Structure-Magnetism Relations in Selected Iron-based Alloys: A New Base for Rare Earth Free Magnetic Materials

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Structure-Magnetism Relations in Selected Iron-based Alloys

A New Base for Rare Earth Free Magnetic Materials

Licentiate Thesis

Johan Cedervall

Department of Chemistry – Ångström Laboratory

Uppsala University, 2015

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Abstract

Materials for energy applications are of great importance for a sustainable future society. Among these, stronger, lighter and more efﬁcient magnetic materials will be able to aid mankind in many applications for energy conversion, for example generators for energy production, electric vehicles and magnetic refrigerators. Another requirement for the materials is that they should be made from cheap and abundant elements. For these reasons temperature induced magnetic transitions for three materials were studied in this work; one for permanent magnet applications and two magnetocaloric materials.

Fe ₅ SiB 2 has a high Curie temperature and orders ferromagnetically at 760 K, providing possible application as a permanent magnet material. The ordering of the magnetic moments were studied and found to be aligned along the tetragonal c-axis and Fe 5 SiB 2 undergoes a spin transition on cooling through a transition temperature (172 K), where the spins reorient along the a-axis in an easy plane.

AlFe ₂ B ₂ orders ferromagnetically at 285 K, making it a candidate for the active material in a magnetic refrigerator. The order of the magnetic transition has been studied as well as the mag- netic structure. It was found that the magnetic moments are aligned along the crystallographic a-axis and that the magnetic transition is of second order.

FeMnP 0 .75 Si 0 .25 undergoes a ﬁrst order magnetic transition around 200 K and the transition

temperatures on cooling are different for the ﬁrst cooling/heating cycle than for following cy-

cles. This so called ”virgin effect” has been studied and found to originate from an irreversible

structure change on the ﬁrst cooling cycle through the ferromagnetic transition temperature.

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”I love deadlines. I like the whooshing sound they make as they ﬂy by.”

- Douglas Adams

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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.

Submitted

II 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.

Submitted

III Irreversible structure change of the as prepared FeMnP 1 −x Si _x - structure 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)

Reprints were made with permission from the publishers.

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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 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 III. I performed all structural characterisation and took part in the dis- cussions and writing of the manuscript.

Other publications to which the author has contributed.

Phase diagram, structures and magnetism of the FeMnP 1 −x Si _x -system V. Höglin, J. Cedervall, M. S. Andersson, T. Sarkar, M. Hudl, P. Nordblad, Y.

Andersson, M. Sahlberg

RSC Advances, 5, 8278-8284 (2015)

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Abbreviations

A list of the abbreviations used in this thesis:

ΔS mag Magnetic entropy change DFT Density functional theory FWHM Full width at half maximum H Magnetic ﬁeld strength H c Coercive ﬁeld

IR Irreducible representations

μ B Bohr magnetron

M Magnetisation

M sat Saturation magnetisation MCE Magnetocaloric effect

MPMS Magnetic property measurement system NPD Neutron powder diffraction

PPMS Physical property measurement system RA Representational analysis

RT Room temperature

SQUID Superconducting quantum interference device T c Curie temperature

VSM Vibrating sample magnetometer

XRD X-ray diffraction

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1. Introduction

The study of materials and their properties has been ongoing for as long as the existence of mankind itself. Already during the the stone age, men used stones as materials for tools to improve their lives. However, better tools could be made when man learned to melt copper and tin to make bronze ( ∼2000 B.C.) [1]. Since then alloys and compounds have played an integral role in creating the society that we have today.

Intermetallic compounds are compounds with metallic bonding and with different a crystal structures than the respective crystal structures of the origi- nal elements [2]. In the binary phase diagram for iron and silicon different in- termetallic 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 dif- fers from the starting elements and the physical properties of intermetallics are therefore also interesting to study. Some of the many interesting applications for intermetallic compounds include hydrogen storage, superconductivity, en- ergy storage (e.g. batteries) and magnetism [4]. Magnetism is included among the applications due to the fact that intermetallic compounds often are com- posed of metallic atoms, or ions, that have magnetic moments.

1.1 Magnetic materials

Magnetism is an invisible force that since ancient times has fascinated and

puzzled mankind. Even today most people use magnets daily without even

knowing so: in hard disk drives, electric motors and generators to mention

a few applications [5]. In a magnetic material the magnetic properties come

from unpaired electrons that are rotating and thus inducing a magnetic mo-

ment [6]. The magnetic moments of these unpaired electrons can either be

unaffected by each other and point randomly in space, that is paramagnetism,

or couple to each other. The coupling can, in the simplest way, be with all

moments in parallel to each other, a phenomenon called ferromagnetism and

the material is said to be ferromagnetic. The spins can also couple in anti-

parallel with each other and the total magnetisation will then be zero. This

is called anti-ferromagnetism. A special case of anti-ferromagnetism is ferri-

magnetism, which has the same coupling mechanism as anti-ferromagnetism

but non-equal magnitude of the magnetic moments for the different directions,

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H

_c

M

r

Applied magnetic field Magnetisation

M

_sat

Figure 1.1. Schematic magnetisation loops for hard magnets (red curve) and soft magnets (black curve).

which in turn gives the material a net-magnetisation. For the applications stud- ied in this thesis only ferromagnetic materials are considered.

With increasing temperature a ferromagnetic material loses its magnetisa- tion and the material becomes paramagnetic. The point when this happens is referred to as the Curie point or Curie temperature (T c ).

Ferromagnetic compounds is often divided into two categories; hard and soft magnets. The difference becomes apparent when the hysteresis loop, ob- tained from plotting magnetisation as a function of applied magnetic field, is studied, see figure 1.1. The hard magnet (red curve) has a broad hysteresis when sweeping the magnetic field, whereas the soft magnet (black curve) in- creases its magnetisation linearly up until the point where the magnetisation is saturated (M sat ).

Today magnets are used in a large number of applications, not only to hold postcards and notes on peoples refrigerators. For hard magnets the main uses are in energy applications, e.g. generators harvesting energy from wind or wa- ter, or in electric vehicles [7]. Soft magnets are used in the same applications as hard magnets to enhance the magnetic properties, but also in transform- ers (as magnetic shielding) and for magnetic cooling. This makes all types of magnetic materials important for efﬁcient energy production and consumption [7].

1.1.1 Magnetostructural properties

Below the ordering temperature in a crystalline magnetic compound the mag-

netic moments can have long-range order, e.g. repetitions of the magnetic

spins are formed with a regular periodicity. This way a magnetic unit cell is

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formed and for commensurate structures the magnetic unit cell can coincide, or be related to an integer number of the crystalline unit cell. If the number of crystalline unit cells to describe the magnetic unit cell is not an integer the structure is said to be incommensurate. The symmetry elements used for con- ventional space groups are not valid to describe magnetic structures, but there is a convention to use Shubnikov groups (magnetic space groups) instead.

To minimise the energy of the system in a ferromagnetic compound the magnetic spins arrange (in a uniaxial structure) either along the easy axis or in the basal plane (called an easy plane). The nature of an easy axis or plane is related to the magnetocrystalline anisotropy energy which comes from the coupling mechanisms between the magnetic spins and the electrons orbital.

The anisotropic energy is the basis for magnetic hysteresis.

Upon cooling below the magnetic ordering temperature the sample struc- ture changes (mainly the magnetic structure) and while warming the original structure should be restored. However, sometimes that is not the case and an irreversible structure change takes place during the ﬁrst (and only the ﬁrst) cooling process. This is often refereed to as a ”virgin effect” for the material.

1.1.2 Permanent magnets

To reduce losses in electric motors, actuators and generators and to therefore further a sustainable future society, development of better rare earth free per- manent magnets is a necessity [7]. To make better permanent magnets the magnets energy product (BH _max ) must be optimised for a hard magnetic ma- terial [8]. Addressing that task requires improvements in both the remanent magnetisation (M _r ), figure 1.1, the magnetisation curve at zero applied field after M sat , and the coercive field (H c ), i.e. the applied negative field where the magnetisation is zero. Anisotropy in a magnet is an interesting to study since H _c is anisotropy dependent. 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 (1.1) where θ is the angle between the magnetisation and the easy axis of magneti- sation 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 eliminated. The anisotropy energy can be estimated from M vs. H curves with the law of approach to saturation [9].

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 % [10]. A magnetic cooling device exploits the magnetocaloric effect

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1 2

3 4

Expelled Expelled heat

heat Heat load

(refridgerator)

Magnetic field off Magnetic

field on

Figure 1.2. Schematic view of the magnetic refrigeration cycle.

(MCE) [11]. The MCE can be quantiﬁed with two parameters, the magnetic entropy change ( ΔS mag ) and the adiabatic temperature change ( ΔT ad ) [12].

ΔS mag is the entropy change 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 1.2 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 material disordered and cool down (4) taking heat from inside the refrigerator which then in turn will cool down, closing the cycle. To avoid energy losses through- out the cooling cycle, soft magnetic materials should be used. The discovery of the giant magnetocaloric effect (GMCE) [13] was a trigger for the research into new sustainable materials for magnetic cooling devices.

1.2 Studied materials

The materials studied in this thesis are all intermetallic compounds made from abundant and cheap elements. The main magnetic element is iron and the other elements are there to provide appropriate atomic and magnetic structure and, in paper III, to tune the physical properties.

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1.2.1 Permanent magnet materials

In this thesis one material, Fe 5 SiB 2 has been studied with the aim of using this as a permanent magnet. The magnetic structure as well as its magnetic properties have been investigated.

Fe 5 SiB 2

Fe 5 SiB 2 is a tetragonal intermetallic compound which was the focus for the study in paper I. Its discovery was made in 1959 [14], when the ternary com- pounds in the Fe-Si-B system were investigated. Fe ₅ SiB ₂ crystallises within the Cr 5 B 3 -type structure [14, 15] with the space group I4/mcm [16]. The unit cell is elongated, with the tetragonal c-axis longer than the a-axis (unit cell pa- rameters: a = 5.5498 Å and c = 10.3324 Å), and early Mössbauer spectroscopy studies showed that the compound is ferromagnetic below 784 K [17, 18]. Low temperature Mössbauer investigations 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 [19]. The high Curie temperature and the uniaxial crystal structure makes this material a good candidate for permanent magnetic applications.

1.2.2 Magnetocaloric materials

Two material systems have been studied within this thesis for magnetic re- fridgeration, one compound of the hexagonal Fe ₂ P-type and one layered or- thorhombic compound from the AlM ₂ B ₂ -class materials.

AlM 2 B 2

The AlM 2 B 2 (M = Fe, Mn, Cr) are compounds in which layers of aluminium are alternating with slabs of (M 2 B 2 ) along the b-axis in the orthorhombic space group Cmmm [20, 21, 22, 23]. The unit cell parameters have, in previous in- vestigations of AlFe 2 B 2 , been determined to be 2.9233, 11.0337 and 2.8703 Å for a, b and c respectively [20]. The magnetic properties has also been studied and the Curie temperature has been found to vary from 282 to 320 K [21, 22, 23] with an entropy change of -4.1 and -7.7 J/K kg at an applied magnetic ﬁeld of 1600 and 4000 kA/m, respectively [22]. The magnetic mo- ment on the iron site has been estimated from magnetisation measurements to be within 0.95-1.25 μ B /Fe-atom. The suggested ﬁrst-order magnetic tran- sition of this compound [24] makes it an interesting candidate for magnetic refrigeration purposes.

FeMnPSi

Another group - or class of materials studied for magnetocaloric purposes in-

cludes compounds of the hexagonal Fe 2 P type [25]. With substitutions of the

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constituent elements for manganese and silicon, compounds of the composi- tion (Fe 1 −x Mn x ) 2 P 1 −y Si y can be studied. Previous studies of these materials have shown tunability of the Curie temperature and the magnetic properties, including the direction and order of the magnetic moments [26, 27, 28, 29].

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2. Aims

The aims of this thesis were to investigate the crystalline and magnetic struc- ture transitions induced by temperature. The magnetic properties were also investigated to obtain a better understanding of what happens during the mag- netostructural transitions. These studies have been performed to gain valuable knowledge for the intended applications for the investigated materials. The goal for the investigated materials are that they potentially can be used as new materials for two different applications; permanent magnets and magne- tocaloric materials.

Magnetostructural transition in Fe 5 SiB 2

Fe ₅ SiB 2 is a ferromagnetic compound with uniaxial structure which undergoes two magnetic transitions. The magnetic structures of this compounds have been determined as well as the transitions themselves. Also the possibility of using this material as a permanent magnetic material has been studied.

Magnetic structure of AlFe 2 B 2

AlFe ₂ B ₂ is a new class of materials exhibiting the magnetocaloric effect. The aim of this study was to determine the magnetic structure and what type of magnetostructural transition takes place at the transition temperature. Also the magnetocaloric properties have been examined.

Virgin effect in the FeMnPSi-system

Fe ₂ P-based compounds are magnetocaloric materials with tunable magne- tocaloric properties with respect to composition. In this project the aim was to investigate the change in T c and crystalline structure as a function of cooling cycles, especially the shift after the ﬁrst cooling cycle was examined.

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3. Methods

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 paper II. For the samples in paper I and II 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 paper I and II in this thesis were arc melted in an arc furnace, see 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 used in paper III, arc melting is not a good synthesis option due to the rapid evaporation of these elements. Therefore, the drop synthesis technique [30] was employed instead, see ﬁgure 3.1 (b). In this technique the non-volatile elements (iron and silicon) were placed in an alumina crucible and melted in an induction furnace.

When the melt was stable small pieces of phosphorous and manganese were dropped into the melt and reacted instantaneously.

3.1.3 Heat treatment

Due to the nature of the arc melting technique (which generates very high tem-

peratures and high cooling rates) heat treatment is often necessary to improve

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(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).

the crystallinity and phase homogeneity of the samples. All samples in this thesis were crushed, pressed into pellets and heat treated in evacuated silica ampoules, see ﬁgure 3.1 (c). To evacuate the silica tubes an oil-vacuum pump was used, the duration of the pumping was at least 0.5 hours. 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 brine.

3.1.4 Post annealing treatments

For the samples in paper II a post annealing treatment was necessary to en- hance the phase purity. This was done by etching the samples in ∼6 mol/cm ³ hydrochloric acid (HCl) for ten minutes. By doing this the amount of sec- ondary 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 for crystalline materials. The diffrac- tion phenomenon was discovered in 1912 [31] 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) constructive and destructive interference will occur and give a recordable pat- tern, 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.

Diffraction is, however, not only a x-ray method. It also works with elec- trons or neutrons, if they are accelerated to high enough velocities (due to the particle/wave duality).

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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 pruducing 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 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 wave- length experiment is performed, the lattice points that intersects the Ewald sphere will show up when the angle is scanned in a diffraction experiment.

From equation 3.4 the distance between the planes of lattice points can also be extracted, since

d ^∗ _hkl = ha ^∗ + kb ^∗ + lc ^∗ (3.5) where h, k and l are integers indexing the lattice planes that the diffracted peak belongs to.

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Origin Incident

beam

Diffracted beam

1/λ k0

k^f 2θ d*

Figure 3.2. The basics of the diffraction phenomena with the circle giving a two dimensional cut of the Ewald sphere.

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 need 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 _λ ^θ

^hkl

) and f ^j ( ^sin _λ ^θ

^hkl

) are the occupation, the displacement and the atomic scattering factor for the j ^th atom while x ^j , y ^j and z ^j are the frac- tional coordinates for the j ^th atom. The factor f ^j ( ^sin _λ ^θ

^hkl

) 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 different results will be obtained compared to with x-

rays. Neutrons interact mainly with the nuclei of the atoms and are sensitive

to isotopic differences (compare hydrogen and deuterium in ﬁgure 3.3). Dif-

ference isotopes of the same element can also have different absorption coef-

ﬁcients, which is the case for boron. The isotope ¹⁰ B has a absorption value of

3835 compared to the ¹¹ B-isotopes absorption of 0.0055, making the absorp-

tion value for natural boron (with 20% ¹⁰ B) 767. In ﬁgure 3.3 the scattering

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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.

power for different atoms appears more random for neutrons, and the scatter- ing length can even be negative (due to a phase shift of the beam). Neutrons also have a magnetic moment and therefore interact with unpaired electrons, making neutrons sensitive to magnetism.

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 CuK α 1 radiation ( λ = 1.540598 Å). This setup also hava 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 [32] 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 corrections 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-

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tainer shape was used to minimise absorption from boron in the sample. Diffrac- tion patterns were recorded at the D1B beamline at ILL (Grenoble, France). A pyrolytic graphite monochromator (reﬂection 002) was used, giving a wave- length 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 [33] was used to 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 [34], 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 [35].

In agreement with Bragg’s law (equation 3.4) peak positions should appear, however, that is not always the case. This is due to imperfections in the ex- perimental set-up, such as sample displacement or absorption. This makes determination of background and instrumental parameters necessary in the re- ﬁnement 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 corrects 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, that is a

convolution of a Gaussian and a Lorentzian function. Due to computational

expense a pseudo-Voigt function is normally used which is a linear combi-

nation 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

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(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 experimen- tal diffraction pattern a number of agreement indices (or R values) are obtained in the refinement [36]. 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 [37].

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 [38] 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 paper I and II were found with the program SARAh [39].

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3.4 Magnetic characterisations

Superconducting quantum interference device (SQUID) magnetometry is a common method for magnetic characterisations. A SQUID uses the quan- tisation of magnetic flux in a closed loop of superconducting materials us- ing Josephson junctions to measure the magnetic fields. Since magnetisa- tion (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). In this thesis magnetic measurements were performed with a Quan- tum Design PPMS using a vibrating sample magnetometer (VSM) option or a Quantum Design MPMS SQUID magnetometer.

3.5 Electronic structure calculations

Density functional theory (DFT) is a purely theoretical method that can be used to calculate physical properties of compounds using quantum physics.

The electronic structure and the magnetic properties of AlFe 2 B 2 in paper II were calculated using the spin polarised relativistic Korringa-Kohn-Rostoker (SPR-KKR) method [40].

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4. Results and discussion

This section has been divided into two main parts; the ﬁrst one focusing on permanent magnetic materials and the second one on magnetocaloric mate- rials. In the ﬁrst part, the results of paper I on the compound Fe ₅ SiB ₂ are summarised. The second part is divided in two subparts, one on AlFe 2 B 2

(paper II) and one on the FeMnPSi-system (paper III).

4.1 Permanent magnet materials

Of the studied materials included in this thesis one is aimed to be used as a new material for permanent magnet applications. This material is the fer- romagnetic compound Fe 5 SiB 2 , which has a high concentration of magnetic iron atoms and a uniaxial unit cell suitable as an easy axis for the magnetic moments. One unit cell contains 4 formula units of Fe 5 SiB 2 which in turn means that the cell contains 20 iron atoms that can contribute to the total mag- netisation. The iron atoms are located at two different sites in the structure, Fe1 at the 4c site (0, 0, 0) and Fe2 at the 16l site (x, x + ¹ ₂ , z).

4.1.1 Fe ₅ SiB ₂

Fe ₅ SiB 2 has been investigated with focus on the magnetic structure, based on neutron diffraction and the magnetic properties, including the magnetocrys- talline energy constants with magnetic measurement techniques.

Atomic and magnetic structure

The atomic and magnetic structures of Fe ₅ SiB ₂ were investigated with a com- bination of powder XRD and NPD. Two samples were synthesised, one with natural boron and one with isotopically pure ¹¹ B for NPD investigations.

The quality of both samples were investigated using high resolution pow- der XRD at the I711 beamline [32] of the Max IV laboratory. The reﬁne- ment using the Rietveld method revealed that the sample with natural boron was very pure (<2% of a secondary phase, Fe 3 Si), while the isotopically pure

11 B-sample contained ∼5% of the secondary phase Fe 4 .7 Si ₂ B. The difference

between the phase-content of the samples is due to that although the ¹¹ B was

isotopically pure it was not as chemically pure as the natural boron used to

produce the samples. The XRD patterns are shown in ﬁgure 4.1. The XRD

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a) b)

Figure 4.1. Powder XRD patterns of for two samples of Fe ₅ SiB 2 , one with natural boron (a) and one with isotopically pure ¹¹ B (b), reﬁned with the Rietveld method.

Black dots, red and blue lines, and black bars correspond to the observed, calculated pattern, difference between observed and calculated data and the theoretical Bragg peak positions respectively. λ = 0.9940 Å.

investigation confirmed that Fe ₅ SiB 2 crystallises in the space group I4/mcm with unit cell parameters a = 5.5541(1) Å and c = 10.3429 Å. Since previous studies on this compound showed a magnetic structure transition at ∼140 K [19], the possibility of a structural transition was investigated using tempera- ture dependent powder XRD, see figure 4.2. The low temperature structural investigations show that the transition is purely magnetic and not coupled to a structural transition since neither the Bragg positions nor the relative inten- sities differ between the temperatures. This becomes even clearer from the change in the unit cell parameters which only exhibit the expected reduction with decreasing temperature (figure 4.2).

To study the magnetic transition in detail NPD experiments were performed at the D1B beamline at ILL, Grenoble. This revealed different magnetic con- tributions fore some reflections at 16 K compared to 300 K, below and above the magnetic transition respectively. The differences are shown in the right part of figure 4.3 mainly for the 004, 211 and 114 reflections. The structural refinements describing the magnetic phases in the Shubnikov groups I4/mc’m’

and Iba’m’ for 300 and 16 K, respectively, with the Fe atoms described using

Fe ³ ⁺ form factors are shown in the left part of ﬁgure 4.3. The direction and

size of the magnetic moments were extracted from the peaks with magnetic

contribution to the total intensities for both temperatures. For 300 K (high

temperature magnetic phase) the moments were found to couple ferromag-

netically along the c-axis with a size of 2.06(7) μ B and 1.72(5) μ B for Fe1

and Fe2 respectively. This gives a mean value of 1.79 μ B /Fe-atom for the

total magnetic moment. For the low temperature (16 K) magnetic phase the

moments were also found to couple ferromagnetically, in agreement with pre-

vious Mössbauer spectroscopy analysis [19], although the direction was dif-

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20 30 40 50 60 70 80 90

0 50 100 150 200 250 300

5,535 5,540 5,545 5,550 10,334 10,336 10,338 10,340 10,342 10,344

Unitcellparameter(Å)

Temperature (K) c a

Intensity(arb.units)

2-theta (deg)

16 K 100 K 150 K 200 K 300 K Bragg positions

Figure 4.2. Temperature dependent XRD patterns for Fe 5 SiB 2 showing that no crystal- lographic structure transition occurs around 172 K. The black bars indicate the Bragg positions for Fe 5 SiB 2 at room temperature. The inset shows how the unit cell param- eters vary with temperature with the dashed line representing the magnetic transition.

λ = 1.540598 Å.

ferent. The moments were found to be in the easy plane along the a-axis. The sizes of the moments were calculated to 2.31(6) μ B and 2.10(4) μ B for Fe1 and Fe2 respectively. The mean value per iron atom is therefore 2.14 μ B for Fe ₅ SiB ₂ at 16 K. The models used in the reﬁnements are shown in ﬁgure 4.4.

20 40 60 80 100 120

Y_obs Y_calc Y_calc-Y_obs Bragg reflections

300 K

2-theta (deg) Y_obs

Y_calc Y_calc-Y_obs Bragg reflections

16 K

Normalized intensity (arb.u.)

0 5 10 15 20

Diffraction angle 2θ ( ° )

58 60 62 64 66 68 70 72 74

16K Yobs

16K Ycalc

16K magnetic 300K Yobs

300K Ycalc

300K magnetic 004

114

202 211

Figure 4.3. Neutron powder diffraction patterns of Fe ₅ Si ¹¹ B 2 . Patterns reﬁned with the Rietveld method at 300 K (upper) and 16 K (lower) in the left part of the ﬁgure.

The right part of the ﬁgure shows an enlargement of the strongest magnetic reﬂections revealing the magnetic transition. λ = 2.52 Å.

Magnetic properties

The temperature at which the spin reorientation (T _t ) and T _c occurs was deter-

mined from magnetisation measurements in which the magnetic susceptibility

( χ) was recorded at a low magnetic ﬁeld as a function of the temperature, as

is seen for the Fe 5 Si ¹¹ B 2 -sample in ﬁgure 4.5 (a). From the plot of 1/ χ versus

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Figure 4.4. Magnetic structures for Fe 5 SiB 2 at 300 K (left) and 16 K (right). The length of the arrows corresponds with the size of the magnetic moments.

T, T _c was determined to be 800 K. The maximum in the magnetic suscepti- bility occured at 169 K and the χ values before and after the maximum differ which supports the NPD results. The natural boron sample was also studied and the corresponding values for T c and T t were 760 and 172 K respectively.

This shows that the temperature at which this magnetic transitions occurs is dependent on the sample composition and presence of secondary phases.

Since the magnetocrystalline energy constants are different for an easy axis and an easy plane a maximum in the χ vs. T plot will occur during the tran- sition, due to a change of sign during the transition. Therefore the K 1 values have been estimated from magnetisation curves recorded for both samples, ﬁg- ure 4.5 (b). The results show that the magnitude of the K 1 -values was higher at a low temperatures than above the T _t . That is 0.33 MJ/m ³ compared to 0.30 MJ/m ³ for the sample with natural boron. This is also in agreement with the higher susceptibility below T t . The M sat value determined from the M vs. H curves gives magnetisations of 1.87 and 1.75 μ B /Fe-atom for 10 and 300 K respectively, in good agreement with the values obtained from NPD.

Unfortunately, since all magnetisation loops indicate a soft magnetic material, Fe 5 SiB 2 ’s usefulness as a permanent magnet material is therefore low.

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(a) (b)

Figure 4.5. Fe ₅ Si ¹¹ B 2 low ﬁeld susceptibility χ = M/H vs. T, H = 40 kA/m (a). The inset shows a detailed view of χ at T c . M vs. H curves for both samples, Fe ₅ SiB 2 , T

= 10 K (solid black line) and T = 300 K (solid red line); Fe 5 Si ¹¹ B 2 , T = 10 K (dashed black line) and T = 300 K (dashed red line) (b)

4.2 Magnetocaloric materials

The other two compounds discussed in this thesis are both potential materials for magnetic refrigeration. Of the two, one is based on the well known hexag- onal Fe ₂ P-structure, FeMnP ₀ _.75 Si ₀ _.25 . The other compound, less studied as a magnetocaloric material, is the orthorhombic layered compound AlFe 2 B 2 .

4.2.1 AlFe ₂ B ₂

AlFe ₂ B ₂ contains 2 formula units per unit cell and has the iron, boron and aluminium atoms located at the positions 4j (0, y, 0.5), 4i (0, y, 0) and 2a (0, 0, 0). Here, the magnetic structure has been studied as well as the magnetic properties, including magnetocaloric properties, to evaluate the discrepancies between of the T _c and ΔS values found in the literature.

Atomic and magnetic structure

Two samples of AlFe ₂ B ₂ were produced, one with natural boron and one with isotopically pure ¹¹ B for the NPD experiments. The quality of the samples was investigated with powder XRD, as is shown in figure 4.6 for the natural boron sample. The diffraction pattern indicates that the produced sample was of high quality and XRD confirm that AlFe 2 B 2 crystallises in the orthorhombic space group Cmmm with the unit cell parameters 2.9256(4), 11.0247(4) and 2.8709(2) Å for a, b, and c respectively. The Rietveld refinement revealed that the y-coordinates were 0.3543(1) and 0.2112(1) for Fe and B respectively and that all positions were fully occupied.

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20 30 40 50 60 70 80 90

2-theta (deg) Y_obs Y_calc Y_calc-Y_obs Bragg reflections

Figure 4.6. X-ray powder diffraction pattern of AlFe ₂ B 2 and the crystal structure model reﬁned with the Rietveld method. The black dots and red line correspond to the observed and calculated pattern respectively. The blue line shows the difference between observed and calculated data. The bars show the theoretical Bragg peaks of AlFe 2 B 2 . λ = 1.540598 Å.

The literature suggests that a ﬁrst order magnetic transition occurs in AlFe 2 B 2 [24] and that the lattice parameters change abruptly at T c . To study the lattice parameters temperature dependency XRD patterns were recorded at low temperatures and the calculated lattice parameters for all temperatures are shown in ﬁgure 4.7. The lattice parameters a and b decreased with decreas- ing temperature, whereas c increased with decreasing temperature. However, none of the previously reported discontinuities cuold be seen around T c .

0 50 100 150 200 250 300

92,35 92,40 92,45 92,50 92,55 92,60 92,65

0 50 100 150 200 250 300

2,870 2,875 2,880 2,915 2,920

2,925 a

b c

Temperature (K)

Unitcellparameter(Å)

10,985 10,990 10,995 11,000 11,005 11,010 11,015 11,020 11,025 11,030

Unitcellparameter(Å) Unitcellvolume(Å3)

Temperature (K) V

Figure 4.7. The development of the unit cell parameters (left) and unit cell volume (right) as a function of temperature for AlFe 2 B 2 . The vertical dashed lines marks T c .

Neutron diffraction intensities for a pure ¹¹ B sample were recorded at the

D1B diffractometer at ILL, and the diffractograms at 320 and 20 K are shown

in ﬁgure 4.8. There were some additional phases in the sample ( ∼5%). Most

of the peaks can be explained by small amounts of tetragonal boron

(a = 8.917(2) Å, c = 5.025(7) Å, in the space group P¯4n2 [41]), and the

additional peaks can be indexed using an additional orthorhombic unit cell

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(a =17.081(7) Å, b = 11.354(8) Å, c = 2.288(1) Å, Space group = Pnma).

The phase could not be identiﬁed even though all reported binary and ternary phases in the Al-Fe-B system were tested, as well as their oxides, hydrox- ides and chlorides. Therefore, the additional peaks seem to originate from an previously unknown phase.

20 40 60 80 100 120

Yobs

Ycalc

Ycalc-Yobs

Bragg reflections 320 K

2-theta (deg.) Yobs

Ycalc

Ycalc-Yobs

Bragg reflections 20 K

Figure 4.8. Neutron powder diffraction patterns of AlFe 2 B 2 reﬁned with the Rietveld method at 320 K (upper) and 20 K (lower). λ = 2.52 Å.

!

"" !

"#$ !"% !

&& !

'(')* )+

Figure 4.9. Difference curve for the temperatures 320 K and 20 K, the 20 K dataset has been shifted by -0.2 ^◦ to compensate for thermal expansion effects (a) and a com- parison of the reﬁnements for the different magnetic models (b). λ = 2.52 Å.

The only features in the the difference plot, ﬁgure 4.9 (a), between 320 and

20 K that cannot be explained with a thermal expansion/contraction of the lat-

tice parameters are the 001 and 040 peaks. These two peaks have magnetic

contributions to the total intensities and since all the magnetic peaks coincide

with the crystallographic unit cell, the magnetic unit cell has the same dimen-

sions as the crystallographic unit cell. To determine the magnetic structure

several models were tested, ﬁgure 4.9 (b), where the magnetic moments were

aligned along the different unit cell axis as well as in the ab-plane. The model

that gives the best agreement with the experimental intensities is when the

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magnetic moments couple ferromagnetically along the a-axis of the AlFe ₂ B ₂ unit cell, as is shown in ﬁgure 4.10. The Shubnikov group Cmm’m’ was used to describe the magnetic structure. This gives the magnetic moment 1.4(3) μ B /Fe-atom. This model is similar to the model found for Fe 5 SiB 2 in paper I.

Al

B Fe

Figure 4.10. Two unit cells of AlFe 2 B 2 with arrows indicating the magnetic spins at 20 K.

Magnetocaloric properties

To determine T _c for AlFe ₂ B ₂ magnetisation data were recorded as a function of temperature in the field cooled cooling (FCC) and field cooled warming (FCW) modes using two different magnetic fields, 4 kA/m and 800 kA/m, as is shown in figure 4.11 (a) and (b) respectively for the ¹¹ B-sample. The insets show the derivative of the magnetisation for the FCC measurement and the low field curve was used to determine T c . T c was thus extracted to a value of 285 K. The corresponding value for the natural boron sample was 295 K, however; the natural boron sample had fewer secondary phases. This clearly shows that T c is composition dependent and this is also an indication of its tuning possibilities. No thermal hysteresis was found for this compound (figure 4.11), a first indication that the magnetic transition has second order characteristics. This contradicts the proposed first order transition reported by Lewis et al. [24].

To determine the order of the magnetic transition and the entropy change, a

number of M vs. H curves were recorded at temperatures ranging from 260 to

305 K, with intervals of 2.5 K as is shown in ﬁgure 4.12. The M vs. H curves

were used to construct an Arrot plot, ﬁgure 4.12 (b), which, due to the positive

slope of the plotted M ² vs. H/M, indicates that the sample undergoes a second

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T (K)

270 280 290 300

dM/dT

x 10^-3

-3 -2 -1 0

T (K)

270 280 290 300

dM/dT

-0.02 -0.01 0

a b

Figure 4.11. Magnetisation as a function of temperature using a ﬁeld of (a) 4 kA/m and (b) 800kA/m. The insets show the temperature derivative of the magnetisation during cooling (FCC) for the respective magnetic ﬁelds.

order magnetic transition, since the sign would change if the transition were of the ﬁrst order [42].

M vs. H curves (figure 4.12 (a)) were also used to estimate the entropy change of the sample which is plotted as a function of temperature in figure 4.12 (c). The maximum entropy change was observed around T _c = 285 K, and the ΔS-values were -1.3 and -4.5 J/kg K for a magnetic field change from 0 to 800 kA/m and from 0 to 4000 kA/m respectively. In previous studies ΔS (from 0 to 4000 kA/m) were determined to -7.7 J/kg K [22], which is higher than the value reported here. This difference might be explained by the difference in the synthesis methods since the reported sample as made using Ga flux with might lead to a (partial) substitution of the Al-site.

H/M (kg/m³)

0 200 000 400 000

M2 (A2m4/kg2)

0 500 1000

a

1500

b c

260 K

305 K

Figure 4.12. (a) Magnetisation as a function of magnetic ﬁeld at temperatures between 260 and 305 K (steps of 2.5 K). (b) An Arrot plot of the data shown in (a). (c) ΔS as function of temperature estimated using the data shown in (a) for a ﬁeld change of 0 to 800 kA/m and 0 to 4000 kA/m, respectively.

A M vs. H curve was also recorded at 10 K to determine the saturated magnetisation. From this measurement the magnetic moment was extracted to 0.9 μ B /Fe-atom, which is signiﬁcantly lower that the value from the NPD measurements. The discrepancy may originate from the secondary phases in the sample, which were nonmagnetic and did not contribute to the magnetic properties of the sample.

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Electronic structure

Electronic structure calculations were performed to further evaluate the AlFe 2 B 2 -phase. The calculations gave lattice parameters that were in good agreement with the parameters extracted from the powder XRD measure- ments. Furthermore, the size and direction of the magnetic moments were calculated to 1.077 μ B /Fe-atom in the a-direction, in good agreement with the results of the NPD investigation. The calculations also showed a strong dependence on the distances between the Fe-atoms, so substitutions of the non-magnetic elements may have a big impact on the magnetic properties.

4.2.2 FeMnPSi

The irreversible structure change, also known as the virgin effect, of the com- pound FeMnP 0 .75 Si 0 .25 during the initial cooling down through the Curie tem- perature (T _c = 250 K on heating) has been investigated. This compound is of FeMnPSi-type based on Fe ₂ P, crystallising within the space group P¯6m2.

Virgin effect

The T _c value was different on cooling for the first cooling/heating cycle com- pared to the following cycles, see figure 4.13. However, T c was the same on heating for all temperature cycles. To determine the origin of this behaviour powder XRD patterns were collected at different temperatures for the as pre- pared sample. The virgin powder XRD patterns can be seen in figure 4.14 where the room temperature pattern is displayed as well as that for the first cycle in the inset. The inset shows abrupt changes of peak positions and extra peaks appearing upon cooling down through the magnetic transition. This is a consequence of magnetostriction in combination with a structural transition that accompanies the ferromagnetic ordering. The effect gives an irreversible structural change even when the sample is re-heated to a paramagnetic state.

0 100 200 300 400

0 40 80 120 160

FCC (I) FCH (I) FCC (II) FCH (II) FCC (III) FCH (III) FCC (IV) FCH (IV)

H = 1 T M a gnetization (A.m

2

/k g)

Temperature (K)

Figure 4.13. M vs. T curves for FeMnP 0 .75 Si 0 .25 under an applied magnetic ﬁeld of 1 T.

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Figure 4.14. X-ray powder diffractogram of FeMnP _0.75 Si _0.25 obtained at 298 K. The inset shows a sequence of diffractograms recorded upon cooling the sample down through T c . Silicon (*) was added as an internal calibration standard.

In figure 4.15 the permanent structural change is displayed for the room temperature diffractograms for the as prepared pattern together with the corre- sponding pattern obtained after the first cooling/heating cycle. Peak splitting occured at high angles due to the presence of two separate phases. These phases were very similar, but there was a small but significant difference in the lattice parameters. This subtle change could easily have been overlooked, and even disregarded, if silicon had not been used as an internal calibration standard.

The irreversibility of the structural transition is further illustrated in the diffratograms recorded at 150 K for the virgin and second cooling cycle, see figure 4.16. These diffractograms show that the peaks for the magnetically ordered phase were stronger during the second cycle, indicating that a higher fraction of the samples phases was ordered magnetically on the second cooling cycle than on the virgin cycle. The relative intensities were normalised to the paramagnetic peaks to facilitate a comparison of the cycles. This is an extra confirmation of what is shown in figures 4.13 and 4.14. Additionally, this transition occurs over a broad temperature range 175-75 K (virgin cooling) and 200-100 K (second and subsequent cooling events), which means that one can expect to find a higher proportion in a magnetically ordered state at 150 K during the second cooling than for the virgin cooling. That the transition is so broad is probably an effect of magnetisation nucleating in different grains of the sample at different temperatures.

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Figure 4.15. Room temperature powder XRD patterns of FeMnP _0.75 S _0.25 recorded before (lower scan) and after (upper scan) the virgin cooling cycle. The inset shows the minute changes of the high angle peaks. Silicon (*) was added as an internal calibration standard.

Figure 4.16. XRPDs during the magnetostructural transition for the virgin cooling cycle and the 2nd cycle measured at 150 K. The contribution from the magnetically ordered phase (arrows) is higher for the 2nd cycle than for the virgin cycle, conﬁrming that a larger fraction of the sample was ordered during the second cycle. The data was normalized against paramagnetic diffraction peaks so that the contribution of the magnetically ordered phase could be extracted. Si was used as an internal calibration standard for the peak positions.

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5. Summary and future outlook

Structural transitions, atomic and magnetic, induced by temperature changes have been studied within this thesis. The studies have been carried out with three different compounds suitable for two different future applications. They are the permanent magnetic material Fe ₅ SiB ₂ and the two magnetocaloric ma- terials AlFe 2 B 2 and FeMnP 0 .75 Si 0 .25 , which are discussed individually below.

Fe 5 SiB 2

For Fe ₅ SiB 2 , a reorientation of the magnetic spins, occuring at 172 K, has been found using powder XRD and NPD as well as from magnetisation measure- ments. It has been seen that the magnetisation is along the tetragonal c-axis at room temperature and that it ﬂips down to the ab-plane (along the a-axis) upon cooling down below the magnetic transition temperature at 172 K. Fur- thermore the magnetocrystalline anisotropy for both magnetic structures has been studied, and were found to be far too low to result in hard magnetic prop- erties. Therefore, the usefulness as a permanent magnetic material is limited.

However, it might be possible to boost the magnetocrystalline anisotropy by substitution of the iron atoms with other magnetic atoms, e.g. cobalt, which might in turn be interesting to study further.

AlFe 2 B 2

NPD and electronic structure calculations have been used to extract the di- rection of the magnetic moments for the magnetocaloric material AlFe 2 B 2 . The magnetic spins orient ferromagnetically along the crystallographic a-axis.

Magnetic measurements show that the sample undergoes a second order mag- netic phase transition at 285 K. Indications of this were also found from the development of lattice parameters upon cooling where no dramatic change is found at T c , something that occurs with ﬁrst order transitions. This decreases the usefulness of the material as a magnetocaloric material. However, elec- tronic calculations indicate that the order of the magnetic transition might be dependent on the distance between the magnetic atoms, making it interesting to look at the effect of substitution at both the iron site as well as the aluminium site.

FeMnP 0 .75 Si 0 .25

The temperature dependence of the ﬁrst order magnetocaloric material

FeMnP 0 .75 Si 0 .25 has been studied with magnetic measurements and temper-

ature dependent powder XRD. The results show that the differences in ther-

mal hysteresis for this material were induced by a minute structural change

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that became permanent after the ﬁrst cooling cycle. The magnetic transition temperature (on cooling) then became slightly higher on the following cool- ing/heating cycles.

Structure-Magnetism Relations in Selected Iron-based Alloys: A New Base for Rare Earth Free Magnetic Materials