Magnetic and electrical transport properties of irradiated thin (Ga,Mn)As films

(Ga,Mn)As films

S´ ergio Luis de Abreu Mello

PhD thesis submitted to the Programa de P´ os- gradua¸ c˜ ao em F´ısica of the Instituto de F´ısica of Universidade Federal do Rio de Janeiro - UFRJ, as a partial fulfillment of the require- ments for the degree of Doctor of Science - Ph.D.

- (Physics)

Supervisor: Marcelo Martins Sant’Anna

Rio de Janeiro

February 2015

M527m

Mello, S´ ergio Luis de Abreu

Magnetic and electrical transport properties of irradiated thin (Ga,Mn)As films / S´ ergio Luis de Abreu Mello. – Rio de Janeiro, 2015.

77 f.: il.

Orientador: Marcelo Martins Sant’Anna

Tese (Doutorado) - Universidade Federal do Rio de Janeiro, Instituto de F´ısica, Programa de P´ os-Gradua¸c˜ ao em F´ısica, 2015.

1. Ion Irradiation 2. Diluted Magnetic Semiconductor 3. Transport

Measurement 4. SQUID Measurement 5. Annealing. I. Sant’Anna,

Marcelo Martins, orient. II. T´ıtulo.

ABSTRACT

Magnetic and electrical transport properties of irradiated thin (Ga,Mn)As films

S´ ergio Luis de Abreu Mello Advisor: Marcelo Martins Sant’Anna

Abstract of PhD thesis submitted to the Programa de P´ os-gradua¸c˜ ao em F´ısica, In- stituto de F´ısica, Universidade Federal do Rio de Janeiro - UFRJ, as a partial fulfillment of the requirements for the degree of Doctor of Science - Ph.D. - (Physics).

The effect of ion-beam irradiation on magnetic and electrical transport properties of thin Ga

Mn

As films (x ∼ 0.05) was investigated. The samples were irradiated at room temperature with ions from a Tandem electrostatic accelerator. SQUID magnetization and (magneto)transport measurements were carried out on the irradiated samples (and also on as-grown specimens for comparison). Both the magnetization and the conductivity of such samples decrease as a result of increase of defect density in the system caused by the irradiation process. While penetrating the film, the impinging ions collide with the host atoms of the material. These atoms become displaced, and can either vibrate and return to their original sites, or they can be removed from the original position, resulting in lattice defects. The amount of defects left in the crystalline structure of the material depends on the irradiation parameters, for example, the ion fluence (measured in ions/cm

), the ion energy, and the atomic number Z of the projectile ion. In this study we have varied these parameters in a systematic manner. For instance, several ion fluences were used with different ion energies, for the same projectile ion (i.e., the same Z). As a result, the irradiated samples span the range from metallic to highly insulating behavior.

The different natures of defects created by ions of low- and high-energies were investi- gated. As an example, keV ions stop within the thin Ga

Mn

As film, while MeV ions have enough energy to cross it and bury themselves in the bulk of the substrate. These two regimes have distinct effects on the thermomagnetic curves measured by SQUID.

We have also investigated the recovery of such irradiated samples, by measuring their

magnetic and transport properties before and after annealing. Transport measurements

on annealed-irradiated samples show significant enhancement of the transport properties of the films (revealed by the increase of conductivity and of the critical temperature).

Comparison of resistivity ρ(T ) curves (T is the temperature) of annealed-irradiated and annealed-non-irradiated samples indicates that most defects created by low fluences of ion beams are similar to those created while growing the samples. This is evidenced by the fact that ρ(T ) of annealed-irradiated and annealed-non-irradiated samples nearly match.

Keywords: Ion Irradiation, Diluted Magnetic Semiconductor, Transport Measurement, SQUID Measurement, Annealing.

Rio de Janeiro

February 2015

RESUMO

Propriedades magn´ eticas e de transporte el´ etrico de filmes finos de (Ga,Mn)As irradiados

S´ ergio Luis de Abreu Mello

Orientador: Marcelo Martins Sant’Anna

Resumo da Tese de Doutorado submetida ao Programa de P´ os-gradua¸c˜ ao em F´ısica, Instituto de F´ısica, da Universidade Federal do Rio de Janeiro - UFRJ, como parte dos requisitos necess´ arios ` a obten¸c˜ ao do t´ıtulo de Doutor em Ciˆ encias (F´ısica).

O efeito da irradia¸c˜ ao com feixes de ´ıons sobre as propriedades magn´ eticas e de trans- porte el´ etrico de filmes finos de Ga

Mn

As (x ∼ 0.05) foi investigado. As amostras foram irradiadas ` a temperatura ambiente com ´ıons produzidos por um acelerador ele- trost´ atico do tipo Tandem. Medidas de magnetiza¸c˜ ao com SQUID e medidas de (mag- neto)transporte foram realizadas nas amostras irradiadas, assim como em outras n˜ ao ir- radiadas para compara¸c˜ ao dos resultados. Tanto a magnetiza¸c˜ ao quanto a condutividade das amostras diminuem como resultado do aumento da densidade de defeitos causados pelo processo de irradia¸c˜ ao. Ao penetrar o filme, os proj´ eteis colidem com os ´ atomos da rede. Esses ´ atomos s˜ ao deslocados, podendo vibrar e, em seguida, retornar para seus s´ıtios de origem, ou se acomodar em interst´ıcios, resultando em defeitos na rede cristalina. A quantidade defeitos produzidos no material depende dos parˆ ametros de irradia¸c˜ ao, como a dose de ´ıons (medida em ´ıons/cm

), a energia e o n´ umero atˆ omico Z do proj´ etil. Esses parˆ ametros foram variados de maneira sistem´ atica nesse estudo. Por exemplo, v´ arias doses foram usadas para cada energia de irradia¸c˜ ao, mantendo o mesmo proj´ etil (ou seja, o mesmo Z). Como resultado, as amostras irradiadas assumem comportamentos desde met´ alico at´ e altamente isolante.

As naturezas diferentes dos defeitos criados por proj´ eteis de baixa e de alta energia foram investigadas. Por exemplo, ´ıons de keV param no filme de Ga

Mn

As, enquanto

´ıons de MeV s˜ ao energ´ eticos o suficiente para cruzar o filme e se enterrar no substrato.

Esses dois regimes de energia apresentam efeitos distintos sobre as curvas termomagn´ eticas

medidas com SQUID. A recupera¸c˜ ao estrutural das amostras irradiadas foi tamb´ em inves-

tigada. Para isso, as propriedades magn´ eticas e de transporte das amostras foram medidas antes e depois de se realizar tratamento t´ ermico sobre elas. As medidas de transporte rea- lizadas ap´ os o tratamento t´ ermico mostraram uma melhora significativa das propriedades de transporte do filme (revelada pelo aumento da condutividade e da temperatura cr´ıtica).

Uma compara¸c˜ ao entre as curvas de resistividade ρ(T ) (T ´ e a temperatura), medidas antes e depois do tratamento t´ ermico das amostras, sugere que os defeitos criados por doses de ´ıons baixas s˜ ao similares ` aqueles criados durante o crescimento dos filmes. Isso est´ a evidenciado pelo fato de que ρ(T ) ap´ os o tratamento t´ ermico ´ e praticamente igual ao obtido antes do tratamento, para doses baixas.

Palavras-chave: irradia¸c˜ ao iˆ onica, semicondutor magn´ etico dilu´ıdo, medida de transporte, medida de magnetiza¸c˜ ao, tratamento t´ ermico.

Rio de Janeiro

Fevereiro de 2015

Agradecimentos

Ao orientador e amigo Marcelo Martins Sant’Anna, por toda sua paciˆ encia, por seu apoio e suas orienta¸c˜ oes, e tamb´ em por seu exemplo de entusiasmo para com a Ciˆ encia.

Aos professores Jacek Furdyna e Xinyu Liu por terem me recebido na University of Notre Dame, EUA. E aos meus colegas de laborat´ orio, Xiang Li, Si-Ning Dong e Taehee Yoo, pela troca de conhecimentos cient´ıficos e culturais, e pelos momentos de divers˜ ao.

Aos meus companheiros de sala, B´ arbara, Camilla, e Anderson, pelo conv´ıvio divertido e harmonioso ao longo desses anos de doutorado.

A professora Thereza Paiva (UFRJ), pela generosa revis˜ ` ao do texto (em tempo record:

uma noite).

A professora Tatiana Rappoport pelas dicas de como me virar em Notre Dame. ` Ao Instituto de F´ısica da UFRJ. Em especial, ao Pedro e ao Cas´ e da secretaria de p´ os-gradua¸c˜ ao.

Ao CNPq e ` a CAPES pelo suporte financeiro.

A minha am´ ` avel esposa, Roberta Parrini, pela amizade, o companheirismo e a coragem de largar tudo para me acompanhar durante meu doutorado sandu´ıche. Vocˆ e tornou essa jornada prazerosa.

A todos, muito obrigado!

List of figures xi

List of tables xv

Introduction 1

1 Basics of Ga

Mn

As 6

1.1 Diluted magnetic semiconductors . . . . 6

1.2 Ga

Mn

As background . . . . 7

1.3 Hole-mediated ferromagnetic coupling . . . . 8

1.4 Molecular beam epitaxy . . . . 10

1.5 Defects in Ga

Mn

As . . . . 11

2 Experimental methods 15 2.1 Ion beam irradiation . . . . 15

2.1.1 Standard Tandem accelerator . . . . 15

2.1.2 High-enery ion beam: standard procedure . . . . 17

2.1.3 Low-energy ion beam: our modus operandi . . . . 18

2.1.4 Mass spectrometry . . . . 19

2.1.5 Extraction of heavy ion beam . . . . 22

2.2 Magnetotransport measurements . . . . 24

2.3 SQUID magnetometry . . . . 26

2.4 Post-growth annealing . . . . 28

3 Synthesis and modification of Ga

Mn

As samples 29 3.1 Ion-beam irradiation of thin Ga

Mn

As films . . . . 29

3.2 Defects produced by ion-beam irradiation . . . . 31

3.3 Irradiation inhomogeneities for low-energy and high-energy ions . . . . 32

3.4 Nanofabrication . . . . 33

4 Magnetic and transport properties 35 4.1 Magnetization measurements . . . . 35

4.1.1 Dependence of the magnetization on the ion fluence . . . . 39

4.1.2 Cross section for beam-induced removal of Mn

estimated from magnetization measurements . . . . 40

4.2 Electrical transport measurements . . . . 42

4.2.1 Annealing studies . . . . 44

4.2.2 Ion-created and growth-created defects comparison . . . . 48

4.2.3 Dependence of the sheet resistance on the ion fluence . . . . 49

5 Magnetotransport studies 52 5.1 Magnetoresistance . . . . 52

5.2 Anomalous Hall effect . . . . 56

5.3 Hall magnetization . . . . 58

6 Recent advances at LaCAM. Conclusion and outlook 63 References 68 A Small angle correction to the Wien filter 75 A.1 Equations of motion . . . . 75

A.2 Possible trajectories and calibration curve . . . . 76

A.2.1 Circular trajectory . . . . 76

A.2.2 Parabollic trajectory . . . . 77

1 Depth profile of implanted Mn ions in ZnO for different implantation energies. 3 1.1 Schematic picture of a (a) nonmagnetic semiconductor and (b) a diluted

magnetic semiconductor. . . . 7 1.2 Schematic illustration of the hole-mediated ferromagnetic interaction

among local Mn spins in diluted magnetic semiconductors. . . . 8 1.3 Schematic energy band diagram of Ga

Mn

As as a function of the Mn

content. . . . 9 1.4 Schematic phase diagram showing the relation between properties of LT-

MBE grown (Ga,Mn)As and the growth parameters. . . . . 11 1.5 Ga

Mn

As unit cell with defects: As

is an As antisite, and Mn

is an

interstitial Mn. . . . 12 1.6 Mn

-Mn

pair in the GaAs structure. . . . . 14 1.7 The nearest four cation and six anion neighbors for anion in the tetrahedral

interstitial position in the zinc-blende lattice. . . . 14 1.8 The six (three cations and three anions) nearest neighbors and the next four

cations and four anions for an ion in the hexagonal interstitial position in the zinc blende lattice. . . . 14 2.1 Schematic representation of a Tandem accelerator and its main components. 16 2.2 Charge state fractions H

, H, and H

as a function of the stripper pressure,

obtained from the collision of a 1 MeV H

ion beam with He gas in the stripper. . . . 19 2.3 User interface of the LabView program used for mass spectrometry. . . . . 20 2.4 Scan of the initial beam from the ion source for a crucible that contained

graphite. . . . 21

2.5 Calibration curve for the peaks in Fig. 2.4. . . . 21

2.6 Scan of Au beam revealing various Au

clusters. . . . 23

2.7 Schematic diagram of the measurement system setup for magnetotransport measurements. . . . 25

2.8 Sample holder loaded with Ga

Mn

As samples. . . . 25

2.9 MPMS XL system and probe components. . . . 27

2.10 Schematic setup for annealing Ga

Mn

As samples. . . . 28

3.1 Depth profile of implanted ions in GaMnAs film and GaAs substrate. . . . 30

3.2 Estimation of irradiation-induced damage inhomogeneities in Ga

Mn

As samples, according to the irradiation energy and irradiation fluence. . . . . 33

3.3 100 µm (left) and 10 µm (right) Hall bar fabricated on Ga

Mn

As samples. 34 3.4 Nanofabricated stripes on a Ga

Mn

As sample. . . . 34

4.1 Temperature dependence of magnetization of the as-grown and ion- irradiated Ga

Mn

As samples, measured with an applied magnetic field of 20 Oe along the [1¯ 10] direction in the sample plane. . . . . 36

4.2 Temperature dependence of magnetization of the reference sample for three different orientations of the applied magnetic field. . . . 38

4.3 Temperature dependence of magnetization of sample A1 for three different orientations of the applied magnetic field. . . . 38

4.4 Magnetization (measured at T = 10 K and in H = 20 Oe) of ion-irradiated Ga

Mn

As samples as a function of the density of Mn vacancies. . . . . 39

4.5 Magnetization (measured at T = 10 K and in H = 20 Oe) of high-energy irradiated Ga

Mn

As samples as a function of the ion fluence f . . . . 41

4.6 Cross section for ion-beam removal of Mn

in Ga

Mn

As as a function of the atomic number Z

of the projectile. . . . 41

4.7 Temperature dependence of the resistivity of irradiated Ga

Mn

As sam- ples and the reference sample. The inset shows the samples resistivity at room temperature as a function of the ion fluence. . . . 43

4.8 Temperature dependence of the magnetization and the resistivity of the

reference sample. . . . 43

4.9 Temperature dependence of the resistivity of Ga

Mn

As samples irradi- ated by 100 keV/amu F

ions, before and after annealing. . . . 46 4.10 Temperature dependence of the resistivity of Ga

Mn

As samples irradi-

ated by 1 keV/amu F

ions, before and after annealing. . . . 47 4.11 Temperature dependence of the sheet resistance of as-grown Ga

Mn

As

samples. . . . 49 4.12 Ion fluence dependence of the resistivity of Ga

Mn

As at room temper-

ature. . . . . 50 5.1 Temperature dependence of the resistivity of the reference sample in zero-

field and in a magnetic field of 7 kOe. . . . 53 5.2 Magnetic field dependence of the resistivity of the reference sample mea-

sured at various temperatures. . . . 53 5.3 Field dependence of the magnetoresistivity of the samples A2, A5, and the

reference sample measured at 25 K. The inset shows the zero-field ρ(T ) curves of these samples. . . . . 55 5.4 Field dependence of the magnetoresistivity of the samples A2, A5, and the

reference sample measured at 80 K. The inset shows the zero-field ρ(T ) curves of these samples. . . . . 55 5.5 Skew scattering and side jump mechanisms. . . . . 57 5.6 ρ

vs. H curves at various temperatures for sample A2. . . . 59 5.7 Arrott plot of (ρ

/ρ

)

vs. H/(ρ

/ρ

) at various temperatures for the

reference sample. . . . 59 5.8 Temperature dependence of the Hall magnetization and of the magnetiza-

tion measured by SQUID for an as-grown Ga

Mn

As. . . . 61 5.9 Temperature dependence of the Hall magnetization for ion-irradiated

Ga

Mn

As samples. . . . . 61 6.1 Temperature dependence of the longitudinal resistance of Hall bar pattern

Ga

Mn

As. The inset shows the low-temperature region of the resistance curve. . . . . 64 6.2 User interface of a LabVIEW program written to control transport mea-

surement system of the LaCAM. . . . 64

A.1 Schematic representation of the velocity selector. . . . 75

1 Works in the literature which deal with ion irradiation of Ga

Mn

As. . . 4

3.1 Parameters of irradiated Ga

Mn

As samples. . . . . 30

Semiconductor materials form the basis of the present electronics. They can be found ev- erywhere: in computers, television sets, microwave ovens, vehicles, mobile phones, medical equipments, etc. One of the main characteristics of semiconductors is that their electrical properties can be tailored by doping process (e.g., by ion implantation). Semiconductor- based electronic devices use the charge of electrons and holes (provided by dopants) to process information. Magnetic materials have also a prominent role in current electronics.

For instance, the increasing volume of information stored in magnetic medium has sur- passed by far the volume of information stored in any other medium, such as paper and optical medium. In this case, the spins of magnetic ions are used for information storage.

Thus, it appears logical to combine the properties of magnetic and semiconductors ma- terials in a single device with enhanced functionalities. The field that emerges from this connection is called spintronics. In spintronic devices both charge carriers and spin of magnetic elements are explored simultaneously. In this context, the Ga

Mn

As system appears as a promising candidate on developing spintronic devices. This is our system of interest. It will be studied throughout this thesis.

Ion beams are widely used for materials processing and analysis, for example, in in-

dustry, with a purpose of fabricating microelectronic devices as well as in basic research,

in the study of beam-induced modification of magnetic and transport properties of thin

films. The employed techniques consist in the ion bombardment of solid substrates. The

bombarding ion energy commonly ranges from a few thousands of electron-volt (keV) to

millions of electron-volt (MeV). The applications depend on the ion energy range, which is

generally limited by the apparatus. In material analysis, for example, the techniques em-

ployed are Rutherford back scattering (RBS) and particle-induced x-ray emission (PIXE),

with ion beams in the MeV energy range. In materials synthesis and interface modifica-

tion, as is the case of doping of thin films and ion implantation near the surface, keV ions are used.

In general, energetic ion beams are extracted from linear particle accelerators. Such accelerators are usually classified as: (i) low-energy accelerator (ion implanter), producing ions with energy < 500 keV; and (ii) high-energy accelerator (e.g., Van der Graaff and Tandem accelerator), with ions in the range of 0.5 – 100 MeV.

We have spent considerable research time developing and improving techniques to modify and characterize thin films inside an ion irradiation chamber. A Tandem acceler- ator, located at the Laborat´ orio de F´ısica Atˆ omica e Molecular (LaCAM) – UFRJ, was used as a tool for material synthesis and modification. The referred machine is optimized to provide ion beams from a few hundred keV to several MeV per ion. This allows the structural modification in the lattice of thin films by the passage of swift ions through the film (i.e. irradiation process). However, as will be seen in Chapter 2, the extraction of lower energy ions (few keV) is also possible. The combination of keV and MeV energy ranges is desirable and offers a series of advantages. For example, one may use a single end-station to perform ion irradiation and implantation. Another example is the creation of a homogeneous doping layer within a solid sample by means of a set of implantations with different energies. The depth profile of implanted ions in a solid is approximately Gaussian for each ion energy. Thus, the superposition of these profiles results in a final profile approximately rectangular, as illustrated in Fig. 1. The thickness of the doping layer can be as broad as is the energy range accessible to the accelerator.

Ion-beam irradiations in both keV and MeV energy ranges are currently used, for example, in the processing of CMOS devices. They can be used for locally modifying semiconductor samples, either by appropriately focusing the beams or combined use of masks and lithography. With regard to magnetic materials, ion beams can be used to introduce artificial length scales to tailor the magnetic properties. For instance, ripple structures (with wavelengths of 25–175 nm) are created on the material surface by means of ion irradiation at certain conditions [2]. Films of magnetic materials (e.g. Permalloy) grown on this ripple morphology have induced uniaxial anisotropy. Ion irradiation can

1This classification is generally adopted in atomic and molecular physics. In particle physics, however, the limit between low and high energy is orders of magnitude greater.

Figure 1.

Depth profile of implanted Mn ions in ZnO for different implantation energies.

(Adapted from [1].)

also be used to either reduce [3] or increase [4] the exchange bias field in structures such as FeNi/FeMn. In this work we compare the two energy ranges (keV and MeV) for ion-beam modification of Ga

Mn

As, and we explore their specific properties.

Ga

Mn

As is a ferromagnetic semiconductor which has been broadly studied for more than a decade [5]. Its main feature relies on the fact of sharing the same proper- ties of GaAs (widely used in electronics) and, simultaneously, being ferromagnetic below some critical temperature. These combined properties make Ga

Mn

As suitable for spin-electronic applications [6, 7]. The incorporation of Mn substitutionally for Ga into the host GaAs semiconductor provides free carriers (holes) in the band structure of the material. It is well established that such holes are responsible for both electrical transport and the coupling between local Mn magnetic moments. On the other hand, when Mn ions enter the crystal lattice at interstitial positions, this compensates the charge carriers, causing suppression of both transport and magnetic properties [8]. The fraction of substi- tutional Mn is therefore an important parameter in investigating this system. Ion-beam irradiation of Ga

Mn

As films is a tool for introducing defects in a controlled manner and to change this parameter as the projectiles interact with the sample [9, 10, 11, 12].

Independent instrumental control of projectile energy and fluence (quantified in ions/cm

)

allows control of the depth profile and of the density of defects.

In the present work, we compare the effects of keV and MeV fluorine ions used in the irradiation. In the former case, the projectiles deposit all their energy in the Ga

Mn

As layer. A very large cascade of secondary dislocations then occurs within the thin film in a region roughly coinciding with the beam penetration range. In the latter case, the projectiles traverse the Ga

Mn

As layer and are implanted much deeper in the bulk of the substrate. While the beam crosses the film, some target atoms are displaced from their original crystalline positions, and cascades of secondary events are occasionally produced.

The trajectory of the projectile in the epilayer region is in this case reasonably described by a straight line, along which a cylindrical track of defects is formed [13].

There are a few works (including earlier works from our group [9, 10]) which deal with ion irradiation of Ga

Mn

As films in the literature. They are summarized in Table 1. In those previous works ions and irradiation energies different than those presented here were used. Unlike those previous studies, where low-energy and high-energy irradiations were used indistinguishably, in the present work we compare the effects of these two energy ranges on the magnetic and transport properties of Ga

Mn

As.

The first chapter of this thesis starts with a brief introduction to diluted magnetic semiconductors, more specifically to Ga

Mn

As. We describe the possible mechanisms that lead to hole mediated ferromagnetism in this system. Growth parameters and their effects on the magnetic and transport properties of Ga

Mn

As are discussed. The chapter ends with an overview of the most known defects in the Ga

Mn

As.

Table 1.

Works in the literature which deal with ion irradiation of Ga

Mn

As.

Ref. Low energy High energy

Kato et al. [14, 15] 30 keV Ga

Mayer et al. [16] 33 and 110 keV Ne

Li et al. [11, 12] 650 keV He

Sinnecker et al. [9] and Sant’Anna et al. [10]

100 keV H

, 700 keV Li

, and 1 MeV H

Present work 19 keV F

1.9 MeV F

In Chapter 2 the experimental methods for modification and characterization of the magnetic and transport properties of Ga

Mn

As are described. All modifications (ex- cept annealing) were performed at LaCAM (UFRJ), using ion beams from a Tamdem accelerator. The characterizations, on the other hand, were carried out at the University of Notre Dame (UND) during the visit of the candidate as a visiting PhD student (Science without Borders program).

Chapter 3 deals with the samples specifications and the experimental details of the ion irradiation of the Ga

Mn

As samples. We provide a comparison between the effects of low-energy and high-energy irradiations on damage creation in Ga

Mn

As. It was found that in both cases (low and high energy) the lowest ion fluence used may result in irradiation inhomogeneities within the film. Pattern-fabricated Ga

Mn

As samples from UND will be shown. As these samples were not irradiated yet, they will not be discussed in detail in this thesis.

In Chapters 4 and 5 the results are discussed. In Chapter 4 we discuss results obtained by SQUID magnetization measurements and results from transport measurements. To get a better insight into the interpretation of our results, we compare them with similar ones found in the literature (i.e., those that deal with ion-irradiated Ga

Mn

As). In Chapter 5 we discuss results from magnetotransport measurements. A careful analysis of the data has allowed us to extract information regarding the ferromagnetic ordering of the samples, which could not be obtained by SQUID magnetization measurements.

In Chapter 6 we present the recent advances with regard to the transport measurement

system which was built at LaCAM. In this system, resistivity is measured as a function of

temperature down to 6 K. The whole mounting is consistent with in-situ measurements

in the irradiation chamber connected to the accelerator. One of the pattern-fabricated

samples, which has been characterized by transport measurements at the UND, was also

studied using the measurement system at LaCAM for comparison. It allowed us to test

the accuracy of our temperature measurements. An outlook is provided in the end of the

chapter.

Basics of Ga _1−x Mn _x As

1.1 Diluted magnetic semiconductors

The incorporation of magnetic elements sparsely into a nonmagnetic semiconductor (as pictorially illustrated in Fig. 1.1) gives rise to a new class of material, known as diluted magnetic semiconductor (DMS) or, in the early literature, semimagnetic semiconductor.

The resulting structure forms an alloy between the host semiconductor and the magnetic impurities diluted into one of the sublattices of the semiconductor compound. The first studies on DMS (in the 1970s and 1980s) focused primarily on II–VI-based materials as the host semiconductor (such as those based on HgTe, CdTe and ZnSe) and transition metal ions of the iron group (e.g. Mn, Fe, and Co) as magnetic impurities [17]. Typical examples of such compounds are Hg

Fe

Se, Cd

Mn

Te, and Cd

Co

Se. In II–VI DMSs the valence of the II-group cations matches that of the magnetic ions, which has two direct consequences: (1) they are easy to prepare either in the bulk form or in the form of thin epitaxial layers (thin films) on a substrate; (2) they lack charge carriers nec- essary for electrical transport. With regard to the latter, carriers have to be added to the compounds by extra doping, so as to make them p-type or n-type semiconductors. How- ever, in dealing with II–VI compounds, this is not an easy task [18, 19]. The interaction among the magnetic moments in II–VI DMSs is therefore dominated by antiferromagnetic superexchange, which results in paramagnetic, antiferromagnetic, or spin-glass behavior [17, 20].

The III–V host semiconductors, on the other hand, have a fundamental problem:

the solubility of transition metals like Mn is very low in III–V semiconductors (of the

Figure 1.1.

Schematic picture of a (a) nonmagnetic semiconductor and (b) a diluted magnetic semiconductor.

order of 10

cm

or less, while the average density of a solid is 10

cm

). From the development of epitaxial growth methods at low temperature the first successful growths of ferromagnetic III–V DMSs were obtained: In

Mn

As in 1992 [21], and Ga

Mn

As in 1996 [22]. The latter is our system of interest. Thus, some important results on Ga

Mn

As in the literature will be discussed in the following sections.

1.2 Ga _1−x Mn _x As background

In the Ga

Mn

As system, a small fraction x (typically 5%) of Ga is ideally substituted by Mn in the GaAs host semiconductor. In these circumstances, Mn is referred to as substitutional Mn (Mn

). The elements of the Ga

Mn

As compound have nominal electronic configuration [Ar] 3d

4s

p

for Ga, [Ar] 3d

4s

for Mn, [Ar] 3d

4s

p

for As.

It is generally accepted that a manganese impurity enters the lattice as an ion Mn

that has a half-filled d shell, which results (according to Hund’s rule) in a total spin quantum number S = 5/2 and a total angular momentum L = 0 (i.e., all five 3d electrons with different magnetic quantum number m

ranging from -2 to +2, according to Pauli exclusion principle). Owing to the absence of a 4p electron, the substitutional Mn

acts as an acceptor, thus doping the system with a hole. There is a general consensus that these holes are responsible for mediating the ferromagnetic coupling among the local Mn

moments in the Ga

Mn

As compound [23]. This is supported by several experimental

results. For example, it is found that T

goes to zero when holes are compensated, and also

that T

is higher for higher hole concentrations [24]. In addition, in n-type In

Mn

As,

as well as in fully carrier compensated Ga

Mn

As with Sn doping, the local Mn spins

couple antiferromagnetically [25, 26].

1.3 Hole-mediated ferromagnetic coupling

Because local magnetic Mn moments are very diluted (∼5%) in the Ga

Mn

As system, they present a negligible direct interaction. Therefore, the ferromagnetic coupling found in Ga

Mn

As results from indirect exchange mechanisms such as double exchange and Zenner’s p − d exchange. Although both mechanisms lead to hole-mediated ferromagnetic coupling between the local Mn spins (Fig. 1.2), the Zenner’s p − d exchange is found to be dominant for typical Mn concentrations. The relevant interactions behind this mechanism are discussed bellow.

Figure 1.2.

Schematic illustration of the hole-mediated ferromagnetic interaction among local Mn spins in diluted magnetic semiconductors. (Extracted from [27].)

sp − d exchange interaction

Due to the presence of d states of incorporated transition metals, DMSs present sp − d exchange interaction between sp-band carries of the host semiconductor and d-shell carriers of the magnetic impurities. The magnitude of the sp − d interaction is expressed as N

α for s − d and N

β for p −d exchange interaction, where N

is the cation ion density, and α and β are exchange integrals. The s − d exchange is due to direct (or potential) interaction between electrons in the conduction band (s-state) and localized d-electrons of transition metals. This interaction, in conjunction with the Pauli exclusion principle, gives rise to ferromagnetic coupling between the delocalized s-state and the localized d- state. Its magnitude is about 0.2 eV. The p −d exchange interaction, on the other hand, is dominated by other exchange mechanism: p−d hybridization, i.e., repulsion of states with parallel spins and attraction of states with opposite spins. The resulting coupling for this mechanism depends on the configuration of the p- and d-states in the host semiconductor.

In the case of Ga

Mn

As, for example, the coupling of p- and d-states (for Mn

in the

Ga lattice site) is always antiferromagnetic. Its magnitude is determined to be N

β ≈ −1

eV from photoemission measurements [28]. A brief explanation of how p −d hybridization

arises in the case of Ga

Mn

As is given below.

p − d hybridization in Ga

Mn

As

The energy band of the Ga

Mn

As as function of the Mn content x is schematically illustrated in Fig. 1.3. For low Mn concentrations, the electronic ground state of a Mn impurity in the GaAs semiconductor is A

(d

+h), i.e., a Mn

ion along with a moderately bound hole. This is a neutral state (ionization energy of 112 meV) with regard to the cation host sites (Ga lattice sites). As x is increased the Mn impurity levels in the band gap start to form an impurity band. At a certain point, this impurity band merges into the valence band which results in the hybridization of the d-wave function of the magnetic impurities with the p-wave function of the As atoms (since As are the nearest neighbors with which Mn forms a tetrahedral configuration). Consequently, those holes weakly bound to the Mn

ions in the neutral state become free holes in the valence band, with a strong As 4p character as observed by photoemission experiments [28, 29]. The new state of such Mn

ions with a missing hole is, therefore, A

(d

).

Figure 1.3.

Schematic energy band diagram of Ga

Mn

As as a function of the Mn content.

E_a

is the acceptor energy level introduced by a single Mn. (Adapted from [27]).

1.4 Molecular beam epitaxy

As already mentioned, the solubility of transition metals is very low in III–V semicon- ductors (e.g. Mn into GaAs). In the particular case of Ga

Mn

As the main reason for the low solubility is because MnAs phase segregation occurs, thus inhibiting the 2- dimensional (2-D) layer-by-layer growth of uniform GaMnAs alloy [30]. In equilibrium growth conditions, which require a substrate temperature T

of approximately 580

C, the formation of such MnAs clusters are energetically more favorable than Mn

. The approach then used to avoid the formation of MnAs is to grow the Ga

Mn

As films by molecular beam epitaxy at relatively low temperatures far from equilibrium. This method is called low-temperature molecular beam epitaxy (LT-MBE).

Fig. 1.4 shows the schematic phase diagram for the properties of MBE grown Ga

Mn

As with respect to the growth parameters: substrate temperature and Mn concentration [31]. At temperatures higher than 300

C, the maximum Mn concentration is very limited (∼ 0.015 or lower), so that no magnetic ordering is expected, even in metal- lic Ga

Mn

As samples. The ferromagnetic ordering is generally achieved in films whose Ga

Mn

As epitaxial layers were grown at temperatures below 300

C. On the one hand, the low temperature increases the solubility of Mn into GaAs, on the other hand, it also increases the density of point defects, which no longer have sufficient thermal energy to move. Therefore, the optimal growth parameters correspond to points in the diagram just below the segregation limit [the line which separates metallic (Ga,Mn)As from formation of MnAs], i.e., the minimum density of defects possible for a given Mn concentration. Al- though this phase diagram predicts correctly most metallic samples grown from different groups, it turns out to be outdated since good metallic samples were grown with higher Mn concentrations (up to x = 0.2 [32]).

For further details regarding the growth of Ga

Mn

As films and post-growth an- nealing procedure, see references [27, 30, 33].

One should note in this connection that the implantation of Mn ions into the GaAs host can also be considered a nonequilibrium approach for increasing the solubility of Mn.

However, solid phase regrowth of the amorphous layer caused by implantation damage

requires thermal annealing up to 800

C for a duration of several seconds. This process

becomes thermodynamically similar to epitaxial growth at high temperature, thus making

Figure 1.4.

Schematic phase diagram showing the relation between properties of LT-MBE grown (Ga,Mn)As and the growth parameters (substrate temperature

and Mn concentration

the formation of secondary phases (MnGa and MnAs) energetically favorable during this annealing schedule [34]. The combined use of ion beam implantation and pulsed laser melting, on the other hand, has shown to be a successful method to synthesize DMSs such as Ga

Mn

As [35]. The short timescales involved during melting and recrystallization prevents secondary phase formation.

1.5 Defects in Ga _1−x Mn _x As

As discussed above, LT-MBE grown Ga

Mn

As have a considerable amount of point defects. The most important of them are known to be the arsenic antisite (As

), when an As atom takes the place of a Ga atom, and the interstitial manganese (Mn

), when a Mn enters at an interstitial position in the lattice (Fig. 1.5). Both of these defects act as double donors [37], i.e., each one can compensate two free holes. It is worth recalling that each hole is provided by a Mn ion located at a Ga site (Mn

). By considering those compensating effects on the hole concentration p, the net balance is

p = [Mn

] − 2([As

] + [Mn

]), (1.1)

Figure 1.5.

Ga

Mn

As unit cell with defects: As

is an As antisite, and Mn

is an interstitial Mn. (Extracted from [36].)

where the [ ] symbol represents the concentration. Of course, the maximization of the hole concentration is desirable, since holes are responsible for the electrical transport and for the long-range ferromagnetic coupling of Mn spins. Maximizing p requires both maximum concentration of Mn

and minimum concentration of As

and Mn

defects.

These two demands are in fact contradictory, since increasing Mn content in Ga

Mn

As requires a reduced growth temperature which in turn promotes the formation of As antisite defects. Thus, there is a Mn concentration that provides a compromise between these two tendencies. Experimental evidence suggests that this optimum Mn content is in the range of about 12% [30].

As antisite, As

The As antisite defects are well established in GaAs layers grown by LT-MBE. The MBE

growth is performed in excess flux of one of the components, that is As in case of GaAs, as

well as GaMnAs. Post-growth annealing might be an option to reduce the density of As

defects in GaAs. However, this is not applicable to Ga

Mn

As, since the temperature

required to remove As

is high (above 400

C), then MnAs precipitates are likely to

form. Other alternative is to keep the As

/Ga flux ratio nearly stoichiometric during the

Ga

Mn

As growth. Best results are found for an As

/Ga flux ratio of 2. [30].

Mn interstitial, Mn

It has been shown theoretically that interstitial Mn does not contribute to the Zener-type Mn–Mn exchange due to its negligible p− d coupling [38]. Moreover, because Mn

is highly mobile and positively charged it is expected that it drifts to interstitial sites adjacent to the negatively charged Mn

[those in state A

(d

)] to form antiferromagnetic Mn

-Mn

pairs, thus canceling the magnetic moment of Mn

([34] and refs. therein). Fig. 1.6 shows a Mn

-Mn

pair in the GaAs host structure.

Unlike As

, Mn

defects may be effectively removed by applying post-growth anneal- ing at low temperatures (close to the Ga

Mn

As growth temperature). Some results in the literature, along with our own results of ion-irradiated Ga

Mn

As samples, will be discussed further in this dissertation.

In addition to the defects discussed above, some studies suggest the formation of

complex Mn defects [37, 38, 39, 40] such as Mn interstitial with As anions as nearest

neighbors in tetrahedral and in hexagonal configuration (Figs. 1.7 e 1.8).

Figure 1.6.

Mn

-Mn

pair in the GaAs structure. (Extracted from [38].)

Figure 1.7.

The nearest four cation and six anion neighbors for anion in the tetrahedral interstitial position in the zinc-blende lattice. (Extracted from [38].)

Figure 1.8.

The six (three cations and three anions) nearest neighbors and the next four

cations and four anions for an ion in the hexagonal interstitial position in the zinc blende

lattice. (Extracted from [38].)

Experimental methods

In this Chapter we describe the experiments carried out in the study of ion-irradiated Ga

Mn

As films. Particular attention is given for the methods used to irradiate the samples.

2.1 Ion beam irradiation

In this work, we have used a 1.7 MV Tandem accelerator model 5SDH from National Electrostatics Corporation (NEC). The machine is located at the Laborat´ orio de Colis˜ oes Atˆ omicas e Moleculares (LaCAM) of the Instituto de F´ısica of Universidade Federal do Rio de Janeiro. The standard operational use of the accelerator will be briefly discussed in the following sections, along with a couple of modifications we have implemented in order to enhance its versatility, for example, by allowing us to extract low-energy ion beams (∼keV). Low-energy ions are useful to perform shallow implantations, thus being a suitable tool for materials synthesis and modification. In this study we have used low- energy ions to perform implantations into the thin Ga

Mn

As film (∼50 nm). High- energy ions (∼MeV) were also used by operating the accelerator in its standard way. In this case the ions cross the Ga

Mn

As film and bury themselves in the bulk of the substrate, far away from the film-substrate interface.

2.1.1 Standard Tandem accelerator

We begin by illustrating the Tandem accelerator and its main components in Fig. 2.1.

From left to right:

Figure 2.1.

Schematic representation of a Tandem accelerator and its main components.

• Source of Negative Ions by Cesium Sputtering (SNICS II). The source is mounted outside the accelerator and is biased down to –30 kV relative to ground.

• The velocity selector is composed by a pair of parallel conducting plates and a pair of magnetic bars, which produce a region of transverse magnetic and electric fields. The magnitude of the magnetic field is fixed, while that of the electric field is controlled by the potential between the plates. Negative particles from the ion source enter the velocity selector obliquely (owing to a small misalignment of the source with respect to the selector), and only those with appropriate charge-to-mass ratio leave it.

• The accelerator tank has both ends at ground and the high-voltage terminal (achiev- ing nominally 1.7 MV) in the middle.

• The electromagnet is primarily used for selecting different charge state beams, but it can also separate same charge state beams of different energies.

• There are two beamlines for neutral and charged species at 0

and 15

lines, respec- tively. We use a 6-way cross chamber for irradiation located at the 15

line.

A Faraday cup is mounted on a mechanical arm that goes onto the chamber through one of its flanges. (Details about the setup may be found in ref. [41].) As will be discussed further in the chapter, the zero degree line has been used for mass spectroscopy.

A general explanation of how to extract ion beams is presented in the following section.

For a detailed discussion regarding limits and operational parameters of the LaCAM

1A spherical chamber [41] has been implemented for materials analysis at -15^◦ line (not shown in figure).

accelerator see references [42, 43].

2.1.2 High-enery ion beam: standard procedure

In the standard operational use of a tandem accelerator, positive MeV ion beams are achieved via a two-stage acceleration process. Firstly, negative keV ions, injected into the accelerator from the ion source, are accelerated towards the positive potential V

at the high-voltage terminal. The beam gains an energy eV

in this stage. At the center of the terminal there is gas stripper responsible for changing the charge state of the ions in the beam. A distribution of positively charged ion beams in various charge states thus emerges from the stripper (i.e. X

→ {X

, X

, X

, . . .}). Secondly, these positive beams are accelerated towards the tank end (at ground). The energy gained in this second stage is given by qeV

, where q is the charge state (q = 1, 2, 3, etc.). By controlling the current applied in the electromagnet, one can select the charge state of the beam supposed to escape from the accelerator through the beamline at the 15

line. The energy of the outgoing beam ranges from tens of keV to few MeV, according to the voltage V

set on the high-voltage terminal. The usual expression to calculate the total energy of the beam is

E

= E

+ (1 + q)eV

, (2.1)

where E

is the energy of ions coming from the source. For instance, a 2.0 MeV proton beam, entering the accelerator with energy E

= 20 keV, is obtained by setting V

= 990 kV on terminal.

The above configuration is standard for Tandem-like accelerators and allows several

ion beam applications such as nuclear reaction analysis (NRA), Rutherford Backscattering

(RBS), and particle-induced X-ray emission (PIXE). Note that all the previous examples

deals with high-energy ion beams, i.e., beyond 0.5 MeV. Many other applications, on the

other hand, require ion beams in the energy range of few keV, which cannot be achieved

by operating the machine as described previously. This is the case of ion beam materi-

als processing, for instance, doping of semiconductors, secondary ion mass spectrometry

(SIMS), and synthesis of novel materials.

2.1.3 Low-energy ion beam: our modus operandi

In order to extract keV ions from a Tandem-like accelerator, we begin by analyzing Eq.

(2.1) that gives the total energy of the ion beam, according to the terminal voltage V

and the selected charge state q. Note that the minimum energy which could theoretically be achieved by following the standard procedure is E

, when zero voltage is set on the terminal. The extraction of ion beams, however, relies on the high-voltage terminal to direct the ions through the accelerator tank. If no voltage is set, the beam enters the accelerator but diverges before reaching the exit.

A better approach is to keep some voltage on the terminal but to take the stripper gas out. Once there is no gas in the stripper the beam cannot change its charge state and, as a consequence, it enters and leaves the accelerator with the same charge as it was in the source (i.e. negatively charged). In this scenario the terminal is used as a set of focusing lenses, i.e., it increases the intensity of the beam without changing its energy.

It is worth mentioning that the electromagnet polarity must be inverted to deflect correctly the negative beams to the 15

line. In addition, one should note that the expression for the total energy given by Eq. (2.1) is still valid for a negative ion beam:

E

= E

for q = −1 (again, the minimum energy). In fact, a generalized version of Eq. (2.1) is obtained by including negative and neutral species in the charge state (q = −1, 0, 1, 2, 3, etc.).

The beam which leaves the accelerator is composed of beams of different charge states.

Their ratio with respect to the initial beam can be controlled by varying the gas pressure in the stripper. For instance, low pressure favors the production of negatively charged beams, since there are not many gas molecules to strip electrons of the incoming beam.

The probability of producing neutrals increases as the pressure is increased. At a certain point, however, the production of positive ions will be favored over that of neutral species.

When it happens, the beam of neutrals decreases as the pressure is increased. This same scenario is reproduced for X

beams over that of X

, and so forth as the pressure is increased. As an example, see in Fig. 2.2 the charge state fractions H

, H, and H

as a function of the stripper pressure, obtained from the collision of a 1 MeV H

ion beam with gas in the stripper.

Although removing thoroughly the stripper gas gives the highest probability of extract-

ing negative ion beams (which have lower energy compared to their neutral and positive

Figure 2.2.

Charge state fractions H

, H, and H

as a function of the stripper pressure, obtained from the collision of a 1 MeV H

ion beam with He gas in the stripper. (Adapted from [42].)

counterparts), we need a little neutral fraction in the final beam for mass spectrometry (described in the next section). Once the mass spectrometry analysis is finished, we can lower the pressure in the stripper to its minimum level ( . 10

Torr) so as to increase the negative ion beam current.

As an example of application, the approach described above to extract low-energy ion beams was successfully used to synthesize (in our Lab) Rh clusters within an Al

O

(alumina) matrix [44]. In that study the need for low-energy ions came from the fact that Rh had to be buried in a thin alumina film, which allowed us to measure their magnetic properties.

2.1.4 Mass spectrometry

The beam is composed of various atomic and molecular species of the compound from

which one wants to extract the ion beam. In addition, the initial beam usually contains

spurious species, for example, those related to copper, from the crucible, and oxygen

and hydrogen, due to the contact of the crucible with the environmental air. The mass spectrometry of this initial beam is obtained with a home-made automated system used for scanning the voltage applied between the plates of the velocity selector and for measuring the neutral beam that leaves the accelerator (Fig. 2.3).

Figure 2.3.

User interface of the LabView program used for mass spectrometry. The graph in the left-hand side shows the voltage scan of the initial beam measured at 0

line (white curve) and at 15

line (red curve) for a given field in the electromagnet.

Neutral species experience no deflection while passing through the electromagnet at the end of the accelerator tank. Consequently, they enter at the zero degree line and travel the whole way until colliding with a metal plate, causing then electron sputtering.

The loss of electrons from the metal plate generates an electrical signal (extracted as a current) which is proportional to the intensity of the neutral beam. That current, the neutral beam one, is that we use for mass spectrometry.

In Fig. 2.4 we plot a scan of the initial ion beam using the mass spectrometry described above. Each peak in the curve is associated with a beam of carbon molecule or atom, measured at the zero degree line. In fact, the identification of the peaks was obtained a posteriori with a calibration equation, viz.,

m = c

(c

+ V )

, (2.2)

where m is the mass of the species, c

and c

are constants, and V is the voltage between

the plates of the velocity selector. The derivation of the above equation is given in

Appendix A.

Figure 2.4.

Scan of the initial beam from the ion source for a crucible that contained graphite.

Figure 2.5.

Calibration curve for the peaks in Fig. 2.4.

Previous knowledge of the compound is helpful to pick actual species for the mass calibration. For instance, despite not knowing a priori which species belongs to a given peak, we could expect, in that example, to find several carbon molecules in the beam since the crucible contained graphite. By analyzing Eq. (2.2), note that light species are associated to high voltages, hence appearing on the right-hand side in Fig. 2.4. On the other hand, heavy species are compressed on the left side (lower mass resolution).

The calibration curve used to identify the peaks in the above example is shown in Fig.

2.5. Note that the data have been linearized by solving Eq. (2.2) for V and by plotting V vs. m

. The straight line represents the best fit for the data by using the least-squares method.

2.1.5 Extraction of heavy ion beam

From mass spectrometry analysis (Figs. 2.4 and 2.5), one can have an idea of the mass limitation for heavy ions, for example, by extrapolating the curve in Fig. 2.5 to zero voltage. The analytical expression for the maximum mass [from Eq. (2.2)] is given by

m

= c

/c

. (2.3)

The constants c

and c

are determined from fitting parameters of the calibration curve (Fig. 2.5). One should note that the mass expression given by Eq. (2.2) only has physical meaning if c

is positive. On the other hand, despite the singularity for (c

+ V ) = 0, c

can in principle assume any value. However, from solving the equations of movement for an ion within the selector, one can show that both constants are positive and depend on geometric and physical parameters of the problem (Appendix A).

As in the case of low-energy ions, we have also created a method that allows us to extract ions with mass heavier than m

(2.3), thus broadening the mass spectrum of the ion beam. As already mentioned, the deflection of ions in the velocity selector is solely controlled by the voltage V between the parallel conducting plates, since the magnetic field is fixed. The plates are symmetrically charged, so that the relation between their voltages is V

= −V

= V /2, resulting in an electric field pointing from the V

plate to the V

plate.

The velocity selector is constructed in such a way that the magnetic force always

deflects the ions in the direction of the selector exit, whereas the electric force deflects

them in the opposite direction. Therefore, the maximum mass that can leave the selector, when V = 0, is only deflected by the magnetic force. That said, the only way to deflect heavier particles is by reversing the polarity of the conducting plates. In this case, the electric force points in the same direction of the magnetic force, which increases the deflection of heavier particles.

In Fig. 2.6 we show the resulting mass spectrometry by using the method described above. The crucible contained a piece of gold wire, thus resulting in several Au

clusters in the beam. Open (closed) symbols correspond to data obtained for reverse (direct) polarity. Note that the beam current for Au

and Au

peaks reached the end of the scale, and that the heaviest mass in the direct polarity was obtained for Au

. Heavier cluster was only found for reverse polarity, as revealed by the mass spectrometry analysis.

Figure 2.6.

Scan of Au beam revealing various Au

clusters. Open (closed) symbols correspond

to data obtained for reverse (direct) polarity.

2.2 Magnetotransport measurements

Magnetotransport measurements on the Ga

Mn

As samples were carried out in the Department of Physics at the University of Notre Dame.

The measurement system allows us to carry out Hall effect measurements under a varying magnetic field of ±8 kOe. The results from Hall effect measurements are presented in Chapter 5. This same system was also used to measure the temperature dependence of the resistivity ρ of the samples (results presented in Chapter 4).

Fig. 2.7 illustrates a schematic diagram of the measurement system setup. A closed- cycle helium flow cryostat, along with a Lakeshore Model 331 Temperature Controller, is used to cool the samples. The minimum temperature reached is 12 K. A Lakeshore Model 632 Bipolar High Power Supply is used to provide current to the electromagnet. The mag- netic field is measured with a Hall sensor placed between the poles of the electromagnet, close to the shroud. The system is capable of measuring four samples simultaneously.

For each sample a set of three instruments is used: a Keithley 220 programmable cur- rent source to apply low DC current (typically on the order of µA), and two Keithley 2001/2000 multimeters to measure the Hall and longitudinal voltages, respectively.

Samples mounting

In order to stabilize quickly the temperature of the samples, they are mounted on a copper sample holder. The sample holder is basically a copper bar embedded into a DIP20 (dual in-line package) socket frame, see Fig. 2.8. A piece of weighing paper covers the bar in order to prevent electrical conduction through the back of the samples. Vacuum grease is utilized to stick the paper on the bar, as well as the samples on the paper/copper. Each specimen is cleaved into a rectangular bar of approximately 5 mm × 1 mm. Pieces of gold wire are used to connect the sample contacts to the socket pins. All contacts are made with In solder (∼ 260

C).

Fig. 2.8 shows the sample holder loaded with three samples. The contacts of one of the samples are numbered according to the order of connection to the socket pins. All samples follow the same connection array. In this configuration, the pair of contacts 1-5 is used to apply current, while the pairs 2-3 and 3-4 are used to measure the transverse

2In Professor Furdyna’s laboratory, under supervision of Professor Xinyu Liu.

Figure 2.7.

Schematic diagram of the measurement system setup for magnetotransport mea- surements. (Adapted from [45].)

Figure 2.8.

Sample holder loaded with Ga

Mn

As samples.

voltage V

(Hall voltage) and the longitudinal voltage V

, respectively. The resistivity ρ and the Hall resistivity ρ

which will appear in the following chapters are defined as

ρ = V

I

wt

l

, (2.4)

ρ

= V

I t, (2.5)

where w is the sample width, t is the film thickness, and l

is the distance between the longitudinal contacts 3-4. The use of ρ

and ρ

in place of ρ and ρ

, respectively, is sometimes preferable.

2.3 SQUID magnetometry

Magnetization measurements were performed on the Ga

Mn

As samples by using a superconducting quantum interference devices (SQUID). The measurements were carried out in the Department of Physics at the University of Notre Dame. The system used in this study was a commercial system named Magnetic Property Measurement System (MPMS) Model XL manufactured by Quantum Design, Inc. The two major hardware components of the system are shown in Fig. 2.9: the MPMS dewar and probe assembly (on the left side), and the associated control system in the MPMS control console (on the upper right corner).

This system is sufficiently sensitive to measure the sample magnet moment as low as

10

emu over a broad range of temperatures (1.9 – 400 K). Its superconducting magnet

is capable of providing fields from -70 to +70 kOe with a stable 0.1 Oe resolution.

Figure 2.9.

MPMS XL system and probe components. (Extracted from [45].)

2.4 Post-growth annealing

In this study ion-irradiated Ga

Mn

As samples (i.e., the set of samples summarized in Table 3.1) were annealed at low temperatures in order to recover their electronic and magnetic properties. The annealing procedure follows the recipe adopted by Furdyna’s group (University of Notre Dame), which consists basically in annealing the samples by an hour under a fixed flow of N

gas of 1.5 SCFH (standard cubic feet per hour); see details in Ref. [34]. The schematic setup used for annealing the samples is illustrated in Fig. 2.10. All the samples were annealed in the same batch in order to minimize effects of temperature change. The annealing temperature was 265±1

C.

Figure 2.10.

Schematic setup for annealing Ga

Mn

As samples.