Magnetization
Ferromagnet shows spontaneous magnetization (M) with or without a magnetic field. The magnetization remains without the field. Usually, the alignment of the magnetic moments of electrons gives spontaneous magnetization. The exchange interaction in quantum mechanics explains the interaction of spin-spin controlled by the Coulomb interaction. The interaction keeps the Pauli principle stable. If the net magnetization is zero in a system that means exchange interaction is zero. If it is high that means all spins are parallel to each other resulting in non-zero magnetization. However, simply if the temperature (T) is increased then thermal energy will randomize the spins and if the T is very high the randomization will be too much resulting in vanishing magnetization. The vanishing of magnetization means the magnetic system is paramagnetic in nature. The temperature at which the magnetic moment of electron spin orientation vanishes is called critical temperature (Tc) or Curie temperature.
Magnetic phase transition
We know that the phase transition is usually governed by pressure, chemical composition, temperature, electric or magnetic field, and connected with order. We see two types of phase transition: one is first order and the other is one-second order. The first-order phase transition is discontinuous with entropy and hence with latent heat. For example, if we heat an ice bar at a constant rate, the temperature remains the same until we reach zero degrees Celsius. The heat we put to become zero degrees is the latent heat of transformation. The first order is also known as sudden volume change. For example, ice enlarges relative to water when they transfer to each other i.e. sudden change in volume. On the other hand, a second-order phase transition does not carry any latent heat with it. The entropy is continuous at a critical temperature. Figure 1 (a) and (b) show the graphical representation of the ferromagnetic and paramagnetic nature of the magnetic moment of electron spin.
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Figure 1: (a) ferromagnetic (b) paramagnetic electron spin moment. Figure 2 shows the first-order and second-order phase transition behaviors concerning temperature.
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Magnetic second-order phase transition evaluation
For technical people, it is necessary to extract magnetization transition temperature for application-related or further consideration-related issues. The detailed process is usually in journal papers or proceedings that do not highlight it. Because that is a technical point usually people keep with them. Therefore, understanding how to evaluate magnetic transition, specifically second-order phase transitions is important and necessary to evaluate properly. We consider magnetic thin film having ferromagnetism which is technologically important for spintronic devices like GMR, TMR, spin FET, or novel applications. First, we can measure (SQUID, VSM methods) the saturation magnetization field from the M-H graph (figure 3). Also, from the M-H result, we can easily extract coercive fields to design magnetic devices.
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| Figure 3: Saturation magnetization determination Second, use the saturation magnetization field as an applied magnetic field and measure temperature-dependent magnetization, and normalize the magnetization by the volume of the magnetic thin film. Sometimes we need to subtract the background part if there are other film or substrate contributions like diamagnetic involved in the sample. Finally, the first derivation of the M-T curve gives a transition temperature at the minimum of the first derivation. The measurement of M-T and extracted graph are shown in figure 4 (a), and (b) respectively. By this technique, one can successfully extract the important Curie temperature of the magnetic thin film. |
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| Figure 4: (a) M-T curve and (b) first derivative of M-T minima is the second-order transition point |
You can also learn about Schottky diode-related related problems.
Good work indeed. I found my understanding
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