UNIVERSITATIS ACTA UPSALIENSIS
UPPSALA
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1585
Magnetic Materials for Cool Applications
Relations between Structure and Magnetism in Rare Earth Free Alloys
JOHAN CEDERVALL
ISSN 1651-6214
ISBN 978-91-513-0123-5
Dissertation presented at Uppsala University to be publicly examined in Häggsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, Friday, 8 December 2017 at 09:00 for the degree of Doctor of Philosophy. The examination will be conducted in English. Faculty examiner: Prof. Paul Henry (The ISIS Facility, STFC Rutherford Appleton Laboratory).
Abstract
Cedervall, J. 2017. Magnetic Materials for Cool Applications. Relations between Structure and Magnetism in Rare Earth Free Alloys. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1585. 70 pp. Uppsala: Acta Universitatis Upsaliensis. ISBN 978-91-513-0123-5.
New and more efficient magnetic materials for energy applications are a big necessity for sustainable future. Whether the application is energy conversion or refrigeration, materials based on sustainable elements should be used, which discards all rare earth elements. For energy conversion, permanent magnets with high magnetisation and working temperature are needed whereas for refrigeration, the entropy difference between the non-magnetised and magnetised states should be large. For this reason, magnetic materials have been synthesised with high temperature methods and structurally and magnetically characterised with the aim of making a material with potential for large scale applications. To really determine the cause of the physical properties the connections between structure (crystalline and magnetic) and, mainly, the magnetic properties have been studied thoroughly.
The materials that have been studied have all been iron based and exhibit properties with potential for the applications in mind. The first system, for permanent magnet applications, was Fe
5SiB
2. It was found to be unsuitable for a permanent magnet, however, an interesting magnetic behaviour was studied at low temperatures. The magnetic behaviour arose from a change in the magnetic structure which was solved by using neutron diffraction. Substitutions with phosphorus (Fe
5Si
1-xP
xB
2) and cobalt (Fe
1-xCo
x)
5PB
2were then performed to improve the permanent magnet potential. While the permanent magnetic potential was not improved with cobalt substitutions the magnetic transition temperature could be greatly controlled, a real benefit for magnetic refrigeration. For this purpose AlFe
2B
2was also studied, and there it was found, conclusively, that the material undergoes a second order transition, making it unsuitable for magnetic cooling. However, the magnetic structure was solved with two different methods and was found to be ferromagnetic with all magnetic moments aligned along the crystallographic a-direction. Lastly, the origin of magnetic cooling was studied in Fe
2P, and can be linked to the interactions between the magnetic and atomic vibrations.
Keywords: Magnetism, Diffraction, X-ray scattering, Neutron Scattering, Permanent magnets, Magnetocalorics
Johan Cedervall, Department of Chemistry - Ångström, Box 523, Uppsala University, SE-75120 Uppsala, Sweden.
© Johan Cedervall 2017 ISSN 1651-6214 ISBN 978-91-513-0123-5
urn:nbn:se:uu:diva-331762 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-331762)
”That which does not kill us makes us stronger.”
- Friedrich Nietzsche
List of papers
This thesis is based on the following papers, which are referred to in the text by their roman numerals.
I Magnetostructural transition in Fe 5 SiB 2 observed with neutron diffraction
J. Cedervall, S. Kontos, T. C. Hansen, O. Balmes, F. J.
Martinez-Casado, Z. Matej, P. Beran, P. Svedlindh, K. Gunnarsson, M.
Sahlberg.
Journal of Solid State Chemistry, 235, 113-118 (2016) II Magnetic properties of the Fe 5 SiB 2 -Fe 5 PB 2 system
D. Hedlund, J. Cedervall, A. Edström, M. Werwi´nski, S. Kontos, O.
Eriksson, J. Rusz, P. Svedlindh, M. Sahlberg, K. Gunnarsson.
Physical Review B. 96 094433 (2017)
III Influence of cobalt substitution on the magnetic properties of Fe 5 PB 2
J. Cedervall, E. Nonnet, D. Hedlund, L. Häggström, T. Ericsson, A.
Edström, M. Werwi´nski, J. Rusz, P. Svedlindh, K. Gunnarsson, M.
Sahlberg.
Submitted
IV Magnetic structure of the magnetocaloric compound AlFe 2 B 2 J. Cedervall, M. S. Andersson, T. Sarkar, E. K. Delczeg-Czirjak, L.
Bergqvist, T. C. Hansen, P. Beran, P. Nordblad, M. Sahlberg.
Journal of Alloys and Compounds, 664, 784-791 (2016) V Mössbauer study of the magnetocaloric compound AlFe 2 B 2
J. Cedervall, L. Häggström, T. Ericsson, M. Sahlberg.
Hyperfine Interactions, 237, 18 (2016)
VI Magnetic and mechanical effects of Mn substitutions in AlFe 2 B 2 J. Cedervall, M. S. Andersson, P Berastegui, S. Shafeie, U. Jansson, P.
Nordblad, M. Sahlberg.
In manuscript
VII Towards an understanding of the magnetocaloric effect in Fe 2 P J. Cedervall, M. S. Andersson, E. K. Delczeg-Czirjak, D. Iu¸san, M.
Pereiro, P. Roy, T. Ericsson, L. Häggström, W. Lohstroh, H. Mutka, M.
Sahlberg, P. Nordblad, P. P. Deen.
In manuscript
Reprints were made with permission from the publishers.
My contributions to the papers
The authors contribution to the papers in this thesis:
Paper I. I planned the study, synthesised the samples and performed all struc- tural characterisations, except for the representational analysis. I wrote the main part of the manuscript and was involved in all discussions.
Paper II. I was involved in the planning of the study, synthesised the samples and performed all structural characterisations. I was involved in all dis- cussions and approved the final manuscript.
Paper III. I planned the study, synthesised the samples and performed all structural characterisations. I wrote the main part of the manuscript and was involved in all discussions.
Paper IV. I planned the study, synthesised the samples and performed all structural characterisations, except for the representational analysis. I wrote the main part of the manuscript and was involved in all discus- sions.
Paper V. I, together with the other authors, planned the study. I synthesised the samples and performed all structural characterisations. I was in- volved in the writing of the manuscript and all discussions.
Paper VI. I planned the study, synthesised the samples and performed all structural and mechanical characterisations. I wrote the main part of the manuscript and was involved in all discussions.
Paper VII. I synthesised the samples and performed all structural character-
isations. I took part in the neutron experiments and was involved in the
data analysis. I also took part in the writing of the manuscript and all
discussions.
Other publications to which the author has contributed.
i Irreversible structure change of the as prepared FeMnP 1-x Si x - struc- ture on the initial cooling through the curie temperature
V. Höglin, J. Cedervall, M. S. Andersson, T. Sarkar, P. Nordblad, M.
Sahlberg.
Journal of Magnetism and Magnetic Materials, 374, 455-458 (2015) ii Phase diagram, structures and magnetism of the FeMnP 1-x Si x
V. Höglin, J. Cedervall, M. S. Andersson, T. Sarkar, M. Hudl, P. Nord- blad, Y. Andersson, M. Sahlberg.
RSC Advances, 5, 8278-8284 (2015)
iii Directly obtained τ-phase MnAl, a high performance magnetic ma- terial for permanent magnets
H. Fang, S. Kontos, J. Ångström, J. Cedervall, P. Svedlindh, K. Gun- narsson, M. Sahlberg.
Journal of Solid State Chemistry 237, 300-306 (2016)
iv Low temperature magneto-structural transitions in Mn 3 Ni 20 P 6 J. Cedervall, P. Beran, M. Vennström, T. Danielsson, S. Ronneteg, V.
Höglin, D. Lindell, O. Eriksson, G. André, Y. Andersson, P. Nordblad, M. Sahlberg.
Journal of Solid State Chemistry 237, 343-348 (2016)
v Magnetic properties of Fe 5 SiB 2 and its alloys with P, S, and Co M. Werwi´nski, S. Kontos, K. Gunnarsson, P. Svedlindh, J. Cedervall, V.
Höglin, M. Sahlberg, A. Edström, O. Eriksson, J. Rusz.
Physical Review B, 93, 174412 (2016)
vi Short-range magnetic correlations and spin dynamics in the para- magnetic regime of (Mn,Fe) 2 (P,Si)
X. F. Miao, L. Caron, J. Cedervall, P. C. M. Gubbens, P. Dalmas de Réotier, A. Yaouanc, F. Qian, A. R. Wildes, H. Luetkens, A. Amato, N.
H. van Dijk, E. Brück.
Physical Review B 94, 014426 (2016)
vii Insights into formation and stability of τ-MnAlZ x (Z = C and B) H. Fang, J. Cedervall, F. J. Martinez-Casado, Z. Matej, J. Bednarcik, J.
Ångström, P. Berastegui, M. Sahlberg.
Journal of Alloys and Compounds 692, 198-203 (2017)
viii AlM 2 B 2 (M=Cr, Mn, Fe, Co, Ni): a group of nanolaminated materi- als
K. Kádas, D. Iu¸san, J. Hellsvik, J. Cedervall, P. Berastegui, M. Sahlberg, U. Jansson, O. Eriksson.
Journal of Physics: Condensed Matter 29, 155402 (2017)
Contents
1 Introduction
. . . .15
1.1 Magnetic materials
. . .16
1.1.1 Magnetostructural properties
. . .18
1.1.2 Permanent magnets
. . . .19
1.1.3 Magnetic refrigeration
. . . .20
1.2 Studied materials
. . .21
1.2.1 M 5 XB 2
. . . .21
1.2.2 AlM 2 B 2
. . .22
1.2.3 Fe 2 P
. . .23
2 Scope of the thesis
. . . .25
3 Methods
. . . .27
3.1 Synthesis
. . .27
3.1.1 Arc melting
. . .27
3.1.2 Drop synthesis
. . .27
3.1.3 Heat treatment
. . . .28
3.1.4 Post annealing treatments
. . .28
3.2 Diffraction
. . .28
3.3 Characterisation by diffraction techniques
. . .31
3.3.1 X-ray powder diffraction
. . . .31
3.3.2 Neutron powder diffraction
. . . .32
3.3.3 Determination of lattice parameters
. . .32
3.3.4 Full pattern refinement using the Rietveld method
. . .32
3.3.5 Representational analysis
. . . .33
3.4 Inelastic neutron experiments
. . . .34
3.5 Magnetic characterisations
. . .34
3.6 Mössbauer spectroscopy
. . . .35
3.7 Electronic structure calculations
. . .36
4 Results and discussion
. . . .37
4.1 M 5 XB 2
. . .37
4.1.1 Magnetic structure of Fe 5 SiB 2
. . .37
4.1.2 Fe 5 SiB 2 as a permanent magnet
. . .39
4.1.3 Phosphorus substitutions in Fe 5 SiB 2
. . . .40
4.1.4 Cobalt substitutions in Fe 5 PB 2
. . .43
4.2 AlM 2 B 2
. . .46
4.2.1 Crystalline structure of AlFe 2 B 2
. . .46
4.2.2 Magnetocaloric properties of AlFe 2 B 2
. . .46
4.2.3 Magnetic structure of AlFe 2 B 2
. . . .48
4.2.4 Manganese substitutions
. . .52
4.3 Fe 2 P
. . . .55
4.3.1 Characterisations of Fe 2 P
. . . .55
4.3.2 Magnetic diffraction
. . .55
4.3.3 Inelastic neutron scattering
. . .57
5 Summary and conclusions
. . .59
6 Sammanfattning på svenska
. . .61
7 Acknowledgements
. . .64
Bibliography
. . . .66
Abbreviations
A list of the abbreviations used in this thesis:
ΔS mag Magnetic entropy change DFT Density functional theory DTA Differential thermal analysis
EDS Energy dispersive X-ray spectrometry EFG Electric field gradient
FWHM Full width at half maximum H Magnetic field strength H c Coercive field
INS Inelastic neutron scattering IR Irreducible representations
μ B Bohr magneton
M Magnetisation
M sat Saturation magnetisation
MAE Magnetocrystalline anisotropy energy
MC Monte Carlo
MCE Magnetocaloric effect
MPMS Magnetic property measurement system MS Mössbauer spectroscopy
NPD Neutron powder diffraction
PPMS Physical property measurement system RA Representational analysis
RT Room temperature
SEM Scanning electron microscope
SQUID Superconducting quantum interference device T C Curie temperature
VSM Vibrating sample magnetometer
XRD X-ray diffraction
1. Introduction
”Not all those who wander are lost.”
- J.R.R. Tolkien Materials have been used, and their properties studied, throughout all exist- ence of mankind. A historic sign of this is the different ages of men, which are named after the typical preferred material. For example, stones were used as tools at the Stone Age, bronze tools at the Bronze Age and iron at the Iron Age.
Since the Bronze Age, when enough heat could be produced to melt copper and tin to form an alloy ( ∼2000 B.C.) [1], compounds and alloys have been studied more and more to improve people’s quality of life. More advanced alloys gave capability of new, more complex, ways of material fabrication.
This has resulted in an exponential development of more complex alloys and compounds until the advanced materials used today.
The materials studied within this thesis are all based on synthesis of inter-
metallic compounds. Intermetallic compounds are compounds with metallic
bonding and with different crystal structures than the respective crystal struc-
tures of the original elements [2]. When mixing two elements the structural
and physical properties will be composition dependant. When examining all
different compositions in the alloy a phase diagram can be built. The phase
diagram is then used to extract which crystal structures an alloy will have at a
certain composition and temperature. To build up a complete phase diagram is
a tedious and time consuming task to do experimentally, which is why compu-
tational studies are mostly used for this today. Commonly, phase diagrams are
built for mixing two or three elements and are therefore referred to as binary
or ternary for two or three elements, respectively. In the binary phase diagram
for iron and silicon different intermetallic compounds (e.g. Fe 3 Si and Fe 5 Si 3 )
can be found, all with different crystal structures than the ones for iron (bcc
at room temperature) and silicon (diamond type) [3]. Very often the physical
properties for intermetallics differ from the starting elements and are therefore
interesting to study. Some of the many interesting applications for intermetal-
lic compounds include hydrogen storage, superconductivity, energy storage
(e.g. batteries) and magnetism [4]. The origin of magnetism in intermetallic
compounds arises due to the magnetic moments of the metallic atoms, or ions,
they contain.
1.1 Magnetic materials
Magnetism is an invisible force that since ancient times has fascinated and puzzled mankind. For example, the discovery that needle shaped magnetic
”stones” on a water film always points north was the birth of the compass in the 11th century [5]. Today, many functions in daily life are based on magnets, often without recognition. Some examples include hard disk drives, electric motors and generators [6]. The magnetic properties in a magnetic material comes from unpaired electrons that are rotating and thus inducing a magnetic moment [7]. The direction of the rotation of the electron will thus determine the direction of the magnetic moment. The possibility of a direction of the magnetic moment lead to it being referred to as a magnetic spin. Adding sev- eral magnetic moments together in a structured way (e.g. in a crystalline struc- ture) gives possibilities of magnetic structures. If the magnetic moments are unaffected by each other, all pointing randomly in space, it is defined as para- magnetism. If the magnetic moments feel the presence of each other, called coupling, they can start to arrange themselves in different magnetic structures.
If the magnetic moments orient themselves all in parallel, it is defined as fer- romagnetism and the compound is said to be ferromagnetic, figure 1.1 (a).
The spins can also couple in anti-parallel with each other and the total mag- netisation will then be zero. This is called anti-ferromagnetism, figure 1.1 (b).
A special case of anti-ferromagnetism is ferrimagnetism, which has the same coupling mechanism as anti-ferromagnetism but non-equal magnitudes of the magnetic moments for the different directions, figure 1.1 (c), which in turn gives the material a net-magnetisation. For the applications aimed at in this thesis ferromagnetic materials are of most importance, however, ferrimagnet- ism can also be of importance.
Nothing is ever static over a period of time, atoms are constantly moving in a gas, and at least vibrating in a solid structure. The same goes for mag-
(a) (b) (c)
(d) (e)
Figure 1.1. General illustrations for magnetic coupling in two dimensions for ferro-
magnetism (a), anti-ferromagnetism (b), ferrimagnetism (c), incommensurate magnet-
ism (d) and frustrated magnetism (e).
netic spins. Independent of the strength of the magnetic coupling the spins will always rotate and result in a fluctuating net magnetisation. Temperature will also affect the fluctuations of the magnetic moments. If a ferromagnetic material is heated, the magnetic moments will vibrate increasingly, until they do not couple to each other at all. At this point the material will have lost its magnetic properties and become paramagnetic. The critical temperature of this transition is called the Curie temperature (T C ). How quick this transition is defines if the transition is said be first or second order. If it is a very sharp transition, almost a step function, it is defined as a first order transition. If it is a continuous transition when going through T C , the transition is of the second order.
Ferromagnetic compounds are often divided in two categories; hard and soft magnets. The difference becomes apparent when the hysteresis loop, obtained from plotting magnetisation as a function of applied magnetic field (applied from an external source), is studied, figure 1.2. The hard magnet (red curve) has a broad hysteresis when sweeping the magnetic field, whereas the soft magnet (black curve) increases its magnetisation linearly up until the point where the magnetisation is saturated (M sat ). For a hard magnet, the demagnet- isation curve is sometimes presented on its own. This is a part of the magnet- isation curve between zero applied field and zero magnetisation at a negative applied field.
Today magnets are used in a large number of applications, not only to hold postcards and notes on refrigerators. The main uses are in energy applica- tions, e.g. generators harvesting energy from wind or water, or in electric vehicles [8]. Soft magnets are used to enhance the magnetic properties of the hard magnets, and also for magnetic shielding in transformers and for mag-
Applied magnetic field Magnetisation
M
satM
rH
cFigure 1.2. Schematic magnetisation loops for hard magnets (red curve) and soft
magnets (black curve).
netic cooling. This makes all magnetic materials important for efficient energy production and consumption [8].
1.1.1 Magnetostructural properties
The structures in the solid state can, in general terms, be either crystalline or amorphous. In both cases the nearest surrounding of an atom will be determ- ined by composition, chemical bonding and so on. This is often referred to as
”short-range ordering” [9]. The difference between an amorphous and crys- talline material is the ”long-range ordering”, where the same local structures repeat themselves to, ideally, infinity. The repetitions in a crystalline material make it possible to describe the whole crystal with just a small part as the rest is just repetitions, the small part is defined as the unit cell. The same structural reasoning also applies to magnetic structures. Below the ordering temperature in a crystalline magnetic compound the magnetic moments can have long- range order, and subsequently repetitions of the magnetic spins. In this way a magnetic unit cell can be formed and for the simplest cases (figure 1.1 (a)- (c)) the magnetic unit cell can coincide, or be related to an integer number of the crystalline unit cell. For these simple cases the magnetic structure is said to be commensurate. If the number of crystalline unit cells to describe the magnetic unit cell is not an integer, the structure is said to be incommen- surate. An example for an incommensurate magnetic structure is represented in figure 1.1 (d), where the magnetic moments follow a sinusoidal behaviour.
Sometimes the magnetic coupling mechanisms can lead to frustration and dif- ferent magnetic structures can arise, in figure 1.1 (e) this is represented in two dimensions. In the description of a normal crystal, a space group is assigned which indicates what symmetry elements exist in the unit cell. From the space group the whole unit cell can be constructed if having only a few atomic posi- tions from which the rest can be generated. The same, again, goes for magnetic structures, but the symmetry elements used for conventional space groups are not valid to describe magnetic structures. Therefore Shubnikov groups (mag- netic space groups) exist so that magnetic structures can be described in an equivalent way [10].
When describing ferromagnetic structures there are certain directions in the
crystal that will be preferable (energetically) for the alignment of the magnetic
spins. This comes from the coupling mechanisms between the spinning elec-
tron and the crystal electric field. For uniaxial structures this coupling results
in that the magnetic moments are aligning preferably along the uniaxial axis
or in the plane perpendicular to it. If the total magnetic energy for aligning
the magnetic moments is lowest along the uniaxial direction that direction is
called an easy axis. If the energy is lowest for a direction perpendicular to
that axis that is defined as an easy plane. That there are certain directions in a
magnetic structure with lower energy than others is a sign of magnetocrystal-
line anisotropy. The energy it would take to rotate a magnetic moment away from an easy direction (which can be done with large enough external mag- netic fields) is defined as the magnetocrystalline anisotropy energy (MAE).
In bulk samples, with no special shapes, the magnetocrystalline anisotropy is what gives coercivity. The coercivity is defined from the coercive field (H c ), which is the negative field required to demagnetise a hard magnet (figure 1.2).
1.1.2 Permanent magnets
To reduce losses in electric motors, actuators and generators and therefore further a sustainable future society, development of better rare earth free per- manent magnets is a necessity [8]. When quantifying the performance of a magnetic material for permanent magnet applications the saturation magnet- isation and the coercivity are two of the most discussed properties. However, the property that really should be optimised is the energy product (BH max ) of the magnet [11]. BH max is a value of how much energy a permanent magnet can store. Here B is the magnetic flux density, i.e. the magnetisation that a magnet can give away for an area at a given distance from the magnet. The magnetic flux density is related to the magnetisation (M) and magnetic field strength (H) (figure 1.2) via
B = μ 0 (M + H) (1.1)
where μ 0 is the magnetic constant. If a plot of B vs. H would be done, BH max
would be found as the area of the biggest possible rectangle that can be fitted in the demagnetisation curve. To really improve BH max , the remanent magnet- isation (M r ), the magnetisation value at zero applied field after M sat , and the coercivity, all need to be as large as possible. Since coercivity is dependent on the anisotropy in the material anisotropy is studied frequently. Anisotropy in general can come from several things. Thin films have a big directional an- isotropy due to one very short axis, the same goes for needle and disk shaped materials. In such materials the magnetic easy axis tends to be along the needle or out of plane from the disk. In a bulk material without any preferred shape the magnetic moments more easily align themselves along an easy axis (mag- netocrystalline anisotropy). When the magnetocrystalline anisotropy is the dominant anisotropy form it can, for uniaxial materials, be expressed as:
E anis = K 1 cos 2 θ + K 2 cos 4 θ (1.2)
where θ is the angle between the magnetisation and the easy axis of magnet-
isation and K 1 and K 2 are anisotropic constants. Often K 2 << K 1 and the term
K 2 cos 4 θ can therefore be disregarded. The anisotropy energy can be estim-
ated from M vs. H curves with the law of approach to saturation, where K 1 is
often expressed as the effective anisotropy constant (K eff ) [12].
1.1.3 Magnetic refrigeration
Cooling devices, such as refrigerators or air conditioner units, consume lots of energy to keep a constant temperature in their surroundings. If a magnetic cooling device could be used instead the energy consumption could be lowered by 20-30% [13]. A magnetic cooling device exploits the magnetocaloric effect (MCE) [14] which means that the material will change its temperature under the action of a magnetic field under adiabatic conditions. The temperature change upon magnetisation is reversible, meaning that the temperature change will have opposite signs if a magnetic field is applied or removed. The MCE can be quantified with two parameters, the magnetic entropy change ( ΔS mag ) and the adiabatic temperature change ( ΔT ad ) [15]. ΔS mag is the entropy differ- ence for an isothermal field change when exposing the material to a change in magnetic field (H) from an initial field H i to a final magnetic field H f (H i < H f ).
In the same way, ΔT ad is the difference in temperature upon a magnetic field change from H i to H f under adiabatic conditions.
Figure 1.3 shows the concept used in a magnetic cooling device. Initially (1) the magnetic moments are randomly oriented and the temperature is T i . After applying a magnetic field the magnetic moments order (2) and the tem- perature in the material rises. After removal of the heat produced the material is ordered and at T i (3); removing the magnetic field will make the mater- ial disordered and cool down (4). The final step will take heat from inside the refrigerator, which then in turn will cool down, heating the material and therefore close the refrigeration cycle. To avoid energy losses throughout the cooling cycle, soft magnetic materials should be used. The discovery of the giant magnetocaloric effect (GMCE) [16] was a trigger for the research into new sustainable materials for magnetic cooling devices.
1 2
4 3
Expelled Expelled heat
heat Heat load
(refridgerator)
Magnetic field off Magnetic
field on
Figure 1.3. Schematic view of the magnetic refrigeration cycle.
1.2 Studied materials
The materials studied in this thesis are all intermetallic compounds made from abundant and cheap elements. For all applications considered uniaxial crys- talline structures are beneficial, or at least structures with one unique axis that is different from the others. Therefore, tetragonal or hexagonal systems are preferred. However, orthorhombic structures with one unit cell axis that dif- fers significantly from the others will also satisfy the criteria. In the studied systems iron is the main magnetic element and the other elements are there to provide appropriate atomic and magnetic structure and to tune the physical properties.
1.2.1 M 5 XB 2
M 5 XB 2 (M = Mn, Fe, Co and X = P, Si) belongs to a tetragonal material system that crystallises within the Cr 5 B 3 -type structure (space group I4 /mcm) [17, 18] where the c-axis is almost the double length of the a-axis. The general structure is shown in figure 1.4 where the two different metal positions are clearly visible. The two different metallic positions in the crystal structure, one 16-fold, 16l (M(1)), and one in a 4-fold, 4c (M(2)), will affect the magnetic properties individually, especially if substitutions can be made on either of the two sites. The X and B atoms occupy the 4a and 8h positions, respectively.
a b
c
Figure 1.4. The crystal structure of M 5 XB 2 viewed along the a-direction. The different
atomic positions are represented with light brown, dark brown, teal and red for M(1),
M(2), X and B, respectively.
In 1959 [17] studies of Fe 5 SiB 2 had already been performed. It was found that the compound adopts the tetragonal structure described in figure 1.4 [17–
19] with the unit cell parameters 5.5498 and 10.3324 Å for a and c, respect- ively. Later, it was found to be a suitable candidate for studies as a perman- ent magnet material due to its ferromagnetic behaviour below its high Curie temperature of 784 K [20, 21]. Low temperature Mössbauer spectroscopy in- vestigations also indicated that a spin-reorientation occurs at 140 K where the magnetisation falls from the c-axis to the ab-plane, when going down below the spin-reorientation temperature [22].
The sister compound of Fe 5 SiB 2 , Fe 5 PB 2 , was discovered at almost the same time, is slightly smaller due to the size difference of silicon and phos- phorus [19]. Fe 5 PB 2 is also ferromagnetic with T C ranging between 615 and 639 K depending on the composition [23, 24], slightly lower than Fe 5 SiB 2 . Similar to Fe 5 SiB 2 , the magnetic moments were found to point along the tet- ragonal c-direction in Fe 5 PB 2 [20] however, there was no spin reorientation at low temperatures. The composition dependency of T C comes from phos- phorus vacancies or a mixing between phosphorus and boron on the two sites.
This was shown with Mössbauer spectroscopy where the peak due to Fe(1) gets split into two. The magnetocrystalline energy constant (K 1 ) for Fe 5 PB 2 was studied with single crystals and was found to be 0.50 MJm −3 at 2 K [25], too low to give any coercivity suitable for permanent magnetic applications.
To increase the coercivity substitutions that alter the magnetic interactions could be employed. Therefore, the effects have been studied, for the whole range Fe 5 Si 1-x P x B 2 and (Fe 1-x Co x ) 5 SiB 2 , by first principle calculations [26].
Also, experimentally, partial substitutions (Fe 4 CoPB 2 , Fe 4 CoSiB 2 ) [27] have been employed.
1.2.2 AlM 2 B 2
AlM 2 B 2 (M = Cr, Mn, Fe) are compounds with an orthorhombic layered struc- ture (space group Cmmm) where slabs of M 2 B 2 are alternated with sheets of aluminium [28–30]. The layers are stacked along the b-direction in the crystal structure, figure 1.5, which is more than double the length of the a and c axes (for AlFe 2 B 2 it is 2.9233, 11.0337 and 2.8703 Å for a, b and c, respectively [30]), making the structure pseudo-uniaxial. When there is only iron on the metal site it exhibits ferromagnetic behaviour with a Curie transition close to room temperature, ranging between 282 and 320 K [31–
33]. It was also shown that the magnetic transition should be first order [34],
making the compound an interesting candidate for magnetic refrigeration. In
addition, substitutions on the metal site have been performed to study the
changes in magnetic properties. It has been found that for high amounts
of manganese in Al(Fe 1-x Mn x ) 2 B 2 , T C drops drastically, down to 43 K for
Al(Fe 0.4 Mn 0.6 ) 2 B 2 [33]. Also substitutions with cobalt have been tested, even
a b
c
Figure 1.5. The crystal structure of AlM 2 B 2 represented with two unit cells viewed along the c-direction. The different atomic positions are represented with white, brown, and red for Al, M and B, respectively.
though no ternary phase in the Al-Co-B phase diagram has been reported. It was found that T C decreases linearly with cobalt content down to 205 K for Al(Fe 0.7 Co 0.3 ) 2 B 2 [35].
The orthorhombic AlM 2 B 2 structure could also be categorised within a big- ger class of materials, the MAB-phases [36]. Which has big similarities with the more familiar MAX-phases where transition metal-carbides or nitrides are stacked between aluminium layers. The similarity becomes even more ap- parent when comparing the deformation mechanisms. When deformed, the (M 2 B 2 )-slabs in AlM 2 B 2 slides over the Al-layers creating a visible delamina- tion (in an electron microscope) [37]. Also similar to the MAX-phases are the low hardness values (10.4(3), 7.3(3) and 9.5(3) GPa for AlCr 2 B 2 , AlMn 2 B 2 and AlFe 2 B 2 , respectively [37]). These are significantly lower than the typical values for metal borides (20-30 GPa) [38].
1.2.3 Fe 2 P
Fe 2 P crystallises in a hexagonal structure (P¯62m) with two iron and two phos-
phorus sites, figure 1.6 [39]. The four atomic positions in the structure make it
a real playground for chemists to tune the properties via substitutions. Several
different substitutions have been performed to enhance the magnetic prop-
erties, most of which have involved the substitution of iron for manganese
to increase the total magnetic moment, and substituting phosphorus with sil-
c
a b
Figure 1.6. The crystal structure of Fe 2 P with the different atomic positions represen- ted with light brown, dark brown, light purple and dark purple for Fe(1), Fe(2), P(1) and P(2), respectively.
icon or arsenic to enhance T C [40–44]. These substitutions were performed to make the compound more suitable for magnetic refrigeration applications, since pure Fe 2 P has a Curie temperature of 216 K [45], much too low for room temperature applications. At T C , Fe 2 P undergoes a first order magnetic transition with a discontinuity in the unit cell parameters at the transition. The discontinuity is also observable with Mössbauer spectroscopy indicating that the local environment of the iron atoms is changing upon magnetisation [46].
The magnetic moments of the iron atoms are oriented in the hexagonal c-
direction [47] and polarized neutron diffraction experiments have shown that
the magnetic moments are 0.92(2) and 1.70(2) μ B for Fe(1) and Fe(2), respect-
ively [48].
2. Scope of the thesis
”Do what you can, with what you have, where you are.”
- Theodore Roosevelt Motivation of the studies
To understand the magnetic behaviour in a material it is a necessity to first understand the structural properties. The structures (both atomic and mag- netic) will effect how the material behaves when exposed to external stimuli, e.g. magnetic fields. When examining materials for magnetic applications it is therefore of utmost importance to understand not only the macro and micro- structure, but also (and more importantly), the crystalline structure. Therefore, within this thesis, the links between structure and physical properties have been studied, whether it is the magnetic or crystalline structure that effects the magnetic or other, more macroscopic, physical properties (hardness, elasticity etc.).
For these reasons, the crystalline structures have been studied with X-ray diffraction and complementary studies with neutron diffraction have also been performed to investigate the magnetic structures. These analysed structures have been linked to the magnetic properties which mainly have been studied with magnetometry. To achieve a deeper understanding of the results first prin- ciple calculations have been performed when necessary. Complementary tech- niques, such as Mössbauer spectroscopy and inelastic neutron scattering have also been performed to get information that would be hard (or impossible) to get from other techniques.
The results from all studies have been evaluated in a perspective of the de- sired applications, that is permanent magnets or magnetic refrigeration, to see if the material meets the criteria of these applications. However, full focus has not always been upon the applications since the basic scientific understanding has always been highly regarded in the work included in this thesis.
Aim of the thesis
The applications studied within this thesis have been evaluated from a crystal-
lographic perspective. I have focused on uniaxial structures made from cheap
and abundant elements where iron have always been present. The main fo-
cus and goal have always been if the physical properties can be improved by
changing the chemistry of the studied compounds. Therefore, answers for the
questions that arises have been investigated. Typical research questions can
then be formulated, like:
• How is the structure of a compound affected by chemical substitutions?
• How will the magnetism change based on the changed chemistry?
• What parameters are most important for a potential application?
• Can given magnetic parameters be controlled by altering the chemistry?
By trying to answer such questions the focus is shifted away slightly from the
intended application and more towards general science. Therefore, it becomes
more interesting to study the origin of the physical phenomena. For instance,
why a material behaves the way it does under certain conditions (temperat-
ure, mechanical pressure, magnetic changes). One example of this is studying
the origin of the magnetocaloric effect, i.e. why does a material change its
temperature when being subjected to a magnetic field? When answering such
questions the focus shifts to structure-magnetism relations. Relations that are
very important to be aware of if one desires to control the physical properties.
3. Methods
”I solemnly swear that I am up to no good.”
- J.K. Rowling
3.1 Synthesis
All samples in this thesis were prepared with the high temperature synthesis techniques described below. However, a post annealing treatment step was only necessary for the samples discussed in papers IV and V. For the samples in papers I and IV both natural boron as well as isotopically pure 11 B were used.
3.1.1 Arc melting
In an arc furnace an electric arc is produced by a discharge involving a high voltage/low current between two electrodes. The discharge causes gaseous atoms to ionise (a plasma carrying the current). Electrically conducting ma- terials can therefore be melted or rapidly sintered using this technique. All samples in papers I-VI in this thesis were (completely or partially) synthes- ised in an arc furnace, figure 3.1 (a), equipped with a tungsten rod (electrode 1) and a water cooled copper plate (electrode 2) upon which the samples were placed. Argon gas was used as both a protective atmosphere and to produce the current carrying plasma. Upon synthesis the samples were melted and remelted five times and turned in between each melting to ensure maximum homogeneity. To ensure that samples were free from oxygen contaminations a titanium ”getter” was first melted for 5 minutes.
3.1.2 Drop synthesis
For highly volatile elements, such as phosphorus and manganese, arc melting is not a good synthesis option due to the rapid evaporation of these elements.
Therefore, the drop synthesis technique [49], figure 3.1 (b), was instead em-
ployed in papers II, III, and VII. In this technique the non-volatile elements
(e.g. iron) were placed in an alumina crucible and melted in an induction fur-
nace. When the melt was stable small pieces of phosphorus were dropped into
the melt where they reacted instantaneously and the desired compound could
be formed.
(a) (b) (c)
Figure 3.1. Schematic setup for the high temperature synthesis route used in the thesis, including arc melting (a), drop synthesis (b) and heat treatment of a pellet inside an evacuated silica ampoule inside a pit furnace (c).
3.1.3 Heat treatment
Due to the nature of the arc melting technique (which generates very high temperatures and high cooling rates) heat treatment is often necessary to im- prove the crystallinity and phase homogeneity of the samples. Most samples in this thesis were crushed, pressed into pellets and heat treated in evacuated silica ampoules, figure 3.1 (c). Some samples where heat treated as crushed pieces for better evaluation of mechanical properties. To evacuate the silica tubes an oil-vacuum pump was used, the duration of the pumping was at least 30 minutes. Afterwards the tubes were sealed and placed in a pit furnace for the heat treatment. After a sufficient time in the furnace the ampoules were taken out and quenched in water.
3.1.4 Post annealing treatments
For the samples in papers IV and V and a post annealing treatment was ne- cessary to enhance the phase purity. This was done by etching the samples in ∼6 mol/dm 3 hydrochloric acid (HCl) for ten minutes. By doing this the amount of secondary phases in the samples could be reduced.
3.2 Diffraction
X-ray diffraction (XRD) is one of the most commonly used techniques when
studying condensed matter, especially crystalline materials. The diffraction
phenomenon was discovered in 1912 [9] when X-rays were diffracted by a
diamond crystal. The technique is based on waves that scatter elastically from
a sample. If the sample is ordered in any way (long range or short range) con-
structive and destructive interference will occur and give a recordable pattern,
a diffraction pattern. The wavelength, λ, of the incoming wave should be well
defined and of the same length scale of the ordered objects to be studied. Dif- fraction is, however, not only a X-ray method. It also works with electrons or neutrons, if they are accelerated to suitable velocities (due to the particle/wave duality).
Diffraction conditions
A crystal can be completely described as a repetition in all dimensions of the smallest unit that contains all of the crystals symmetry elements. This smallest unit is called the unit cell. The dimensions of the unit cell can be described with 6 parameters, 3 unit cell edges (a, b and c) and the angles between them (α, β and γ). If a transformation from direct space into reciprocal space is performed the crystal structure will be transformed into a reciprocal lattice (a set of mathematical points). The reciprocal unit cell can be described with the reciprocal vectors (a ∗ , b ∗ and c ∗ ) where |a ∗ | = 1/a, |b ∗ | = 1/b and |c ∗ | = 1/c.
The scattering that occurs inside the crystal can be described by waves that scatter from the reciprocal lattice. Scattering of an incident wave can occur from any point in the reciprocal lattice and in all directions. However, to obtain constructive interference producing a Bragg peak the scattered wave must hit a lattice point on the surface of a sphere (named the Ewald sphere) from the point of scattering where the radius hits the origin of the reciprocal lattice. This is illustrated in two dimensions in figure 3.2 but is also valid in three dimensions. The radius of the Ewald sphere is 1/ λ and that is equal to the length of both the incident beam (k 0 ) as well as the scattered beam (k 1 ), hence
|k 0 | = |k 1 | = 1/λ (3.1)
is valid. The angle and the length of the vector between k 0 and k 1 are 2 θ and d ∗ hkl (marked in red in figure 3.2) respectively. This infers that the distance between the origin and the diffracted lattice point is d ∗ hkl in reciprocal space, which would correspond to d hkl in normal space ( |d ∗ hkl | = 1/d hkl ). If normal vector addition is performed for k 1 it is found that
k 1 = k 0 + d ∗ hkl (3.2)
which also gives
|k 1 |sinθ = |k 0 |sinθ = 1
2 |d ∗ hkl | (3.3)
and with some rearrangement gives
2d hkl sin θ = λ (3.4)
which is well known as the Bragg equation, or Bragg’s law. If a fixed wavelength experiment is performed, the lattice points that intersects the Ewald sphere will show up when the angle is scanned in a diffraction experiment. From equa- tion 3.4 the distance between the planes of lattice points can also be extracted, since
d ∗ hkl = ha ∗ + kb ∗ + lc ∗ (3.5)
Origin Incident
beam
Diffracted beam
1/λ k0
kf 2θ d*
Figure 3.2. The basics of the diffraction phenomena with the circle giving a two dimensional cut of the Ewald sphere.
where h, k and l are integers indexing the lattice planes that the diffracted peak belongs to.
Structure factor
From equation 3.4 the lattice parameters can be determined but this does not show where the atoms are located. For that the relative intensities in a diffrac- tion pattern needs to be taken into consideration. The intensity is proportional to the scattering power of the atoms in the structure. The scattering power in the crystal can be described with the structure form factor, F hkl :
F hkl = ∑ n
j =1
g j t j
sin θ hkl
λ
f j
sin θ hkl
λ
e 2 πi(hx
j+ky
j+lz
j) (3.6)
where n is the total number of atoms; θ hkl and λ are the angle and wavelength respectively; g j , t j
sin θ
hklλ
and f j
sin θ
hklλ
are the occupation, the displace- ment and the atomic scattering factor for the j th atom while x j , y j and z j are the fractional coordinates for the j th atom. The factor f j
sin θ
hklλ
is highly dependent on the radiation used in the experiment.
X-rays vs. neutrons
X-rays interact with the electrons of the atoms in a sample. An effect of this is that the scattering power will be stronger the more electrons the atoms have, which can be seen in the upper part of figure 3.3. As a consequence, heavy elements will scatter stronger than light elements which makes it hard to crys- tallographically locate light elements (e.g. H, Li, B), especially in a structure containing heavy elements.
If neutrons are used instead of X-rays different results will be obtained.
Since neutrons mainly interacts with the nuclei of the atoms and therefore
X-rays
Neutrons
H D Li O Al Si Mn Fe
Figure 3.3. The difference in elastic coherent cross section of X-rays (upper) and neutrons (lower). The green and red colours for neutron scattering correspond to the negative and positive scattering lengths respectively.
are sensitive to isotopic differences (compare hydrogen and deuterium in fig- ure 3.3). Figure 3.3 also shows a that the scattering power for different nuc- lei appears more random for neutrons, and the scattering length can even be negative (due to a phase shift of the beam). This randomness is not only ob- served for the scattering cross section, but also for the absorption cross section, which can also be seen for different isotopes of the same element, for example boron. The isotope 10 B has an absorption cross section value of 3835 barn (1 barn = 10 −28 m 2 = 100 fm 2 ) compared to the 11 B-isotopes absorption of 0.0055 barn, making the absorption cross section value for natural boron (with 20% 10 B) 767 barn. An effect of this is that isotopically pure 11 B is preferred when performing an experiment with neutrons. Another characteristic of neut- rons (except for them having no electronic charge) is their magnetic moment.
Therefore they can interact with magnetic electrons in a sample and is an ex- cellent tool for mapping magnetic structures and effects in a sample.
3.3 Characterisation by diffraction techniques
3.3.1 X-ray powder diffraction
The XRD experiments were performed with two different set-ups, one in- house and one synchrotron based. The in-house experiments were performed with a Bruker D8 diffractometer equipped with a Lynx-eye position sensitive detector (PSD, 4 ◦ opening) using CuKα 1 radiation (λ = 1.540598 Å). This set-up also have the possibility to vary the temperature from 16 K to 300 K, making temperature dependent XRD experiments possible.
The synchrotron based experiments were performed at the I711 beamline
[50] at the Max II synchrotron of the Max IV laboratory (Lund, Sweden). The
high resolution XRD-patterns were recorded in transmission mode, at 298 K,
in 0.3 mm spinning capillaries, using a Newport diffractometer equipped with
a Pilatus 100K area detector mounted 76.5 cm from the sample (λ = 0.9940 Å).
The detector was scanned continuously, from 5 ◦ to 125 ◦ in approx. 6-10 min, recording 62.5 images/ ◦ (step size 0.016 ◦ ) for each measurement. The true 2 θ position of each pixel was recalculated, yielding an average number of 100000 pixels contributing to each 2 θ value. Integration, applying no correc- tions for the tilt of the detector, provided FWHM values of 0.03-0.08 ◦ from 5 to 125 ◦ .
3.3.2 Neutron powder diffraction
To study magnetic structures neutron powder diffraction (NPD) experiments were performed in double-walled, cylindrical, vanadium containers. This con- tainer shape was used to minimise absorption from boron in the sample.
Diffraction patterns were recorded at the D1B instrument at ILL (Grenoble, France). A pyrolytic graphite monochromator (reflection 002) was used, giv- ing a wavelength of 2.52 Å.
3.3.3 Determination of lattice parameters
Lattice parameters can be determined from the peak positions of a diffraction pattern if the Bravais lattice is known. Determination of the lattice parameters is done via a least square fit of the expected peak positions (calculated with Bragg’s law, equation 3.4) to the observed peaks. In this thesis, the program UnitCell [51] was used to precisely determine the lattice parameters.
3.3.4 Full pattern refinement using the Rietveld method
To determine the contents of a unit cell of a structure that is at least partially known a full pattern refinement can be used. This was first done in 1969 by H. M. Rietveld [52], and hence this method is often called the Rietveld method. The method refines a calculated pattern to an experimental diffraction pattern by fitting the structural and profile parameters using the least square method [53].
In agreement with Bragg’s law (equation 3.4) peaks should appear at given positions, however, that is not always the case. This is due to imperfections in the experimental set-up, such as sample displacement or absorption. This makes determination of background and instrumental parameters necessary in the refinement process. The integrated peak intensities (I hkl ) are dependent of F hkl (for a definition of F hkl see equation 3.6) and a number of other parameters and are calculated as:
I hkl = Kp hkl L θ P θ A θ T hkl E hkl |F hkl | 2 (3.7)
where K is a constant known as the scale factor that is proportional to the
amount of the phase, measurement time and the flux of the incident radiation;
p hkl is the multiplicity for the specific reflection; L θ , P θ and A θ are multipliers that correct for geometry, partial polarisation of the scattered electromagnetic wave and absorption of both the incident and diffracted beam; T hkl is the pre- ferred orientation factor and E hkl is an extinction multiplier (which is usually not important for small crystals.
The shape of the peaks are often described with a Voigt profile, a convolu- tion of a Gaussian and a Lorentzian function. Due to computational expense a pseudo-Voigt function is normally used which is a linear combination of the Gaussian and the Lorentzian functions. The width of the peaks is defined at half intensity of the peak, or the full width at half maximum (FWHM), and is dependent of θ according to:
FW HM =
U tan 2 θ +V tanθ +W (3.8) where U , V and W are constants.
As a reference to how good a refined pattern is compared to the experi- mental diffraction pattern a number of agreement indices (or R values) are obtained in the refinement [54]. The weighted-profile R value, R wp , is defined as:
R wp =
∑ i
w i [y i (obs) − y i (calc)] 2 / ∑
i
w i [y i (obs)] 2
1 /2
(3.9) where y i (obs) and y i (calc) are the observed and calculated intensity at step i and w i is the weight. In an ideal Rietveld refinement the R wp should approch the statistically expected R value, R exp :
R exp =
(N − P)/ ∑ N
i
w i y i (obs) 2 1 /2
(3.10) where N is the number of observations and P the number of refined parameters.
R exp is a value for the quality of the data and the ratio between R exp and R wp
gives another goodness-of-fit parameter, χ 2 ,
χ 2 = R wp /R exp (3.11)
which should approach 1. However, this is not always the case, e.g. if the data have been ”over-collected” (R exp is very small) then χ 2 will be much larger than 1 even though the refinement is very good. In this thesis all structural (nuclear and magnetic) determination and phase analyses were done using the program FullProf [55].
3.3.5 Representational analysis
Determinations of magnetic structures can be very time consuming if done by
trial and error. If a systematic approach is applied, so that only magnetic struc-
tures based on symmetry requirements are tested, the number of possibilities
can be reduced. This is done with representational analysis (RA) based on the Landau thermodynamic theory of second-order transitions [56] and involves the systematic decomposition of a magnetic representation Γ into irreducible representations (IR) of the space group. The number of magnetic structures allowed by symmetry will be the number of all non-zero IR in the final de- composition of Γ. In this thesis the magnetic space groups in papers I, IV and VII were found with the program SARAh [57].
3.4 Inelastic neutron experiments
To study dynamical effects (e.g. vibrations) in a sample diffraction techniques is not a good tool, therefore spectroscopic methods are necessary. One spec- troscopy method, using neutrons, for identifying crystal as well as magnetic vibrations is inelastic neutron scattering (INS). In INS a sample is placed in a neutron beam where the sample-neutron interaction is, as suggested by the name, inelastic. The incoming neutron can give or lose energy to the sample, and the energy gain or loss can be detected by measuring the neutrons flight time from the sample to the detector. By doing this the intensity of scattered neutrons can be measured both as a function of scattering angle and energy.
Around zero energy (no interaction with the sample) the elastic line can be extracted (with the same characteristics as a ”normal” diffraction pattern), and at non-zero energies other phenomena can be recorded. In paper VII this was done to record the temperature dependence of the crystalline (phonons) and magnetic (magnons) vibrations. These experiments were performed at the in- struments IN5 (ILL, Grenoble, France) and TOFTOF (MLZ, Hamburg, Ger- many) at different wavelengths to get different energy resolutions.
3.5 Magnetic characterisations
Magnetometry is a common method to determine the magnetic properties of a
sample. If a magnetic sample passes through a coil it will induce an elec-
tric current that can be measured. This can be done with either a vibrat-
ing sample magnetometer (VSM) or a superconducting quantum interference
device (SQUID). In the VSM the sample is vibrating inside an electromag-
net which records a current proportional to the magnetic moment. A SQUID
measures the magnetic moments based on the quantisation of magnetic flux in
a closed loop of superconducting materials using Josephson junctions. While
a VSM is more easily available a SQUID has a benefit of higher probing fields
since it is based on superconducting magnets. However, the SQUID has to
be cooled down using liquid Helium, making it more expensive and requiring
more care.
Since magnetisation (M) is dependent on both temperature (T) and applied magnetic field (H), M = f (H,T), it is useful to measure M as a function of H (T) at a constant T (H). From measurements versus temperature magnetic ordering temperatures, T C or other magnetic transitions, can be determined.
For field dependent measurements properties like M sat , M r and H c can be ex- tracted directly from the magnetic hysteresis curve. Also anisotropy constants can be estimated using the M vs. H curves. ΔS mag can also be calculated from a number of M vs. H curves at different temperatures close to the Curie transition using
ΔS mag = μ 0 H
fH
i∂M
∂T
H
dH (3.12)
based on the Maxwell relations. In this thesis magnetic measurements were performed with using a LakeShore 7400 VSM equipped with a high temper- ature option, a Quantum Design PPMS using the VSM option or a Quantum Design MPMS SQUID magnetometer.
3.6 Mössbauer spectroscopy
Mössbauer spectroscopy (MS) is based on the recoil-free absorption and emis- sion of γ-rays from nuclei in solids [58]. When a γ-photon emitted from a γ-ray source hits a Mössbauer active nuclei in a solid it might be absorbed if the energy of the γ-photon is right. The nuclei then gets excited and can emit a γ-photon of the same energy, since the position of the nuclei is locked in the solid the recoil for sending out the γ-photon is taken up by the whole crystal.
The reemitted γ-photon can then be detected to record a Mössbauer spectrum.
One common nuclei for this is 57 Fe, an isotope suitable although its low nat- ural abundance (2.2%). A γ-photon emitter with the right energy for 58 Fe is
57 Co. Iron MS is a powerful technique since it is sensitive to the chemical environment of the Fe-atoms. Different crystallographic environments gives different peaks in the spectrum, and also, the local environments give splitting of the peaks (quadrupole splitting) to a doublet-peak. Also magnetic splitting can occur if the Fe-atoms are magnetically ordered. This will be seen as a sextet peak due to the hyperfine splitting. All these split peaks can be used to extract information about the local and magnetic environments in the sample [59]. In papers III, V and VII Mössbauer absorption spectra were obtained with a spectrometer equipped with a constant acceleration type vibrator and a
57 CoRh γ-ray source.
3.7 Electronic structure calculations
To further try to understand solid magnetic systems theoretical modelling is a good tool. This is performed by solving the Schrödinger equation for the sys- tem. However, since exact solutions for is not available for systems with more than one electron models for the Hamiltonian are necessary. Density func- tional theory (DFT) provides a way to model large systems computationally by replacing the complex wavefunctions with electron densities and thereby reducing the computational complexity of the calculations. The electronic and magnetic properties in this thesis (papers II-IV) were modelled with DFT calculations in the generalized gradient approximation (GGA) [60] using the spin polarised relativistic Korringa-Kohn-Rostoker (SPR-KKR) method [61].
Curie temperatures were also estimated with theoretical calculations using
Monte Carlo (MC) simulations [62] (papers II and III). To calculate theoret-
ical phonon spectra in paper VII, first principles calculation using the projector
augmented wave method as implemented in the Vienna Ab initio Simulation
Package (VASP) have been performed [63].
4. Results and discussion
”If you can’t explain it to a six year old, you don’t understand it yourself.”
- Albert Einstein
4.1 M 5 XB 2
The tetragonal compounds M 5 XB 2 (M = Mn, Fe, Co and X = P, Si) were investigated as starting point for new potential permanent magnet materials.
This tetragonal, and therefore uniaxial, structure, figure 1.4, with its two metal positions, is an interesting system with respect to high Curie temperatures and ferromagnetic behaviour for high iron concentrations.
4.1.1 Magnetic structure of Fe 5 SiB 2
The first material to be synthesised in the M 5 XB 2 system was Fe 5 SiB 2 . It was chosen for its high T C and large magnetisation. Therefore this was the subject of study in paper I. Since earlier Mössbauer studies had indicated a spin reorientation at low temperatures [22] two samples were synthesised, one with boron with extremely high chemical purity and one with isotopically pure
11 B. In both cases arc melting followed by prolonged heat treatments were used for the synthesis, figure 3.1. Synthesis of the 11 B sample was done be- cause of the high neutron absorption in 10 B and could therefore be used for neutron diffraction experiments. The two high resolution XRD patterns for the two samples, figure 4.1, reveal that the desired main phase is obtained for both samples. There is, however, a secondary phase in both samples. The sample with natural boron contains Fe 3 Si (<2%) and the 11 B sample contains Fe 4.7 Si 2 B ( ∼5%). The wight percents of the secondary phases come from the Rietveld refinements.
When examining the magnetic behaviour as a function of temperature, fig-
ure 4.2, it was found that the Curie temperature was indeed as high as in
previous studies [20, 21] with a value of 760 K. Also, as seen earlier with
Mössbauer spectroscopy [22], a strange magnetic behaviour was observed at
low temperatures. In figure 4.2 this can be seen as a kink in the magnetisa-
tion curve centred around 172 K. With low temperature XRD no structural
transition could be observed, except for the expected shrinking of the unit cell
upon cooling, and hence, the transition observed from magnetometry can be
concluded to be a pure magnetic reordering.
(a) (b)
