Landau-Lif z-Gilbert vs. Bloch

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In summary, the Landau-Lif****z-Gilbert and Bloch equations have the same form when no damping and relaxation are included. However, Gilbert introduced dissipation using a different approach from the Landau-Lif****z equation. This equation is rarely mentioned in NMR-related discussions.
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BeauGeste
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Landau-Lif****z-Gilbert vs. Bloch

Could anyone elucidate on the difference between the phenomenology of the Landau-Lif****z-Gilbert equations and Bloch equations. When damping and relaxation are not included they have identical form. Are they the same thing? I've been learning about NMR related stuff for a while and I've never heard mention of the Landau-Lif****z-Gilbert equation.

Any help would be appreciated.
 
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  • #2
Landau Lif****z equation is the same as Blochs equation, without dissipation. Gilbert used a different approach, from LL, to introduce dissipation. But I think it reduces to the LL equations.

edit.. Kinda funny that Lif****z is censored
 
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If you don't intend answering the question, then please don't post a reply!
 

FAQ: Landau-Lif z-Gilbert vs. Bloch

What is the difference between Landau-Lifshitz-Gilbert (LLG) and Bloch equations?

The Landau-Lifshitz-Gilbert (LLG) equation describes the dynamics of magnetic moments in a ferromagnetic material, taking into account the effects of damping and an external magnetic field. On the other hand, the Bloch equation describes the precession of a single spin in an external magnetic field without considering damping. In other words, the LLG equation is a more comprehensive model that includes the effects of damping, while the Bloch equation is a simplified version that only considers the precession of a single spin.

How do the LLG and Bloch equations differ in their mathematical forms?

The LLG equation is a second-order differential equation, while the Bloch equation is a first-order differential equation. This means that the LLG equation takes into account the time derivative of the magnetization, while the Bloch equation only considers the first derivative. Additionally, the LLG equation includes the effects of damping, which is not present in the Bloch equation.

Which equation is more commonly used in research and why?

The LLG equation is more commonly used in research because it provides a more accurate description of the dynamics of magnetic moments in a ferromagnetic material. It takes into account the effects of damping, which is an important factor in many magnetic systems. Additionally, the LLG equation can be extended to include other parameters such as temperature and spin-transfer torque, making it a more versatile model.

What are the limitations of the Bloch equation?

The Bloch equation is a simplified model and does not take into account the effects of damping, which is an important factor in many magnetic systems. It also assumes that the magnetic moments are perfectly aligned with the external magnetic field, which is not always the case in real systems. Additionally, the Bloch equation only applies to single spins and cannot be extended to describe the dynamics of a system with multiple interacting spins.

When should I use the LLG equation and when should I use the Bloch equation?

The choice between using the LLG or Bloch equation depends on the specific research question and the system being studied. If the effects of damping are negligible and the system can be described by a single spin, the Bloch equation may be sufficient. However, if the system has significant damping and multiple interacting spins, the LLG equation would provide a more accurate description. It is important to carefully consider the assumptions and limitations of each equation before deciding which one to use.

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