# Weiss Theory Of Ferromagnetism (Cc-12 Unit-2(2) Lec-7)

Hello students. Welcome to my YouTube channel, integrated Fuji studies IPS Ethereum already lost to second year, syllabus complete core research, plus 3, CBC online classes, raw videos, subscribe foreign. These are the substances, which can be magnetized and retain their magnetism, even after removal of the external magnetic unit volume, m, which is produced in such substances is very high. And even in weak magnetic fields here available. The second point, the value of m is not linearly proportional to the.

Applied magnetic field that is BA, or in other words, their magnetic susceptibility chi m is which is equal to mu 0, m by b. An s, I unit is not constant. But a very caribou with respect to the applied field above a certain critical temperature, but transition temperature. So a point which curie point that is TC c stands for critical. It has like critical temperature.

They behave as a paramagnetic substance. Critical temperature, rupees, paramagnetic, substance, susceptibility at any temperature. Which is higher than critical is given by the query west law that is chi, m is equal to c by t, minus TC. Okay. And now the susceptibility has a singularity at t, equal to TC.

When I add critical temperature, the susceptibility is a singular value. Okay. And at this temperature and below there exists a spontaneous magnetization, because if the susceptibility chi m is infinite, then we have finite, m for zero value of the applied field. Ba, okay.

So this is due to the interaction between the magnetic ions, which. Is strong enough to align their magnetic moments against the disorder, which is produced by the thermal effects. Okay. Now, the query temperature actually is the temperature, which is above which the spontaneous magnetization vanishes. Okay, query temperature for a spontaneous magnetization. Venice, corridor.

Okay. So the paramagnetic substance will have behaved query. So it separates the disorder paramagnetic phase at temperature above through temperature. Okay, less than pure temperature. Rehab. Okay. So, yeah, There are basic features, ferromagnetic substances.

Now let us come to the main topic waste field theory of ferromagnetism ferromagnetic, which are spontaneously magnetized. Now, within each domain is spontaneous magnetization. Actually, it is due to the alignment of the magnetic moments of adjacent atoms.

How is almost a magnetic moment got a particular direction? Okay. Now the interaction, which aligns the magnetic moments is actually quantum mechanical in origin. Okay, the introduction to quantum. Mechanical interaction, and it is due to the exchange properties of electron wave function.

Okay, exchange interaction. And it arises when the wave function of two atoms overlap only image on two electrons, hoodie formula. So they are indistinguishable, and they belong to both the atoms. So in such cases, the symmetry or anti-symmetry of the wave function strongly influence the energy of the system. And it is the exchange symmetry between the spins and the extent of overlap of the wave function, which. Determines the nature and extent of exchange interaction, which is proportional to the magnetization m within a domain.

Thus, in this mean field approximation, each atom will experience a magnetic field, which is proportional to the magnetization. So I mean, m, lambda is proportionality constant waste constant, which is independent of temperature. Now if the external applied field b, effective so applied field, which is externally applied, how internal field ether or addition for delay, I'm, a particular.

Effective field so b, a plus lambda, m now, edge, b, b, a b, e, r, m, all are vectors. So they act along the same direction. So we can write their magnitude like this b, equal to b, a plus b, e, which is equal to b, a plus lambda, m. Now suppose a unit volume of ferromagnetic material, which contains n atoms. So every monopoly parameter case would expiration python about the magnetization in terms of Brillouin function. See the keyboard m, equal to n, g, j into j, mu, b, b, j, x. It is j. X, singular do line function.

Its value. H this much, okay, you can write its value directly. Okay. So extra value in case of ferromagnetic, substance, angular mu, b by. Kt, so mu. Now for spontaneous magnetization, when there is no external applied field, 180 b, lambda, x, zero. Okay.

Now suppose, when all the domains are aligned along the magnetic field, then the magnetic moment per unit volume, which is known as saturation magnetic moment. I mean, m, s, s for saturation and g, j into j. Mu, b, okay. So everything compare curry by equation, a one. Okay. So the. Simultaneous solution of equation, five and six can be obtained by plotting, the ratio, m by m. S, against x.

How are you plotting acid? This is in accordance with equation 7 upon a pylon for the value of temperature, which is greater than the critical temperature, also equal to critical temperature and also less than critical temperature. Okay? So the plot of this ratio, m by m. S, against x is in accordance with equation, five for t, equal to t, c. Okay.

So 7 equation 7 gives a straight line with different values of. T, and that of equation 5 gives a curve, okay, accordingly critical, which is given by equation, seven as you can see in this figure it is equal to TC. It has changed your straight line out against the marker line function equation. Five. So this straight line is actually tangent at origin to this blue line. Function curve.

Top ray, a straight line is slope. It is given by m by ms, which is equal to this much so at t, equal to TC. It replaces for low value of x such that.

If x is very less than one taller, Line function reduced into j, plus one by three j into x. Okay. It is so tangent to the curve at origin will be having a slope given by b, j, x by x, which is equal to j, plus 1 by 3, j. Okay, this much so that we can calculate for the value of critical temperature. Tc.

Their value is magnetic moment per atom. And it is given by mu j, equal to GJ mu b, square root of j into j. Plus one. Okay, here we value those two waste theory of parameters. Okay.

And this shows that TC is proportional to the waste field constant. That is lambda. Okay, top second case, Allah below temperature that is at a temperature less than TC. Okay. So below cure temperature, I'm a straight line. Jo by la, given by equation, seven it.

I actually say, coco, intersect Corsica, okay, which is given by equation. Five so ATM is x equal to zero. And p, as you can see in this figure, it has g below temperature. Dc. Another straight line track or could data point at zero. And at p, data point, tray intersection, x-ray value.

So the intersection at origin x equal to. Zero is classically unstable condition, Tojo intersection at p. It corresponds to spontaneous magnetization. Thus, below the critical temperature, spontaneous magnetization results in ferromagnetic materials, even in the absence of magnetic field substitute k by n, g, square, j, square, mu, b, square by mu, mu b, square, lambda, equal to one by t, c into j, plus one by three j. Okay. So eBay. It is t by TC into j, plus 1 by 3 j into x. Okay.

So age of equation by the equation 11 at e. M, s, will be maximum value of. Spontaneous magnetization as for spontaneous, and it gives the dependence of this spontaneous magnetism on temperature. But however, a microscopic sample Judy amended. It is generally not magnetized. Okay, mostly at a magnitude. It only becomes a magnet under the influence of an external magnetic field. Okay.

So this behavior is due to the fact that ferromagnetic material is usually subdivided into small regions without domain. So each of this domain is spontaneously magnetized, even in the absence of. External magnetic field. Okay, ISO magnetic domains within the material. They are so arranged as to form closed chains. And they cancel the magnetic effect of each other total magnetism.

It will be zero. Hence, the whole material will be on magnetized or neutral. Okay, temperature for temperature, t, greater than TC magnetic field. So that there will be disordered arrangement equation like this m into 1, minus t, c by t, which is equal to c by mu zero. T, b, a h, o, c. Good data.

Constant. Yeah. This much. Okay. Constant. Okay, so that mu zero, m by b, an into t, minus t, c by t is equal to c by t, mu, zero, m by b, susceptibility, chi, m. So you have a value of similar c by t, minus p c. So a German formula topic.

This is your q, d, west law, for the case of para magnetism. Okay, according to this law, one by chi m is equal agency. This law agrees quite accurately with the experimental results.

But there is slight curvature or deviation near the query point, TC. Okay. And this light curvature leads to distinction between ferromagnetic and. Paramagnetic theory points, okay, deviation collapse straight line.

Now in case of iron, nickel cobalt, their values in kelvin are given like this. It is your curie temperature. Ferromagnetic temperature, parametric by temperature is slightly lower than your paramagnetic curie temperature. Okay. So this is all about your waste theory of ferromagnetism.

Thank you.

Dated : 09-May-2022