# Why does the magnetisation orient itself in the -y direction

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• shedrick94
In summary, when a 90 degree pulse is applied in the x direction in magnetic resonance, the magnetization vector, which was originally oriented in the z direction, is precessing around in the X-Y plane. The direction of this rotation can be determined using the relationship between the time derivative of a vector in the laboratory frame and the rotating frame. Additionally, the angular momentum of the magnetization is equal to the magnetization multiplied by the gyromagnetic ratio, and the solution for the magnetization is that it rotates at a frequency of -gamma B about the magnetic field vector.

#### shedrick94

In magnetic resonance, if we apply a 90 degree pulse in the x direction when we have a magnetisation orientated in the z direction. Why do we get the magnetisation then orientated in the -y direction immediately after the pulse?

I don't understand why it would not be in the +Y direction

Upon applying a 90 degree pulse, the entire magnetization, (from the nuclear spins), that has been rotated away from the z-direction, is precessing around in the X-Y plane if I remember the result correctly. (The large static field in the z-direction causes this precession. The large static field in the z-direction is effectively canceled only in the rotating frame. ## M \times B_z ## will supply the necessary torque to cause the precession.) During the application of the r-f signal at resonance in the x-direction, the magnetization vector is precessing around in the laboratory frame, while in the rotating frame, it appears to simply make a 90 degree rotation from the z-direction to the X-Y plane. The direction the magnetization rotates in the rotating frame can be readily computed. Hopefully your textbook correctly computed it.

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Besides what I mentioned in post #2, there are a couple of additional items that might be of interest. One important item in the derivations is the relationship between the time derivative of a vector ## \vec{r} ## in the laboratory frame versus the rotating frame: ## [d \vec{r}/dt]_o=d \vec{r} /dt +\omega \times \vec{r} ##. One other item is that the angular momentum ## J ## from magnetization ## M ## is ## M=\gamma J ##, so that ## dJ/dt=M \times B ## becomes ## dM/dt=\gamma M \times B ##. It should be noted in the last equation, that the solution for ## M ## is that it rotates at frequency ## \omega=-\gamma B ## about the vector ## B ##. Notice from the first equation above that ## dM/dt=0 ## in the rotating frame (## M ## is constant), but ## [dM/dt]_o=\omega \times M ## in the laboratory frame.

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## 1. Why does the magnetisation orient itself in the -y direction?

The magnetisation of a material is caused by the alignment of its atomic or molecular magnetic moments. These magnetic moments are influenced by the surrounding magnetic field, which causes them to orient themselves in a specific direction. In the case of the -y direction, it means that the magnetic moments are aligned perpendicular to the direction of the magnetic field.

## 2. What determines the direction of the magnetisation?

The direction of the magnetisation is determined by the crystal structure and chemical composition of the material, as well as the strength and direction of the external magnetic field.

## 3. Why is the -y direction important for magnetisation?

The -y direction is important for magnetisation because it allows for the creation of a net magnetic moment in a material. When the magnetic moments of individual atoms or molecules align in the same direction, it creates a macroscopic magnetic field that can be used for various applications, such as in data storage or medical imaging.

## 4. Can the direction of magnetisation be changed?

Yes, the direction of magnetisation can be changed by applying a stronger external magnetic field or by heating the material above its Curie temperature, which disrupts the alignment of the magnetic moments.

## 5. How does the direction of magnetisation affect the properties of a material?

The direction of magnetisation can affect the magnetic properties of a material, such as its strength, stability, and response to external magnetic fields. It can also determine the material's behavior in different applications, such as whether it is suitable for use in electronic devices or as a permanent magnet.