Dynamical phase transitions study in a Co(1−x)Rux magnetic system of two-dimensional Ising type
ABSTRACT: The study of the magnetic properties in new materials has allowed great advances from the technological and industrial point of view. Therefore, the understanding of the physical phenomena that involve magnetism is a challenge that is still in force and that increasingly includes more rese...
- Autores:
-
Marín Ramírez, Juan Marcos
- Tipo de recurso:
- Doctoral thesis
- Fecha de publicación:
- 2020
- Institución:
- Universidad de Antioquia
- Repositorio:
- Repositorio UdeA
- Idioma:
- eng
- OAI Identifier:
- oai:bibliotecadigital.udea.edu.co:10495/19522
- Acceso en línea:
- http://hdl.handle.net/10495/19522
- Palabra clave:
- Ising model
Phase transformations (Statistical physics)
Mean field theory
Kerr effect
Magnetismo
Magnetism
Magnetización
Magnetization
Sistemas dinámicos
http://id.loc.gov/authorities/subjects/sh85068376
http://id.loc.gov/authorities/subjects/sh85100646
http://id.loc.gov/authorities/subjects/sh96010226
http://id.loc.gov/authorities/subjects/sh85072072
- Rights
- openAccess
- License
- Atribución-NoComercial-CompartirIgual 2.5 Colombia (CC BY-NC-SA 2.5 CO)
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dc.title.spa.fl_str_mv |
Dynamical phase transitions study in a Co(1−x)Rux magnetic system of two-dimensional Ising type |
dc.title.alternative.spa.fl_str_mv |
Estudio de las transiciones dinámicas de fase en sistemas magnéticos de Co(1-x)Rux del tipo Ising bidimensional |
title |
Dynamical phase transitions study in a Co(1−x)Rux magnetic system of two-dimensional Ising type |
spellingShingle |
Dynamical phase transitions study in a Co(1−x)Rux magnetic system of two-dimensional Ising type Ising model Phase transformations (Statistical physics) Mean field theory Kerr effect Magnetismo Magnetism Magnetización Magnetization Sistemas dinámicos http://id.loc.gov/authorities/subjects/sh85068376 http://id.loc.gov/authorities/subjects/sh85100646 http://id.loc.gov/authorities/subjects/sh96010226 http://id.loc.gov/authorities/subjects/sh85072072 |
title_short |
Dynamical phase transitions study in a Co(1−x)Rux magnetic system of two-dimensional Ising type |
title_full |
Dynamical phase transitions study in a Co(1−x)Rux magnetic system of two-dimensional Ising type |
title_fullStr |
Dynamical phase transitions study in a Co(1−x)Rux magnetic system of two-dimensional Ising type |
title_full_unstemmed |
Dynamical phase transitions study in a Co(1−x)Rux magnetic system of two-dimensional Ising type |
title_sort |
Dynamical phase transitions study in a Co(1−x)Rux magnetic system of two-dimensional Ising type |
dc.creator.fl_str_mv |
Marín Ramírez, Juan Marcos |
dc.contributor.advisor.none.fl_str_mv |
Arnache Olmos, Oscar Luis Campillo Figueroa, Gloria Eugenia |
dc.contributor.author.none.fl_str_mv |
Marín Ramírez, Juan Marcos |
dc.subject.lcsh.none.fl_str_mv |
Ising model Phase transformations (Statistical physics) Mean field theory Kerr effect |
topic |
Ising model Phase transformations (Statistical physics) Mean field theory Kerr effect Magnetismo Magnetism Magnetización Magnetization Sistemas dinámicos http://id.loc.gov/authorities/subjects/sh85068376 http://id.loc.gov/authorities/subjects/sh85100646 http://id.loc.gov/authorities/subjects/sh96010226 http://id.loc.gov/authorities/subjects/sh85072072 |
dc.subject.unesco.none.fl_str_mv |
Magnetismo Magnetism |
dc.subject.lemb.none.fl_str_mv |
Magnetización Magnetization |
dc.subject.proposal.spa.fl_str_mv |
Sistemas dinámicos |
dc.subject.lcshuri.none.fl_str_mv |
http://id.loc.gov/authorities/subjects/sh85068376 http://id.loc.gov/authorities/subjects/sh85100646 http://id.loc.gov/authorities/subjects/sh96010226 http://id.loc.gov/authorities/subjects/sh85072072 |
description |
ABSTRACT: The study of the magnetic properties in new materials has allowed great advances from the technological and industrial point of view. Therefore, the understanding of the physical phenomena that involve magnetism is a challenge that is still in force and that increasingly includes more research. This continuous search has been focused on the development and study of new experimental techniques, analytical and/or theoretical models that can provide the necessary tools to transcend current technological barriers and demands. Hence, the manufacture of nano-structured materials has led to the discovery of new and exciting magnetic properties and devices. That is why, in the first part of this thesis, we will try to elaborate and develop a methodological procedure that allows the use and adaptation of advanced materials manufacturing tools, which will enable the synthesis of nano-structured magnetic thin films. This thin films have a high reproducibility and also are ferromagnetic at room temperature, a relevant aspect for a technological perspective. Likewise, these ultrathin systems can be structurally manipulated to modify the critical magnetic transition temperature or Curie Tc temperature, an intrinsic property of all ferromagnetic materials. Furthermore, for the study of these systems it is necessary to develop an understanding of how the magnetization process occurs and its magnetization reversal (change of sign) in systems with a high anisotropy, that is, systems that have an easy axis of magnetization. These materials are currently widely used in magnetic recording processes. Combined with this last fact and the current demands for more information and speed capability of electronic devices by the final consumer, it is essential to understand the dynamic processes of magnetization under the effect of time-dependent magnetic fields. Therefore, in the second part of our work we will find some important peculiarities of the study of magnetic transitions in low dimensional systems using external excitations with temporal dependence. For this, we will take advantage of the Kerr magneto-optical effect or MOKE, as our main study tool. This phenomenon consists of the change of polarization in an electromagnetic wave when reflected by a magnetized surface, allowing more information about some fundamental magnetic observables even at the limit of monolayers (a few atoms). Therefore, by employing the Kerr effect in conjunction with a suitable series of test samples, we are able to study the dynamic magnetic behavior in the vicinity of the dynamic phase transition (DPT). Likewise, by changing the intrinsic Curie temperature in our thin film systems, i.e. the reduced temperature T/Tc we can access experimentally to a wider portion of the dynamic phase diagram which has not been addressed before either theoretically or experimentally for dynamic magnetic systems. For this purpose, we have fabricated Co1−xRux (1010) epitaxial thin films with uniaxial in-plane anisotropy by means of sputter deposition in the concentration range 0.0 ≤ x ≤ 0.26. All samples are ferromagnetic at room temperature, exhibit an abrupt magnetization reversal along their easy axis, and represent a unique Tc and thus T/Tc-ratio according to their Ru concentration. The dynamic magnetic behavior was measured by using an ultra-sensitive transverse magneto-optical detection method, and the resulting dynamic states were explored as a function of the applied magnetic field amplitude H0 and period P, as well as an additional bias field Hb, which is the conjugate field of the dynamic order parameter Q. Our experimental results demonstrate that the qualitative behavior of the dynamic phase diagram is independent from the T/Tc-ratio, and that for all T/Tc values, we observe metamagnetic anomalies in the dynamically paramagnetic state. These anomalies are characterized by a rapid rise in the order parameter in a small region of bias field, which are not present in the corresponding thermodynamic phase diagram. However, quantitatively these metamagnetic anomalies are very strongly dependent on the T/Tc-ratio, leading to an about 20-fold increase in magnitude for the metamagnetic fluctuations in the paramagnetic regime as the T/Tc-ratio increases from 0.37 to 0.68. Also, the phase space range, in which these anomalous metamagnetic fluctuations occur, extends closer and closer to the critical point as T/Tc increases. |
publishDate |
2020 |
dc.date.issued.none.fl_str_mv |
2020 |
dc.date.accessioned.none.fl_str_mv |
2021-05-05T17:36:02Z |
dc.date.available.none.fl_str_mv |
2021-05-05T17:36:02Z |
dc.type.spa.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
dc.type.hasversion.spa.fl_str_mv |
info:eu-repo/semantics/acceptedVersion |
dc.type.coar.spa.fl_str_mv |
http://purl.org/coar/resource_type/c_db06 |
dc.type.redcol.spa.fl_str_mv |
https://purl.org/redcol/resource_type/TD |
dc.type.local.spa.fl_str_mv |
Tesis/Trabajo de grado - Monografía - Doctorado |
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http://hdl.handle.net/10495/19522 |
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http://hdl.handle.net/10495/19522 |
dc.language.iso.spa.fl_str_mv |
eng |
language |
eng |
dc.rights.spa.fl_str_mv |
info:eu-repo/semantics/openAccess |
dc.rights.*.fl_str_mv |
Atribución-NoComercial-CompartirIgual 2.5 Colombia (CC BY-NC-SA 2.5 CO) |
dc.rights.uri.*.fl_str_mv |
http://creativecommons.org/licenses/by-nc-sa/2.5/co/ |
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openAccess |
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Medellín, Colombia |
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Arnache Olmos, Oscar LuisCampillo Figueroa, Gloria EugeniaMarín Ramírez, Juan Marcos2021-05-05T17:36:02Z2021-05-05T17:36:02Z2020http://hdl.handle.net/10495/19522ABSTRACT: The study of the magnetic properties in new materials has allowed great advances from the technological and industrial point of view. Therefore, the understanding of the physical phenomena that involve magnetism is a challenge that is still in force and that increasingly includes more research. This continuous search has been focused on the development and study of new experimental techniques, analytical and/or theoretical models that can provide the necessary tools to transcend current technological barriers and demands. Hence, the manufacture of nano-structured materials has led to the discovery of new and exciting magnetic properties and devices. That is why, in the first part of this thesis, we will try to elaborate and develop a methodological procedure that allows the use and adaptation of advanced materials manufacturing tools, which will enable the synthesis of nano-structured magnetic thin films. This thin films have a high reproducibility and also are ferromagnetic at room temperature, a relevant aspect for a technological perspective. Likewise, these ultrathin systems can be structurally manipulated to modify the critical magnetic transition temperature or Curie Tc temperature, an intrinsic property of all ferromagnetic materials. Furthermore, for the study of these systems it is necessary to develop an understanding of how the magnetization process occurs and its magnetization reversal (change of sign) in systems with a high anisotropy, that is, systems that have an easy axis of magnetization. These materials are currently widely used in magnetic recording processes. Combined with this last fact and the current demands for more information and speed capability of electronic devices by the final consumer, it is essential to understand the dynamic processes of magnetization under the effect of time-dependent magnetic fields. Therefore, in the second part of our work we will find some important peculiarities of the study of magnetic transitions in low dimensional systems using external excitations with temporal dependence. For this, we will take advantage of the Kerr magneto-optical effect or MOKE, as our main study tool. This phenomenon consists of the change of polarization in an electromagnetic wave when reflected by a magnetized surface, allowing more information about some fundamental magnetic observables even at the limit of monolayers (a few atoms). Therefore, by employing the Kerr effect in conjunction with a suitable series of test samples, we are able to study the dynamic magnetic behavior in the vicinity of the dynamic phase transition (DPT). Likewise, by changing the intrinsic Curie temperature in our thin film systems, i.e. the reduced temperature T/Tc we can access experimentally to a wider portion of the dynamic phase diagram which has not been addressed before either theoretically or experimentally for dynamic magnetic systems. For this purpose, we have fabricated Co1−xRux (1010) epitaxial thin films with uniaxial in-plane anisotropy by means of sputter deposition in the concentration range 0.0 ≤ x ≤ 0.26. All samples are ferromagnetic at room temperature, exhibit an abrupt magnetization reversal along their easy axis, and represent a unique Tc and thus T/Tc-ratio according to their Ru concentration. The dynamic magnetic behavior was measured by using an ultra-sensitive transverse magneto-optical detection method, and the resulting dynamic states were explored as a function of the applied magnetic field amplitude H0 and period P, as well as an additional bias field Hb, which is the conjugate field of the dynamic order parameter Q. Our experimental results demonstrate that the qualitative behavior of the dynamic phase diagram is independent from the T/Tc-ratio, and that for all T/Tc values, we observe metamagnetic anomalies in the dynamically paramagnetic state. These anomalies are characterized by a rapid rise in the order parameter in a small region of bias field, which are not present in the corresponding thermodynamic phase diagram. However, quantitatively these metamagnetic anomalies are very strongly dependent on the T/Tc-ratio, leading to an about 20-fold increase in magnitude for the metamagnetic fluctuations in the paramagnetic regime as the T/Tc-ratio increases from 0.37 to 0.68. Also, the phase space range, in which these anomalous metamagnetic fluctuations occur, extends closer and closer to the critical point as T/Tc increases.RESUMEN: El estudio de las propiedades magnéticas en nuevos materiales ha permitido grandes avances desde el punto de vista tecnológico e industrial. Por ende, el entendimiento delos fenómenos físicos que involucran el magnetismo es un reto aún vigente y que cada vez abarca mayor investigación. Esta continua búsqueda, está enfocada en el desarrollo y estudio de nuevas técnicas experimentales, de modelos analíticos y/o teóricos, que provean las herramientas necesarias para trascender las barreras y demandas tecnológicas actuales. De allí, que la fabricación de materiales nano-estructurados ha dado pie al descubrimiento de nuevas y excitantes propiedades desde el punto de vista magnético. Es por ello, que en primera instancia esta tesis tratará de elaborar y desarrollar un proceso metodológico que permita la utilización y adaptación de herramientas de fabricación de materiales avanzadas. Esto, permitirá la sinterización de películas delgadas magnéticas nano-estructuradas, con una alta reproducibilidad y además ferromagnéticas a temperatura ambiente. A su vez, estos sistemas pueden ser manipulados estructuralmente para modificar la temperatura critica de transición magnética o temperatura de Curie Tc, propiedad intrínseca de todos los materiales ferromagnéticos. Igualmente, para el estudio de estas películas delgadas es necesario desarrollar un entendimiento de cómo se da el proceso de magnetización y su inversión (cambio de signo) en sistemas con alta anisotropía, esto es, que presentan un eje fácil de magnetización. Estos materiales son actualmente ampliamente utilizados en procesos de grabación magnética. Combinado con este último hecho y las demandas actuales de mayor información y rapidez en la velocidad de dispositivos electrónicos por parte de sus consumidores, hace que el entender los procesos dinámicos de la magnetización bajo el efecto de campos magnéticos dependientes del tiempo, sea fundamental. Por ende, en la segunda parte de nuestro trabajo encontraremos algunas particularidades importantes del estudio de transiciones magnéticas en sistemas de baja dimensionalidad utilizando excitaciones externas con dependencia temporal. Para ello, aprovecharemos el efecto Kerr magneto-óptico o MOKE (por sus siglas en inglés), como herramienta de estudio principal. Este fenómeno, consiste en el cambio de la polarización en una onda electromagnética al ser reflejado por una superficie magnetizada, permitiendo mayor información sobre algunos observables magnéticos fundamentales incluso en el límite de las monocapas (unos pocos átomos). Por lo tanto, al emplear el efecto Kerr magneto-óptico junto con una serie adecuada de muestras, podemos estudiar el comportamiento magnético dinámico en las proximidades de la transición dinámicas de fase. Del mismo modo, al cambiar la temperatura intrínseca de Curie en nuestras películas delgada, es decir, la temperatura reducida T/Tc, podemos acceder experimentalmente a una porción más amplia del diagrama de fase dinámico que no se ha abordado antes ni teóricamente ni experimentalmente en el estudio de la dinámica de sistemas magnéticos. Es por esto, que hemos fabricado una serie de películas delgadas epitaxiales de Co1−xRux (1010) utilizando la técnica de Sputtering en un rango de concentración de 0.0 ≤ x ≤ 0.26. El dopaje con Rutenio (x) permite modificar la Tc de las películas sin alterar sustancialmente las propiedades estructurales de las películas, en especial aquellas relacionadas con la epitaxialidad del sistema. Luego, todas nuestras muestras son ferromagnéticas a temperatura ambiente y exhiben un cambio abrupto en el sentido de la magnetización (inversión en su signo) a lo largo del eje fácil de magnetización, además representan un valor único de Tc (T/Tc). Debido a estas singulares características, fue posible investigar su comportamiento dinámico usando una magnetómetro Kerr transversal ultrasensible, y los estados dinámicos resultantes se exploraron en función de la amplitud del campo magnético aplicado H0 y el período P, así como un campo de independiente del tiempo adicional Hb, que es el campo conjugado del parámetro de orden dinámico Q. Finalmente, nuestros resultados experimentales demuestran que el comportamiento cualitativo del diagrama de fase dinámico es independiente de la relación T/Tc, y que para todos los diferentes valores de T/Tc, observamos anomalías metamagnéticas incremento rápido en el parámetro de orden en un pequeño rango de campos) en el estado dinámicamente paramagnético, que no existen en su correspondiente termodinámico. Sin embargo, cuantitativamente estas anomalías metamagnéticas dependen en gran medida de la relación T/Tc, lo que lleva a un aumento de aproximadamente 20 veces en los valores de las fluctuaciones metamagnéticas en el régimen paramagnético a medida que la relación T/Tc aumenta de 0.37 a 0.68. Además, el rango comprendido por el espacio de fase, en el que ocurren estas fluctuaciones metamagnéticas anómalas, se extiende cada vez más cerca del punto crítico a medida que aumenta T/Tc.113application/pdfenginfo:eu-repo/semantics/acceptedVersioninfo:eu-repo/semantics/doctoralThesishttp://purl.org/coar/resource_type/c_db06https://purl.org/redcol/resource_type/TDTesis/Trabajo de grado - Monografía - Doctoradoinfo:eu-repo/semantics/openAccessAtribución-NoComercial-CompartirIgual 2.5 Colombia (CC BY-NC-SA 2.5 CO)http://creativecommons.org/licenses/by-nc-sa/2.5/co/http://purl.org/coar/access_right/c_abf2https://creativecommons.org/licenses/by-nc-sa/4.0/Ising modelPhase transformations (Statistical physics)Mean field theoryKerr effectMagnetismoMagnetismMagnetizaciónMagnetizationSistemas dinámicoshttp://id.loc.gov/authorities/subjects/sh85068376http://id.loc.gov/authorities/subjects/sh85100646http://id.loc.gov/authorities/subjects/sh96010226http://id.loc.gov/authorities/subjects/sh85072072Dynamical phase transitions study in a Co(1−x)Rux magnetic system of two-dimensional Ising typeEstudio de las transiciones dinámicas de fase en sistemas magnéticos de Co(1-x)Rux del tipo Ising bidimensionalMedellín, ColombiaDoctor en FísicaDoctoradoFacultad de Ciencias Exactas y Naturales. Doctorado en FísicaUniversidad de AntioquiaORIGINALMarinJuan_2020_TransicionDinamicaFase.pdfMarinJuan_2020_TransicionDinamicaFase.pdfTesis doctoralapplication/pdf10630675http://bibliotecadigital.udea.edu.co/bitstream/10495/19522/1/MarinJuan_2020_TransicionDinamicaFase.pdf751d684aded21d9160709e3bc22a6a85MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-81051http://bibliotecadigital.udea.edu.co/bitstream/10495/19522/4/license_rdfe2060682c9c70d4d30c83c51448f4eedMD54LICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://bibliotecadigital.udea.edu.co/bitstream/10495/19522/5/license.txt8a4605be74aa9ea9d79846c1fba20a33MD5510495/19522oai:bibliotecadigital.udea.edu.co:10495/195222021-05-05 13:14:28.552Repositorio Institucional Universidad de Antioquiaandres.perez@udea.edu.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 |