Index of /rozprawy2/10792

Pełen tekst

(1)Faculty of Physics and Applied Computer Science. Doctoral thesis Tomasz Kołodziej. The impact of orbital ordering on the Verwey transition in magnetite Supervisor: prof.dr hab. Andrzej Kozłowski. Krakow 2014.

(2) This PhD thesis has been completed within the framework of the Human Capital Operational Program POKL.04.01.01-00-434/08-02 co-financed by the European Union.. 2.

(3) Oświadczenie autora rozprawy:. Oświadczam, świadomy odpowiedzialności karnej za poświadczenie nieprawdy, że niniejszą pracę doktorską wykonałem osobiście i samodzielnie i że nie korzystałem ze źródeł innych niż wymienione w pracy.. data, podpis autora. Oświadczenie promotora rozprawy:. Niniejsza rozprawa jest gotowa do oceny przez recenzentów.. data, podpis promotora rozprawy. 3.

(4) 4.

(5) I dedicate this dissertation to prof. J. M. Honig: All that I have experienced about the Verwey transition was possible only thanks to his perfect single crystals of magnetite.. 5.

(6) Acknowledgements In this place, I would like to thank all those people who helped me to reach the final point of my Ph.D. studies, on the one hand from a scientific point of view, and from a personal one on the other. First of all, I would like to thank my supervisor, Prof. Andrzej Kozłowski, for his constant help, support, encouragement and patience. He has really spent a lot of time teaching me not only physics, but also how to move within science in general. I am really grateful for all what he has done for me, both in scientific and in personal areas. I also want to thank my other great teacher, Wojtek Tabiś, who taught me how to work with many experimental techniques. I was really fortunate to have an opportunity to learn from him, which was always a great pleasure and a lot of fun. Thanks to Prof. Barbara Lavina I could travel to the USA and learn of high pressure science; this was one of my biggest scientific adventures. She is a truly good teacher, great person, and I really owe her my gratefulness. Emilio Lorenzo is the person thanks to whom I first attended an experiment with synchrotron radiation. Thanks to Prof. Józef Korecki I was able to see the dynamics of the magnetic domain structure on the surface of magnetite, which was exciting. I am also indebted to Prof. Andrzej Wiśniewski, Prof. Roman Puźniak and Jarosław Piętosa, Ph.D., thanks to whom I measured magnetization under pressure, which is an important part of this thesis. I gratefully acknowledge Zbigniew Kąkol, Zbigniew Tarnawski, Przemek Piekarz, Marcin Sikora, Joachim Kusz, Stuart Gilder and Waldemar Tokarz for constructive “brain storms”. I think I really learned a lot during those sessions. I am grateful to the Coordinators of my Interdisciplinary Ph.D. Studies. At the end of the scientific part I would like to express my great gratitude to my primary and high school physics teachers: Mr Jan Barszczak and Mr Michał Uberman, who really triggered my love and passion for science, one of my most important feelings. Apart from the scientific part, here I would like to thank all the people who supported me in my private life and without whose help I would have never been able to get to this point. First of all, I really want to thank my wife Kasia, my parents and brothers for all their support, patience and belief in me. It is very important to me and I am hoping for more. Without you, for sure, I would not be the person I am now. I want to thank all my friends. I thank you for your friendship and I want to say that without you my life in Kraków would not have been interesting at all over last ten years. More personally, I really want to thank Piotrek and Klaudia Ramza, Kuba Ramza and Szymek Pysz for discussions, support and help in hard times, and a lot of fun in good times. During all the times complicated 6.

(7) by problems with accommodation in Kraków I could always count on Ania and Piotrek Mazur and their parents. I really appreciate all their help, and I thank them for the music we were able to play. I want to thank Ewelina Bednarz for our conversations and for the dance classes we attended together. It was absolutely relaxing. With Asia Stępień I always had a nice discussions, tea sessions and fast table tennis games. I always could count on coffee in the great company of Ola Szkudlarek, Kamila Kollbek and Karolina Gąska. Krzysztof Antoszek taught me at the beginning in the dormitory, how to effectively learn the guitar. Thanks for nice jams and the first discovery of the electric guitar, which is still my greatest hobby. Magda Kaczmarska did all my job with the scholarships in the Ph.D. students council when I was away from Kraków; she is a really reliable person and I greatly appreciate her help. I could also always count on Jola Knecht, and discuss new books releases with her. I was sharing the office with Ewa Wilke, Iza Biało and Akyana Britwum and thanks to them we had an absolutely nice atmosphere there. I also want to thank Ania Chramiec, Rafał Wojtasik, Marek Szybiak, Tomek Król, Marcin Stachowski, Grzesiek & Ewelina Ukarma for the friendship since school times, lasting even for 20 years now. And to my AGH fellows: Bartek Kwieciński, Marcin Kawala, Agnieszka Jamrozik, Marcin Perzanowski, Dominika Augustyńska, Paweł Pędrak and Łukasz Klita. I owe something to every single person, and really appreciate that we had a possibility of studying together.. 7.

(8) Contents Preface: Thesis aim and the main concept____________________________. 11. Chapter 1. The Verwey transition in magnetite and its observation____. 14. 1.1. Verwey transition in magnetite: the existing state of affairs___________________. 14. 1.2. Verwey transition in statu nascendi______________________________________. 22. 1.3. Axis switching______________________________________________________. 24. Chapter 2. Thermal expansion and magnetostriction of magnetite with first and second order Verwey transition_____________________________. 31. 2.1. Introduction________________________________________________________. 31. 2.2. Previous results: literature data___________________________________________. 31. 2.3. Samples___________________________________________________________. 32. 2.4. Experiment_________________________________________________________. 34. 2.5. Data Presentation____________________________________________________. 36. 2.6. Experimental results__________________________________________________. 37. 2.6.1. Field sweeps____________________________________________________. 38. A. Magnetic field dependence of the size at 10K caused by magnetic domain movement or magnetization rotation________________________________. 39. B. Magnetic field dependence of the size at 90K (70K) caused by magnetic domain movement, magnetization rotation and the change of c axis direction______________________________________________________. 41. C. Magnetic field dependence of the size at 102K (127K), i.e. in the region above the transition temperature, but below the isotropy point TIP_________. 45. D. Magnetic field dependence of the size at 290K________________________. 46. 2.6.2. Temperature sweeps______________________________________________. 47. 2.6.3. Discussion and conclusions_________________________________________. 50. A. Thermal shrinking on cooling______________________________________. 51. B. The axis switching difference in I and II order samples__________________. 54. C. Unit cell size changes under the applied magnetic field__________________. 55. 8.

(9) Chapter 3: Nuclear inelastic scattering studies of lattice dynamics in magnetite with first and second order Verwey transition______________. 58. 3.1. Literature data_______________________________________________________. 59. 3.2. Samples___________________________________________________________. 60. 3.3. Nuclear inelastic scattering of synchrotron radiation at ID18 in ESRF___________. 61. 3.4. NIS data processing__________________________________________________. 63. 3.5. Results______________________________________________________________. 65. 3.5.1. Time spectra______________________________________________________. 66. 3.5.2. Results of NIS measurements_________________________________________. 68. 3.5.3. Phononic density of states___________________________________________. 69. 3.6. Discussion_________________________________________________________. 73. 3.6.1. Heat capacity____________________________________________________. 74. 3.6.2. Temperature dependence of DOS____________________________________. 75. 3.6.3. Further comments on the mechanism of the Verwey transition_____________. 78. 3.7. Conclusions________________________________________________________. 79. Chapter 4: Axis switching in magnetite under pressure p < 1.2GPa____. 80. 4.1. Introduction________________________________________________________. 80. 4.2. Literature survey_____________________________________________________. 81. A. Structure______________________________________________________. 83. B. The Verwey transition temperature_________________________________. 84. C. Magnetic interactions____________________________________________. 84. D. AC magnetic susceptibility_______________________________________. 85. E. Magnetic anisotropy_____________________________________________. 86. F. Elastic constans_________________________________________________. 86. 4.3. Experiment_________________________________________________________. 87. 4.3.1. Apparatus______________________________________________________. 87. 4.3.2. Samples________________________________________________________. 88. 4.3.3. Experiment preparations___________________________________________. 91. 4.4. Results of measurements______________________________________________. 93. 4.4.1. Stoichiometric magnetite, mg05N#2W________________________________ 4.4.2. Zinc doped magnetite, 459-3#1w, x = 0.011_________________________ 9. 93 100.

(10) 4.4.3. Zinc doped magnetite, 448#1BW, x = 0.011__________________________. 101. 4.5. Discussion_________________________________________________________. 103. Chapter 5: Conclusions______________________________________________. 109. Streszczenie (summary in Polish)_____________________________________. 112. Appendix: Author’s publications_____________________________________. 115. References___________________________________________________________. 116. 10.

(11) Preface: Thesis aim and the main concept Magnetite (Fe3O4) is the first magnetic material found by mankind. This discovery triggered a tremendous change in human civilization by allowing for an independent means to orient in the world, though Nature itself had discovered it first: magnetite compasses are also present in living creatures. Magnetite is also a promising material for spin electronics and will possibly be used to heat and destroy cancer cells. Finally, it presents one of the most striking phase transformations, the Verwey transition at TV = 124K where practically all physical characteristics behave anomalously. The aim of this thesis is to discuss the role played by the orientation of 3d iron orbitals (orbital ordering, OO) on the properties of magnetite in the vicinity of the Verwey transition. The author’s experimental results, as well as the literature data gathered so far, both discussed below, give grounds to say that orbital ordering and its change with doping, is an important factor in the complex mechanism of the Verwey transition, in some cases responsible for the spectacular anomalies related to this transition. The Verwey transition1, so called after Evert Johannes Willem Verwey, the author of the first systematic studies, is reflected in a huge peak in heat capacity, a jump of resistance by two orders of magnitude, a step in the AC magnetic susceptibility and anomalies in practically all physical properties. Also the structure changes at the transition: from high temperature (high-T) cubic Fd-3m to monoclinic Cc, which, among other factors, leads to the doubling of the unit cell along one of <100> axes (that becomes the monoclinic c axis) while cooling. Since its discovery in 1939, it has been clear that structural and electronic aspects of the transition are interwoven. Actually, the original model, first set up by Verwey and the one that, for 60 years, has created the standard of the transition metal oxides description saw the transition as a freezing out of strongly correlated electrons. Those electrons, one from each of the two iron octahedral (B) positions, were supposed to travel relatively freely between iron B cations at T > TV (resulting in rather high conductivity) and to freeze on particular positions at T < TV, changing the lattice symmetry and causing a two orders of magnitude increase in resistance . This freezing of octahedral electrons results in a certain electronic pattern that establishes the details of the low temperature (low-T) structure and other orientation-dependent properties, such as the magnetic anisotropy axis. It was found, and slowly started to be understood in the 50-ties that this pattern, and, consequently, all pattern-related properties (c axis and magnetic anisotropy 1. In subsequent parts of the thesis, the Verwey transition sometimes is denoted as „VT”, for convenience.. 11.

(12) axis) may be changed when external magnetic field is applied: this is the Axis Switching (AS) phenomenon, described and studied in details in this thesis. The clear Verwey-like view of magnetite starts to complicate if dopands or vacancies, already in minute amounts, are introduced into the magnetite lattice. Namely, the Verwey transition changes its character, from first to second order, with increased doping or departure from stoichiometry. The problem why the transition order is changed, still unsolved, will play an important role in the thesis.. With the outbreak of a new millennium, an increased number of papers, in particular those based on microscopic probes like NMR and resonant X-ray scattering, showed that no clear-cut, as in the Verwey model, charge ordering exists, revealing, at the same time, many new interesting facts. It was also suggested that the orbital ordering (OO) of iron 3d states exists at T < TV and is coupled with the charge ordering. The complex character of the charge/orbital ordering is revealed in a recently solved low-T structure of magnetite: orbitally- and charge-ordered states are coupled in trimerons (three octahedral Fe cigar-like atom chains), which are connected in a very complicated, yet longrange, manner. Although the “trimerons lattice” seems to be very rigid, it may be susceptive to even very slight lattice distortions, as those caused by vacancies and dopands. It suggested that the author should seek here a possible reason for the above mentioned change of the Verwey transition character with doping/nonstoichiometry and the complex character of the transition in general. The attempts to follow this line of reasoning are described below.. First, based on the published elastic constant studies as well as on the author’s magnetostriction data, it is suggested that the Verwey transition is linked to interatomic forces and, with solely those forces present, it would be the continuous phase transformation at ca 66K, with a pronounced change of lattice symmetry and size, but, possibly, without a major electric manifestation. The orbital ordering, which is a more subtle reorganization of those interatomic forces, stabilizes the low-T structure causing a substantial increase in the transition temperature and bringing about, depending on the doping level/nonstoichiometry, large anomalies in physical characteristics. This idea is outlined in Chapter 1 where the low-T structure and literature data are described, and fully developed in Chapter 2 where magnetostricion data are presented. The remaining part of this thesis describe experimental proofs of this concept.. 12.

(13) Since interatomic forces are suggested to be akin to the basics of the Verwey transition, the consequences of these forces, the lattice vibrations, should be measured first. The results of Fe lattice vibration studies (based on Nuclear Inelastic Scattering, NIS) are described in Chapter 3. It was found that doping, even in the second order transition regime, has negligible effect on the lattice vibrations. And that, actually, the phononic density of the states below and above TV, and for magnetite exhibiting the transition of the first and second order2, are mainly different below E = 12meV, the energy comparable to the transition temperature. Based on these findings, the role of orbital ordering in the explanation of the literature heat capacity data and peculiarities of the Verwey transition was suggested.. While elastic constants and lattice vibrations are used to observe interatomic forces, the axis switching phenomenon was proposed as a means to observe orbital ordering. In other words, whenever some physical characteristics are affected by axis switching (like the sample size described in Chapter 2), this changing parameter is linked to orbital ordering and may be used for the orbital ordering characterization. Apart from the sample size, the other parameter that is affected by the axis switching, i.e. that can serve to characterize the orbital ordering, is a sample magnetization. It had already been studied before and it was shown that this phenomenon may be used to quantify the AS by the definition of two parameters: the switching field, Bsw and the activation energy U. In author’s further attempts to observe the orbital ordering via AS, these characteristic parameters were measured when external pressure was exerted (Chapter 4). Although, despite interesting results, the interpretation proved not to be easy, I am confident that the main idea of my thesis (orbital ordering impact on the natural transition due to interatomic forces) was, at least partially, confirmed. This is stated in the concluding remarks gathered in Chapter 5.. 2. Magnetite samples used for the investigations presented in this thesis consist of magnetite exhibiting the first-order Verwey transition (sharp anomalies at the transition with a large latent heat), as well as magnetite exhibiting the second order Verwey transition (without a latent heat, i.e. without a sharp peak in heat capacity). For a convenience, in subsequent parts of the Thesis, the shorter forms (‘first (I) order magnetite’ and ‘second (II) order magnetite’) are being used, respectively.. 13.

(14) 1. The Verwey transition in magnetite and its observation Probably none of the naturally existing minerals was utilized by mankind more in its pristine form than magnetite. When first discovered ca 200 years BC, the “lodestone” was used to navigate the world, i.e. copying the nature who has already used it in the brains of virtually all living creatures from the very start of their existence [Baumgartner2013]. Apart from orientation, magnetite was “used” as a storage medium: it stored the memory of the past in the magnetic order formed while cooling down from the liquid state. Also this feature of information storage was exploited by mankind: already in 70-ties, magnetite appeared in traditional recording media. Finally, it started to play a prominent role in the emerging field of spin electronic applications [Gupta1999]. Apart from its role in civilization, magnetite displays yet another fascinating feature: the Verwey transition. At this first order phase transformation the resistivity drops two orders of magnitude when heated above TV = 124K (Fig. 1.1a). Surprisingly, all groups of magnetite "application" and the Verwey transition are interwoven: in spin electronics cooling down magnetite below TV results in a drastic drop of electric conductivity. And the thermal cycling across the transition greatly diminishes coercive force, i.e. magnetic memory (see e.g. [Muxworthy2000]). However the Verwey transition not only may hinder everyday magnetite application: the dependence of TV on stoichiometry, altered by annealing conditions, was used by Carporzen and coworkers as the precise indicator of the Vredefort crater creation history [Carporzen2006]. Thus, apart from the fascinating problem of its own, the Verwey transition in magnetite is vital for several applications of this material. This transition is a subject of extensive studies of the research group which the author belongs to.. 1.1.. Verwey transition in magnetite: the existing state of affairs Not only resistivity jumps at TV; the spectacular anomalies are also observed practically in. all physical characteristics. In particular, there is a huge peak in heat capacity, proving first order character of the transition (Fig. 1.1b). The step in AC magnetic susceptibility is also observed (Fig. 1.1c) and the important changes undergo in the magnetic anisotropy energy: at T = 130K the change of the easy axis from <111> to <100> takes place that survives also below TV (Fig 1.1.d). Finally, the structure symmetry changes from high-T cubic to low-T monoclinic Cc (Fig. 1.2). The high temperature magnetite structure was found to be an inverse spinel type, with Fd3m symmetry and with Fe residing in tetrahedral (or A) and octahedral (or B) positions, as 14.

(15) shown in Fig. 1.2. When cooled below TV the cubic symmetry lowers to the monoclinic by the slight atomic displacements resulting in monoclinic c axis doubling one of cubic edges and the a and b axes along cube diagonals (Fig. 1.2). Note that c axis may point along any edge, so, inevitably, in a free-cooled sample structural domains will appear: this will constitute the key point of the thesis. 7,5. 100000. Fe3O4. 4,5 C(mJ/K*g). log (ρ) (Ωcm). 6,0. 3,0 1,5 0,0. 10000. 1000. -1,5 -3,0. 4. 8. 12. 16. 20. 24. 75 100 125 150 175 200 225 250 275 300 325. -1. 1000/T (K ). T(K). Fig. 1.1a. The main landmark of the Verwey transition: ∼100 times resistivity drop on heating.. Fig. 1.1b. Specific heat of stoichiometric single crystalline magnetite (after [Tarnawski2004]) suggesting the first order transition with a large latent heat. 0. 0,0012. -1. 0,0010. Magnetic anisotropy. -2. Fe3(1-δ)O4. 5. χ'AC [V]. 3. K1 (10 erg/cm ). 0,0014. 0,0008 0,0006. -3. δ=0 δ=0.0045 δ=0.0077. -4. 0,0004. 80. 100. 120. 140. 160. 0. 180. T (K) Fig. 1.1c. Magnetic AC susceptibility change at TV [Balanda2005]; the shape of it is used here as an indication of the sample quality.. 100. 200. 300. 400. 500. 600. 700. 800. Temperature (K). Fig. 1.1d. Cubic anisotropy term K1 as a function of temperature for Fe3(1-δ)O4. The values below TV (except at T≈0) are calculated assuming that K1 term in the cubic anisotropy is preserved even in low temperature phase. (after [Kakol1994]). With such an interesting phenomenon as the Verwey transition it was natural that models explaining it were formulated very shortly after its observation. Already in the first papers of Verwey [Verwey1939, 1941] the mechanism of the transition, that survived for half a century, was formulated. According to this, magnetite was regarded as the ionic compound in which in tetrahedral oxygen surroundings in the inverse spinel lattice Fe+3 cations were situated, while in octahedral positions (see Fig. 1.2a) both Fe+2 and Fe+3 were present and arranged in a certain order. Due to the postulated interionic strong Coulomb repulsion [Anderson1956], in each 15.

(16) tetrahedron of octahedral positions two were supposed to be Fe+2, and the other two Fe+3 (so called “Anderson criterion”, see Fig. 1.2b). Since in Fe+2 noncentrosymmetric orbitals were present, both charge and orbital ordering, as well as the lattice distortion (of the more symmetric high-T cubic) were postulated. This concept survived all subsequent experimental and theoretical findings, although the ordering charges differ by 0.6e at best, not by 1 as in the Verwey model. On heating above TV, the "additional" electrons (those released from Fe2+) were supposed to resonate between adjacent octahedral positions (order-disorder transformation), what resulted in a drastic increase of electric conductivity. The high-T electron movement was also regarded as strongly correlated [Anderson1956] (Anderson criterion was still valid) and the short range order was believed to be present even above TV.. Fig. 1.2a. High-T magnetite (Fd-3m, spinel lattice) elementary cell; in particular, Fe arrangements in tetrahedral (green) and octahedral oxygen arrangements are shown (right). When cooled below TV, the symmetry lowers to monoclinic (showed schematically, in the lower panel, as high-T cube embedded in a new elementary cell) with one high T cube edge doubled. Note that c is no longer perpendicular to a as a result of small atomic rearrangements.. Fig. 1.2b. Schematic electronic arrangement on the octahedrally surrounded iron. Above TV the mean iron valance state, Fe+2.5, can be understood as a minority spin electron jumping between adjacent octahedral positions, freezing out on specified positions below TV. Octahedral sites are arranged in tetrahedrons; here one possible arrangement, suggested originally by Verwey (and not realized in practice; note the fulfillment of the Anderson criterion for this order: in each tetrahedron two ions are Fe+2, and two are Fe+3) is shown.. This picture of strongly correlated electrons freezing at TV was partially supported by the existing literature data. First, the entropy released at the transition was Rln2 [Shepherd1991], instead of 2Rln2 in case of no order at all was present above TV. Second, in the older NMR results 16.

(17) [Mizoguchi1966] two frequencies observed below TV coalesced into one above. The theoretical band models based on the strongly correlated electron concept [Aragon1988, Song1995] were quite successful in rationalizing the transition and explaining some experimental facts, e.g. the temperature dependence of resistivity [Ihle1986]. Finally, and it was the strongest argument in favor for the ionic model, the experimentally determined total magnetic moment of magnetite formula unit agreed well with that calculated from this model [Kakol1989]. However, the NMR and the X ray resonance scattering experiments carried out at the outbreak of the new millennium [Novak2000, Garcia2001, 2011] questioned both isolated ion notion as well as fast electronic jump in the disordered phase. Although many puzzles remain to be solved, the general idea, posed very early by Verwey, that both charge and orbital ordering, as well as the lattice distortion (to more symmetric high temperature cubic) exist below TV, is still valid with the ordering charges, however, differing by a smaller value than 1 elementary charge, as in the original Verwey model. Up to the early eighties considerable conflicting experimental data about the Verwey transition were accumulated. It was even suggested that this phase transition is in fact a set of two or several closely spaced transitions. Most of these controversies were rationalized when it was found, based on heat capacity data [Shepherd1991], that even very small departures from the ideal 3:4 cation to anion ratio may largely alter the nature of the transition. Namely, studies at Purdue showed that the nonstoichiometry of the level 3δ < 0.012 in Fe 3(1−δ) O 4 ≡ (Fe3+ )[Fe13++6δ Fe12−+9δ ]O 4 linearly lowers the transition temperature and the same is valid for Ti dopands in Fe3-xTixO4 ≡ (Fe3+ )[Fe13−+2x Fe12++x Ti 4x+ ]O 4 and Zn in Fe3-xZnxO4≡ (Fe13-+x Zn 2x+ )[Fe13++x Fe12−+x ]O 4 . Here, parentheses () denote tetrahedral lattice sites and brackets [], octahedral lattice sites. The number of Fe3+ and Fe2+ on octahedral and tetrahedral sites were calculated based on charge and mass neutrality conditions and as a result of precise magnetic measurements [Kakol1989]. Many other dopands were checked [Brabers1998], but zinc, titanium and nonstoichiometry level were found to play a special role: even though the number of "additional" electrons or holes (due to different dopand valence) created by these elements, and the place they enter are different, a striking universal compositional correspondence x ⇔ 3δ was found with respect to the transition temperature TV (see Fig. 1.3a). Also, for 3δ = xZn = xTi > 0.012 the nature of the Verwey transition changes from first to second order (what causes the characteristic drop in TV vs. x), while for a perturbation level higher than 0.036 the transition disappears altogether. The attribution of the Verwey transition temperature changes to the number of defects is, however, not justified, since other dopants [Brabers1998] do not follow this “universal” dependence.. 17.

(18) The clear difference between first and second order magnetite was also evident from the heat capacity results (Fig. 1.3b) obtained in author’s group and published in nineties [Kozlowski1996]. Namely, below TV the heat capacity baseline for first order magnetite diminishes abruptly, contrary to the case for the second order where the baseline at T < TV can be extrapolated from its trend at higher temperatures. For T > TV this heat capacity baseline is virtually identical for both classes of magnetite samples. This behaviour constitutes probably the most clear, apart from the universal TV vs. x relation, Verwey transition order identification parameter. No universal explanation for such a disturbing effect of extraneous elements on the Verwey transition is suggested until now, but the minute perturbation level substantially changing magnetite properties called for special precautions in sample preparations. For these reasons the results of all experiments presented below are obtained on the 5N purity magnetite single crystals grown by skull melter crucibleless method at Purdue University [Harrison1978]. This technique allows for the control of the oxygen partial pressure during growth, thereby ensuring that the melt remains within the stability range of the material. After preparation the crystals are subjected to subsolidus annealing under CO/CO2 gas mixtures to establish the appropriate metal/oxygen ratio [Aragon1983]. 130. 0.8. Fe3-xZnxO4. 0.7. Fe3-xTixO4. 100 90. 0,00. 0,01. 0,02. 0,03. Fe3-xZnxO4. 0.6 2. Zn doped. Cp/T (J/mol K ). 110. Tv ( K ). Fe3(1-δ)O4. 0,04. 0.5 0.4. 500. 0.2 0.1. X, 3δ. 550. 0.3. θD ( K ). 120. 40. x=0 x = 0.010 x = 0.028. 60. 80. 450. 80 100 120 Temperature ( K ). 100. 120. 140. 140. Temperature (K). Fig. 1.3a. Universal TV vs 3δ = x relation (based on [Aragon1986] with subsequent results added). Note the change in transition order manifested by the two slopes in otherwise linear relation. The composition of the samples used for the present studies are marked by large bullets. Sample formulas are shown below, where also the impact of doping on the “mobile” electron density is indicated by green (lowering) and red (rising) arrows.. Fig. 1.3b. Temperature dependence of heat capacity in Fe3−x ZnxO4.([Kozlowski1996] ). The baseline for x = 0.028 (second-order transition) at T < TV is larger than for firstorder samples as better seen in the T dependence of Debye θD (the inset; the peak is removed for clarity). For T >TV , the backgrounds are identical.. 18.

(19) In the quest of what other interactions, on top of Coulomb electron correlations, intervene in the Verwey transition, the crystal lattice was considered first. Apart from the lattice and electronic transition acting simultaneously, the substitution of 43% of normal. 16. O by the heavier. 18. O. isotope, resulted in the increase of TV by ca. 5K [Terukov1979]. Also, the diffuse scattering was observed above TV that showed two distinct temperature dependences. The first was diffuse scattering [Fujii1975, Shapiro1976], observed in noncommensurate positions, that already started as high as 80 K above TV and have critically gained in strength until TV. Below TV, depending on the transition order, either went immediately to zero (first order VT) or proceeded with no change of its strength [Aragon1993], see Fig. 1.4b. This phenomenon was further studied and observed up to room temperature [Bosak2014]. It was also found to be connected to phonon modes that, according to the ab initio study, show a strong softening for larger amplitudes in the presence of local electron interactions in the Fe(3d) [Hoesch2013]. All these suggest that the lattice low-T short range order proceeds up to very high temperatures, but also additionally suggest that the Verwey transition is triggered by a cooperative electron-phonon mechanism in the presence of large Coulomb electron correlations. The other, basically different phenomenon, was the spot like diffuse scattering (Fig. 1.4a), that appeared at the Bragg peaks positions a few K above TV. 800. 1,25. I (8 0 0.75) (counts/2 min). 1/I (arb. units). 1,00. Fe3O4 E=0.0 meV Q=(4,0,0.5). 0,75 0,50. Q=(8,0,0.75). 0,25 TV 0,00 100. 120. 140. 160. 180. 200. T (K). Fe O 3(1-δ) 4 δ = 0.000 δ = 0.006. 600. 400. (8 0 3/4). 200. background 0. 100. 150. 200. T (K). Fig. 1.4a. Temperature dependence of the inverse intensity of the diffuse scattering (solid line) compared with spotlike scattering (red line) (after [Shapiro1976]). Fig. 1.4b. Temperature dependence of the diffuse scattering at (8,0,¾) for first (δ = 0) and second (δ = 0.006) order Verwey transition (after [Aragon1993]).. This dichotomous character of the lattice dynamics aspect of the Verwey transition was also visible in the results of the lattice elastic constants studies. As for the diffuse scattering, this analysis showed that c44 starts to behave in a critical way already at room temperature, in the same manner for both classes (Fig. 1.5a), showing typical Landau relation. c44 = c044. T − TC , T −θ. 19. (1.1).

(20) for continuous phase transitions with a linear coupling between strain and the order parameter. Here θ (= 56K) is the temperature of the phase transition predicted by Landau theory and TC (= 66K) is a real critical temperature resulting from coupling of the order parameter to strain. These two characteristic temperatures are identical for all three samples measured previously, of first- and second-order character and underline the universality of high temperature interactions. 1,1. c44(T)/c44(270 K). x=0 x=0.02. 1,0. Fe3-xZnxO4. 0,9 0,8 0,7 0,6. x=0.032 0. 50. 100. 150. 200. 250. 300. 350. T [K] Fig. 1.5a. The temperature dependence of c44 elastic constant for Zn doped magnetite showing similar approach to the transition, irrespective to its order. (after [Schwenk2000]). Fig. 1.5b. Magnetite total energy diminution with X3 and ∆5 phonon mode amplitude. (after [Piekarz2007]). This picture of strongly correlated electron-phonon system was rationalized by the theoretical symmetry analysis [Piekarz2006, Piekarz2007]. Three vital phonon modes were identified that, together with the strongly coupled electrons, drive the transition. A X3 phonon optic mode, mainly composed of iron vibrations, has been shown to considerably lower the electronic energy, leading ultimately to the change of structure (Fig. 1.5b). The mode closely related to c44 critical behavior above TV was identified as the optic mode of T2g symmetry and the mode ∆5 was found to be possibly responsible for the critical behavior a few K above TV. The analysis showed again that the low-temperature insulating phase of magnetite is due to instability driven by the electron-phonon coupling in the presence of strong electron interactions. The multicharacter phase of the Verwey transition was further revealed by resonant X ray scattering studies [Lorenzo2008] of three Bragg reflections specific to the lattice distortion at TV, charge ordering and orbital ordering, i.e. those three types of entities that order at TV (Fig 1.6a). The main conclusion gained from these studies was that the lattice disorders first on heating as if being less supported by still existing, but highly weakened charge and orbital ordering that, as known from diffuse scattering studies [Bosak2014], survive up to room temperature (Fig 1.6b).. 20.

(21) Fig. 1.6a. Energy scans at three different Q positions, (0, 0, 1/2 ), (0, 0, 1) and (0, 0, 7), and at T = 50K. At Fe K absorption edge of 7.119 keV. Note that (001) peak, reflecting charge order, is highly amplified at resonance, while the “orbital order peak” (0, 0, 1/2 ) is only visible at resonance. (after [Lorenzo2008]).. Fig. 1.6b. Temperature dependence of the intensity of the three different orders: lattice distortion, charge ordering and orbital ordering. (after [Lorenzo2008]).. With this clear experimental and theoretical evidence of the important role of the lattice coupled with electrons in the mechanism of the Verwey transition, the quest for the exact atomic pattern at low temperature must have finally succeeded after almost 80 years since the transition was discovered. The description of the low-T structure was difficult since not only c, but also other monoclinic axes could be along different directions and 24 crystallographic domains were present. The successful refinement [Senn2012] was possible when the crystal size was reduced down to 40 µm and the sample became single domain; even in this case almost 100 thousands peaks must have been analyzed to get the reasonable refinement. The structure is very complicated and the iron atoms on octahedral sites are arranged in characteristic three atoms cigar-like structures, trimerons (Fig. 1.7a, b), with valences of 2.3-2.95 within one trimeron. Generally, the central atom is less positive ("2+"), the end atoms more positive and the trimerons share those „3+” ions. According to the authors, the structure is static: the arrangement, although complicated, does not change with time. But the general impression is that this is also very fragile: a small perturbation, as e.g. a small amount of nonstoichiometry or doping, may either ruin or change this arrangement. This fact is, possibly, reflected in the abrupt transfer from magnetite of first to second order for the certain critical defect concentration. This also asks for its observation from all perspectives and also for the action that can change the trimeron order by the external mean and to check if the whole atomic and electronic arrangement is also altered. Such observation was performed both by our group and by others.. 21.

(22) Fig. 1.7a. Trimeron (cigars) distribution in the low temperature magnetite structure, with Fe2+ and Fe3+ states shown as blue and yellow spheres, respectively. The trimerons are mainly endlinked through Fe3+ ions, but one trimeron is terminated by an Fe2+ ion (circled). Some Fe3+ sites do not participate in any trimerons. [Senn2012]. 1.2.. Fig. 1.7b. Trimeron structure as a coupled distribution of a minority-spin electron (with approximate atomic populations indicated by the sizes of blue t2g orbitals) and associated atomic displacements (purple arrows). Orbital order at the central Fe2+ site (blue) localizes the minorityspin electron in one of the t2g orbitals and elongates the four Fe–O bonds perpendicular to the local axis. Weak bonding interactions transfer minority-spin density into coplanar t2g orbitals at two neighbouring B sites (shown as yellow Fe3+) and shorten the Fe–Fe distances. The minority-spin electron density is approximated by a scalene ellipsoid encompassing the three Fe sites. Other Bsite Fe2+ or Fe3+ neighbours (black spheres) do not participate. [Senn2012]. Verwey transition in statu nascendi In the author’s research group the Verwey transition in the process of its emergence was. observed by AC magnetic susceptibility with, simultaneous, resistivity measurements, and, separately, using the combined coherent X ray diffraction simultaneously with AC magnetic susceptibility. In these studies, a large latent heat, allowing for the sample temperature stabilization for a long time, was exploited. During the time when the temperature was stable and the transition proceeded, all the most important ongoing processes were traced as a function of time. Part of those results where both AC susceptibility and the resistivity were traced this way, is shown in Fig. 1.8a. They suggest that, on cooling, a strong lattice reaction goes past some other processes that cause the AC susceptibility to diminish, i.e. to some extend supporting the results from [Lorenzo2008] on the decoupled three stages of the Verwey transition. Also, the time recording of the peak on CCD clearly shows a structural domains dynamics (Fig. 1.8b). As mentioned above, such an observation naturally asks for the way of not only to see, but also to intervene in the transition by some external mean and, again, for the observation how the process develops in time. To the author’s best knowledge, there are two situations described in 22.

(23) the literature3 where the Verwey transition was treated this way, i.e. was caused by the external trigger: First, high electric field bias was applied to magnetite thin film [Lee2007] and magnetite nanocrystals below TV causing the onset of conductance switching, i.e. the transfer to the high-T phase. In the second, more recent case described in two papers [Pontius2011, Jong2013] a strong burst of energy below the Verwey transition was applied. This ultimately resulted in an ultrafast transfer to the high temperature metallic phase. With moderate energy burst an ultrafast (< 300 fs) punching of holes in the trimeron lattice takes place, followed by a ca 1.50 ps rearrangement of residual trimerons and their decay back to the original state. In the case the energy burst is stronger, the trimeron lattice melts and the characteristic signal in optical reflectivity develops that proves the occurrence of the high-T state. The lattice and electronic order responses are probed using soft X-ray diffraction at the linac coherent light source.. 129. χ'(t). 1,0. 50000. Temperature (K). 128 40000. 127. 0,9. T(t). 126. 30000. 125. 0,8 20000. 124. I(t). 123. 0,7. 0. 122 200. 10000. 250. 300. 350. 400. 450. 500. 550. time (s). Fig. 1.8a. Temperature (A) and temporal (B) dependences of the averaged (1 1½ 2) peak intensity (integrated over main part of CCD screen), and χAC across the Verwey transition on cooling. In (B), also the sample temperature plateau due to latent heat is presented. 3. Fig. 1.8b. Evolution of the (1 1½ 2) superstructure peak on cooling. Left: the peak profiles obtained from the CCD camera at different stages of the phase transition. The brighter color (online) indicates the stronger peak intensity. Right: full time evolution of the superlattice peak: each 2D CCD (as on the left) image has been projected on 1D space (on the horizontal axis) and each row represents one 2D image. The lower line (green online) indicates the beginning of the transition and the other one the end of it.. In one case [Mertens2005] when the external magnetic field was changed from B = 1.5 to 3T at T = 123.6K (i.e. very close to the transition) the electrical resistance jump from 1.8 to1.4 kΩ was noticed and interpreted by the authors as a proof of the transition from low-T phase to high-T phase. However, the paper was not aimed on the deliberate manipulation in the transition, as the papers mentioned above.. 23.

(24) Apart from the fact that the switching of conductivity at the picosecond timescale makes these systems faster than the best graphene transistors [Jong2013] developed so far, it also shows, that the external intervention (energy or electric field) can switch low-T magnetite phase to the highT one and that the process of the system reorganization under this intervention can be observed. In author’s opinion this intervention may be realized also by magnetic field application at temperature slightly lower than TV in the process of axis switching; this process and the early observation of it by author’s group is presented below. In this thesis the extension of those studies motivated by author’s claim that, by this means, it is possible to manipulate the orbital and charge orders are presented.. 1.3.. Axis switching The axis switching (AS) is the change of both easy magnetic and monoclinic c axes. caused by the application of a magnetic field. This is possible due to the coupling of magnetic moment with orbital order. For these reasons, the magnetism in magnetite should be described first.. Fig. 1.9. Symbolic representation of magnetite magnetic anisotropy on top of the temperature dependence of primary magnetic anisotropy constant K1 (after [Abe1976]).. Fe3O4 is a ferrimagnetic material, with spin-only magnetic moment of a total value 4.06 µB /f.u.. At high temperatures magnetic easy, intermediate and hard axes are along cubic <111>, 24.

(25) <110> and <001> directions, respectively (Fig. 1.9). This situation changes at the isotropy point of TIP = 130K (the main anisotropy constant K1 diminishes to zero) and below this temperature magnetic moment points toward <100> direction [Aragón1992,Novak2000]. When magnetite sample is cooled below TV and when the lattice distortion occurs, each of cubic <100> can become an easy magnetic axis and the c monoclinic axis as well. As a result, the material breaks into 24 structural domains unless the external magnetic field H > 2 kOe along the particular [001] is applied [Calhoun1954]. This direction becomes the unique c axis [Król2006, Krol2007] with some charge and orbital arrangement (shown schematically in Fig. 1.10 and in 1.11), e.g. in the form of trimeron lattice.. Fig. 1.10. Top panel: the sequence of events that can occur once the cubic magnetite structure is cooled below TV in B = 0 (twins occur with c along three edge directions) and in B vertical (unique c axis). In case magnetic field is applied along the other cube edge the axis switching may ultimately occur for strong B. This is easily observed in magnetization measurements when B is along other cube edge: there is a clear break in M(B) relation (shown by the arrow in the lower right panel).. On the other hand, when the unique c axis has been established and the magnetite sample is magnetized along one of the other <100> directions, then at temperatures slightly lower than TV, a reorientation of easy magnetic and monoclinic c axes, takes place and this <100> direction becomes a new easy- and monoclinic c axis (Fig. 1.10 and, in a less schematic way, also in Fig. 1.11). This axis switching (AS) phenomenon, first described by Calhoun [Calhoun1954] in early fifties and subsequently studied in [Vittoratos1971], was, from the very beginning, considered as 25.

(26) the reorganization of the electronic arrangement that defines both axes, as presented in Fig. 1.11. Thus, the observation of it gives the unique possibility to study the transformation of charge and orbital order at the transition. Since this is best observed by the magnetization studies, they are summarized below; the author’s own magnetic studies, aimed to observe it under pressure will be shown in Chapter 4.. Fig. 1.11. Symbolic representation of the charge order change caused by the axis switching. The original low T elementary cell (shown in the left panel by the simplified P2/c unit cell [Huang2006]), is suggested to rotate (right panel) forced by external magnetic field (blue arrows); note that the atomic arrangement changed. Cubic cell is shown in green. 20. Bsw/T (T/K). 100. M (emu). 15. Fe3O4,Bll[100] 10. after FC Bll[001] Bsw_ext. 5. 10. 4K 55 K 60 K 65 K. 0 0,0. 0,2. 0,4. activation energy U/k = 353 K. 0,6. 70 K 70 K, Bll[001] 80 K 0,8. 1,0. 1,2. 8. 1,4. B (T) Fig. 1.12a. M(B) isotherms along [100] measured after field-cooling in B = 1T along [001] across TV (easy axis establishing). As long as the axis switching does not occur, M(B) is reversible and typical for an unspecified magnetic direction (T = 4, 55K). The arrow shows the onset of axis switching and defines Bsw; for still higher field and with field lowering, the data reproduce an easy direction (grey triangles), proving the permanent character of AS.. 26. 10. 12 14 1000/T (1/K). 16. 18. Fig. 1.12b. Temperature dependence of switching field, supporting the relation proposed by Calhoun [Calhoun1954]. (after [Krol2010]).

(27) In Fig. 1.12a the results of many isothermal magnetization measurements at different temperatures are presented. In each case, once M is measured along <100> cubic axis that is not the magnetic easy direction, the moment slowly increases and, at some switching field Bsw, deviates to the universal M(B) curve for the easy direction (which is shown here as grey triangles; see also Fig. 1.10); then, when B lowers, the universal curve is followed. With increasing temperature the field at which the axis switches gets lower. As already stated above and originally proposed by [Calhoun1954], the atomic arrangement defining c axis is a result of a certain charge pattern, probably linked to octahedral sites. So, if the magnetic field is applied, then some unsuitable electron positions would tend to change to make the energy lower. But there is an energy barrier U it has to jump over or tunnel through. As a result, for a given T, the field required to switch the axis is Bsw = cTexp(U/kT). So, log(B/T) vs. inverse temperature should be linear, as supported by the experiment (see Fig. 1.12b). The energy barrier U is ca. 350K, i.e. is of the same order of magnitude as the Verwey transition temperature. It may mean that switching the axis causes the manipulation of those entities that will start to rearrange by themselves a few kelvins above at the Verwey transition. To check it and also to shed some light on the axis switching mechanism its dependence on those factors that change the transition temperature, samples doping, were primarily studied. The results of axis switching observation of doped or nonstoichiometric samples, measured by field dependant magnetization, are presented in Fig. 1.13a; the activation energy increases with the lowering Verwey temperature, contrary to the first estimation. Apparently, the axis switching link with the Verwey transition is not straightforward. Namely the activation energy for the axis switching is not a simple measure of the strength of the processes preventing the Verwey transition to occur as the system is heated. Then, in the stoichiometric sample the frequent axis switching was performed in two perpendicular directions and two characteristic parameters, U and Bsw, were obtained. As presented in Fig. 1.13b, the switching field for the first process is considerably higher than for others, while the activation energy (slope of straight lines) remains constant. It was thus suggested [Krol2010] that the first AS process slightly changes those entities (e.g. orbital order) that move during the AS. In other words, the “rigidity” of the electronic surroundings of those atoms that are involved in AS lowers, what is equivalent to the additional internal magnetic field that adds up the one already existing.. 27.

(28) 750 0.2. 650 0.0. 600. log(B sw /T). activation energy U(K). 700. 550 500 450 400 350. stoich. magnetite nonstoich. magnetite Zn doped magnetite. -0.2 -0.4 1 AS, U=354 K 2 AS, U=357 K 3 AS, U=328 K. -0.6. 300. -0.8 9. 110 112 114 116 118 120 122 124 126. TV(K). 10. 11. 12. 13. b). 1000/T. a). Fig. 1.13a. Correlation of the activation energy and Verwey temperature adjusted by doping or nonstoichiometry.. Fig. 1.13b. Activation energy log(Bsw/T) vs.1000/T dependence for successive axis switching scans (marked 1,2,3). Note that while U stays constant, the switching field Bsw lowers.. Since the crystal structure of Fe3O4 affects electrical conductivity (which results e.g. in polaronic conductivity [Ihle1986, Walz2002]) the attempt of a direct inspection how the changing crystal structure influences the electrical conductivity was obvious. The extensive studies were performed [Krol2009, Kolodziej2009, Kolodziej2009#2], where the resistivity was measured simultaneously along [100] and [010] directions (in the setup shown in Fig. 1.14a) while the axis switching was triggered by the magnetic field set perpendicular to c axis. 825. Fe3O4 r B⊥c T=99K. 950. 800. R[100] (Ω). R[010](Ω). 900 850. 775. 800. 750. 750. 725. 700 -4. -3. -2. -1. 0. 1. 2. 3. 4. B(T) Fe3O4 T=99K. 825. r B⊥c 800. R[010](Ω). 900 850. 775. 800. 750. 750 700 -0.3. 725 -0.2. -0.1. 0.0. 0.1. 0.2. 0.3. R[100](Ω). 950. Fig. 1.14. a) The experimental setup for AS observation by the sample resistance; the electrical contacts are marked as blue and red dots. b) The results of resistance measurements in two perpendicular directions (coinciding with [100] and [010] axes) of stoichiometric magnetite sample under magnetic field set normal to c direction. c) The expanded view of the highlighted region from b Note that AS, starting here at ca 0.1T, causes rapid resistance contortions. (after [Kolodziej2009#2]).. B(T). 28.

(29) The representative results, at 99K, presented in Fig. 1.14b and c show that, indeed, the carriers feel the changing structure, although the clear description and the explanation of this process was not reached. Finally, the AS was observed microscopically by the NMR measurements [Chlan2010] performed on the sphere-shaped magnetite single crystal in the arrangement that allowed to adjust the magnetic field along any chosen direction within the (001) plane. Since tetrahedral Fe atoms are nearest neighbors of octahedral sites where the changing arrangements was expected, Fe tetrahedral atoms acted here as probes observing undergoing processes and only the spectra from those Fe positions were analyzed. The results of measurements at 20K and in external magnetic field of 0.3T are presented in Fig. 1.15, together with the schematic representation of possible charge arrangement.. Fig. 1.15. Axis switching detection by NMR; T = 20K. Spectra a and c (tetrahedral sites) correspond to the external magnetic field 0.3 T, set along the easy axis while in the spectrum b the external field is perpendicular to the easy axis. Between the measurements b and c, the sample was heated up to 80 K, and the field of 1.3 T was applied to switch the easy axis. The schematic representation of tetrahedral Fe (left panel; the red dot) watching the surrounding describes the steps of the experiment and the changing octahedral arrangement. (based on [Chlan2010]). Once the c axis was uniquely set by cooling in field4, (Fig. 1.15, upper panel) there is some accompanying charge and orbital order on octahedral positions, and an external magnetic field, pointing along c axis, both observed by tetrahedral Fe nucleus probe (shown symbolically by the. 29.

(30) red dot in Fig. 1.15). NMR spectrum consist of 8 tetrahedral lines, two almost coinciding. The rotation of magnetic field into the other <100> cubic direction (still at 20K) results in a different surrounding of the probe due to different B direction, without, however, affecting charge order (the temperature and magnetic field are too low to cause the axis switching to occur): the NMR spectrum is now substantially different than before. If now the sample is heated to 80K (still far below the Verwey transition temperature, although close enough for AS) and the magnetic field is increased to 1.3T, the axis switching occurs and the magnetic field direction becomes the new c axis. Indeed, the subsequent cooling to 20K and application of 0.3T as before gives NMR spectrum almost identical to that for the first case.. The majority of experiments described above suggest that when magnetite is cooled from high temperatures there exist interactions and their fluctuations (reflected by the diffuse scattering) that drive the system to the second order phase transition at ca 60K (elastic constants studies results). This process is rapidly broken by the nucleation of a new phase that can be triggered by those fluctuations, but otherwise has no relation to the critical, high-temperature behavior. Besides, the major processes present at the Verwey transition, charge and orbital orderings (the results of XRS measurements), can be observed in the process of axis switching. The author claims that the charge and orbital order is to some extend separate from the high temperature interactions and that there is some coupling between them that prevents the Verwey transition to occur at ca 60K, as predicted from high T. These two sites of the Verwey transition may be, to some extend, studied separately, as described below. To prove it, the macroscopic size observation, by strain gauge technique, will be described first. The idea that will be revealed from these studies will be tested and presented in succeeding chapters.. 4. In next sections the procedure of cooling in an external magnetic field is denoted as „FC” (field-cooling), while cooling without magnetic field aplication – „ZFC” (zero-field cooling).. 30.

(31) Chapter 2. Thermal expansion and magnetostriction of magnetite with first and second order Verwey transition 2.1. Introduction The idea presented in the Chapter 1 that the main interactions between atoms are identical for stoichiometric and doped magnetite, and that they lead, at some low temperature, to some kind of a phase transformation, should be now tested from several points of view, focused both on those interactions and on those processes that trigger the transition of a different order. Since, as will be described later on, magnetic field influence on magnetite properties is pronounced and the AS phenomenon will be argued to test orbital ordering impact on magnetite properties, the straightforward impact of magnetic field on magnetite lattice, in the form of magnetostriction, should be measured first. In this chapter the results of magnetostriction measurements are presented, but it also comprises the results of a simple measurements of the size changes with temperature. In both kinds of experiments the size was measured with the strain gauge, the alternative to the diffraction methods. The results of those experiments are, in author’s opinion, vital: the two-fold character of the Verwey transition is clearly revealed and the axis switching phenomenon, easily observed in size vs. magnetic field data, distinguishes the Verwey transition of different character.. 2.2. Previous results: literature data Magnetostriction and thermal expansion measurements below room temperature were already performed before. Bickford [Bickford55] (Fig. 2.1a) measured magnetostriction on natural and synthetic single crystals. The samples were (110) plane circular disks and the measurements were done in the temperature range 120K to 300K. Magnetostriction was measured as a function of crystal orientation with respect to an applied static magnetic field of 0.35 T. High temperature magnetostriction of natural and synthetic magnetite crystals (and also titanomagnetites) was measured by Moskowitz [Moskowitz1971]; representative results are shown in Fig. 2.1b. Similar measurements to those presented in this thesis, but on polycrystalline materials, were done by Aksienova [Aksienova1987]. The results are presented in Figs. 2.1c, d, showing clear anomalies in the vicinity of the Verwey transition. The authors associate these anomalies with the fielddependent Fe2+ orbital ordering below TV, i.e. the effects that are also present in AS. The axis switching was also used to partly interpret the results of low T magnetostriction measurements in 31.

(32) twinned magnetite by Vittoratos [Vittoratos71]. No effort was made to at least partly detwin the crystal.. Fig. 2.1a. λ100, λ111 and λ110 versus temperature for synthetic magnetite single crystal. (after [Bickford55]). ZFC, T=77K. FC 1.8T, T=120K. Fig. 2.1b. High-T magnetostriction results of two synthetic policrystals as measured in [Moskowitz1971].. 1: 88K. B=1.8T. 2: 106K. 3: 114K 6: 157K 5: 131K 4: 117K. B=0. Fig. 2.1c. Temperature dependence of thermal expansion and magnetostriction in polycrystalline magnetite [Aksienova1987].. Fig. 2.1d. Isothermal magnetostriction of polycrystalline magnetite samples in the T region around the Verwey transition temperature [Aksienova1987].. 2.3. Samples The samples (Figs. 2.2 a,b) were Zn doped magnetite single crystals (x = 0.008, with TV = 113K, and x = 0.022, TV = 92K,) grown with skull melter technique, annealed for stoichiometry and cut to have the (001) plane exposed. The samples quality was checked by the routine AC magnetic susceptibility measurements. The results are presented in Fig. 2.2 c, d, together with their TV values on top of the universal TV vs. composition relation (Fig. 2.3). The samples composition was chosen to cover first, and second order Verwey transition regime. The samples were thin plates (thickness below 1 mm, in comparison to ca 5X5 mm other size). Consequently, infinitesimally small demagnetization field was assumed.. 32.

(33) a). b). 12. 40. Tv=112.6K. 35 χ' (a.u.). 10 χ' (a.u.). TV=92.1K. 45. 14. 8 6. 30. 460-2#1 Fe3-xZnxO4 x=0.022. 25 20. 4. 459J#3 Fe3-xZnxO4, x=0.0085. 2 106. 108. 110. 112. 114. 116. 118. 120. 15 10 80. 122. 85. 90. 95. 100. T(K). T(K). d). c). e) Fig. 2.2 a, c, e. The sample, AC magnetic susceptibility results and the Laue pattern for the zinc ferrite with x = 0.008 (459J#3). The data suggest that the sample falls within I order Verwey transition regime. The (100) misalignment is ca 20.. f) Fig. 2.2 b, d, f. The samplle, AC magnetic susceptibility results and the Laue pattern for the zinc ferrite with x = 0.022 (460-2#1). The data suggest that the sample falls within II order Verwey transition regime. The (100) misalignment is ca 20. 130 Fe3(1-δ)O4 Fe3-xZnxO4. 120. Fe3-xTixO4 magnetostriction. Tv ( K ). 110 100 90 80 0.000. 0.013. 0.026. Fig. 2.3 TV of the samples where magnetostriction was measured black spheres) on top of universal TV vs composition relation. The data suggest that 459J#3 falls within I order Verwey transition regime, while 460-2#1 is of the second order.. 0.039. X, 3δ. 33.

(34) 2.4. Experiment Size dependence on temperature (in T range 10-300K) and magnetic field (up to 8T) was measured by the strain gauge [Vishay] glued along [010] direction (Figs. 2.4 and 2.5a) with the Mbond 600 glue [Mbond]. To account for strain gauge temperature characteristics, the same sensor was glued to Si single crystal and measured simultaneously. The measurements of sensors resistances were performed in PPMS using Horizontal Rotator option that enabled magnetic field be aligned along [010] and [100] directions. In general, both the strain gauge and samples mounting as well as the data elaboration were identical to those in refs [Serrate2005] and [Serrate2007]. The resistive response of the strain gauge mounted on the sample can be expressed as the sum of strain gauge thermal coefficient of resistivity and differential expansion coefficients of sample and strain gauge as follows [TN-513-1]: ∆RS ( T ) = [β G + ( α s − α G ) ⋅ FG ]∆T RS. (2.1). where: ∆RS is the strain gauge (mounted on the sample) resistance change;. βG is the thermal coefficient of resistivity of grid material (i.e. strain gauge and substrate), α s − αG =. ∆Ls 1 ∆L 1 − G Ls ∆T LG ∆T. is the difference in thermal expansion coefficients between. specimen and grid, respectively, FG is a gauge factor of the strain gauge, ∆T is the temperature change from arbitrary initial reference temperature (in our case 300K; in what follows all the size changes are relative to the sample size at 300K). Since βG is uncertain, the reference sample, quartz, was used, for which the same relation as that above holds. Subtracting both sites of those equations one gets: ∆RS ( T ) ∆Rq ( T ) − = ( α s − α G − α q + α G ) ⋅ FG ∆T RS Rq. (2.2). where ∆Rq and αq are the resistance change for the strain gauge on quartz and quartz thermal expansion coefficient. Thus: ∆LS ∆Lq 1 ∆RS ∆Rq − = ( − ) LS Lq FG RS Rq. (2.3) ,. and the linear magnetostriction can be obtained since both FG and ∆Lq/Lq are known [TN-513-1]. The linear expansion coefficient αq = (1/Lq)*dLq/dT of quartz (in the form of Infrasil glass [Englisch1989]) can be used to calculate ∆Lq(T)/Lq (relative to Lq at 300K) based on the formula: 34.

(35) ∆Lq ( T ) Lq. T. = exp( ∫ αdT ) − 1 T0. (2.4) .. Since this is small, comparing to the value for magnetite (see Fig. 2.6), and the difference does not affect the most important conclusions, this is set to zero in the forthcoming results presentation. In all the data below the magnetostriction of magnetite, ∆Ls/Ls will be presented in 10-6 units and referred as microstrain (µst). The resistance of both gauges were measured by 4-point standard PPMS setup. Fig. 2.4. The overall shape of the fully encapsulated K-alloy gauge with solder dots (SK-09-031DE-350) used in magnetostriction measurements. The encapsulation (the foil) was trimmed to the sample shape and dimensions. The red arrow shows [010] direction, i.e. the direction of size monitoring. Gage Length = 0.79mm, Overall Length = 3.56, Grid Width = 0.81mm, Overall Width = 0.81mm, Matrix Length = 6.9mm, Matrix Width = 3.0mm. The excitation current for resistance measurements of strain gauges was set automatically by the equipment but was generally ca. 250µA. The number of readings per experimental point was initially set to 50, due to severe time constrains of the equipment; most of the data for both samples was measured under these conditions, what resulted in a considerable data scattering easily seen in the results. Since the additional time was granted for x = 0.022 (460-2#1) sample, the number of readings was increased to 100, what greatly diminished the noise. However, once the same experiment was repeated, it resulted in 5% upward shift of the results. Treating this shift as an artifact, the new data were shifted to previous position that made all new magnetic field runs fully coinciding with the previous results (as long as the comparison was possible: the new data were much less noisy): this is shown in Fig. 2.13. Isothermal magnetostriction studies were performed at temperatures 10K, 90K (x = 0.008), 70K (x = 0.022) (i.e. the temperatures where AS could be observed), 127K (x = 0.008), 102K (x = 0.022), i.e. just above TV, and 290K, specific to the phenomena that were aimed to investigate.. Fig. 2.5a, . Sample holder from horizontal rotator option of PPMS with the sample (grey) and quartz, and with strain gauges glued to them. Note the definition of magnetite crystal orientation.. 35. Fig. 2.5b.Sample holder (green) position on the horizontal rotator in PPMS. Magnetic field direction is shown by the red arrow..

(36) 2.5. Data Presentation The sample configuration on the “dorsal fin-like” sample holder and the way it is placed on the horizontal rotator are shown in Fig. 2.5. The strain gauge is glued along [010] cubic axis. It means that the sample's size along [010] will always be measured, while the c axis may be set either along [010] or along [100], depending on the direction of magnetic field applied on cooling. The real “physical problem” is: how the size of the sample, in the direction along and perpendicular to the easy c axis, changes when magnetic field is applied either along or perpendicular to c. The graphical coding (see the Table 2.1) and the main labeling of figures will be this “physical problem” oriented. In particular, the results (at T < TV) after the field was applied along c axis will be in blue (bulk symbols for the case when the size is observed along c, ∆Lc,Bc, while open symbols when the size is observed perpendicular to c, i.e. is measured in the a-b plane, ∆Lab,Bc) and those with the field within a-b plane (perpendicular to c axis) will be in red (bulk, when the size along c is observed ∆Lc,Bab, open otherwise, ∆Lab,Bab). The data presented below look very noisy; again, however, the most important conclusions of the thesis are clear and are not affected by this noise. For this reason, in most of cases the results were not a subject of smoothing nor data reduction. All the data, relevant to the discussed topic, are presented. For data presentation, the graphical codes, describing the experiments and undergoing physical processes may be useful. Some of those codes, with the description, are presented in the Table 2.1. The others, not shown, are obvious and follow the same style. a) These refer to the magnetostriction measurements, at specified temperature, when B (changed from 0 to 4 or 8T and back to 0) is applied in a-b plane (Bab, left figure; the data will be in red or in redtint color), or along c (Bc, right figure; the data will be in blue or in blue-tint color) and the size is measured along a-b plane (left; labeled ∆Lab; open red symbols, ∆Lab , Bab,), or along c (right; labeled ∆Lc; bulk blue symbols, ∆Lc, Bc,). B c ,. b) This refers to thermal expansion measurements with B (usually 2T or 0.01T) applied along c (blue color) and with size measured along ab plane (∆Lab ,Bc; open blue symbols). More codes for the temperature sweeps are presented in the Table 2.2.. c B. c) When the sample is zero-field-cooled, the c axis is not defined. In this case, the size can be measured in the direction either parallel (∆L||B) or perpendicular (∆L⊥B) to the magnetic field direction.. ,. 36.

(37) d) In case the temperature is not far from TV, the axis switching may occur. Initially, the field is applied along a-b (i.e. the curve will be red) and the size along a-b is monitored (open red symbols, ∆Lab,Bab), but the c axis may switch to the field direction. Note that the final results should resemble those from a) (right figure) if the c axis switch means that the whole crystal was rotated, as NMR and X ray data suggest.. e) AS may also occur when the previously ZFC sample (three domains with c axes in all <100> axes present) are treated by the field at T slightly below TV, as above. f) In case T is from the range TV to TIP, all <100> directions are easy magnetic axes. The data points are marked with various colors and symbols, and labeled ∆Lll in case the size is measured along B (as in the figure) or ∆L⊥ when the size perpendicular to B is measured.. g) If T > TIP all <100> directions are hard magnetic axes and the easy axes are <111>. No special color code was applied here. Table 2.1. Selected graphical codes used in the presentation of magnetostriction and temperature expansion data.. 2.6. Experimental results The most general result of size dependence on temperature is that in both cases of c vs. magnetic field direction, the size along c (∆Lc) and perpendicular to c (∆Lab) shrinks on cooling with the mean sample change ∆Ls/Ls. 5. of the order of 10-3 at lowest temperatures (i.e. when. ∆T = 290K); this is presented in Fig. 2.6. Here both the results based on volume changes for the samples with the c axis not defined during cooling (zero-field-cooled, i.e. “unoriented sample”. Measuring field during heating was set to 0.01T; it was checked that the same results were obtained in case the field was 0) and the samples where c axis was set (in this case the field 2T was applied along c axis on heating) are presented. Also, the data for c-defined samples are shown both in case the shrinking of quartz reference sample is not taken into account (i.e. ∆Lq(T)/Lq = 0; bulk black squares) and when the expansion of quartz was taken into account. In case of “unoriented sample” only the data with “quartz correction” included is shown.. 5. ∆Ls/Ls =(∆V/V)1/3, ∆V/V= (∆Lc/L)* (∆Lab /L)2. 37.

(38) 0 0. x=0.008. x=0.022. Relative change of volume. -200. c axis defined; B=2T. -400. 1/3. with ∆V for quartz set to 0 with ∆V for quartz subtracted. 10 *(∆V/V). -600. c axis not defined; B=0.01T. -800. 0. 50. 100. 150. 200. 250. with ∆V for quartz set to 0 with ∆V for quartz subtracted. -600 -800. c axis not defined; B=0.01T. -1000. with ∆V for quartz subtracted. -1000. c axis defined; B=2T. -400. 6. 6. 10 *(∆V/V). 1/3. -200. 300. Relative change of volume. with ∆V for quartz subtracted 0. 50. 100. 150. 200. 250. 300. T (K) T (K) Fig. 2.6. Mean linear sample direction ∆Ls/Ls = (∆V/V)1/3 for the samples (x = 0.008, left panel; x = 0.022 right panel) with well defined c axes (black symbols; in this case the samples were measured with B = 2T along c axis on heating) and with the domains present (ZFC samples, cyan stars). In the first case the data both with quartz correction (open symbols) and without are presented.. Note that for the first order sample no significant volume change is present for unoriented sample, but not for the second order one in the same condition. As already mentioned above, all the data presented below do not have the “quartz correction” included, since the difference, although present, does not affect any important conclusions of this thesis. 2.6.1. Field sweeps. In general, magnetostriction data were analyzed based on the following issues: 1. Magnetic field dependence of the size, at 10K, caused by magnetic domain movement or magnetization rotation, i.e. in case the magnetic field can not have any irreversible effects on the sample. 2. Magnetic field dependence of the size, at 90K (x = 0.008) and 70K (x = 0.022), caused by magnetic domain movement, magnetization rotation and axis switching (these temperatures were chosen so as to allow the AS to happen). It will be shown that although the first order sample behaves predictably, some extraordinary features are found for the second order sample. 3. Magnetic field dependence of the size, at 127K (x = 0.008) and 110K (x = 0.022), caused by magnetic domain movement, magnetization rotation. 4. Magnetic field dependence of the size, at 290K, caused by magnetic domain movement, magnetization rotation in case <111> are the easy axes.. 38.

(39) A. Magnetic field dependence of the size, at 10K, caused by magnetic domain movement or magnetization rotation. The collected data, in each configuration of magnetic field B vs. c axis and vs. measured dimension is presented on cumulative Fig. 2.7. Here also the data for the zero-field-cooled sample (no unique c axis defined) is shown. The most important details are presented also in Fig. 2.8, while the direct comparison between samples is shown in Fig. 2.9. The main result is that both samples shrink on cooling, more in case of II order sample, and more in direction of monoclinic c axis than in the a-b plane. Also, no visible magnetic field dependence of size is found when magnetization process is solely due to domain walls movement. ∆Lab,Bab -400. ∆Lab,Bc. -950. -500. ∆Lab,Bab. ∆Lab,Bc. -1000. ∆L ⊥B. -1050. x=0.008, T=10K. -700 -800. ∆LllB. ∆LllB µst. µst. -600. -1100. -900 -1000. ∆L ⊥B. x=0.022, T=10K. ∆Lc,Bab. ∆Lc,Bc. ∆Lc,Bab 0. 1. 2. 3. ∆Lc,Bc. -1150. 4. 0. B(T). 1. 2. 3. 4. B(T). Fig. 2.7. Isothermal size dependence upon B at T = 10K. All configurations, i.e. when the field is applied along c (blue and bluish symbols) and in a-b plane (red and reddish) with the size measured along and perpendicular to c are shown. Presented are also the data when the sample was ZFC (c axis was not defined) and the size was measured along (orange) or perpendicular (dark cyan) to the B vector.. In Fig. 2.8 the details of the magnetization process shown in Fig. 2.7 is presented. Note that the size along c (Fig. 2.8 a,b) or perpendicular to c (Fig. 2.8 c,d) is observed while the B vector is applied in different directions. Comparison between the results for both samples in the same scale are shown in Fig. 2.9 together with the graphical representation of cooling and field impact on size.. 39.