Single layered perovskites with the chemical formula La2−xSrxTO4 (T = transition metal) exhibit a variety of intriguing ordering phenomena. The most outstanding is the occurrence of high temperature superconductivity in La2−xSrxCuO4, which can be considered as the prototype system for the more complex cuprates. Some cuprates show incommensurate static charge order at low temperatures [38–40]. For others it is believed that charges are dynamically correlated [39, 147, 259]. Such effects are difficult to measure if the charges fluctuate. In contrast to the cuprate La2−xSrxCuO4 the isostructural nickelates and cobaltates remain insulating over a wide doping range [112, 134, 135, 138]. While incommensurate charge stripe order is long known for the nickelates, recently also evidence for charge stripes in cobaltates has been published [174]. Single crystal rods, with ≈10cm length and ≈0.8cm diameter, have been grown by the traveling solvent floating zone technique using an optical four mirror furnace. We investigated strontium doped nickelates in the range 0.15 ≤ x ≤ 0.22. In addition, also co-doped nickelates have been investigated. A large number of samples with different doping concentrations enabled us to systematically characterize the sample properties. Powder X-ray diffraction measurements were used to determine the lattice parameters. For the nickelates we could confirm the doping dependence of the lattice constants reported in literature [202]. The main interest for the cobaltate system was in the strontium doping range 1/3 ≤ x ≤ 1/2. It was previously reported that the ab-lattice parameter exhibits an anomalous peak around a Sr doping x ≈ 1/3 [140]. We could not confirm such an anomaly for our samples and, instead, we observe a strictly monotonic doping dependence of the lattice parameters which we attribute to the close to perfect stoichiometry of our samples. Samples with the 214-layered perovskite structure can be synthesized over a wide range of oxygen off-stoichiometry. However, the oxygen content can have similarly strong influence on the sample properties as strontium doping. It is therefore essential for data interpretation to determine the oxygen off stoichiometry. EDX and WDX measurements were used to confirm the oxygen content in our nickelates to be nearly stoichiometric. The oxygen content determination of the cobaltates is somewhat more difficult. Thermogravimetry measurements in a flow of Ar/H2 confirmed a nearly stoichiometric oxygen content δ in La2−xSrxCoO4+δ for all samples. We used neutron diffraction measurements to determine the magnetic order in our nickelate samples. In stripe ordered nickelates a small titanium co-doping of the order of 5% is suficcient to supress the incommensurate magnetism and restore antiferromagnetic order. Within the series of zinc co-doped nickelates three samples exhibit an incommensurability epsilon ≈ 1/8, indicating the stabilization of an intermediate stripe pattern with an eightfold unit cell. Compared to the epsilon ≈ 1/3 regime the correlation length is greatly reduced. The magnon dispersion of two samples within the intermediate stripe phases with epsilon ≈ 1/8 and epsilon ≈ 1/4 has been measured with neutron spectroscopy. The observed dispersion neither resembles the one in the undoped nor the 1/3 strontium doped samples. Despite the amount of disorder in our co-doped nickelate materials there are no clear signs for the emergence of hourglass spectra which is most likely caused by a strong exchange interaction across the holes. We investigated the charge and magnetic order in the incommensurate regime of La2−xSrxCoO4 with doping 0.33 ≤ x ≤ 0.5 by elastic neutron scattering and hard X-ray synchrotron measurements. In contrast to the established opinion that this phase is characterized by charge stripe order we were able to show that no charge stripes are present. Instead we found that checkerboard charge order, which is most stable at x = 1/2, persists to a much lower doping than previously thought. The absence of charge stripes is also in agreement with the dispersion of the top most Co-O bond stretching phonon mode. Charge order can induce an anomaly in this branch according to the modulation vector ~q. We observed a softening at ~q = (1/2 1/2 0), which is consistent with our expectations for a checkerboard charge ordered phase. Inelastic neutron measurements revealed an additional high energy part of the hourglass dispersion which has not been reported so far. The entire lowenergy spin excitations that belong to the classical hour-glass dispersion are mostly in-plane excitations, the newly discovered high-energy magnon mode arises from out-of-plane excitations. The resemblance between the low energy excitations below the neck of the hourglass with the excitations in La1.5Sr0.5CoO4 and similarly between the high energy excitations with those observed in La2CoO4 suggests that the observed dispersion is not a single dispersion, but instead consists of two dispersions with distinct origin. In this model the low-energy dispersion arises mainly from magnetic excitations of hole doped regions and the high-energy part would be connected to magnetic excitations within the undoped islands. The absence of charge stripe order in the insulating cobaltates in combination with an unmagnetic low spin state for Co+3 requires a different explanation for the presence of incommensurate magnetic order. We propose a picture on the basis of the ideal checkerboard charge order of the half doped reference system. Decreasing the strontium concentration requires the replacement of Co+3 by Co+2, effectively resulting in the competition between the antiferromagnetic order of the undoped and the antiferromagnetic order of the half doped compound. The induced frustration can be released by a twisting of magnetic moments away from their antiferromagnetic orientation, ultimately leading to the observed incommensurate magnetic order.

Im Rahmen dieser Arbeit wurden thermodynamische Modellationen, Synthesen und Strukturuntersuchungen zu Lanthanoidpolysulfiden und den selenärmeren Lanthanoid-polyseleniden durchgeführt. Bereits bekannte thermodynamische Daten der Lanthanoidpolysulfide, welche durch Gesamtdruckmessungen ermittelt wurden, konnten genutzt werden, um neue Synthesewege zur Darstellung der Lanthanoidpolysulfide thermodynamisch zu modellieren. Im Rahmen dieser Modellierungen wurde für Praseodym exemplarisch gezeigt, dass ein chemischer Gasphasentransport der Polysulfide unter Zugabe von Br2(l) und unter der Ausbildung des Transportmittels SBr2(g) möglich ist. Des Weiteren konnte die Synthese der Verbindungen LnS1.9 (Ln = La – Nd, Gd) unter Verwendung von HgS als Sulfiddonor durchgeführt und anhand der entwickelten elektrochemischen Spannungsreihe anorganischer sulfidischer Festkörper sowie weiterführender thermodynamischer Rechnungen rationalisiert werden. Die durch thermodynamische Rechnungen optimierten Synthesen lieferten Kristalle guter bis hervorragender Qualität, welche durch anschließende Röntgen¬beugungsexperimente charakterisiert wurden. Anhand dieser Daten konnten die Kristallstrukturen einer Vielzahl von Lanthanoidpolychalkogeniden LnQ2–δ (Ln = La – Ho, Y; Q = S, Se; 0 £  £ 0.15) gelöst und verfeinert werden. Die Strukturtypen, welche im Rahmen dieser Arbeit für die Lanthanoidpolychalkogenide gefunden wurden, sind der CeSe2-Typ, der CeSe1.9-Typ, eine niedersymmetrische Form des GdSe1.875-Typs und eine inkommensurabel modulierte Variante des PrSe1.85-Typs. Da es sich bei allen beschriebenen Verbindungen um Überstrukturen des ZrSSi-Typs handelt, wurden zur Veranschaulichung dieser Tatsache Bärnighausen-Stammbäume für die gefundenen Strukturtypen aufgestellt. Anhand dieser Stammbäume wurde illustriert, wie sich die Atomlagen der niedersymmetrischen Überstrukturen aus denen des hochsymmetrischen Aristotyps ableiten lassen.

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This thesis, submitted to the University of Manchester, covers a range of topics related to current research in two-dimensional materials under the title: 'Investigations into the interfacial interaction of graphene with hexagonal boron nitride.'In the last decade, two-dimensional materials have become a rich source of original research and potential applications. The main advantage lies in the ability to produce novel composite structures, so-called 'layered heterostructures', which are only a few atomic layers thick. One can utilise the unique properties of several species of crystal separately, or how they interact to realise a diverse range of uses. Two such crystals are graphene and hexagonal boron nitride. Hexagonal boron nitride has, so far, been used primarily as a substrate for graphene, allowing researchers to get the most out of graphene's impressive individual properties. However, in this thesis, the non-trivial van der Waals interaction between graphene and hexagonal boron nitride is examined. The interface potential reveals itself as a relatively large-scale, orientation-dependant superlattice, which is described in chapters 1 and 2.I In Chapter 4, the effect of this superlattice is examined by measurement of its effect upon the electrons in graphene, where its modulation leads to the creation of second and third generation Dirac points, revealing Hofstadter's Butterfly. As well as an excellent example of the physics possible with graphene, it also presents a new tool with which to create novel devices possessing tailored electronic properties. II In chapter 5, the consequential effect of the superlattice potential on the structure of graphene is studied. Results are discussed within the framework of the Frenkel-Kontorova model for a chain of atoms on a static background potential. Results are consistent with relaxation of the graphene structure leading to the formation of a commensurate ground state. This has exciting consequences for the production of heterostructures by demonstrating that alignment angle can have large effects upon the physical properties of the crystals. III In chapter 6, the van der Waals potential is shown to be responsible for the self-alignment of the two crystals. This effect is important for the fabrication of perfectly aligned devices and may lead to new applications based on nanoscale motion.

<p>Thin metal films have found their use in many magnetic devices. They form pseudo two-dimensional systems, where the mechanisms for the magnetic interactions between the layers are not completely understood. Layered crystal structures have an advantage over such artificial systems, since the layers can be strictly mono-atomic without any unwanted admixture. In this study, some model systems of layered magnetic crystal structures and their solid solutions have been investigated by x-ray and neutron diffraction, Mössbauer and electron spectroscopy, heat-capacity and magnetic measurements, and first-principle electronic structure calculations, with the goal of deepening our understanding through controlled chemical synthesis.</p><p>The compounds TlCo₂S₂, TlCo₂Se₂ and their solid solution TlCo₂Se_2-xS_x, all containing well separated cobalt atom sheets, order with the moments ferromagnetically aligned within the sheets. In TlCo₂S₂, the net result is ferromagnetism, while TlCo₂Se₂ exhibits antiferromagnetism. The inter-layer distance is crucial for the long-range coupling, and it was varied systematically through Se-S substitution. The incommensurate helical magnetic structure found for TlCo₂Se₂ (x = 0) prevails in the composition range 0 ≤ x ≤ 1.5 but the pitch of the helix changes. The accompanying reduction in inter-layer distance on sulphur substitution varies almost linearly with the coupling angle of the helix. An additional competing commensurate helix (90°) appears in the medium composition range (found for x = 0.5 and 1.0).</p><p>The systems TlCo_2-xMe_xSe₂ show helical magnetic ordering for Me = Fe or Cu, while a collinear antiferromagnetic structure occurs for Me = Ni. Magnetic order is created by iron substitution for copper in the Pauli paramagnetic TlCu₂Se₂, but now with the moments perpendicular to the metal sheets.</p><p>TlCrTe₂ forms a quite different crystal structure, with intra-layer ferromagnetic alignment and net collinear antiferromagnetism. In contrast to the other phases, the values of the moments conform well to a localised model for Cr³⁺.</p>

In this thesis I have studied some problems of condensed matter at high pressures and temperatures by means of numerical simulations based on Density Functional Theory (DFT). The stability of MgCO3 and CaCO3 carbonates at the Earth's mantle conditions may play an important role in the global carbon cycle through the subduction of the oceanic crust. By performing ab initio electronic structure calculations, we observed a new high-pressure phase transition within the Pmcn structure of CaCO3. This transformation is characterized by the change of the sp-hybridization state of carbon atom and indicates a change to a new crystal-chemical regime. By performing ab initio Molecular Dynamics simulations we show the new phase to be stable at 250 GPa and 1000K. Thus, the formation of sp3 hybridized bonds in carbonates can explain the stability of MaCO3 and CaCO3 at pressures corresponding to the Earth's lower mantle conditions. We have also calculated phase transition sequence in CaCO3, SrCO3 and BaCO3, and have found that, despite the fact that these carbonates are isostructural and undergo the same type of aragonite to post-aragonite transition, their phase transformation sequences are different at high pressures. The continuous improvement of the high-pressure technique led to the discovery of new composite structures at high pressures and complex phases of many elements in the periodic table have been determined as composite host-guest incommensurate structures. We propose a procedure to accurately describe the structural parameters of an incommensurate phase using ab initio methods by approximating it with a set of analogous commensurate supercells and exploiting the fact that the total energy of the system is a function of structural parameters. By applying this method to the Sc-II phase, we have determined the incommensurate ratio, lattice parameters and Wyckoff positions of Sc-II in excellent agreement with the available experimental data. Moreover, we predict the occurrence of an incommensurate high-pressure phase in Ca from first-principle calculations within this approach. The implementation of DFT in modern electronic structure calculation methods proved to be very successful in predicting the physical properties of a solid at low temperature. One can rigorously describe the thermodynamics of a crystal via the collective excitation of the ionic lattice, and the ab initio calculations give an accurate phonon spectra in the quasi-harmonic approximation. Recently an elegant method to calculate phonon spectra at finite temperature in a self-consistent way by using first principles methods has been developed. Within the framework of self-consistent ab initio lattice dynamics approach (SCAILD) it is possible to reproduce the observed stable phonon spectra of high-temperature bcc phase of Ti, Zr and Hf with a good accuracy. We show that this method gives also a good description of the thermodynamics of hcp and bcc phases of Ti, Zr and Hf at high temperatures, and we provide a procedure for the correct estimation of the hcp to bcc phase transition temperature.

Thin metal films have found their use in many magnetic devices. They form pseudo two-dimensional systems, where the mechanisms for the magnetic interactions between the layers are not completely understood. Layered crystal structures have an advantage over such artificial systems, since the layers can be strictly mono-atomic without any unwanted admixture. In this study, some model systems of layered magnetic crystal structures and their solid solutions have been investigated by x-ray and neutron diffraction, Mössbauer and electron spectroscopy, heat-capacity and magnetic measurements, and first-principle electronic structure calculations, with the goal of deepening our understanding through controlled chemical synthesis. The compounds TlCo2S2, TlCo2Se2 and their solid solution TlCo2Se2-xSx, all containing well separated cobalt atom sheets, order with the moments ferromagnetically aligned within the sheets. In TlCo2S2, the net result is ferromagnetism, while TlCo2Se2 exhibits antiferromagnetism. The inter-layer distance is crucial for the long-range coupling, and it was varied systematically through Se-S substitution. The incommensurate helical magnetic structure found for TlCo2Se2 (x = 0) prevails in the composition range 0 ≤ x ≤ 1.5 but the pitch of the helix changes. The accompanying reduction in inter-layer distance on sulphur substitution varies almost linearly with the coupling angle of the helix. An additional competing commensurate helix (90°) appears in the medium composition range (found for x = 0.5 and 1.0). The systems TlCo2-xMexSe2 show helical magnetic ordering for Me = Fe or Cu, while a collinear antiferromagnetic structure occurs for Me = Ni. Magnetic order is created by iron substitution for copper in the Pauli paramagnetic TlCu2Se2, but now with the moments perpendicular to the metal sheets. TlCrTe2 forms a quite different crystal structure, with intra-layer ferromagnetic alignment and net collinear antiferromagnetism. In contrast to the other phases, the values of the moments conform well to a localised model for Cr3+.

Demands for new, energy-efficient appliances have greatly increased in response to our growing need for a more environmentally friendly society. Magnetic refrigeration is a technique that utilizes the magnetocaloric effect, with possible energy savings of up to 30% compared to commercial gas compression refrigerators. A material appropriate for commercial magnetocaloric devices should be both cheap and non-toxic; it should also exhibit a first-order magnetic transitions close to room temperature. The magnetic properties of Fe2P-related materials can be relevant in this context, since their magnetic properties can be finely tuned through the substitution of Fe by Mn and P by Si, As, Ge or B to meet the general requirements for a magnetocaloric device. An in-depth study has therefore here been made of the structural and magnetic properties of the (Fe,Mn)2(P,Si)-system. The phase diagram of the FeMnP1-xSix-system has been carefully re-examined. It is found to contain two single-phase regions: an orthorhombic Co2P-type structure (x &lt; 0.15) and a hexagonal Fe2P-type structure (0.24 ≤ x &lt; 0.50). Selected compounds within the Fe2P-type region of the phase diagram have been shown to exhibit potential for use in magnetic refrigeration applications. Neutron powder diffraction has here been used to determine the magnetic structures of selected crystalline compositions within the FeMnP1-xSix-system to gain a better understanding of its magnetic properties. The Fe2P-type region is mainly ferromagnetic, but an incommensurate antiferromagnetic structure has also been identified close to the Co2P/Fe2P-type phase border for x ≈ 0.25. The so-called ''virgin effect'' in the Fe2P-type region of the FeMn(P,Si) phase diagram is found to be accompanied by an irreversible structural phase transition induced by magnetostriction. This new phase is found to be preserved during successive cooling-heating cycles. Furthermore, the magnetic properties of the substituted Fe2P-type structure changes significantly for metal:non-metal ratios away from 2:1. Such deviations could well explain the apparently conflicting structure-property relationships described in earlier literature for the FeMnP1-xSix-system.

Ce manuscrit a pour sujet principal la diffraction par rayons X des matériaux ondes de densité de charges (ODC). Nous avons étudié le cristal quasi-1D NbSe3 ainsi que le quasi-2D TbTe3. Plusieurs grands instruments ont été utilisés pour cette étude, le synchrotron ESRF de Grenoble sur la ligne ID01 ainsi que le laser à électron libre LCLS à Stanford. Premièrement, grâce à la cohérence du faisceau X à LCLS, nous avons pu observer une perte de cohérence transverse dans NbSe3 lors de l’application d’un courant électrique au-dessus d’un certain seuil ainsi qu’une compression longitudinale de l’ODC. Ensuite, à l’ESRF, nous avons utilisé un faisceau X focalisé au micromètre par une Fresnel zone plate pour scanner l’ODC localement par diffraction sur NbSe3 puis ensuite sur TbTe3. Lorsqu’un courant est appliqué sur l’échantillon, nous avons observé une déformation transverse indiquant que l’ODC est bloquée au niveau de la surface de l’échantillon dans NbSe3. Dans le cas de TbTe3, l’ODC tourne sous courant présentant un cycle d’hystérésis lorsque le courant passe continument de positif à négatif. Nous avons aussi pu constater dans plusieurs régions, toujours pour TbTe3, la création de défauts d’irradiation localisés induisant une compression-dilatation de l’ODC. Dans une dernière partie théorique, nous montrons comment la théorie du transport électrique de l’ODC par un train de solitons portants chacun une charge ainsi que la prise en compte du blocage de l’ODC sur la surface de l’échantillon que nous avons vu expérimentalement permet de comprendre plusieurs mesures de résistivité en fonction des dimensions de l’échantillon trouvées dans la littérature. Nous présentons ensuite plusieurs idées pour expliquer du blocage de l’ODC sur les surfaces au niveau microscopique et proposons l’hypothèse d’une ODC commensurable en surface (et incommensurable dans le volume). / The main subject of this manuscript is the X-ray diffraction of charge density wave (CDW) materials. We studied the quasi-1D NbSe3 crystal and the quasi-2D TbTe3. Several large instruments facilities were used for this study, the ESRF synchrotron in Grenoble on the ID01 line and the LCLS free electron laser in Stanford. First, thanks to the coherence of the X-beam at LCLS, we were able to observe a loss of transverse coherence in NbSe3 when applying an electrical current above a certain threshold as well as a longitudinal compression of the CDW. Then, at the ESRF, we used an X-ray beam focused on the micrometer scale by a Fresnel zone plate to scan the CDW locally by diffraction on NbSe3 and on TbTe3. When a current is applied to the sample, we observed a transverse deformation indicating that the CDW is pinned on the sample surface in NbSe3. In the case of TbTe3, the CDW rotates under current showing a hysteresis cycle when one is continuously changing from positive to negative current. We have also observed in several regions, in TbTe3, the creation of localized irradiation defects inducing a compression-dilation of the CDW. In a last theoretical part, we show how the theory of electric transport in the CDW state by a train of charged solitons, as well as taking into account the CDW pinning on the surface of the sample that we have seen experimentally, allows us to understand several resistivity measurements, found in the literature, made on samples with different dimensions. Finally, we present several ideas for an explanation of the CDW pinning at the surfaces on a microscopic level and propose the hypothesis of a commensurate CDW on the surface (and incommensurate in volume).

Les alliages à base de Ni-Mn-In ont attiré une attention considérable en raison de leurs propriétés multifonctionnelles depuis leur découverte en 2004, telles que l’effet de mémoire de forme métamagnétique (Metamagnetic shape memory effect MMSME), l'effet magnétocalorique (MCE) et l'effet de magnétorésistance (MR). Cependant, certaines connaissances fondamentales sur ces alliages manquent toujours jusqu'à présent, telles que la structure cristalline de la martensite, les caractéristiques cristallographiques de microstructure et de transition magnétostructurale. Dans cette thèse, les caractéristiques cristallographiques, les comportements mécaniques et les propriétés magnétiques des alliages Ni-Mn-In base ont été étudiés théoriquement et expérimentalement. Tout d'abord, les structures cristallines des alliages Ni-Mn-In ont été déterminées avec précision par la méthode de Rietveld dans le cadre de la théorie du superespace. Ensuite, la microstructure de la martensite, notamment l'organisation et l'interface des variantes, ainsi que les caractéristiques cristallographiques de la transformation martensitique, telles que les relations d'orientation (OR), le chemin de déformation de la transformation et la compatibilité géométrique entre l'austénite et la martensite, ont été systématiquement étudiés. Enfin, avec cette connaissance fondamentale sur les alliages Ni-Mn-In, les comportements et les mécanismes de sélection /réarrangement des variantes de martensite sous deux types de stratégies de chargement mécanique, à savoir le chargement à l'état martensitique et le chargement durant la transition structurelle, et les effets du recuit sur l'effet MCE et les pertes d'hystérésis associées ont été explorées. Les principaux résultats sont les suivants. La martensite modulé a une structure cristalline incommensurable avec la structure cristalline 6M et le groupe de superespace I2/m(α0γ)00 qui peut être approximée par un modèle de superstructure de multiplicité 3 dans l'espace à tridimensionnel. La microstructure de martensite est en forme de plaques et auto-organisée en colonies. Chaque colonie a quatre variantes d'orientations distinctes. Le maximum de 6 colonies distinctes et 24 variantes peut être généré à l'intérieur d'un grain austénitique. Bien que jusqu'à 14 types de relations de maclage sont proposées dans le cadre des théories cristallographiques de transformation martensitique, seuls trois types de relations de maclage sont généralement observés, à savoir des macles de type I, type II et composées. Les interfaces des variantes sont définies à l'échelle mésoscopique par leur plan de maclage K1 correspondant. Cependant, à l'échelle atomique, la macle de type I a une interface cohérente, alors que celles de type-II et les macles composées ont des interfaces étagées. Les deux relations d'orientations K-S et Pitsch sont appropriés pour décrire la correspondance de réseau entre austénite et martensite dans les alliages Ni-Mn-In. Cependant, le chemin de déformation lié à la relation de Pitsch est mis en évidence pour être efficace pour la déformation de la structure. Avec le chemin de transformation déterminé, le mécanisme sous-jacent de l'organisation des variantes est révélé. À travers la transformation martensitique, en dépit de l'existence d'une relativement large couche contrainte (de l'ordre de 20 nm), le plan d'habitat est bordé par une variante de martensite simple avec l'austénite plutôt que la structure généralement observée "en sandwich", ce qui suggère une relativement bonne compatibilité géométrique entre les phases correspondantes. Pour le chargement en compression à l'état martensitique, l'arrangement des variantes est réalisé par des processus de démaclage. Il est démontré que l'état de variante unique dans certaines colonies pourrait être obtenu lorsque l'orientation de chargement est située dans la zone de Facteur de Schmid (SF) positif commune pour les trois systèmes de démaclage. [...] / Ni-Mn-In based alloys have attracted considerable attention due to their multifunctional properties since its discovery in 2004, such as metamagnetic shape memory effect (MMSME), magnetocaloric effect (MCE) and magnetoresistance (MR) effect. However, some fundenmental knowledge on these alloys is still missing until now, such as crystal structure of martensite, crystallographic features of microstructure and magnetostructural transition. In this dissertation, the crystallographic features, mechanical behaviors and magnetic properties of Ni-Mn-In based alloys were studied theoretically and experimentally. First, the crystal structures of Ni-Mn-In alloys were accurately determined by Rietveld method in the frame of superspace theory (Chapter 3). Then, the microstructure of martensite (Chapter 4), such as variant organization and interface structure, and the crystallographic features of martensitic transformation, such as orientation relationship (OR), transformation strain path and geometrical compatibility between austenite and martensite, were systematically studied (Chapter 5). Finally, with this fundamental knowledge on Ni-Mn-In alloys, the behaviors and mechanisms of martensite variant rearrangement/ selection under two kinds of mechanical loading strategies, i.e. loading at martensite state and loading across the structural transition, and the effects of annealing on MCE and its related hysteresis loss were explored (Chapter 6). The main results are as follows. The modulated martensite has an incommensurate 6M crystal structure with superspace group I2/m(α0γ)00 that can be approximated by a three-fold superstructure model in the three-dimensional space. The microstructure of martensite is in plate shape and self-organized in colonies. Each colony has four distinct orientation variants. The maximum of 6 distinct colonies and 24 variants can be generated within one austenite grain. Although as many as 14 kinds of twin relations are suggested in the frame of crystallographic theories of martensitic transformation, only three types of twin relations are generally detected, i.e. type-I, type-II and compound twin. Variant interfaces are defined by their corresponding twinning plane K1 at mesoscopic scale. However, at atomic scale, the type-I twin has a coherent interface, whereas type-II and compound twins have “stepped” interfaces. Both the K-S and Pitsch ORs are appropriate to describe the lattice correspondence between austenite and martensite in Ni-Mn-In alloys. However, the strain path related to the Pitsch relation is evidenced to be the effective for the structural distortion. With the determined transformation path, the underlying mechanism of variant organization is revealed. Across the martensitic transformation, despite the existence of a relative wide stressed layer (around 20 nm), the habit plane is bordered by single martensite variant with austenite rather than the generally observed “sandwich-like” structure, implying a relative good geometrical compatibility between the corresponding phases. For compressive loading at martensite, variant arrangement is realized by the detwinning process. It is evidenced that a single variant state in some colonies can be obtained when the loading orientation is located in the common positive Schmid factor (SF) zone of the three detwinning systems. For loading across the structural transition, the prestrain is obtained by variant selection in which the number of colonies is significantly reduced and the variant organization within colony is greatly changed. The SF for transformation strain path is introduced to evaluate the possible selection of variants. Heat treatment can significantly enhance the magnetic entropy change ΔSM but simultaneously increase the magnetic hysteresis loss. For ΔSM, the chemical ordered degree should play a prominent role [...]