How Does Increasing Length Affect Spin Hall Voltage in Materials?

In summary, the spin Hall voltage equation only takes into account the spin Hall angle, length of the material, charge current density, and spin magnetic moment. Increasing the length of the material while keeping the charge current density fixed will result in a linear increase in the spin Hall voltage, but in real materials, the relationship may be non-linear. The dimensions of the equation should be [ML^3 T^-2 I^-1], which is the dimension of voltage.
  • #1
ubergewehr273
142
5
Hi!

I'm trying to understand the dependence of spin hall voltage on various parameters of the material. I have been going through this paper, and it is mentioned that $$V_{SH} = 2 \pi R_s L j_x n \mu_B$$

In the equation, only ##L## and ##j_x## seem to be the variables. Does increasing ##L## keeping ##j_x## fixed, increase the spin hall voltage linearly (as seen from the equation)? If I simply increase ##L##, is it correct to say that I cannot magically increase the spin Hall voltage simply because ##j_x## will decrease as ##L^{-2}##?

Also, from the paper, doing a quick dimension analysis, I get the RHS as ##[IL T^{-1}]## whereas voltage has a dimension of ##[ML^2 I T^{-3}]##. Where am I going wrong?
 
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  • #2


Hello there!

Thank you for bringing up this interesting question. The equation you have mentioned is a simplified form of the spin Hall voltage equation and it only takes into account the spin Hall angle (##R_s##), the length of the material (##L##), the charge current density (##j_x##), and the spin magnetic moment (##\mu_B##). Other parameters such as the material's conductivity, mobility, and carrier density are not included in this equation.

To answer your first question, yes, increasing the length of the material while keeping the charge current density fixed will result in a linear increase in the spin Hall voltage. This is because the spin Hall voltage is directly proportional to the length of the material in this equation. However, in real materials, the spin Hall angle and other parameters may also change with the length, resulting in a non-linear relationship.

As for your second question, the dimensions of the equation are indeed not correct. The correct dimensions for the RHS should be [ML^3 T^-2 I^-1], which is the dimension of voltage. This is because the spin Hall voltage is a product of current density (I/L^2), spin Hall angle (dimensionless), length (L), and spin magnetic moment (I/T). Therefore, the final dimension should be [ML^3 T^-2 I^-1].

I hope this helps clear up your doubts. Keep exploring and asking questions!
 

FAQ: How Does Increasing Length Affect Spin Hall Voltage in Materials?

1. What is spin Hall voltage?

Spin Hall voltage is a phenomenon in which an electric field induces a spin polarization in a material, resulting in a voltage difference across the material. This effect is caused by the spin-orbit coupling, which is the interaction between the spin of an electron and its motion.

2. How is spin Hall voltage measured?

Spin Hall voltage can be measured using various techniques, such as the spin Hall effect measurement, spin pumping measurement, or spin Seebeck effect measurement. These methods involve applying an electric field or temperature gradient to the material and measuring the resulting spin polarization or voltage difference.

3. What are the applications of spin Hall voltage?

Spin Hall voltage has potential applications in spintronics, a field that aims to use the spin of electrons in addition to their charge for information processing and storage. It can also be used in spin-based logic devices, spin-based memory devices, and other emerging technologies.

4. What factors affect spin Hall voltage?

The magnitude of spin Hall voltage is influenced by several factors, including the material properties, the strength of the spin-orbit coupling, and the applied electric field or temperature gradient. The direction of spin Hall voltage can also be affected by the crystal structure and magnetic properties of the material.

5. Can spin Hall voltage be controlled?

Yes, spin Hall voltage can be controlled by adjusting the material properties, such as the thickness or composition, or by changing the external conditions, such as the applied electric field or temperature gradient. Researchers are also exploring ways to manipulate spin Hall voltage using magnetic fields or light.

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