥푓𝑖푙푚 and ∆푥푛표푟 is the normalized shift divided by the diffraction index. Also, the last column shows the out-of-plane lattice expansion ratio calculated from HRXRD, which is more accurate than RSM measurements. Compared with samples grown on (001) GGG substrates, the samples grown on (111) substrate show almost no in-plane lattice relaxion, in other words, they are fully strained. Assuming their unit cells have the same volume, then it’s expected that the samples on (111) substrates should have larger expansion, which is verified in the last column.

21 Table 2-2 RSM summary of all six samples.

001 훿푑

408 116 푑

푥푓𝑖푙푚 푥푠푢푏 ∆푥 ∆푥푛표푟 푥푓𝑖푙푚 푥푠푢푏 ∆푥 ∆푥푛표푟 45 nm 3.911 3.949 0.038 0.00925 0.991 1 0.009 0.009 2.366 80 nm 3.907 4.001 0.094 0.0235 0.984 1.003 0.019 0.019 2.522 160 nm 3.909 4.003 0.094 0.0235 0.980 1.002 0.022 0.022 2.624 111 훿푑

664 642 푑

푥푓𝑖푙푚 푥푠푢푏 ∆푥 ∆푥푛표푟 푥푓𝑖푙푚 푥푠푢푏 ∆푥 ∆푥푛표푟 23 nm 0.665 0.665 0 0 1.998 1.998 0 0 3.242 38 nm 0.684 0.684 0 0 2.019 2.018 0.001 0.002 3.106 74 nm 0.670 0.669 0.001 0.0015 2.013 2.013 0 0 3.113

22 3. Magnetism Analysis

In this section, magnetic properties and temperature dependency of off-stoichiometric YIG samples are discussed, primarily focusing on (111) direction samples. Samples grown on (001) and (110) directions need further experiments to verify, which is not available due to limited access to lab at this special time of COVD-19. All magnetic measurements are conducted on MicroSense Vibrating Sample Magnetometer (VSM) with silica sample holder and temperature is controlled by air heating oven and thermocouple inside the oven.

3.1 Room Temperature Measurements

Figure 3.1 In-plane hysteresis loop of off-stoichiometric and standard YIG samples.

In order to directly observe the effects of Y substitution and O deficiency to the magnetic properties of samples, 53nm YIG sample is grown from standard Y3Fe5O12 target with 100 푚푇표푟푟 O2 for reference. The HRXRD data of this reference sample could be found in the Appendix section, which shows that high quality epitaxial YIG film is grown on the (111) GGG substrate. The

23 magnetization of samples is normalized by sample volume, where the thickness is obtained from XRR fitting mentioned in Chapter 2 and the area is calculated from the measured dimensions of film using digital caliper (~75 − 80% of substrate area).

After subtracting the linear background from paramagnetic GGG substrate, the in-plane hysteresis loop measurements shown in Figure 3.1 indicate that compared with the standard YIG sample, the coercivity 퐻푐 of off-stoichiometric YIG samples do not show apparent changes and remain less than 1 푂푒. However, the saturation magnetization 푀푣 of the off-stoichiometric YIG samples is ~30 − 50 푒푚푢/푐푐 depending on sample thickness, in stark contrast to the standard YIG value.

Near external field 퐻푒 ≈ 0 푂푒, the off-stoichiometric YIG samples do not show an obvious opening like standard YIG sample. One reason is that the step size of magnetic field while measuring the off-stoichiometric YIG samples is large, so the details of magnetization reversal is missing near 퐻푒 ≈ 0 푂푒. Another reason is that the coercivity of off-stoichiometric YIG samples is indeed smaller than that of standard YIG sample, which has exceeded the resolution of magnetic field of VSM in our lab. If this is true, it is easier for the off-stoichiometric YIG sample to reverse magnetization when changing external field, which means that the energy barrier required to overcome for magnetization is smaller.

The saturation magnetization 푀푣 of off-stoichiometric samples differs ~20 푒푚푢/푐푐 depending on film thickness. One possible reason of this is that there exists a ~6푛푚 ‘dead’ layer at the interfacial between GGG substrate and YIG thin film, which comes from the interfacial diffusion of cations Gd3+ 22. Therefore, the thickness of effective sample is smaller than the XRR fitting value and the thinner the film, the larger the error is for estimation of volume, which can qualitatively explain the 23nm sample has smaller saturation magnetization 푀푣 and the other two samples almost have the same 푀푣. Another possible reason is the uncertainty from measuring film thickness and film area. For the first approximation, the uncertainty of every measurements is 2%, which is a good estimation for digital caliper and XRR fitting. Then according to uncertainty chain rules:

2 2 2 ∆푥 = √(∆푥1) + (∆푥2) + (∆푥3)

24 the uncertainty of 푀푣 is ~4%, which cannot explain the 20 푒푚푢/푐푐 difference when the thickness of off-stoichiometric samples decreases.

For samples grown on (001) directions, although the three samples shown in Figure 2.2a show similar HRXRD data and high quality epitaxial garnet phase thin films, their magnetization varies a lot. One reason is that the 45nm sample was grown at a lower laser power with repetition rate 5Hz and the 80nm and 160nm samples were grown at a higher laser power with repetition rate 10Hz, therefore, the growth rate of the 45nm is significantly lower. The 45nm sample on (001)

GGG substrate shows similar magnetic properties to (111) direction with 푀푣~40 푒푚푢/푐푐 , however, the 80nm and 160nm samples grown on (001) direction with higher growth rate do not show any magnetism in-plane direction. Therefore, further experiments are needed to draw a safe conclusion about samples grown on (001) direction. Besides, the analysis of RSM in Chapter 2 shows that the samples grown on (001) substrate are not fully strained as on (111) substrate, which may explain why the magnetic properties of (001) direction off-stoichiometric YIG samples are sensitive to the growth conditions.

3.2 Temperature Dependence

Figure 3.2 Temperature dependence of standard (a) and off-stoichiometric (b) YIG

By measuring the in-plane saturation magnetization 푀푠 from room temperature to the Curie temperature (where the magnetization disappears), the temperature dependence of saturation

25 magnetization of standard and off-stoichiometric YIG samples grown on (111) substrates are shown in Figure 3.2 a and b separately.

Although the sample for reference here is grown from standard Y3Fe5O12 target with 100 푚푇표푟푟

O2 atmosphere and shows 푀푠~135 푒푚푢/푐푐, the Curie temperature is ~ 450 퐾, which is 100 퐾 lower than the bulk value. It indicates that the reference YIG is still not perfect instead is off- stoichiometric. One possible reason is that the 100 푚푇표푟푟 O2 atmosphere is still not high enough there is O deficiency in the crystal. Also, the Y to Fe ratio may not be strictly 3:5 as the target. Elemental analysis and temperature calibration are needed to further verify the assumptions.

Compared with the ‘good’ YIG sample, the Curie temperature of off-stoichiometric YIG decreases significantly to ~310 퐾 (40 ℃), which means that the super-exchange interaction between a site and c site Fe has been weakened by the substitution of Y and existence of O deficiency.

3.3 Explanation

In this section, the effect of non-magnetic ion Y substituting magnetic ion Fe will be discussed and compared with the standard YIG sample, the reduced saturation magnetization 푀푠 and Curie temperature 푇푐 will be qualitatively explained according to the model developed in Dionne’s book2.

The ferrimagnetism of YIG comes from the antiparallel coupling between the Fe3+ sitting in the tetrahedral and octahedral sublattice. Based on this, a two-lattice model shown in Figure 3.3 is used to explain how magnetic properties of YIG are changed by the substitution of non-magnetic ion to Fe3+ ion. A 2D model with two sublattices antiferromagnetic aligned is shown in Figure 3.3a and we denote the blue sublattice (spin up) j and yellow sublattice (spin down) i. In real 3D YIG, the single magnetic moment of ion sitting in i and j is the same but with the numerous ratio 3:2, resulting in the ferrimagnetism. Assume that one magnetic ion in the j sublattice is substituted by a non-magnetic one and that the substitution fraction is small, then the ‘ripple’ effect of the substitution is shown in Figure 3.3b, with the transparent blue site missing magnetic moment and the nearest i site neighbors and j site neighbors affected.

26 The ferrimagnetic order of the a and d site cations of YIG is maintained by the super-exchange interaction, therefore, there exists the possibility that the local breakdown will put an ‘domino effect’ to the long-range order. For example, a missing j site (by substitution) will reduces the exchange field (molecular field) felt by the nearest i site neighbors, which makes the collective behavior of remaining magnetic ions weaker. In other words, the missing j site could weaken the ferrimagnetism of crystal and make the nearest i site neighbors behave partly paramagnetically. An equivalent representation of this effect is that the nearest i site effective magnetic moment is reduced, or canted as shown in Figure 3.3b.

Figure 3.3 Un-canted (a) and canted (b) spin illustration.

However, the canting effect has more ripples in the nearby regions which can be summarized as follows: a) Direct Reduction of Exchange Field: Strictly speaking, the non-magnetic substitution weakens the super-exchange interaction between a and d site cations, thereby, the lower thermal energy is needed to overcome the barrier to behave ‘independently’. In the YFO grown samples, to

the first approximation, the Fe3+ sublattice is greatly diluted by the non-magnetic Y3+, therefore,

the super-exchange between the remaining Fe3+ is greatly reduced, which can explain why the

Curie temperature 푇푐 of off-stoichiometric samples is 31~0 퐾, which is 250퐾 lower than the standard YIG.

27 b) Inter-sublattice Spin Canting: the missing magnetic site j will offer its neighboring i site some freedom to behave ‘independently’, which results in a smaller effective magnetic moment. c) Intra-sublattice Spin Canting: the parallel alignment in each separate sublattice is also achieved by exchange coupling. The missing in j site and canting in i site will also put an effect on their own sublattice to reduce the effective magnetic moment of their own types. But the probability and reduction of this intra-sublattice canting should be smaller than the inter-sublattice one, because the a-d site super exchange interaction is the dominant one in YIG.

Also, the O deficiency will change partially the Fe3+ to Fe2+ because the Y3+ is the stable valent state, therefore, the net spin angular momentum will reduce from 5휇퐵 to 4휇퐵. Considering the ionic relation: 푟푌3+ > 푟퐹푒3+, the unit cell is swelled by the Y3+ and has a larger volume. Combing all the factors discussed above, the saturation magnetization 푀푣 of the off-stoichiometric samples is reduced to ~30% of standard YIG value.

More quantitative model to explain the substituted-YIG samples could be found in Gilleo and Geller’s original work, although focusing on polycrystalline samples, while the model is still useful and inspiring to the work here.

28 4. Other Characterization

Figure 4.1 AFM characterization of (111) 38nm sample.

As shown above in Error! Reference source not found., the off-stoichiometric YIG samples grown on (111) substrates show the ripple structure under AFM characterization. The width of the stripe is ~1 휇푚 and the depth of groove is ~1푛푚. It’s possible that the wavy structures come from the artifacts of equipment. Therefore, more AFM characterization on the sample should be conducted to rule out the possibility of artifacts. However, the AFM of (111) samples with groove depth ~1푛푚 and the zoomed view scans on the right showing sub-nanometer smooth surface are consistent with the HRXRD analysis in Chapter 2.

Figure 4.2 Depth profile of (110) sample.

Figure 4.2 shows the atomic ratio of C, O, Fe, Y versus depth beneath sample surface by X-Ray Photoelectron Spectrum (XPS). The longer the etching time, the deeper the sample will be exposed to X-Rays to collect data. At the surface (푥 = 0), carbon dominates because the sample is rinsed with IPA and acetone. With deeper and deeper in the sample, the carbon drops to zero at etching cycle 4 and the Y to Fe ratio stables at ~1: 1. Here, Fe3p level and Y3d level are used for the quantization of the atomic ratio. Further analysis is needed to make sure this choice is reliable and accurately calibrated.

30 5. Summary

By ablating perovskite phase target YFO (YFeO3), Y rich and Fe deficiency garnet phase thin films are epitaxially grown on the GGG (Ga3Gd5O12) substrates with different orientations: (001), (110) and (111). Compared with standard YIG grown on GGG substrate, the off-stoichiometric

YIG samples show larger out-of-plane expansion ratio resulting from the swelling of Y3+ substitution and O deficiency. The in-plane relaxation depends on the substrate orientation and film thickness: samples grown on (111) GGG substrates with thickness from 23nm to 74nm maintain fully strained; however, samples grown on (001) GGG substrates show different levels of relaxation depending on film thickness.

Also, the magnetic properties are dramatically changed by these substitutions: The off- stoichiometric samples show reduced saturation magnetization 푀푠~40 푒푚푢/푐푐 and lowered

Curie temperature 푇푐~310 퐾, in stark contrast with the values of standard YIG (푀푠~140 푒푚푢/푐푐 and 푇푐~560 퐾).

Therefore, it seems impossible to directly grow perovskite phase (YFO) on garnet substrate (GGG). Then what about growing garnet on the perovskite substrates? Standard YIG target is used to ablate and deposit on STO (SrTiO3) substrate but no garnet phase is found except perovskite. Combining these two experiments, the perovskite and garnet structures seem very tolerant of off-stoichiometry. To achieve nano-composite made up of garnet and perovskite phase, other strategies are under research such as: engineering nucleation site of substrate and patterning the substrate surfaces with amorphous silica.

Although the original goal of co-deposition of garnet and perovskite phase together on the single substrate has not been achieved so far, the journey of exploring all choices is fruitful and rewarding. I’d like to end my thesis with Theodore von Kármán’s quote:

‘Scientists discover the world that exists; engineers create the world that never was.’

31 6. Appendix

Figure 6.1 HRXRD of off-stoichiometric YIG on (110) GGG substrates

The crystallization of off-stoichiometric YIG on GGG (110) substrate is not as good as on (001) and (111) substrates. Laue fringes exist besides the film peak but not as sharp as samples grown on (001) and (111) substrates. But epitaxial garnet phase is still formed on the substrate.

Figure 6.2 GIXRD of off-stoichiometric YIG samples on (001) and (111) substrates.

No peak but noises are shown in the GIXRD characterization, and combined with HRXRD result, it’s concluded that epitaxial garnet phase is formed on the GGG substrates.

32 Reflectivity Profile 0 Measurement 1.0 x10 Calculation Residual 4

3 -2 1.0 x10

1 -4

1.0 x10 Reflectivity (normalized) Reflectivity

0 Residual delta ( log10 ( intensity ) ) intensity ( log10 ( delta Residual

-1 -6 1.0 x10

-2

0 1 2 3 4 5 6

2-theta (deg) Figure 6.3 XRR simulation and fitting result in GlobalFit.

The red curve is experimental measured data and the blue curve is simulation and fitting by adjusting the thickness of YIG film and roughness. Only the bright region is used for fitting because at high angles, noises will dominate and lower the quality of fitting.

Figure 6.4 (111) HRXRD with YIG on GGG substrates.

HRXRD of reference YIG sample in Chapter 3 together with other samples are shown above to verify the epitaxial growth.

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