Propriétés statiques et dynamiques des chaînes aimants

The size reduction of magnetic units able to store information is an important issue for the design of high-density data storage devices. The discovery of molecules that show slow relaxation of their magnetization, similar to classical magnets, is a great breakthrough in terms of molecular scale information storage. The work presented in this thesis is devoted to the study of the magnetic properties of Single Chain Magnets. Single Chain Magnets can be viewed as a one-dimensional assembly of anisotropic magnetic units linked by magnetic interactions. Beyond their potential applications, Single Chain Magnets are interesting prototypes for the fundamental study of spin chains. The first chapter of this manuscript summarizes some known static and dynamic properties of Single Chain Magnets. Chapter II is devoted to the static properties of domain walls, which link the magnetic domains in spin chains, considering various magnetic topologies. Chapter III is dedicated to the dynamic properties of Ising spin chains. In the Single Chain Magnet literature, the Glauber model is used to describe the dynamic properties of such spin chains. However, there exists an infinite number of dynamic Ising models. In this chapter, three dynamic models are studied in detail. We show that the presence of a magnetic field allows us to discern different magnetization relaxation behaviors associated with each dynamic model. These results allow us to establish two experimental protocols in order to determine the most suitable dynamic model to describe the properties of Single Chain Magnets.Dans le domaine du stockage de l'information, la miniaturisation de l'unité magnétique portant l'information est un enjeu capital. Ainsi, la découverte de molécules possédant des propriétés de relaxation lente de leur aimantation, comparables à celles des aimants classiques, constitue une avancée majeure suscitant l'espoir de pouvoir un jour stocker l'information à l'échelle moléculaire.Cette thèse a pour but d'étudier les propriétés magnétiques des chaînes aimants. Ces chaînes sont constituées d'unités magnétiques liées par des interactions magnétiques au sein d'un réseau unidimensionnel. Au delà de leurs potentielles applications, les chaînes aimants sont parfaitement adaptées à l'étude fondamentale des chaînes de spins. Le premier chapitre de ce manuscrit constitue un rappel des propriétés statiques et dynamiques des chaînes aimants connues à ce jour. Le deuxième chapitre décrit les propriétés statiques des parois séparant les différents domaines d'aimantation dans des chaînes de spins de topologies magnétiques variées. Le troisième chapitre de ce manuscrit décrit les propriétés dynamiques des chaînes de spins d'Ising. Bien que seul le modèle de Glauber soit utilisé dans la littérature associée aux chaînes aimants, il existe une infinité de modèles dynamiques d'Ising.Grâce à l'étude détaillée de trois modèles, il est montré dans ce chapitre que l'application d'un champ magnétique permet de révéler différentes dynamiques de relaxation de l'aimantation pour chacun des modèles considérés. Ces résultats permettent enfin de proposer deux protocoles expérimentaux à même de déterminer le modèle dynamique le plus adapté à l'étude des chaînes aimants

Static and dynamic properties of Single-Chain Magnets with sharp and broad domain walls

We discuss time-quantified Monte-Carlo simulations on classical spin chains with uniaxial anisotropy in relation to static calculations. Depending on the thickness of domain walls, controlled by the relative strength of the exchange and magnetic anisotropy energy, we found two distinct regimes in which both the static and dynamic behavior are different. For broad domain walls, the interplay between localized excitations and spin waves turns out to be crucial at finite temperature. As a consequence, a different protocol should be followed in the experimental characterization of slow-relaxing spin chains with broad domain walls with respect to the usual Ising limit.Comment: 18 pages, 13 figures, to be published in Phys. Rev.

Static and dynamic properties of Single Chain Magnets

Dans le domaine du stockage de l'information, la miniaturisation de l'unité magnétique portant l'information est un enjeu capital. Ainsi, la découverte de molécules possédant des propriétés de relaxation lente de leur aimantation, comparables à celles des aimants classiques, constitue une avancée majeure suscitant l'espoir de pouvoir un jour stocker l'information à l'échelle moléculaire.Cette thèse a pour but d'étudier les propriétés magnétiques des chaînes aimants. Ces chaînes sont constituées d'unités magnétiques liées par des interactions magnétiques au sein d'un réseau unidimensionnel. Au delà de leurs potentielles applications, les chaînes aimants sont parfaitement adaptées à l'étude fondamentale des chaînes de spins. Le premier chapitre de ce manuscrit constitue un rappel des propriétés statiques et dynamiques des chaînes aimants connues à ce jour. Le deuxième chapitre décrit les propriétés statiques des parois séparant les différents domaines d'aimantation dans des chaînes de spins de topologies magnétiques variées. Le troisième chapitre de ce manuscrit décrit les propriétés dynamiques des chaînes de spins d'Ising. Bien que seul le modèle de Glauber soit utilisé dans la littérature associée aux chaînes aimants, il existe une infinité de modèles dynamiques d'Ising.Grâce à l'étude détaillée de trois modèles, il est montré dans ce chapitre que l'application d'un champ magnétique permet de révéler différentes dynamiques de relaxation de l'aimantation pour chacun des modèles considérés. Ces résultats permettent enfin de proposer deux protocoles expérimentaux à même de déterminer le modèle dynamique le plus adapté à l'étude des chaînes aimants.The size reduction of magnetic units able to store information is an important issue for the design of high-density data storage devices. The discovery of molecules that show slow relaxation of their magnetization, similar to classical magnets, is a great breakthrough in terms of molecular scale information storage. The work presented in this thesis is devoted to the study of the magnetic properties of Single Chain Magnets. Single Chain Magnets can be viewed as a one-dimensional assembly of anisotropic magnetic units linked by magnetic interactions. Beyond their potential applications, Single Chain Magnets are interesting prototypes for the fundamental study of spin chains. The first chapter of this manuscript summarizes some known static and dynamic properties of Single Chain Magnets. Chapter II is devoted to the static properties of domain walls, which link the magnetic domains in spin chains, considering various magnetic topologies. Chapter III is dedicated to the dynamic properties of Ising spin chains. In the Single Chain Magnet literature, the Glauber model is used to describe the dynamic properties of such spin chains. However, there exists an infinite number of dynamic Ising models. In this chapter, three dynamic models are studied in detail. We show that the presence of a magnetic field allows us to discern different magnetization relaxation behaviors associated with each dynamic model. These results allow us to establish two experimental protocols in order to determine the most suitable dynamic model to describe the properties of Single Chain Magnets

Static and dynamic properties of Single Chain Magnets

Dans le domaine du stockage de l'information, la miniaturisation de l'unité magnétique portant l'information est un enjeu capital. Ainsi, la découverte de molécules possédant des propriétés de relaxation lente de leur aimantation, comparables à celles des aimants classiques, constitue une avancée majeure suscitant l'espoir de pouvoir un jour stocker l'information à l'échelle moléculaire.Cette thèse a pour but d'étudier les propriétés magnétiques des chaînes aimants. Ces chaînes sont constituées d'unités magnétiques liées par des interactions magnétiques au sein d'un réseau unidimensionnel. Au delà de leurs potentielles applications, les chaînes aimants sont parfaitement adaptées à l'étude fondamentale des chaînes de spins. Le premier chapitre de ce manuscrit constitue un rappel des propriétés statiques et dynamiques des chaînes aimants connues à ce jour. Le deuxième chapitre décrit les propriétés statiques des parois séparant les différents domaines d'aimantation dans des chaînes de spins de topologies magnétiques variées. Le troisième chapitre de ce manuscrit décrit les propriétés dynamiques des chaînes de spins d'Ising. Bien que seul le modèle de Glauber soit utilisé dans la littérature associée aux chaînes aimants, il existe une infinité de modèles dynamiques d'Ising.Grâce à l'étude détaillée de trois modèles, il est montré dans ce chapitre que l'application d'un champ magnétique permet de révéler différentes dynamiques de relaxation de l'aimantation pour chacun des modèles considérés. Ces résultats permettent enfin de proposer deux protocoles expérimentaux à même de déterminer le modèle dynamique le plus adapté à l'étude des chaînes aimants.The size reduction of magnetic units able to store information is an important issue for the design of high-density data storage devices. The discovery of molecules that show slow relaxation of their magnetization, similar to classical magnets, is a great breakthrough in terms of molecular scale information storage. The work presented in this thesis is devoted to the study of the magnetic properties of Single Chain Magnets. Single Chain Magnets can be viewed as a one-dimensional assembly of anisotropic magnetic units linked by magnetic interactions. Beyond their potential applications, Single Chain Magnets are interesting prototypes for the fundamental study of spin chains. The first chapter of this manuscript summarizes some known static and dynamic properties of Single Chain Magnets. Chapter II is devoted to the static properties of domain walls, which link the magnetic domains in spin chains, considering various magnetic topologies. Chapter III is dedicated to the dynamic properties of Ising spin chains. In the Single Chain Magnet literature, the Glauber model is used to describe the dynamic properties of such spin chains. However, there exists an infinite number of dynamic Ising models. In this chapter, three dynamic models are studied in detail. We show that the presence of a magnetic field allows us to discern different magnetization relaxation behaviors associated with each dynamic model. These results allow us to establish two experimental protocols in order to determine the most suitable dynamic model to describe the properties of Single Chain Magnets

Single-Chain Magnets and Related Systems

In this chapter, the static and dynamic magnetic properties of singlechain magnets and related systems are reviewed. We will particularly focus on the so-called Ising limit for which the magnetic anisotropy energy is much larger than the energy of the intrachain exchange interactions. The simple regular chain of ferromagnetically coupled spins will be first described. Static properties will be summarized to introduce the dominant role of domain walls at low temperature. The slow relaxation of the magnetization will be then discussed using a stochastic description. The deduced dynamic critical behavior will be analyzed in detail to explain the observed magnet behavior. In particular, the effect of applying a magnetic field, often ignored in the literature, will be discussed. Then, more complicated structures including chains of antiferromagnetically coupled magnetic sites will be discussed. Finally, the importance of interchain couplings will be introduced to discriminate between a “real” single-chain magnet and a sample presenting both a magnet-type property and a three-dimensional antiferromagnetic ordered state at low temperature

Domain walls in single-chain magnets

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Magnetic tetrastability in a spin chain

Bistability in magnetism is extensively used, in particular for information storage. Here an alternative approach using tetrastable magnetic domains in one-dimensional (1D) spin systems is presented. Using numerical and analytical calculations, we show that a spin chain with a canting angle of π/4 possesses four energy-equivalent states. We discuss the static properties of this canted 1D system such as the profile and the energy of the domain walls as they govern the dynamics of themagnetization. The realization of this π/4 canted spin chain could enable the encoding of the information on four bits, which is a potential alternative toward the increase of storage density

Evaluating growth and risk of relapse of intracranial tumors

As cancer evolution is challenging to evaluate, there is dire need of novel approaches offering clinicians a better insight on the disease. For instance, having an estimation of the growth of slowly evolving tumors that have to be monitored or of the risk of relapse after treatment may be invaluable for clinicians. In this article, two approaches (statistical learning and mechanistic modelling) are presented that aim at addressing these clinical questions. As we wish to use data available in the clinical routine for solid tumors, medical images will be a major source of insight on the disease

Spatial mechanistic modeling for prediction of the growth of asymptomatic meningioma

Mathematical modeling of tumor growth draws interest from the medical community as they have the potential to improve patients' care and the use of public health resources. The main objectives of this work are to model the growth of meningiomas-slow-growing benign tumors requiring extended imaging follow-up-and to predict tumor volume and shape at a later desired time using only two time examinations. We propose two variants of a 3D partial differential system of equations (PDE) which yield after a spatial integration systems of ordinary differential equations (ODE) that relate tumor volume with time. Estimation of models parameters is a crucial step for obtaining a personalized model for a patient that can be used for descriptive or predictive purposes. As PDE and ODE systems share the same parameters, they are both estimated by fitting the ODE systems to the tumor volumes obtained from MRI examinations acquired at different times. A population approach allows to compensate for sparse sampling times and measurement uncertainties by constraining the variability of the parameters in the population. Description capabilities of the models are investigated in 40 patients with benign asymptomatic meningiomas who had had at least 3 surveillance MRI examinations. The two models can fit to the data accurately and more realistically than a naive linear regression. Prediction performances are validated for 33 patients using a population approach. Mean relative errors in volume predictions are less than 10% with ODE systems versus 12.5% with the naive linear model using only two time examinations. Concerning the shape, the mean Sørensen-Dice coefficients are 85% with the PDE systems in a subset of 10 representative patients

Spatial mechanistic modeling for prediction of the growth of asymptomatic meningioma

Mathematical modeling of tumor growth draws interest from the medical community as they have the potential to improve patients' care and the use of public health resources. The main objectives of this work are to model the growth of meningiomas-slow-growing benign tumors requiring extended imaging follow-up-and to predict tumor volume and shape at a later desired time using only two time examinations. We propose two variants of a 3D partial differential system of equations (PDE) which yield after a spatial integration systems of ordinary differential equations (ODE) that relate tumor volume with time. Estimation of models parameters is a crucial step for obtaining a personalized model for a patient that can be used for descriptive or predictive purposes. As PDE and ODE systems share the same parameters, they are both estimated by fitting the ODE systems to the tumor volumes obtained from MRI examinations acquired at different times. A population approach allows to compensate for sparse sampling times and measurement uncertainties by constraining the variability of the parameters in the population. Description capabilities of the models are investigated in 40 patients with benign asymptomatic meningiomas who had had at least 3 surveillance MRI examinations. The two models can fit to the data accurately and more realistically than a naive linear regression. Prediction performances are validated for 33 patients using a population approach. Mean relative errors in volume predictions are less than 10% with ODE systems versus 12.5% with the naive linear model using only two time examinations. Concerning the shape, the mean Sørensen-Dice coefficients are 85% with the PDE systems in a subset of 10 representative patients