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Microscopio de fuerza magnética

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El microscopio de fuerza magnética (MFM) es una variedad de microscopio de fuerza atómica, en el cual, una punta afilada magnetizada escanea una muestra magnética; las interacciones magnéticas entre la punta y la muestra son detectadas y posteriormente se utilizan para reconstruir la estructura magnética de la superficie de la muestra. Muchos tipos de interacciones magnéticas se miden por MFM, incluyendo la interacción dipolo-dipolo magnético. El escaneo a través de MFM utiliza menudo el modo sin contacto AFM (NC-AFM).

Contentido [hide] 1 Visión general 2 Fechas importantes 3 Componentes del MFN 4 Procedimiento para el escaneo 5 Modos de operación 5.1 Modo estático (DC) 5.2 Modo dinámico (AC) 6 Generación de imágenes 6.1 Calculo de las fuerzas que interactuán en la punta magnética. 7 Muestro de imágenes 8 Ventajas 9 Limitaciones 10 Avances 11 Referecia 12 Links externos Overview[edit]

En las mediciones realizadas por el MFM, la fuerza magnética entre la punta del microscopio y la muestra se puede expresar como: [1][2]

\vec F=\mu_o (\vec m \cdot \nabla ) \vec H \,\! where \vec m \, \! es el momento mágnetico de la punta (aproximado como un dipolo punto), \vec H \, \! el campo magnético de la superficie de la muestra, y µ0 el a permeabilidad del medio en un espacio libre.

Debido a que el campo magnético de dispersión de la muestra puede afectar el estado magnético de la punta, y viceversa, la interpretación de la medición MFM no es sencilla. Por ejemplo, la geometría de la punta de magnetización debe ser conocida para el análisis cuantitativo.

La resolución típica que se puede lograr es de 30 nm , [3], aunque resoluciones tan bajas como 10 a 20 nm también son alcanzables.[4]

Fechas importantes[edit] Un aumento en el interés por los MFM fue resultado de las siguientes invenciones:[1][5][6]

1982 - Microscopio de efecto de túnel (MET)

La corriente túnel entre la punta y la muestra se utiliza como la señal. Tanto la punta y la muestra debe ser conductores de corriente.

1986 - Microscopio de fuerza atómica (AFM)

Fuerzas (atómica / electrostáticas) entre la punta y la muestra se detectan a partir de las deflexiones de una palanca flexible (en voladizo). La punta en voladizo vuela por encima de la muestra con una distancia típica de decenas de nanómetros.

1987 - Microscopio de fuerza magnética (MFM)[7]

Deriva del MFA. Se detectan las fuerzas magnéticas entre la punta y la muestra.[8][9] La imagen del campo magnético del material se obtiene mediante el escaneo de la punta imantada sobre la superficie de la muestra en una exploración de barrido.[10]

Componentes del MFM[edit]

Los principales componentes de un sistema de MFM son: la exploración piezoeléctrica

Mueve la muestra en un direcciones x, y, z. El voltaje se aplica a los electrodos separados para diferentes direcciones. Por lo general, un potencial de 1 voltio resultados en 1 a 10 nm desplazamiento. La imagen se arma escaneando lentamente la superficie de la muestra, a través de un barrido. Las áreas de escaneo varían desde uno poco dentro del rango de hasta 200 micrómetros. Los tiempos de imagen van desde unos pocos minutos a 30 minutos. La restauración de constantes de fuerza en la gama voladizo de 0,01 a 100 N / m en función del material del voladizo. El magnetizado de la punta en un extremo de una palanca flexible (cantilever); en general, es una sonda de MFA con un recubrimiento magnético.

En el pasado, las puntas estaban hechas de metales magnéticos grabados en metales particulares como el níquel. Hoy en día, las puntas están fabricadas por lotes (punta-cantilever), utilizando una combinación de micromecanizado y fotolitografía. Como resultado, se obtienen puntas más pequeñas , y también un mejor control mecánico de la punta en voladizo. [11] [12] [13] El voladizo puede estar hecho de silicio monocristalino, dióxido de silicio (SiO2), o nitrato de silicio (Si3N4). Los módulos en voladizo de punta de Si3N4 suelen ser más duraderos y tienen constantes de fuerza de recuperación más pequeños (k). Las puntas están recubiertas con una (<50 nm) de película magnética delgada (tal como Ni o Co), generalmente de alta coercitividad, de modo que la punta estado magnético (o de magnetización M) no cambia durante la formación de imágenes. El módulo de punta en voladizo es impulsado cerca de la frecuencia de resonancia por un cristal piezoeléctrico con frecuencias típicas que van desde 10 kHz a 1 MHz [5].

Scanning procedure[edit]

The scanning method when using an MFM is called the "lift height" method.[14] When the tip scans the surface of a sample at close distances (< 10 nm), not only magnetic forces are sensed, but also atomic and electrostatic forces. The lift height method helps to enhance the magnetic contrast through the following:

First, the topographic profile of each scan line is measured. That is, the tip is brought into a close proximity of the sample to take AFM measurements. The magnetized tip is then lifted further away from the sample. On the second pass, the magnetic signal is extracted.[15]

Modes of operation[edit]

Static (DC) mode[edit]

The stray field from the sample exerts a force on the magnetic tip. The force is detected by measuring the displacement of the cantilever by reflecting a laser beam from it. The cantilever end is either deflected away or towards the sample surface by a distance Δz = Fz/k (perpendicular to the surface). Static mode corresponds to measurements of the cantilever deflection. Forces in the range of tens of piconewtons are normally measured.

Dynamic (AC) mode[edit]

For small deflections, the tip-cantilever can be modeled as a damped harmonic oscillator with a proof mass (m) in [kg], an ideal spring constant (k) in [N/m], and a damper (D) in [N·s/m].[16] If an external oscillating force Fz is applied to the cantilever, then the tip will be displaced by an amount z. Moreover, the displacement will also harmonically oscillate, but with a phase shift between applied force and displacement given by:[5][6][9] F_z=F_o \cos(\omega t), \; z=z_o \cos(\omega t + \theta)\,\! where the amplitude and phase shifts are given by:

z_o= \frac{{\frac{F_o} {m}}}{\sqrt{(\omega_n^2 - \omega^2) + (\frac{\omega_n \omega} {Q})^2}}, \; \theta=\arctan\left [\frac{\omega_n \omega} {Q(\omega_n^2 - \omega^2)} \right ]\,\! Here the quality factor of resonance, resonance angular frequency, and damping factor are:

Q=2 \pi \frac{\frac{1} {2} k z_o^2} {\pi D z_o^2 \omega_n} = \frac{1} {2\delta}, \; \omega_n=\sqrt{\frac{k} {m}}, \; \delta=\frac{D} {2\sqrt{mk}}\,\! Dynamic mode of operation refers to measurements of the shifts in the resonance frequency. The cantilever is driven to its resonance frequency and frequency shifts are detected. Assuming small vibration amplitudes (which is generally true in MFM measurements), to a first-order approximation, the resonance frequency can be related to the natural frequency and the force gradient. That is, the shift in the resonance frequency is a result of changes in the spring constant due to the (repelling and attraction) forces acting on the tip. \omega_r=\omega_n \sqrt{1-\frac{1} {k} \frac{\partial F_z} {\partial z}} \approx \omega_n \left (1-\frac{1} {k} \frac{\partial F_z} {\partial z} \right )\,\! The change in the natural resonance frequency is given by

\Delta f= f_r - f_n \approx -\frac{f_n} {2k} \frac{\partial F_z} {\partial z}\,\!, where f=\frac{\omega} {2\pi}\,\! For instance, the coordinate system is such that positive z is away from or perpendicular to the sample surface, so that an attractive force would be in the negative direction (F<0), and thus the gradient is positive. Consequently, for attractive forces, the resonance frequency of the cantilever decreases (as described by the equation). The image is encoded in such a way that attractive forces are generally depicted in black color, while repelling forces are coded white.

Image formation[edit]

Calculating forces acting on magnetic tips[edit] Theoretically, the magneto-static energy (U) of the tip-sample system can be calculated in one of two ways:[1][5][6][17]

One can either compute the magnetization (M) of the tip in the presence of the magnetic stray field (H) of the sample or Compute the magnetization of the sample in the presence of the magnetic stray field of the tip (whichever is easier) Then, integrate the (dot) product of the magnetization and stray field over the interaction volume as

U=-\mu_o\int\limits_V {\vec M \cdot \vec H\, dV}\,\! and compute the gradient of the energy over distance to obtain the force F. Assuming that the cantilever deflects along the z-axis, and the tip is magnetized along a certain direction (e.g. the z-axis), then the equations can be simplified to

F_i=\mu_o\int\limits_V {\vec M \cdot \frac{\partial \vec H} {\partial x_i}\, dV}\,\! Since the tip is magnetized along a specific direction, it will be sensitive to the component of the magnetic stray field of the sample which is aligned to the same direction.

Imaging samples[edit]

The MFM can be used to image various magnetic structures including domain walls (Bloch and Neel), closure domains, recorded magnetic bits, etc. Furthermore, motion of domain wall can also be studied in an external magnetic field. MFM images of various materials can be seen in the following books and journal publications:[5][6][18] thin films, nanoparticles, nanowires, permalloy disks and recording media.

Advantages[edit]

The popularity of MFM originates from several reasons, which include:[2]

The sample does not need to be electrically conductive. Measurement can be performed at ambient temperature, in ultra high vacuum (UHV), in liquid environment, and at different temperatures. Measurement is nondestructive to the crystal lattice or structure. Long-range magnetic interactions are not sensitive to surface contamination. No special surface preparation or coating is required. Deposition of thin non-magnetic layers on the sample does not alter the results. Detectable magnetic field intensity, H, is in the range of 10 A/m Detectable magnetic field, B, is in the range of 0.1 gauss (10 microteslas). Typical measured forces are as low as 10−14 N, with the spatial resolutions as low as 20 nm. MFM can be combined with other scanning methods like STM.

Limitations[edit]

There are some shortcomings or difficulties when working with an MFM, such as:

The recorded image depends on the type of the tip and magnetic coating, due to tip-sample interactions. Magnetic field of the tip and sample can change each other's magnetization, M, which can result in nonlinear interactions. This hinders image interpretation. Relatively short lateral scanning range (order of hundreds micrometers). Scanning (lift) height affects the image. Housing of the MFM system is important to shield electromagnetic noise (Faraday cage), acoustic noise (anti-vibration tables), air flow (air isolation), and static charge on the sample.

Advances[edit]

There have been several attempts to overcome the limitations mentioned above and to improve the resolution limits of MFM. For example, the limitations from air flow has been overcome by MFMs that operate at vacuum.[19] The tip-sample effects have been understood and solved by several approaches. Wu et al., have used a tip with antiferromagnetically coupled magnetic layers in an attempt to produce a dipole only at the apex.[20]

References[edit]

^ Jump up to: a b c D.A. Bonnell, Scanning Probe Microscopy and Spectroscopy (2000). "7". (2 ed.). Wiley-VCH. ISBN 0-471-24824-X. ^ Jump up to: a b D. Jiles (1998). "15". Introduction to Magnetism and Magnetic Materials (2 ed.). Springer. ISBN 3-540-40186-5. Jump up ^ L. Abelmann, S. Porthun, et al. (1998). "Comparing the resolution of magnetic force microscopes using the CAMST reference samples". J. Magn. Magn. Mater. 190: 135–147. Bibcode:1998JMMM..190..135A. doi:10.1016/S0304-8853(98)00281-9. Jump up ^ Nanoscan AG, Quantum Leap in Hard Disk Technology ^ Jump up to: a b c d e H. Hopster, and H.P. Oepen, Magnetic Microscopy of Nanostructures (2005). "11-12". Springer. ^ Jump up to: a b c d M. De Graef, and Y. Zhu (2001). "3". Magnetic Imaging and Its Applications to Materials: Experimental Methods in the Physical Sciences 36. Academic Press. ISBN 0-12-475983-1. Jump up ^ Magnetic Force Microscopy Jump up ^ Y. Martin and K. Wickramasinghe (1987). "Magnetic Imaging by Force Microscopy with 1000A Resolution". Appl. Phys. Lett. 50 (20): 1455–1457. Bibcode:1987ApPhL..50.1455M. doi:10.1063/1.97800. ^ Jump up to: a b U. Hartmann (1999). "Magnetic Force Microscopy". Annu. Rev. Mater. Sci. 29: 53–87. Bibcode:1999AnRMS..29...53H. doi:10.1146/annurev.matsci.29.1.53. Jump up ^ History of Probing Methods Jump up ^ L. Gao, L.P. Yue, T. Yokota, et al. (2004). "Focused Ion Beam Milled CoPt Magnetic Force Microscopy Tips for High Resolution Domain Images". IEEE Transactions on Magnetics 40 (4): 2194–2196. Bibcode:2004ITM....40.2194G. doi:10.1109/TMAG.2004.829173. Jump up ^ A. Winkler, T. Mühl, S. Menzel, et al. (2006). "Magnetic Force Microscopy Sensors using Iron-filled Carbon Nanotubes". J. Appl. Phys. 99 (10): 104905. Bibcode:2006JAP....99j4905W. doi:10.1063/1.2195879. Jump up ^ K. Tanaka, M. Yoshimura, and K. Ueda (2009). "High-Resolution Magnetic Force Microscopy Using Carbon Nanotube Probes Fabricated Directly by Microwave Plasma-Enhanced Chemical Vapor Deposition". J. NanoMaterials 2009: 147204. doi:10.1155/2009/147204. Jump up ^ Magnetic Force Microscopy (MFM) manual Jump up ^ I. Alvarado, "Procedure to Perform Magnetic Force Microscopy (MFM) with VEECO Dimension 3100 AFM", NRF, 2006 Jump up ^ Cantilever Analysis Jump up ^ R. Gomez, E.R. Burke, and I.D. Mayergoyz (1996). "Magnetic Imaging in the Presence of External Fields: Technique and Applications". J. Appl. Phys. 79 (8): 6441–6446. Bibcode:1996JAP....79.6441G. doi:10.1063/1.361966. Jump up ^ D. Rugar, H.J. Mamin, P. Guenther, et al. (1990). "Magnetic Force Microscopy: General Principles and Application to Longitudinal Recording Media". J. Appl. Phys. 68 (3): 1169–1183. Bibcode:1990JAP....68.1169R. doi:10.1063/1.346713. Jump up ^ http://www.hitachi-hitec-science.com/documents/technology/probe_microscope/poster_2005_01.pdf Jump up ^