what is the " duhas - van alfan effect " in solid state physics?

Question

calculation of electronic band

Answer 1

The correct name is de Haas-van Alphen effect. Alphen is also spelled as Alfven.

These physicists, de Haas and van Alphen, observed in 1930 that under special conditions (very low temperatures) the magnetization M caused in a sample by external magnetic field B did not change linearly with B.

More specifically, the ratio M/B was going up and down, being a periodical function of 1/B. This happens only in diamagnetic materials, not in para- or ferromagnetic ones.

The effect was explained theoretically by (Soviet physicist) Lev Landau, as a result of quantum effects in charged particle motion in magnetic field (so called Landau quantization).

Here is the relevant quote from (very long) article [3]:


The de Haas-van Alphen (dHvA) effect is an oscillatory variation of the diamagnetic susceptibility as a function of a magnetic field strength (B)...

The first experimental observation of this behavior was made by de Haas and van Alphen (1930). They have measured a magnetization M of semimetal bismuth (Bi) as a function of the magnetic field (B) in high fields at 14.2 K and found that the magnetic susceptibility M/B is a periodic function of the reciprocal of the magnetic field (1/B).

This phenomenon is observed only at low temperatures and high magnetic fields. Similar oscillatory behavior has been also observed in magnetoresistance (so called the Shubnikov-de Haas effect).

The dHvA phenomenon was explained by Landau1 as a direct consequence of the quantization of closed electronic orbits in a magnetic field and thus as a direct observational manifestation of a purely quantum mechanics. The phenomenon became of even greater interest and importance when Onsager2 pointed out that the change in 1/B through a single period of oscillation was determined by the remarkably simple relation.