Control of Magnetic Behavior in LaMnO3 Thin Films
through Cationic Vacancies
A Thesis
Submitted to the Faculty
of
Drexel University
by
Cerina Gordon
In partial fulfillment of the
requirements for the degree
of
Master of Science in Materials Science and Engineering
June 2017
© Copyright 2017
Cerina Gordon. This work is licensed under a Creative Commons Attribution 4.0
International License. ii
Acknowledgements
I would like to express thanks to all those who helped me and stood by me during the production of this work. In particular I’d like to thank Mark Scafetta and Dr. Steve
May for providing the opportunity to study this problem, Mark for growing the films and
Dr. May for prompting the study of this problem and providing the resources to study it.
Growth of the films by Mark S. was funded by the National Science Foundatin (DMR-
1151649)
I’d also like to thank my lab group for providing training on several of the tests performed, assisting in characterization and providing useful discussion and moral support. Similarly, I’d like to thank my committee members, Dr. Steve May, Dr. Goran
Karapetrov and Dr. Garritt Tucker for the valuable discussion following my defense.
Finally, I’d like to thank my friends and family for providing support and sticking it out with me, and providing an outside perspective to remind me of exactly what a general audience does and does not know. iii
Table of Contents List of Tables ...... v
List of Figures ...... vi
Abstract ...... viii
1. Introduction ...... 1
2. Background ...... 3
Magnets and Magnetization ...... 3
Definition of a Magnet ...... 3
Types of Magnetic Behavior in Materials ...... 4
Ferromagnetic Behavior ...... 6
Antiferromagnetic Behavior ...... 8
Perovskites ...... 9
Charge balancing ...... 9
Defects ...... 10
Magnetic and Electronic Behavior in Perovskites ...... 11
Lanthanum Manganite ...... 14
Bulk LaMnO3 ...... 14
LaMnO3 Thin Films ...... 15
3. Experimental ...... 18
Samples ...... 18
Synthesis and Processing ...... 19
Thin Film Deposition via Molecular Beam Epitaxy (MBE) ...... 19
Annealing ...... 21 iv
Characterization ...... 21
Rutherford Backscattering Spectroscopy (RBS) ...... 22
X-ray Diffraction (XRD) ...... 22
X-ray Reflectivity (XRR) ...... 24
Vibrating Sample Magnetometry ...... 26
4. Results and Discussion ...... 29
Structural Analysis ...... 29
X-Ray Diffraction ...... 29
Effect of Annealing ...... 32
X-Ray Reflectivity ...... 33
Magnetic Behavior ...... 35
Moment vs Applied Field (MvH) ...... 35
Moment vs Temperature and the Paramagnetic Transition Temperature ...... 41
5. Conclusion and Future Work ...... 46
v
List of Tables
Table 2.1: Categorization of magnetic materials by alignment of adjacent spins ...... 4
Table 3.1: List of samples by LaMnO3 film cation ratios ...... 18
Table 4.1 Summary of x-ray diffraction results ...... 31
Table 4.2 Film thickness as obtained through x-ray reflectivity analysis ...... 34
Table 4.3 Transition temperatures ...... 42 vi
List of Figures
Figure 1.1 Slowdown in hard-drive improvements ...... 1
Figure 1.2 Seagate's 2008 technology roadmap ...... 1
Figure 1.3 IBM hard drive architecture for perpendicular writing ...... 2
Figure 2.1 Alignment and growth of magnetic domains in a ferromagnetic material ...... 6
Figure 2.2 Typical magnetic moment (M) vs. applied field (H) behavior for ferromagnetic materials ...... 7
Figure 2.3 Example spin canting in a G-type antiferromagnetic material ...... 8
Figure 2.4: Crystal structure of an ideal perovskite ...... 9
Figure 2.5 d-orbitals and corresponding energy levels ...... 12
Figure 2.6: p-orbitals ...... 12
Figure 3.1 Sample XRR data with simulated fit ...... 25
Figure 4.1: X-ray diffraction data for LaMnO3 films on SrTiO3 ...... 29
Figure 4.2 X-ray diffraction peaks following ozone annealing ...... 32
Figure 4.3 XRD spectra for LaMnO3 near the (001) substrate peak ...... 33
Figure 4.4 Sample fit of x-ray reflectivity data ...... 34
Figure 4.5 Magnetization vs applied field at 10K for LaMnO3 films ...... 35
Figure 4.6 Comparison of AF sample to AF behavior reported in [11] ...... 36
Figure 4.7 Saturation magnetic moment vs thickness for LaMnO3 films on SrTiO3 ...... 37
Figure 4.8 Saturation magnetic moment as a function of composition ...... 37
Figure 4.9 Saturation moment as a function of manganese valence state ...... 38
Figure 4.10 Phase diagram for strontium-doped LaMnO3 ...... 39 vii
Figure 4.11 Change in saturation magnetic moment due to ozone annealing, as a function of manganese average oxidation state ...... 40
Figure 4.12 Film moment vs temperature under an applied field of 0.1 T ...... 41
Figure 4.13 Determination of transition temperature via trend line ...... 42
Figure 4.15 Film moment […] vs transition temperature ...... 43
Figure 4.16 Manganese oxidation state vs transition temperature ...... 44
Figure 4.17 Film thickness vs transition temperature ...... 44
Figure 4.18 Film moment vs temperature for a constant applied field of 0.1 T, following annealing in ozone ...... 45 viii
Abstract
Control of Magnetic Behavior in LaMnO3 Thin Films through Cationic Vacancies Cerina Gordon
The magnetic behavior of lanthanum manganite thin films (LaMnO3) deposited on strontium titanate (SrTiO3) was explored as a function of manganese oxidation state, as controlled by the presence of cation and oxygen vacancies. This was done in response to the inconsistent magnetic properties found in literature. The films were characterized using Rutherford backscattering spectroscopy, wide-angle x-ray diffraction, x-ray reflectivity and vibrating sample magnetometry. The films were found to exhibit an antiferromagnetic to ferromagnetic transition consistent with that found in strontium- doped LaMnO3 systems, where the manganese oxidation state is controlled by the fraction of strontium present.
1
1. Introduction
Thin film magnetic devices have revolutionized data storage in much the same way thin film semiconductor devices have revolutionized computing. Between
1990 and 2005, hard drive data storage areal density increased from 100 Mbit/in2 to 110 Figure 1.1 Slowdown in hard-drive 2 Gbit/in . This was accompanied by a 1000-fold improvements, as compared to predictions a la Kryder's law. [2] decrease in data storage price per byte. This regular improvement was called Kryder’s law, as an analogue to Moore’s law, describing the exponential increase in areal density of transistors. [1] [2] [3]
In recent years, this projected increase in areal density has slowed as hard drive technologies approach fundamental limits. Continued improvements rely on the development of new technologies, including changes Figure 1.2 Seagate's 2008 technology roadmap for to hard drive architecture, changes to continued improvements in hard drive storage capacity. Heat-assisted magnetic recording (HAMR) has not yet data storage mechanism and been realized in a consumer product. [2] improvements to the material systems being used.
One of the biggest advances in hard drive storage capacity in recent years was due to the development of perpendicular writing. In this configuration bits are magnetized 2 perpendicular to the platter surface, rather than the parallel orientation used in the past.
This technology relies on several exotic behaviors including giant magnetoresistance.
Additionally, layers with a variety of well-controlled magnetic behaviors are required, including layers showing soft ferromagnetism and antiferromagnetic behavior. Use of this technology moves the theoretical maximum areal density
Figure 1.3 IBM hard drive architecture for for magnetic hard drives from ~100 perpendicular writing. [3] Gbits/in2 to over 500-600 Gbits/in2. [4]
In addition to driving a need for the development of a variety of magnetic materials, thin films and heterostructures, the development of perpendicular writing illustrates the need for continued research into basic physical phenomena such as those that form the basis of the emerging field of spintronics. A material system that has gained interest is that of perovskite oxides, as they are massively tunable due to a large number of degrees of freedom and many compounds exhibit exotic behaviors such as superconductivity and ferroelectricity. [5]
One material, lanthanum manganite (LaMnO3), when grown as a thin film, can be tuned from antiferromagnetic to ferromagnetic under a wide variety of circumstances using a range of techniques. The characterization and origin of this behavior is explored within this work. 3
2. Background
Magnets and Magnetization
Definition of a Magnet
Magnetic materials are any materials whose electrons align themselves in response to an applied external magnetic field. These materials can be classified into several broad categories: ferromagnetic, antiferromagnetic, ferrimagnetic, paramagnetic and diamagnetic. These categories represent distinct frameworks for ordering with implications with regards to their magnetic susceptibility, spin exchange energy and magnetic domain structure as well as macroscopic properties such as their saturation magnetization and coercivity.
The origin of magnetism is the motion, and internal angular momentum, of electrons. According to Ampere’s Law,
∇ × � = � � ( 2.1 )
where B is a magnetic field, µ is the vacuum permeability constant and J is total current density, electric currents create magnetic fields. By using the definition of current as the flow of charged particles it can be seen that there is a current associated with the motion of a single electron. Thus, electrons in orbitals can lead to the exhibition of an orbital moment.
The intrinsic magnetic moment of an electron, independent of its orbital motion, is called an electron’s spin, and has a magnitude of one Bohr magneton. While electrons in filled orbitals will pair up such that these moments nullify one another, according to Hund’s rules, electrons in partially empty orbitals will align their spins to maximize their collective spin angular momentum, maximizing their collective magnetic moment. These small 4 moments can, depending on various material properties, align with the moments of electrons orbiting adjacent atoms, resulting in macroscopic magnetic behavior.
Types of Magnetic Behavior in Materials
When examining magnetism on this atomic scale it is possible to define the five previously mentioned types of magnetism by how adjacent spins align after application and removal of an applied magnetic field: in ferromagnetic materials adjacent spins align parallel to one another, in antiferromagnetic materials adjacent spins of equal magnitude align opposite one another, in ferrimagnetic materials adjacent spins of unequal magnitudes align opposite one another with the larger spins aligned. The spins in paramagnetic and diamagnetic materials do not align without an applied magnetic field, but while a field is applied paramagnetic materials show a slight net moment in alignment with the applied field, while diamagnetic materials show a slight moment opposed to the applied field.
Table 2.1: Categorization of magnetic materials by alignment of adjacent spins
Alignment of Net Magnetic adjacent spins Moment Ferromagnetic ↑↑↑↑↑↑↑↑↑↑ large, + Antiferromagnetic ↑↓↑↓↑↓↑↓↑↓ zero Ferrimagnetic ↑↓↑↓↑↓↑↓↑↓↑↓ meduim, + Paramagnetic ~ small, + Diamagnetic ~ small, -
5
This aligned-opposed behavior is typically modeled with a parameter called exchange energy, representing the energy associated with aligning spins between adjacent atoms and defined as
� = −�� ∙ � ( 2.2 )
where � ∙ � represents the relative angle between adjacent spins and J represents the exchange integral, which is a material property. If J is positive then there is a reduction in energy for � ∙ � > 0, which corresponds to aligned spins, with a minimum at � ∙ � = 1, the vectors being exactly parallel. This is the definition for ferromagnetic materials.
Similarly, for negative J the lowest energy configuration is for adjacent spins to line up opposite one another, this being the case in antiferromagnetic and ferrimagnetic materials.
The alignment behavior of adjacent spins becomes entropy-controlled at higher temperatures, with the temperature being dependent on the magnitude of the exchange integral. Above the temperature at which behavior becomes entropy-controlled, ferromagnetic, ferrimagnetic and antiferromagnetic materials become paramagnetic. In ferromagnetic materials this transition temperature is called the Curie transition temperature; in antiferromagnetic materials this is the Néel temperature. In addition to the observation of the disappearance of spin ordering, this transition may be observed as a discontinuity in the first derivative of a material’s magnetic susceptibility.
Magnetic susceptibility is defined as the ability for an external field to magnetize a sample,
� = �� ( 2.3 ) 6 where M is the magnetization of the sample, B is the applied field and χ is the susceptibility.
This is a bulk property which changes with temperature, in accordance with the relationship to entropy/exchange energy described above, and is distinct for each of the previously described types of magnetic behavior. In paramagnetic and diamagnetic materials, this property is typically constant with respect to temperature and applied field, being a positive constant in paramagnetic materials and negative in diamagnets. Magnetization, and therefore susceptibility in antiferromagnetic materials is small, increasing with temperature to reach a sharp peak at the Néel transition. Magnetization in ferromagnetic materials is more complicated and as a result susceptibility is a non-linear equation. [6]
Ferromagnetic Behavior
In ferromagnetic materials, an applied field may cause all the unpaired spins to become aligned with that field; with no more spins to align, magnetization cannot increase and susceptibility becomes essentially zero. The degree of magnetization in this condition is called the saturation magnetization. This can be seen in both the formation and development of their domain structure and the shape of magnetic moment vs applied field graphs.
The unpaired spins in ferromagnetic materials show local alignment within regions called domains. These domains vary in size and Figure 2.1 Alignment and growth of magnetic domains in a ferromagnetic material. The left- most sample has reached saturation alignment direction. Prior to application of a magnetization. Repurposed from [6] magnetic field these domains are randomly oriented, with their net moment typically 7 summing to zero across the sample. On application of a magnetic field, the domains aligned with the field grow while those aligned oppositely shrink, resulting in a net magnetic moment in the direction of the applied field.
When a magnetic field is applied to a non-magnetized sample, a linear increase in magnetization is observed, similar to that observed in paramagnetic materials. At some applied field this magnetization will reach a maximum which, when normalized with the number of contributing atoms in the sample, is slightly less than 1 µB per unpaired electron per atom. For example, nickel in its ground state has an electronic configuration of 3d8 4s2, meaning it has 2 unpaired electrons in its d-shell. This corresponds to a theoretical maximum magnetization of 2 µB/Ni. On removal of the applied field the magnetization of the sample will decrease linearly, similar to the path seen when the field was initially applied. However, the sample will retain some net magnetization at zero applied field, called the remanence; without any driving Figure 2.2 Typical magnetic moment (M) vs. applied field (H) behavior for ferromagnetic materials. Repurposed from force the domains will remain aligned. Some field, [6] called the coercive field, must be applied in the other direction to return the sample to zero magnetization. Further application of a magnetic field in the opposite direction results in the same saturation behavior seen in the other direction.
8
Antiferromagnetic Behavior
While there is only one way of arranging spins so that adjacent spins have opposite orientations in 1D space, when moving to 2D or 3D space more configurations become available. For example, three forms of ordering in antiferromagnetic materials are: A-type, representing parallel alignment in 2 axes, antiparallel in the third, C-type, representing parallel alignment in 1 axis, antiparallel in the other 2, and G-type, antiparallel alignment Figure 2.3 Example spin canting in a G-type antiferromagnetic in all 3 axes. As a result, it is possible to have a net magnetic material. This material would show a slight magnetic moment in the positive x direction. moment along one axis or within a plane while having no net Repurposed from [7] magnetization across the entire sample. However, the magnetic moment observed in most antiferromagnetic materials is the result of a different phenomenon called spin canting.
Spin canting refers to a slight (<300) off-axis tilt which can appear systematically throughout a sample. As in ferromagnetic materials it is possible for the moments arising from spin canting to negate one another across the sample or to be aligned via application of a magnetic field, resulting in a small net magnetization and ferromagnet-like behavior.
[7]
9
Perovskites
Perovskites are materials with the general chemical formula ABX3 where A and B are cations, A being larger than B, and X being oxygen, nitrogen, carbon, hydrogen or a halogen gas. [8] [9] As the oxide is the most common form it is the only one that will be mentioned here forward. The cation on the A-site is of an element that can take the oxidation states +1, +2, +3 or some combination of those, while the cation on the B Figure 2.4: Crystal structure of an ideal perovskite. Repurposed from [9] site is generally a transition metal.
These materials are distinguished from other materials of matching composition by their crystal structure: crystals in this group typically take the cubic structure, which may be represented as corner-sharing octahedra with B-cations in the center and A-cations in the vacancies between clusters, or as cubic crystals with an A cation in the body center location, B cations at the corners and oxygen at the center of each edge. While the material can take on an orthorhombic, rhombohedral or tetragonal structure [8] the relative positions of these atoms remains mostly constant.
Charge balancing
Perovskites are typically described as ionic solids, meaning the atoms are fully ionized and the formula may be charge balanced in order to determine the oxidation states of the individual components. As oxygen can only take the oxidation state -2, this is the 10 starting point. The sum of the oxidation states of the A and B cations is therefore +6, as there are 3 oxygens per formula unit. Since B is frequently transition metals which can take on multiple oxidation states, mixed oxidation states are frequently observed, for example