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Materialanalytik Praktikum Vibrating Sample Magnetometry B512 Stand: 23.09.2015 Aim: Magnetic characterization of ferromagnetic samples by Vibrating Sample Magnetometry. Contents 1. Introduction 2 2. Basic 4 3. Experiment 7 4. Analysis 8 5. Report 9 6. References 9 1.1. 2.1 2.1.1 2.1.2 2.2 2.3 3.1 3.2 Measurement principle 2 Ferromagnetic materials Magnetic domains Hysteresis Demagnetization Units 4 4 5 6 6 Equipment Procedure 7 8 1 B512: Vibrating Sample Magnetometry 1. Introduction Vibrating Sample Magnetometry (VSM) is a measurement technique which allows to determine the magnetic moment of a sample with very high precision. The aim of this lab course is to introduce this widespread technique and to characterize ferromagnetic samples. Therefore, an understanding of the measurement principle and the properties of ferromagnets is required. 1.1. Measurement principle Vibrating Sample Magnetometry (VSM) is based on Faraday's law which states that an electromagnetic force is generated in a coil when there is a change in flux through the coil [1]. In the measurement setup, a magnetic sample is moving in the proximity of two pickup coils as indicated in Fig. 1. β vibration Figure1: Schematic representation of a VSM.[1] The oscillator provides a sinusoidal signal that is translated by the transducer assembly into a vertical vibration. The sample which is fixed to the sample rod vibrates with a given frequency and amplitude (60 to 80 Hz and 1 mm, respectively). It is centered between the οΏ½β0 of high homogeneity. two pole pieces of an electromagnet that generates a magnetic field π»π» 6 Field strengths in the range of 10 A/m are commonly possible with laboratory VSM 2 B512: Vibrating Sample Magnetometry systems. Stationary pickup coils are mounted on the poles of the electromagnet. Their symmetry center coincides with the magnetic center of the sample. Hence, the change in magnetic flux originating from the vertical movement of the magnetized sample induces a οΏ½β0 , being constant, has no affect on the voltage but is necessary voltage ππππππππ in the coils. π»π» only for magnetizing the sample. According to Faraday, the voltage in a single winding of the pickup coil can be written as ππππππππ = β βΞ¦ βπ‘π‘ (1) where Ξ¦ is the magnetic flux. For the pickup coils with a flat surface π΄π΄ and πππ€π€ windings, Eq. 1 gives οΏ½β βπ΅π΅ ππππππππ = βπππ€π€ π΄π΄ βπ‘π‘ (2) οΏ½οΏ½οΏ½β οΏ½οΏ½β = β« ππππ ππ ππππ. ππππ (3) οΏ½β = ππ0 (π»π» οΏ½β0 + ππ οΏ½οΏ½β ). π΅π΅ (4) οΏ½β0 , it will be magnetized and have When we bring the sample into the homogeneous field π»π» οΏ½οΏ½β . Here, ππ οΏ½οΏ½β is defined by the resulting magnetic moment ππ the magnetization ππ οΏ½οΏ½β per volume unit οΏ½β near the sample is now The magnetic flux density π΅π΅ οΏ½β0 we have In the constant magnetic field π»π» οΏ½β βπ΅π΅ βπ‘π‘ = οΏ½οΏ½β βππ (5) βπ‘π‘ where the change of magnetic flux in time originates from the vertical sample movement relative to the coils. The flux change detected by the coils is therefore proportional to a number of quantities: the frequency ππ of the vibration and its amplitude ππ, the magnetic moment of the sample ππ οΏ½οΏ½β and the distance to the pickup coils π¦π¦0 . Furthermore, ππππππππ can be increased by increasing the number of windings πππ€π€ and the number of pickup coils ππππ used in the setup. Also, the geometry of the sample influences the induction. ππππππππ (π‘π‘) β β οΏ½οΏ½οΏ½βπππππ€π€ ππππ πΊπΊ cos(ππππ) ππ π¦π¦0 where G is a geometric factor of the sample. (6) The measurement setup is sensitive even to very low magnetic moments. Today's vibrating 3 B512: Vibrating Sample Magnetometry sample magnetometers are able to detect magnetic moments of down to the µemu range, which corresponds to approx. 10-9 g of iron [2]. 2. Basic 2.1 Ferromagnetic materials 2.1.1 Magnetic domains Magnetic materials are distinguished by their behavior in external magnetic fields. For ferromagnets, the ππ(π»π») dependence is characterized by domain wall movement and magnetization rotation. According to the theory of Weiss a non-saturated ferromagnet contains a number of small regions called domains, in which the local magnetization is homogeneous and reaches the saturation value. The direction of magnetization in different domains is not necessarily parallel. Two domains are separated by domain walls which are regions of approx. 100 nm where the magnetization rotates continuously. They are classified by the angle of rotation (90° or 180°) and the mode of rotation (Bloch or Neel). Figure 2: a) Magnetic domain pattern of a Fe whisker, b) Bloch wall, c) Neel wall [3] When applying an external magnetic field, domains with magnetization parallel to the field will grow at the cost of domains with energetically more unfavorable magnetization alignment. As a consequence domain walls move through the sample and the overall magnetization increases. In magnetically soft materials, domain walls are broad and the movement of the walls requires small fields only whereas larger fields are necessary in magnetically hard materials. A second mechanism that increases the magnetization is magnetization rotation within the domains. Due to magnetic anisotropies, certain directions are easier to magnetize than others. The spontaneous magnetization lies preferably along one of these easy directions. If 4 B512: Vibrating Sample Magnetometry the applied external field is not parallel to such an easy direction, the magnetization rotates and aligns along the magnetic flux lines. 2.1.2 Hysteresis a) b) Figure 3: a) Virgin curve, b) Hysteresis loop of a ferromagnetic material. [4] Fig. 3 shows a typical ferromagnetic hysteresis loop and indicates the predominant, underlying mechanisms for each region. The sample is firstly magnetized to saturation in an applied field (virgin curve). The region of highest permeability is governed by domain wall motion whereas magnetization rotation occurs rather at higher magnetic fields. When the applied field is reduced to zero the remanent magnetization ππππ remains. A magnetic field of opposite direction called coercivity field π»π»ππ is needed to macroscopically demagnetize the sample. Thus, the hysteresis loop contains important information about the magnetic properties of the sample. Characteristic quantities include the saturation magnetization πππ π , the remanent magnetization ππππ , the coercivity field π»π»ππ , permeability ππ and the dissipated energy that is necessary to magnetize the sample in the opposite direction. The dissipated energy can be calculated from the area that is included by the hysteresis loop. 5 B512: Vibrating Sample Magnetometry 2.2 Demagnetization In an external magnetic field, the presence of a magnetic material alters the magnetic οΏ½β. If the sample has a finite length, magnetic poles are generated near the ends of induction π΅π΅ the sample. These poles give rise to a magnetic field that opposes the external field and is therefore called demagnetizing field. The strength of the demagnetizing field depends on οΏ½οΏ½β and the geometry of the sample. The field inside the magnetic material the magnetization ππ is now different from the external field and requires correction. The inner field can be calculated by οΏ½βππππ = π»π» οΏ½βππππππ β ππππ ππ οΏ½οΏ½β π»π» (7) οΏ½οΏ½β is the magnetization and ππππ the demagnetizing factor which is only determined by where ππ the sample shape. For thin films, spheres and ellipsoids it is possible to calculate ππππ , whereas for other shapes one needs to approximate. 2.3 Units Geometry Direction Thin film in plane out of plane Sphere π΅π΅π π 0 1 1/3 Quantity Symbol Unit (SI) Unit (cgs) Magnetic flux Flux density / Induction Magnetic field Magnetization Polarization Dissipated energy Permeability Magnetic moment π·π· B H M J BβH ππ ππ Wb = Vs (Weber) T = Wb/m2 (Tesla) A/m A/m T J/m3 Vs/Am A m2 Mx (Maxwell) G (Gauss) Oe (Oersted) emu/cm3 emu/cm3 erg/cm3 G/Oe = 1 emu Conversions Constants 1 T = 104 G 1 A/m = 4ππ 10-3 Oe 1 A m2 = 103 emu ππ0 = 4ππ 10-7 Vs/Am 6 B512: Vibrating Sample Magnetometry 3. Experiment 3.1 Equipment a) b) c) Figure 6: LakeShore VSM 7400 system: a) overview of the setup, b) pick up coils in between pole pieces and c) VSM head with integrated transducer assembly. Components of the LakeShore VSM 7400 system are shown in Fig. 6: the electromagnet (a) with the pole pieces on which the pickup coils are mounted (b) and the vibrating/rotating head with positioning screws to center the vibrating rod (c). The VSM system also comprises a bipolar DC power supply (± 50V, ± 100A), a cooling system for both the electromagnet and the power supply, the VSM controller and a PC with LakeShore "IDEAS VSM" software to control the components and to collect the measured data. 7 B512: Vibrating Sample Magnetometry 3.2 Procedure Before using the VSM, you must carry out a series of configuration steps. β’ Insert the Ni standard into the VSM. The standard is ball-shaped, therefore magnetically isotropic, and has a magnetic moment of 6.92 emu at 5000 Oe. β’ Find the exact position of the standard in respect to the center of the pickup coils. The vibrating rod can be adjusted by three screws on top of the VSM for x, y and z direction. The pickup coils are connected in a way that, the sample being in the center of the coils, there will be a signal minimum along x-, a maximum along y- and a maximum again along z-direction. β’ Run Calibrations β Moment gain to calibrate the instrument, i.e. to convert the measured voltage signal into the correct value of the magnetic moment. After calibration of the VSM, the following measurements aim to address two topics. The first part covers basic magnetic characterization and the information that can be deduced from magnetization curves. The second part cope with demagnetization. 1. Basic magnetic characterization: Record the magnetization curves for three samples provided by the supervisor. Center each sample in between the pickup coils analog to the Ni standard before starting the measurement. 2. Demagnetization: Record the magnetization curve for a thin film sample in two orientations: in plane and out of plane. Determine the volume of each sample that you have measured. 4. Analysis LakeShore software saves all data as ASCII text files (.txt). Copy these files to a USB flash drive of yours. The file format is as follows (in case of a magnetization curve): [Header lines: time stamp etc.] Field(G) 1234.56 Moment(emu) 7.89012 etc. 8 B512: Vibrating Sample Magnetometry 5. Report Please answer to the following assignments: 1. Create a diagram containing the magnetization curve (magnetic polarization in T vs. applied field in A/m) for each of the materials of section 3.2 #1 and a table showing the saturation polarization (in T), the remanent polarization (in T), the coercive field (in A/m) and the dissipated energy (in J/m³). Create a diagram showing the relative permeability as a function of the applied field. 2. Discuss and compare the magnetic properties of these materials with respect to possible applications. 3. Create a diagram containing the magnetization curves for both orientations of the thin film sample. Compare the values for the saturation magnetization obtained from both measurements. 4. Give 3 common measurement errors of the VSM measurement principle and explain how they affect the measured magnetization curve. 6. References [1] K.H.J. Buschow and F.R. de Boer. Physics of Magnetism and Magnetic Materials. Kluwer Academic/Plenum Publishers, 2003. [2] L. Michalowsky. Magnettechnik. Fachbuchverlag Leipzig, 1993. [3] A. Hubert and R. Schäfer. Magnetic Domains. Springer-Verlag, Berlin Heidelberg, 1998. [4] D. R. Askeland. The Science and Engineering of Materials. International Thomson Publishing, 3rd ed., 1994. [5] O'Handley, R. C. Modern magnetic materials : principles and applications. John Wiley & Sons, New York, 2000. [6] D. Jiles. Introduction to Magnetism and Magnetic Materials. Chapman & Hall, 1998. 9