DISSERTATION
zur Erlangung des akademischen Grades
eines Doktors der Naturwissenschaften (Dr. rer. nat.) an der Universit¨at Konstanz
Fachbereich Physik
vorgelegt von
Alexander Barth
Tag der m¨undlichen Pr¨ufung: 26. Juli 2007 Referenten:
Prof. Dr. G¨unter Schatz Prof. PhD. William E. Evenson
Konstanzer Online-Publikations-System (KOPS) URL: http://www.ub.uni-konstanz.de/kops/volltexte/2007/3637/
URN: http://nbn-resolving.de/urn:nbn:de:bsz:352-opus-36373
2.1 The magnetic field . . . 3
2.2 Matter in external magnetic fields . . . 4
2.2.1 Dia- and paramagnetism . . . 7
2.2.2 Ferromagnetism . . . 9
2.2.3 Ferri- and Antiferromagnetism . . . 15
2.3 Finite size effects in thin magnetic films . . . 16
2.3.1 Interlayer exchange coupling . . . 17
2.4 Film growth and epitaxy . . . 18
3 Experimental methods and set-ups 21 3.1 The UHV set-up MEDUSA . . . 21
3.2 Magnetic characterization . . . 24
3.2.1 Superconducting QUantum Interference Device: SQUID . . . 24
3.2.2 X-ray Magnetic Circular Dichroism: XMCD . . . 29
3.3 Structural investigations . . . 36
3.3.1 Scanning Tunneling Microscopy (STM) . . . 36
3.3.2 X-ray diffraction and reflectometry . . . 39
3.3.3 Electron Diffraction: MEED . . . 40
3.3.4 Chemical composition by AES . . . 41
3.3.5 Rutherford backscattering . . . 42
3.3.6 Transmission electron microscopy . . . 44
4 Experimental Results 47
4.1 Sample description and preparation . . . 47
4.2 Thin Gadolinium layers . . . 49
4.3 Structure and morphology of the Gd/Ni-bilayer system . . . 54
4.3.1 X-ray analysis of Gd/Ni/Au thin films . . . 55
4.3.2 In-situ Auger spectroscopy on Gd/Ni bilayers . . . 58
4.3.3 Characterization of the layer structure and chemical com- position by RBS and TEM . . . 59
4.3.4 Investigating the growth of Gd on Al2O3 and Si3N4 by STM 62 4.4 Magnetic characterization of Gd/Ni-bilayers . . . 67
4.4.1 In-plane anisotropy in Gd/Ni bilayers . . . 68
4.4.2 Field dependent magnetization measurements on the exam- ple bilayer system: Gd(50˚A)/Ni(75˚A)/Au(20˚A) . . . 69
4.4.3 Temperature dependence of the magnetic properties of the example system Gd(50˚A)/Ni(75˚A)/Au(20˚A) . . . 72
4.4.4 Element-specific hysteresis loops of an example Gd/Ni bi- layer system . . . 76
4.4.5 Dependence on the nickel layer thickness . . . 83
4.4.6 Influence of the substrate temperature . . . 89
4.5 Proposed model of the bilayered system . . . 95
4.6 Preliminary results on Ni/Gd/Ni-trilayers . . . 96
5 Outlook and conclusions 99
6 Summary 101
7 Zusammenfassung 103
List of figures 109
Bibliography 117
Danksagung 119
A Properties of the GdNi-system 121
B Depth profile by RBS 123
behavior or structure, which was already conducted in the early 1970s. But due to the challenging problems associated with the handling of rare earths like their strong reactivity with water and oxygen, strong alloying with other metals or their high content of impurities was keeping research only to a small number of involved groups and publications per year. Another issue is the non-epitaxial or even amorphous growth of nearly all rare earth elements if evaporated under UHV conditions. As will be shown later in section 4.2 there are only a few sub- strates which allow an epitaxial growth of gadolinium for example. But still the search for materials with high magnetization or either high or low coercivity for magnetic data storage technology or magnetic sensing elements attract notice to this class of elements especially gadolinium.
Gadolinium can be seen as the only room temperature ferromagnet among the rare earth materials due to the highest Curie temperature, which is 16°C. The low value of the coercivity limits its possible applications for data storage. Its permanent magnetic moment amounts to 7.98µB, what exceeds for example the value of nickel by a factor of 12. Its magnetic moment is generated completely by the spin moment µs of the 4f-shell whose complicated RKKY interaction to its neighbors will be described in sections 2.2 and 2.2.2.2. Besides these properties gadolinium possesses other outstanding characteristics that are worth mentioning like the highest cross section for capturing thermal neutrons of 49000 barn or the high magnetocaloric effect. Its physical properties are a density of 7.895 cmg3, a melting point at 1313°C and an atomic weight of 157.25 u. There are 17 isotopes known but only 7 are abundant in natural gadolinium. The hcp structure with the lattice parameters a=3.63 ˚A and c=5.78 ˚A is stable up 1235°C (αGd) above it transforms to its bcc phase (βGd). It was discovered in 1880 by Jean Charles Galissard de Marignac and its main applications are as a contrast agent in med- ical NMR, material for nuclear reactor construction and in microwave devices.
The other magnetic material used in this work, nickel, becomes ferromagnetic
below TC=358°C. Its magnetic moment is 0.606 µB (at T=0 K). The physi- cal properties are: Density 8.908 cmg3, atomic weight 58.69 u and melting point Tm=1455°C and its crystal structure is fcc.
A large number of the publications on gadolinium and its magnetic behavior in the recent decade was on the topic of exchange interactions, either as a pure metal or in alloys with different transition metals, especially iron, cobalt CoNi and Permalloy. Systems containing pure nickel layers are hardly discussed in lit- erature. Possible reasons are the difficulties to determine the interface structure [13], the tendency of alloying [14, 15] and the comparable low Curie temperature of the formed GdNi alloys [16].
Interlayer exchange coupling attracted a lot of interest since the discovery of the giant magnetoresistance effect GMR in 1986 [17, 18]. In this field of application gadolinium can play an important role due to its high magnetic moment, low coercivity and its intrinsically low magnetic anisotropy. The coupling of Gd with ferromagnetic materials is one of the most interesting topics that was investigated in the recent years [19, 20, 21] as well as the coupling of magnetic layers through a gadolinium spacer [14, 15, 22]. The interaction is still only partially understood because of the complex interaction of the 3d and 4f magnetic moments [23], lead- ing to twisted [24] or even helic spin configurations as in the case of Dy and Ho [25, 26].
In this study the magnetic interplay and interactions between thin gadolinium and nickel layers were investigated and their connection to the structural prop- erties of the bilayers. For this, several thin films of gadolinium were studied to investigate the growth on different substrates and two series of Gd/Ni bilayers with varying nickel layer thickness, on two different substrates and two different deposition temperatures. Electron diffraction (MEED, LEED), Auger electron spectroscopy, X-ray diffraction (XRD), transmission electron microscopy (TEM), Rutherford backscattering (RBS) and scanning tunneling microscopy (STM) were applied to examine structural properties on an atomic and microscopic scale. The overall magnetic properties of the whole samples were studied by a superconduct- ing quantum interference device (SQUID) and element-specific by X-ray circular dichroism (XMCD). It will be shown that morphology and magnetic behavior are closely connected in this system and that different coupling schemes can evolve from this.
A short introduction will be given initially to the subject of magnetism and mag- netic materials. Generally three different types of magnetic response of materials are distinguished, namely dia-, para- and ferromagnetism. The basic concepts that lead to these different types will be discussed and the further subtypes ferri- and antiferromagnetism will be introduced to the reader. Special emphasis will be given to the different nature of the ferromagnetic behavior of the so called band- or 3d-transition metal magnet nickel and the 4f- or rare earth magnet gadolinium.
Theoretical predictions at the end of this chapter about the interplay of these two materials will lead to later discussion of the observed experimental results.
2.1 The magnetic field
In the literature one can find two complementary ways of describing magnetic phenomena. One is in terms of circulating currents evolving from Maxwell’s equations and the other in terms of magnetic poles, which are more suitable for describing experimental observations. Even the unit system that is used depends on the choice of the description and development of the theory and definitions of magnetism. Most text books about electrodynamics work with the cgs system (centimeter-gram-second), like [8, 27]. So this is usually used for formulations from Maxwell’s equations. The more phenomenological description in terms of poles is in most cases carried out in the SI-unit system. Since most measurement devices ,that were used in this work like the SQUID-magnetometer, deliver results in cgs units, these units will be used in the following description of magnetism.
A short conversion table is given in table 1.1.
Additional information about the conversion between the two unit systems is comprehensively summed up in [28], where it is written: ”Conversions between
cgs units and mks (SI) units seem to have been designed to torment both the novice and the seasoned professional alike”.
These two formulations can be connected by the definition of the magnetic dipole momentm~ caused by an electrical current density~j(~r):
~ m= 1
2c Z
[~r×~j(~r)]d3r (2.1) The magnetic induction B~ is the response of a material if a magnetic field H~ is applied to it. In vacuum,B~ and H~ are equal in cgs units (in SI B~ =µ0H).~ In para- and diamagnetic materials, their relation is linear. The magnetization M~ of the medium has to be taken into account, leading to the following relation betweenB~ and H:~
B~ =H~ + 4π ~M (2.2)
The magnetizationM~ can have its origin in induced and/or permanent mag- netic moments of the atoms or molecules and is usually expressed as the magnetic moments per unit volume (see table 2.1).
property cgs SI
dipole field H = rp2 [oersted] H = 4πε1
0
p r2
Ampere
m
magnetic induction B~ =H~ + 4π ~M [Gauss] B~ =µ0(H~ +M~) [Tesla]
susceptibility χ M~~
H
emu
cm3oersted
M~
H~ [dimensionless]
Bohr’s magneton µB 2me~
ec = 0.927*10-23 ergOe 2me~
e = 0.927*10-20 JT Table 2.1: Conversion table of characteristic magnetic variables cgs↔SI
2.2 Matter in external magnetic fields
If a material is exposed to an external magnetic field its response can be expressed by the ratio of the magnetization that results and the applied field strength at a fixed temperature. This quantity is called the susceptibility χ:
χ= M
H; h emu cm3Oe
i
. (2.3)
But it’s the magnetic induction B~ what is directly measured. The ratio of B~ and the magnetic field strength H~ is called the permeability µof the material.
it is much weaker and gives rise only to small changes in the electronic structure that can be observed by hyperfine interaction experiments. The origin of the atomic magnetic moment is the orbital moment~land the total spin moment ~s of the electrons. For light to medium elements the individual angular momenta
~li and spins ~si of electrons in open shells add up separately to L~ and S, which~ couple to the total angular momentum J~ = L~ + S. This mechanism is called~ Russell-Saunders- or L-S-coupling.
In heavy elements, the so called jj-coupling appears, where ~land ~s of a single electron first couple to ~j, and then these add up to the total angular momen- tum J~ = P
i~ji of the atom. Both of the materials under investigation, nickel and gadolinium, build up their magnetic moment according to the L-S-coupling.
Although gadolinium is a considerable heavy element this coupling mechanism is valid due to the the fact that the open shells are in low lying 4f orbital.
The magnetic moment arising from the total angular momentum of the elec- tron cloud is given by:
~
m=−gJµB
~
J .~ (2.5)
With the number gJ being the Land´e factor and µB the so called Bohr magneton (see table 1.2). The g-factor can be computed from the quantum numbers J, S and L by
gJ = 1 + J(J + 1) +S(S+ 1) +L(L+ 1)
2J(J + 1) . (2.6)
In order to obtain the values for J, S and L one has to derive the quantum states of all electrons in shells that are not completely filled according to Hund’s rules. But this formalism only applies correctly to free atoms. In a solid, and especially in the magnetic 3d-transition metals, the formation of electronic band structures from delocalized electrons and interactions between the orbitals of neighboring atoms lead to strong deviations from the calculated values, as shown later in the sections sections 2.2.2.1 and 2.2.2.2.
Figure 2.1: Spin and effective magnetic moment: The spin and magnetic moment of the rare earth metals from lanthanum to lutetium [29].
Ion Configuration gp
J(J + 1) [µB] µexp [µB]
Ce3+ 4f15s25p6 2.54 2.4
Pr3+ 4f25s25p6 3.58 3.5
Nd3+ 4f35s25p6 3.62 3.5
Pm3+ 4f45s25p6 2.68 -
Sm3+ 4f55s25p6 0.84 1.5
Eu3+ 4f65s25p6 0 3.4
Gd3+ 4f75s25p6 7.94 7.98
Tb3+ 4f85s25p6 9.72 9.77
Dy3+ 4f95s25p6 10.63 10.6
Ho3+ 4f105s25p6 10.6 10.4
Er3+ 4f115s25p6 9.59 9.5
Tm3+ 4f125s25p6 7.57 7.3
Yb3+ 4f135s25p6 4.54 4.5
Table 2.2: Comparison of calculated and measured magnetic moment from the paramagnetic state per ion of rare earth metals [25]. Eu3+ should have no mag- netic moment, but low lying excited states are occupied, producing a nonzero magnetic moment.
|χ| 1. The sign indicates that the magnetization points opposite to an external magnetic field. Diamagnetism occurs in all materials but is usually dominated by para- and ferromagnetic phenomena. It can be explained by loop currents that are induced in the atoms by the external field, corresponding to spin precession. This current, in turn, produces an induced magnetic moment, which points opposite to the external field according to Lenz’s law. The following expression for the diamagnetic susceptibility can be derived using quantum mechanical perturbation theory [2, 30]:
χdia =−N Ze2 6mec2
r2
. (2.7)
N : Number of atoms/molecules per unit volume Z : Atomic number
hr2i: average quadratic radii of the occupied orbitals in partially filled shells
Typical values forχdia are in the range of 10−6 cmemu3Oe.
In a paramagnetic material the atoms (or molecules) possess a permanent magnetic moment arising from their electronic configuration. These permanent magnetic moments do not interact with each other and can be freely oriented.
This leads to a small but positive value for χpara.
Langevin developed an expression for freely orientable magnetic moments m~ in an external field. Due to thermal excitation, they will not align perfectly to an applied magnetic field. This classical picture leads to the Curie law:
χpara= N m2 3kBT = C
T. (2.8)
C is called the Curie constant.
But due to the quantum mechanical nature of the atomic magnetic moment, the alignment with respect to the external field is quantisized. If this is taken into account the magnetization is given by
Mpara =N gJ µBBJ(x). (2.9) BJ(x) is called the Brillouin function. Its argument is x=JgµBH/kBT. It converges in the limit of J → ∞ to the Langevin function, and the result equa- tion (2.8) is obtained. Equation (2.9) gives us an expression for the susceptibility, incorporating the total angular momentJ of the atoms:
χpara = N g2J(J+ 1)µ2B 3kBT = C
T. (2.10)
But there are additional mechanisms that cause a paramagnetic response to external magnetic fields. The weakly-bound electrons in the conduction band carry a magnetic spin momentm~S = -2µB
~ and cause a temperature-independent paramagnetic behavior called Pauli spin paramagnetism. The energy levels of spins parallel and antiparallel to the external field are shifted by ∆E = 2µBB0. This gives more conduction electrons with m~S parallel than antiparallel to the external fieldB~, as shown in figure 2.2. One thereby finds a net magnetization
MP auli =
N−N↑↓
V
µB = 3N µ2B
2kBTF. (2.11)
N, N↑↓ are the numbers of electrons with magnetic moments parallel and antiparallel to the external field. It should be mentioned that due to the negative g factor of electrons the spin~s and the associated magnetic moment m~s point in opposite directions.
Figure 2.2: Density of states: Without an external field the density of states of the free electron gas is unperturbed and the number of spin-up and spin-down electrons are equal (left graph). An external magnetic field causes a shift of the distribution and there are more electrons with spin antiparallel to the field.
The so called Van Vleck paramagnetism will only be briefly mentioned. It is caused by excited states in atoms that don’t exhibit a magnetic moment in the
In order to describe ferromagnetism, we require additional physics. The depen- dence of M on H for a typical ferromagnetic material is called hysteresis loop.
Starting with a demagnetized sample, the magnetization rises with increasing magnetic field until it reaches a maximum value called the saturation magneti- zation MS. In this state all atomic magnetic moments are aligned. Decreasing the field again to zero, a remaining magnetization, called the remanence MR, can be observed. One has to apply an opposite field HC, the coercivity, in order to obtain a net magnetization of zero again. With increasing field strength the magnetization rises again until all moments are aligned opposite to the saturation before, and the process can be continued to form a loop.
In 1907 Weiss presented a phenomenological model of ferromagnetism, in- troducing an interaction between the permanent magnetic moments of the atoms called ”the molecular field”, which he added to the applied field:
H~tot =H~ext+H~W =H~ext+γ ~M (2.12) γ: molecular field constant.
Introducing this expression into equation (2.10) leads to the Curie-Weiss law, describing the behavior of magnetic materials above their Curie temperature TC, where they are paramagnetic.
M
Hext+γM = C
T ⇒ χ= M
Hext =
CHext
T−Cγ
Hext = C
T −TC (2.13) This can be expanded to the temperature regime below TC by applying the same replacement to the calculations of Langevin for paramagnetic materials. So without an external field there is still the molecular field HW and the spontaneous magnetization is given by the intersection of the following two expressions for M.
M = N mL(α) (2.14)
M = HW
γ (2.15)
The argument of the Langevin function L isα=mH/kBT.
But even the normalized magnetization M/M0 over T/TC is only approxi- mately represented by equation (2.14) (see figure 2.3).
Figure 2.3: The relative spontaneous magnetization of Fe, Co and Ni can be well described by Weiss’s theory with (a) the classical Langevin function or the Brillouin function for (b) J=1 and (c) J=1/2 [6].
This model takes no account of the quantum mechanical nature of the elec- trons which cause the magnetic behavior and gives no explanation for the origin of the postulated molecular field. This major drawback of the theory of Weiss was solved by Heisenberg in 1928 by introducing an exchange interaction between the spins of different atoms.
Hˆex =X
ij
JijS~iS~j (2.16)
Jij is called the exchange integral. The major result of this idea is that it can lead to a parallel alignment of neighboring spins due to this interaction of electrostatic origin. It is a direct result of Pauli’s exclusion principle since elec- trons with parallel spins can’t be at the same place what reduces the electrostatic repulsion. If only the number z of nearest neighbors are taken into account within the molecular field theory, one obtains an expression forJij:
Jij = 3kBTC
2zS(S+ 1). (2.17)
In the case of the three ”classical” ferromagnets Fe, Co and Ni the open shells from which a permanent magnetic moment evolves are the 3d orbitals. But these electrons are in the conduction band and therefore delocalized, which contradicts the idea of localized interacting magnetic moments as in Weiss’s and Heisenberg’s theories. Although the temperature dependence and phase transition are well pre- dicted (see figure 2.3), the magnetic moment per atom and its change from the ferro- to the paramagnetic phase couldn’t be explained.
Stoner introduced his model of band magnetismin 1938 in analogy to Pauli spin paramagnetism of the conduction band electrons. In Fe, Co and Ni the Fermi energy is within the 3d band, making it possible to shift electrons to ex- cited states. The energy needed is taken from minimizing electrostatic repulsion as mentioned in the above paragraph. This is represented by the exchange inter- action in equation (2.16) plus an exchange term that shifts the energy levels for spin parallel or antiparallel. This shift is not equal for both spin states, and by favoring one spin orientation, it causes a spontaneous magnetization:
E↑(~k) = E(~k)−µBB+J N↓ (2.19) E↓(~k) = E(~k)−µBB+J N↑.
This splitting is shown for nickel in figure 2.4 [30]. Here the exchange energy leads to a complete filling of the majority band with 5 electrons and 0.54 holes in the minority band (the missing 0.46 holes are in the 4s-band and do not contribute to the magnetic moment).
Figure 2.4: Energy bands of nickel: Above TC there is an equal number of spin-up and spin-down electrons (left side). At T=0K there is an excess of 0.54 electrons in one of the 3d-subbands [30].
The susceptibility follows from equation (2.3) using D(EF), the density of states at the Fermi level:
χStoner = µ2BD(EF) 1− J D(EF)V
2
| {z }
≥0 Stoner-criterion
. (2.20)
The Stoner criterion is a good measure of wether a material will be ferro- magnetic. The computed values are shown in figure 2.5
Figure 2.5: Values of the Stoner criterion: Elements with D(EF)*J≥ 1 are ferromagnatic [2].
Figure 2.6: The open 4f shell is well shielded from the influence of neighboring atoms in Gadolinium. For comparison the size of the Wigner-Seitz-Cell RW S is inserted. Taken from [26].
This mediation is performed by delocalized electrons in the conduction band and is called Rudermann-Kittel-Kasuya-Yosida coupling, abbreviated RKKY, af- ter the scientists who contributed to its description. First, Rudermann and Kittel developed the idea of an indirect interaction of nuclear magnetic moments via con- duction electrons [31]. Kasuya and de Gennes expanded the model to rare earths [32], and Yosida applied it to transition metal alloys [33].
The basic idea of this coupling is that the spin of the 4f orbital polarizes the conduction electrons, which, in turn transports this polarization to neighboring spins. In the following only a short summary of the RKKY formalism will be given.
The interaction of two localized f-spins l and l’ can be described in a similar manner as in equation (2.16) by:
Hˆf f0 =X
l,l0
j(R~l−R~l0)S~l·S~l0. (2.21)
The sum is over all pairs of spins at the sites R~l and R~l0 in the system. j describes the indirect exchange coupling, depending on the density of states in the conduction band at the two positions. It follows:
j(R~l−R~l0) = 1 N2
X
k,k0
|jsf(~k−~k0)|2D(~k)(1−D(~k0))
Ek0 −Ek ei(~k−~k0)·(R~l−R~l0) (2.22)
jsf : Exchange interaction between localized f- and delocalized s-spins
~k, ~k0 : Wave vectors of the conduction electrons at the two different sites Ek, Ek0 : Their respective energies
D: Density of states.
In order to solve this eingenstate equation analytically, several assumptions have to be made. The direct interactions f↔f and s↔s are neglected; jsf = j = con- stant and the density of conduction electrons is taken to be isotropic. Then equation (2.22) becomes:
j(R~l−R~l0) = 9π j2
EFF(2kF|R~l−R~l0). (2.23) The function F, given below, shows an oscillatory behavior:
F(x) = xcosx−sinx
x4 . (2.24)
It describes well the long range RKKY interaction, as it decreases by R−3. In figure 2.7 the exchange interaction from equation (2.22) is plotted for gadolinium.
Positive values express ferromagnetic and negative antiferromagnetic coupling.
Gadolinium behaves like a ”normal” ferromagnet, i.e. the magnetic moments within a domain are parallel. In most other rare earth materials the indirect coupling forms chiral or cone-helical structures of the magnetic moments, and parts of the magnetic moments cancel each other [34, 35].
Figure 2.7: RKKY ex- change interaction of Gd: The coupling oscil- lates from ferro- to anti- ferromagnetic. Taken from [26].
2.2.3 Ferri- and Antiferromagnetism
In antiferromagnetic materials the coupling between neighboring magnetic mo- ments leads to antiparallel alignment. Thus, there is no net magnetization. Ex- amples are chromium and manganese, that even have a very high magnetic mo- ment per atom. Above the ordering temperature TN, the N´eel temperature, the materials turn paramagnetic. But compounds like Fe2O3 (hematite) can also be antiferromagnetic (like most oxides with Fe, Co, Ni).
In contrast, ferrimagnetic materials have oppositely oriented magnetic moments but they do not cancel each other completely. Instead a net magnetization is left. Ferrimagnetism can occur in oxides like FeO·Fe2O3 (magnetite) or alloys, e.g. CoPt3, CrPt3 and some RE-TM alloys.
The expressions for antiferro- or ferrimagnetic coupling can be extended to multi- layered structures, as has been investigated e.g in [36, 37, 38]. Here the magnetic coupling between neighboring layers of rare earths and transition metals was stud- ied. The interaction of magnetic layers separated by a nonmagnetic spacer can lead to an oscillating coupling depending on the spacer thickness [18, 39, 40].
Examples of this phenomenon are multilayers of Co/Cu or Fe/Ru and Fe/Cr.
2.3 Finite size effects in thin magnetic films
In thin films the dimensionality is reduced to a 2D system. On the other hand, magnetism is an ensemble property, especially ferromagnetic coupling. Thus, strong influence of the macroscopic structure on the magnetic behavior can be expected.
The magnetic anisotropy is one of the properties influenced by the characteristics of a thin layered film. There are three major contributions to magnetic anisotropy:
Magnetocrystalline anisotropy has its origin in the crystal structure and is thereby an intrinsic property of the material. It is caused by different distances to the next neighbors of an atom along different crystal axes. Its contribution is comparatively small, such as Ka=4.2*105 erg/cm3 for iron.
Shape anisotropy dominates in many thin film systems. Large dipole- dipole interactions cause it. If the easy axis lies within the film, the aligned domains can interact throughout the whole film, and a large demagnetizing field can be established . The Gd, Ni and Gd/Ni layered films investi- gated here all show an in-plane magnetization due to shape anisotropy (see figure 4.20 in section 4.4.1).
Surface and boundary anisotropy: Atoms at surfaces and boundaries can interact only on one side with neighboring atoms of the same species.
This asymmetry also leads to a magnetically anisotropic behavior. This effect can be very strong in multilayered systems with very thin magnetic layers like Co/Pd with tCo≤13˚A, as shown in figure 2.8. Above the critical thickness of the Co-layer the easy axis is driven by the shape anisotropy.
All these different contributions are usually summarized by a measurable value of an effective anisotropy Kef f that consists of a volume part KV and a surface/boundary part KS:
Kef f =KV + 2KS
t t = film thickness. (2.25)
Reduced dimensionality influences other properties, too, e.g. decrease of the Curie temperature [42], saturation magnetization MS or critical temperature TC in superconductors [41]. Systems of islands or small grains (see section 2.4) undergo a transition to a superparamagnetic behavior [43].
Figure 2.8: The effective anisotropy Kef f·t changes its sign at tc, so that the easy axis goes from perpendicular to the film surface to parallel [41].
2.3.1 Interlayer exchange coupling
The exchange coupling between magnetic layers has attracted a lot of interest in the past 20 years. Most research has been done on systems of two, in most cases, identical magnetic layers separated by a non-magnetic spacer. These lay- ered structures can exhibit the so called giant magnetoresistance effect GMR, describing the change in conductivity across the layers, depending on their mag- netic alignment. Exchange coupling of magnetic layers was first investigated in the 1970s and especially from the mid-1980s on in the course of magneto-optical devices, in order to stabilize the magnetization of layers containing rare earth metals. They exhibit a high Kerr rotation but are thermally very unstable.
In the following a very brief description of the exchange coupling between two neighboring magnetic layers will be given, introduced by Esho [44] and Kobaya- shi [40]. Only magnetostatic interactions are considered, what is sufficient for the investigated system Gd/Ni. The coupling phenomena in GMR-systems involve a mediation of the magnetizations through the conduction electrons of the spacer layer, according to the RKKY coupling as first described by Gr¨unberg [17] and Parkin in 1986 [18].
The magnetization of each layer is considered to rotate coherently and the easy axis lies in the film plane. The external field H and the field produced by the adjoint layer act on it. The external field is also applied parallel to the film plane.
The total free energy per unit area can then be written as:
E = − Ms1t1Hcosθ1−Ms2t2Hcosθ2
| {z }
Zeeman energies
(2.26)
+ 1
2σw[1±cos(θ1−θ2)]
| {z }
coupling energy
− (Ku1−2πMs12)t1cos2θ1−(Ku2−2πMs22)t2cos2θ2
| {z }
effective anisotropy energies
t1, t2: thicknesses of the layers; Ku1, Ku2: uniaxial anisotropy constants;
θ1, θ2: angles between the applied field H and the magnetization of the single layers.
The stable configurations can then be computed from:
∂E
∂θi = 0 and ∂2E
∂θ2i >0. (2.27) From these equations follows that the stable solutions are:
θ1, θ2 = 0, π. (2.28)
So the magnetic moments align either parallel or antiparallel to each other in this simple model, depending on the sign of the term of the coupling energy in equation (2.26). Helical structures, as they appear in e.g. Dy or Tb can lead to different angles.
2.4 Film growth and epitaxy
In the previous section 2.3 the influence of the limited dimensionality on mag- netism was discussed. But there are more implications for the properties of the material, like altered crystal structures, alloys that do not exist in the bulk mate- rial, or conductivity, superconductivity or optical properties changes that can be tailored. Due to the rising demand for the precise production of thin films sev- eral techniques have been developed. Those used in this work will be presented in the next chapter. Epitaxy is usually performed under at least high vacuum conditions (i.e. p<10−6 mbar) in order to supply a continuous and homogenous flow of atoms (sometimes molecules or small clusters) onto the substrate without deflections or reactions with the residual gas.
In the following, the interactions between the material and the substrate will be
Figure 2.9: Epitaxial growth: Illustration of the three major modes of epitaxial growth, beginning on the left from submonolayers to several monolayers on the right [3].
An effective tension energy can be defined from the following boundary ten- sions: γSV between substrate and vacuum, γAV between adsorbate and vacuum andγSA between substrate and adsorbate. Its sign and value are good indices to predict the growth mode:
∆γ =−γSV +γAV +γSA (2.29)
Volmer-Weber growth: A negative value of ∆γ expresses a stronger interaction between the adsorbed atoms than with the substrate. The ad- sorbate tends to agglomerate and form islands. That’s why this growth mode is called island growth. Nevertheless, films growing in this manner can form very smooth granular structures (e.g. Pt on WSe2 [45]). An ex- ample of the build-up of very rough surfaces is Pb on glass (especially at elevated temperatures).
Frank-van-der-Merve growth: Also known as layer-by-layer growth.
∆γ > 0, i.e. the material tends to accumulate at the substrate. Thus, a first monolayer is established followed by additional layers. Sites at kinks and holes are preferred by the adsorbed atoms, which favors the 2D-growth pattern.
Stranski-Krastanow growth: After forming one or several smooth mono- layers, further deposited atoms form islands. ∆γ ≈ 0 characterizes this behavior.
3.1 The UHV set-up MEDUSA
The samples were all produced in the UHV-chamber MEDUSA, and acronym for Maschinerie zur Erforschung DUenner Schichten and Atomagglomerationen, at a base pressure of pbase=1*10−10 mbar. During evaporation from the compact e-beam evaporators, models EFM3 and EFM4 from Focus GmbH, the pressure did not rise above 1*10−9 mbar. EFM stands for Evaporator with integrated Flux Monitor. A schematic layout of the chamber is shown in figure 3.1.
The samples were introduced into the UHV system through a load-lock that could be evacuated down to 1*10−7 mbar within a few hours. With a substrate heating it is possible to remove gaseous adsorbates from the samples without degrading the vacuum in the main chamber. A manipulator system, manufac- tured by Vacuum Generators, was adapted to the sample transfer system of the MEDUSA. It is used to bring the samples to the evaporation position and is in- stalled in all the measurement devices. The big advantage of this manipulator system is that samples can be heated up to 800 K and cooled by liquid nitrogen down to 100 K. The main chamber is equipped with a set of two EFM evap- orators (see figure 3.2 a). They are positioned in a way to aim at the same spot, where the sample is located. These sources were used for evaporating nickel and gadolinium. In addition, a home-built boat evaporator was installed for the preparation of gold capping layers. But due to poor reliability and the small amount of material that could be stored even if all four available boats were used only for capping material, it was replaced by a water-cooled crucible evapo- rator system, which can be equipped with up to four different materials at a time.
The EFM evaporators are a very compact form of a e-beam evaporation source and it fits to a CF40-flange. Electrons are emitted from a tungsten wire that has a thorium content of 0.5 %. A high voltage is supplied between the
Figure 3.1: Schematic layout of MEDUSA UHV-chamber (top view).
filament and the crucible, usually 800-1000 V, in order to accelerate the elec- trons towards the crucible. The current between the filament and the crucible is monitored to check the applied heating power. The crucible and the filament are suited in a copper cooling shroud to minimize the rise in pressure because of heating the surrounding. On top of the cooling shroud, where the evaporated ma- terial comes through, a chimney is mounted. It collects a part of the electrically charged atoms, and so a current, proportional to the evaporated flux can be mea- sured. Due to the low ionization energies of gadolinium, these atoms are usually 3+ ionized, what gives a much higher current than for nickel. The evaporation of both materials posed great difficulties. The filament is exposed to the evaporated material unlike in most other e-beam evaporators. Gadolinium lowers the work function of the filament dramatically, that’s why the heating up of the crucible has to be monitored very carefully, and the filament current has to be reduced im- mediately as soon as the material is beginning to be evaporated. Nickel tends to alloy with the crucible materials molybdenum and tungsten. This can lead to the destruction of the crucibles. The boat evaporator used was suffering the known drawbacks like poor reliability and that only small amounts of material could be stored. Aside form that materials like Co, Pt or Pd can not be evaporated from this kind of source, due to the high temperatures needed. On the other hand a stable and high flux of gold could be reached within a few minutes and the system needed no cooling. Still it was replaced later by a home-built thermal evaporator, consisting of boron-nitride crucibles surrounded by a tantalum filament. But this
Figure 3.2: Schematics of an EFM evaporator and source alignment in MEDUSA: In part a) the major components of the used EFM evaporators are shown. On the right side in b) the arrangement of all three sources with respect to the sample is sketched.
source needs water cooling and has to be completely unmounted for every refill of materials.
Figure 3.2 b) shows the arrangement of the evaporation sources around the sample position. During deposition of all materials the sample did not need to be moved giving a very good reproducibility of the samples. The sample was mounted on a OMNIAX manipulator manufactured by Vacuum Generators. It can be moved in all directions and is rotatable around the z- and y-direction. As can be seen in figure 3.1 to the left of it (looking through the viewport at the sample stor- age), an AUGER spectrometer from Omicron is mounted in order to investigate the chemical composition of the samples. Its e-gun was also used for electron diffraction under a small angle, called MEED. To the right a LEED system from Omicron is installed to investigate crystal structures with a higher precision.
By a transfer mechanism, samples can be brought into a separate STM chamber in-situ. The STM was manufactured by RHK, but the pictures presented later were all taken with a system by Omicron, situated in another chamber. For this a special transfer adapter was developed for bringing the samples under UHV to the other chamber.
Beside these devices the MEDUSA chamber is also equipped with a sputter gun to clean and smoothen metal substrates and a mass spectrometer for inves- tigating residual gases. A sample storage could hold up to four samples and a
smaller one two samples. By that a whole series of samples could be produced with using the load-lock only once. This assured a very low pressure and espe- cially a very low oxygen content in the chamber. The content of oxygen and water in the residual gas was minimized by using a titanium sublimation pump. The main and STM chamber were pumped by iongetter pumps supplied by Varian and Leybold. The load-lock was equipped with a turbo molecular pump from Pfeiffer which was pre-pumped by a oil-free plunger pump manufactured by Leybold.
3.2 Magnetic characterization
The magnetic behavior of the bilayers produced is the central issue of this work.
The different nature and the very different temperature dependence of gadolinium and nickel is the reason of the very interesting switching behavior. Rare earth and transition metals align antiferromagnatically in many systems investigated in the recent years [46, 47]. Possible applications of these systems range from sensing devices to components in data storage devices.
All samples were thoroughly characterized by a SQUID-magnetometer from Quan- tum Design. Field and temperature dependence of the whole bilayer system could be investigated and so the interplay of the two species was accessible. Experiments with XMCD, X-ray Magnetic Circular Dichroism, were performed to observe the magnetization of each material separately.
In the following the basic concepts and physics, involved in these experimental methods, will be introduced and discussed. Citations for further going literature will be given to the reader, in order to keep this section to a reasonable extent.
3.2.1 Superconducting QUantum Interference Device:
SQUID
SQUID magnetometers represent the most sensitive devices for measuring mag- netic moments and magnetic fields respectively. Moments down to 10−4∗φ0 can be detected. φ0 = h/2e is called the flux quantum (see below). The set-up used was manufactured by Quantum Design (San Jose, CA) and carries the model name MPMS-5S XL. The samples can be magnetized by fields of up to±50 kOe and measurements can be carried out in a temperature range from 1.7 K to 400 K.
Nowadays many different measurement methods for magnetic moments and fields are available like MOKE (Magneto-Optical Kerr Effect), VSM (Vibrating Sample Magnetometry) etc. A brief overview and comparison is given in [48]. The major advantages of SQUIDs are the temperature variability, which was used inten- sively in this work, the high accuracy and good reproducibility. Its disadvantages are long measuring times, high costs for purchase and helium consumption and background signals from substrates and mounting straws. In the following basic
Figure 3.3: Two Josephson contacts forming a SQUID loop.
Figure 3.3 shows a schematic view of a dc SQUID loop consisting of two Josephson junctions arranged to a ring structure. A Josephson junction is an insulating layer between two superconductors, coupling them weakly. From the Ginzburg-Landau theory it can be derived, that a dc current flows through such a junction in absence of neither an external voltage nor magnetic field, the so called dc Josephson effect:
j =jmsinδ0 (3.1)
jm: maximum current density,δ0: phase difference between both sides of the junction.
So without an external voltage applied, a current is flowing across the junc- tion. If an external voltage is applied, the potentials A~ and U in the describing Schr¨odinger equation have to be gauge transformed, leading to the ac Josephson effect.
j =jmsin
δ0− 2eU21
~ t
(3.2) δ0: Phase difference of the field free junction from equation (3.1), U21: Ap- plied external voltage.
An additional oscillating current with the frequencyω = 2eU21/~arises over the junction.
In the presence of a weak magnetic field, i.e. the BCS theory is still valid and the only effect of the vector potential A~ is a position-dependent phase shift can be computed by:
δ=δ0+2π φ0
2
Z
1
A~·d~l φ0 ≡ hc
2e (cgs) (SI: h
2e). (3.3) φ0 is the so called flux quantum. With these three equations (3.1), (3.2) and (3.3) also complex arrangements of Josephson junctions can be described, like a SQUID loop as shown in figure 3.3, applying simple Kirchhoff’s rules. A magnetic fluxφ is flowing perpendicular through the ring. A current going from position 1 to 2 splits up onto the two branches a and b.
I = Ia+Ib =Imasinδa+Imbsinδb (3.4)
= 2Imsin
δb +δa 2
cos
δb−δa 2
The second line evolves from assuming the same maximum current in both branches (Ima=Imb). Following the closed path around the ring (i.e. 1→2→1) the phase can only change by discrete values 2πn, thus the magnetic flux is quantized accordingly.
I
C
∇Φ·~l=δtotal= 2πn (3.5)
The phase differences in the upper and the lower branch are connected to the enclosed magnetic flux by the following equation, which can be computed from the integration of A~·d~lover a half loop.
δa−δb = 2πn+ 2π φ0
I
C
A~·d~l+2π φ0
4πλ2L c
Z
C0
~j·d~l= 2πn+ 2πφ
φ0 . (3.6) C’: Path from the right side of the upper junction to the right side of the lower junction (so without passing an insulator layer), λL: London penetration depth.
I = 2Im
cos πφ φ0
. (3.8)
One can see from equation (3.8) that the detected current oscillates with changing magnetic flux penetrating the SQUID loop by multiples of the flux quantumφ0. From this it is clear, that a device as shown in figure 3.3 can be used to measure very small changes in magnetic fields. But in order to detect fluxes greater than φ0 the SQUID loop is used in the MPMS system in a flux-locked- loop feedback. A magnetic flux, opposite to the one from the sample, is applied to the SQUID with an oscillating component (usually some 100 kHz). If the two constant fluxes cancel each other the frequency of the oscillating component is doubled, due to|cos(x)|. This is detected by a lock-in amplifier. This degenerative feedback makes it possible to detect magnetic fluxes up to the maximum flux, that can be generated by the magnet in the feedback loop.
In the following a short description of the set-up used and the special tech- niques to achieve a resolution down to 10-4∗φ0 will be given. All measurements are controlled by a computer, which is following a previously generated measuring sequence. In figure 3.4 a schematic overview of the used SQUID system is shown.
This inner part is suited in a helium dewar which is insulated by a vacuum gap and a surrounding liquid nitrogen shield.
Straws, made of delrin, which is a purely diamagnetic plastic, are used to mount the samples. The straw, holding the sample, is attached to a rod, which can be moved up and down through the sensing coils. The detected signal is then trans- ferred to the actual SQUID loop, that is positioned at the bottom of the helium dewar. The set-up was equipped with the optional RSO mode (Reciprocating Sample Option).
In the left part of figure 3.5 two types of pick-up coils and and the detected signal, that is recorded if a sample is moved through it, are shown. The used set-up holds a second-order gradiometer, labeled b) in the drawing. The use of such a pick-up coil brings many benefits. Into a simple coil a change in the homogenous external field would already induce a voltage. For comparison a first- order gradiometer is in the picture, too. The first-order coils are insensitive to a change of the homogenous external field, whereas field gradients induce a voltage.
The second-order coil rejects both homogenous fields and linear gradients, but is more complicated in production, since the distances and diameters have to obeyed accurately. Furthermore Vandervoort [52, 53] proved that the noise due to the
Figure 3.4: Schematic overview of the SQUID magnetometer MPMS XL-5S: Right: Probe components; Left: Zoom of the solenoid [52].
resistance of the solenoid is reduced by an order of magnitude.
The right part of figure 3.5 illustrates the RSO mode, which was used for all samples, because the less precise DC mode has a too low resolution. The sample is moved through the pickup coil with a frequency of up to 4 Hz and amplitudes between 0.5 and 4 cm. This oscillation of the detected SQUID voltage is than fed into a second lock-in, improving the resolution by one order of magnitude in comparison with the DC mode. Two positions for adjusting the sample with respect to the coils can be chosen. The center position, where the sample is in the middle of the gradiometer, and the position, where the maximum slope in the detected SQUID voltage. Temperature dependent measurements were all performed at the center position, because it is less sensitive to displacements of the sample. In hysteresis, the sample doesn’t drift due to thermal expansion of the mounting straw, and the more precise maximum slope position can be used.
Figure 3.5: Gradiometer pick-up coils: Left: Gradiometer designs and de- tected voltage over displacement. Right: Illustration of the RSO mode; The sample is moved at up to 4 Hz though the pick-up coils [52].
3.2.2 X-ray Magnetic Circular Dichroism: XMCD
Magneto-optical effects are known since the discovery of the Faraday effect in 1845. John Kerr discovered in 1876 the rotation of the polarization of light, that is reflected at a ferromagnetic surface. This magneto-optical Kerr effect is the basis of nowadays MOKE magnetometers and is driven by the different absorption of left and right circular polarized light. The induced transitions, using optical wavelengths (a few eV), are within the valence band. In 1975 Erskine and Stern proposed the idea of a magneto-optical effect in the x-ray regime of circular polarized light, called XMCD [54]. The first XMCD experiment could be performed in 1987 by Sch¨utz on a thin Fe foil [55]. This was made possible after a tunable x-ray source with a sufficiently high flux was available. Therefore synchrotron radiation is needed for these experiments.
In contrast to experiments using visible light in XMCD electrons in low lying core levels are excited to states in the valence band or the continuum. With the energy levels of the core shells being characteristic for the different elements, this method is element-specific [56]. This was used within this work, in order to record hysteresis loops of nickel and gadolinium, separately.
3.2.2.1 From X-ray absorption XAS to XMCD
X-rays are strongly attenuated in matter according to the Beer-Lambert law I(E, d) =I0e−µd. (3.9) In the energy range of x-rays photon absorption is the dominant contribution to the attenuation, i.e. that electrons are exited from an initial state |ii to a final state|fi and the photon energy is transferred onto them. Contributions by Compton effect and photo effect can be neglected. So there appear characteristic lines in the absorption spectrum that are defined and labeled K, L1, L2, L3, M1...
after the initial states |1s1/2i,|2s1/2i, |2p1/2i, |2p3/2i, |3s1/2i...
The transition probability is described by Fermi’s golden rule:
Γi→f = 2π
~ |hf|H|ii|ˆ 2ρ(Ef). (3.10) From this equation one can see that two quantities determine the transition rate:
The interaction strength, described by the first term, which leads to the selection rules (equation (3.11)) and the density of states near the Fermi level as final states. Here we only consider electric dipole transitions (E1):
∆j = 0;
∆l = ±1;
∆m =
+1 left circular 0 linear
−1 right circular
(3.11)
∆s = 0.
In XMCD the dependence of the absorption on the magnetization is used.
This effect is caused by the different number of final states that are available for electrons with ”spin up” or ”spin down”, due to the different shift in energy of the two subbands (see figure 2.4). Figure 3.6 shows schematically the absorption of a photon with the energy E=~ω at the L2,3-edge in a 3d-transition metal. The possible final states are 4s and 3p.
The definition of the actual XMCD-signal is the difference in the absorption coefficients µ+(E) andµ−(E):
∆µ(E) = µ+(E)−µ−(E) (3.12)
µ+(E) : P~ ↑↑M~ µ−(E) : P~ ↑↓M~
P~: Polarization/helicity of the photons;M~: Magnetization of the sample.
Figure 3.6: Dipole transi- tions in a 3d-metal: Accord- ing to the selection rules tran- sitions to the 4s and 3d or- bitals are possible. The 4s- band is very narrow and by that can not take up many electrons, but is not split due to exchange interactions. The 3d-band splits up into a spin- up and a spin-down branch, making transitions with ∆m=- 1 more likely. Taken from [57].
In the experiments carried out at BESSY, the Berliner Elektronenspeicherring- Gesellschaft f¨ur Synchrotronstrahlung, in the course of this work, the magnetiza- tion of the samples was changed with an external magnetic field and the polar- ization of the incoming photons was kept constant. For simplicity the measured intensity with respect to the ingoing intensity I0 was recorded.
This sensitivity in the number of available states in the valence band is used in NEXAFS experiments, with which the density of states above the Fermi-level can directly be observed.
This difference in the cross-section of the absorption of x-rays between P~ ↑↑ M~ and P~ ↑↓ M~ can lead to a significant difference in the absorption spectrum as shown in figure 3.7.
From the definition equation (3.12) and figure 3.6 one sees, that a difference in absorption is only visible if the magnetization is parallel/antiparallel to the beam direction. Measurements in transmission on the in-plane magnetized system Gd/Ni were carried out under an angle of 45°. So only the projection of M~ on the incident beam~k is detected, lowering the XMCD-signal. Figure 3.8 shows a schematic of the used UHV set-up ALICE at the BESSY.
The synchrotron BESSY, situated at Berlin, offers a large variety of x-ray radiation for different investigation methods. The radiation is generated by elec-
Figure 3.7: XAS and XMCD spectra of Nickel: The XMCD spectrum (bottom) is the normalized difference between the two XAS spectra at the top.
The data was recorded from sample A4, consisting of Gd(50˚A)/Ni(75˚A)/Au(20˚A) on Si3N4.
trons that circulate in packages in the storage ring at an energy of 1.7 GeV and a beam current of up to 400 mA. At 16 straight sections so called wigglers or undu- lators consisting of superconducting magnets are installed that force the electrons on a wiggled trajectory, see figure 3.9. The electrons are accelerated towards the center of each half circle, what causes them to emit the x-ray radiation, which has wide spread spectrum. The arrangement of the magnets determines, wether linear, circular or elliptical radiation is emitted. At each site several experiments are installed in order to optimize the use of the synchrotron. The energy loss
Figure 3.8: UHV-chamber ALICE at BESSY: The sample is rotatable and can be moved in all directions for alignment. The sample holder can hold up to four samples.
Figure 3.9: Layout of an undulator: By changing the arrangement of the for segments the type of the emitted radiation can be changed. Taken from www.bessy.de.
of the electrons, because of the emission of radiation, is compensated by four cavity-resonators along the storage ring. Between the straight sections specially designed permanent magnets focus the e-beam and force it on its circular path through the storage ring, which is kept at a pressure below 1·10-11 mbar.
3.2.2.2 Sum rules
The magnetic moment of an atom can be divided into two contributions, originat- ing from its spin polarization hSzi and its orbital momentum polarization hLzi, according to:
orbital momentum : µL=−µBhLzi spin momentum : µS =−µBhSzi.
(3.13) With the transition probability and the number of electrons in the initial states being different XMCD can be used to determine these two contributions.
In the following a short introduction to the so called sum rules will be given.
More detailed information is given in [57, 58, 59, 60]. The description will be limited to the L2- and L3-edge as they are important for the magnetic transition metals.
Figure 3.10 shows all possible transitions from 2p- to 3d-orbitals. The pro- portionate contribution of the single transitions is indicated by the thickness of the arrows and the percentage value. These differences in the transition proba- bility leads to a spin polarization of the final state, called Fando effect.
The same is true for the orbital momentum l. The selective transition produces a polarization of the orbital momentum of the final state. Both polarizations, derived directly from the calculated transition probabilities, are also given in fig- ure 3.10 as hli and hσifor the case of right circular polarized light.
Starting from the different transition probabilities, one can derive the XMCD spectrum of a sample that has a magnetic moment, which is completely caused by spin polarization and µl = 0. Then the L2 and L3 peak would have different sign, but the same height. Whereas a hypothetical sample withµs= 0 andµl>0 would show two peaks with the same sign but the L2 peak would be twice as high.
In an actual XMCD measurement one would of course observe a superposi- tion of these two cases, leading to a spectrum like in figure 3.7. But the consid- erations above can be used to evaluate the contributions of µl and µs from the ratio of the areas under the peaks.
Figure 3.10: Transition probabilities for 2p→3d: σ+-polarized light excites the initial states with a different probability, indicated by the thickness of the arrows and the percentage of the overall transition strength.
µs = −1
C(A3−2A2)µB µl = − 2
3C(A3 +A2)µB (3.14)
A2 and A3 are the areas under the L2 and L3 peaks. The integration bound- aries are given by the limits of the absorption band of the respective transition.
A3 = Z
L3
µ+(E)−µ−(E)dE A2 =
Z
L2
µ+(E)−µ−(E)dE (3.15)
The constant C cannot be derived from the spectra, but must be evaluated from reference measurements by e.g. SQUID that give a number of the total atomic momentum of the sample.
3.3 Structural investigations
The morphology and crystal structure of the samples influence strongly the mag- netic behavior of the Gd/Ni-bilayer system. In order to resolve the great differ- ences between the samples deposited on Al2O3 and Si3N4 several methods were deployed using diffraction (XRD, XRR, MEED), energy transfer (AES, RBS) or scanning techiques (STM, TEM).
In this section only a brief introduction of these investigation techniques will be given, as far as it is necessary for the understanding of the later presented results.
3.3.1 Scanning Tunneling Microscopy (STM)
The first set-up of an scanning tunneling microscope was developed and pub- lished by G. Binning and H. Rohrer in 1982 [61, 62]. For this they were awarded the nobel prize in 1986. It allows to picture surfaces directly in real space down to atomic resolution. Later they extended the idea of a scanning probe to the atomic force microscope (AFM), that allows to investigate non-conductive sur- faces. Nowadays many subtypes are available to investigate magnetic structures, adhesion forces, etc. or manipulate surfaces on the nanoscale.
Figure 3.11: Illustration of a SPM: Left: conceptional idea; Right: Realization in the case of a STM, using a tunneling current between probe and sample.
The basic idea is to scan the surface with a probe, that has only a few nanometers in diameter, line by line and then bring these lines together to form a picture. Figure 3.11 illustrates this technique. In order to do that, a very accurate positioning of the probe is necessary. This can be achieved by attaching the probe to a piezo tube, as shown in figure 3.12. Applying voltages up to 400 V in case of the used set-up from Omicron the tube bends and can be moved over the surface. The positioning in z-direction is done at some models by the same tube, applying off-set voltages to all segments at a time. The UHV-STM from Omicron uses a separate one. Additionally a coarse positioning system is needed, usually operating with piezo drives, too.
In the case of a STM the measured feedback property is a tunneling current between the tip and the surface, what limits this technique to conductive samples.
The tip in the used set-up consisted of 0.38 mm thick tungsten wire, which was etched in 3m-NaOH to a tip with a curvature below 20 nm. In an ideal picture, as in figure 3.11, the current flows through a single atom at the end of the tip.
SEM pictures of a STM tip are shown in figure 3.13. The curvature at the end is below 10 nm. Although most tips produced were of similar shape, their imaging qualities could be very different. Some problems like a multitip or oxidization could be removed by electric field emission.
Figure 3.13: SEM picture of a STM-tip: The tips produced were of a high constant quality.
A short description of the theoretical background will be given, following the description of a tunneling hamiltonian after Bardeen [63]. If the overlap of the wave functions of the surface atoms and the tip and the applied voltage U are small, perturbation theory can be used, what leads to an expression for the tunneling current.
I ∼U ρtip(EF)ρsurf ace(~r0, EF) (3.16) ρ are the density of states at the Fermi-level in the tip and the surface. So the detected distances, later combined to a picture, is not directly the surface, but the electronic density of states near the Fermi-level.
Figure 3.14: Feedback control in a typical STM: a) Conceptional set-up of a STM, b) constant current mode for feedback, c) constant height mode. Taken from [45].
The density of the surface states decreases exponentially in first order with an effective decreasing lengthκeff in vacuum.
κef f =
r2meB
~2
+|~k|||2 (3.17)
B = Wtip+Wsample
2 − |eU|
2
With B being the barrier height,~k|| the electron wave vector parallel to the cur- rent. By that the tunneling current drops exponentially with increasing distance z to the surface and is therefore a very sensitive measure for the surface structure.
I ∼exp[−2κef fz] (3.18)
