give the specimen take alignment of magnetic moment of anti ferromagnetism and ferrimagnetic
Answers
Explanation:
The magnetism of metals and other materials are determined by the orbital and spin motions of the unpaired electrons and the way in which unpaired electrons align with each other. All magnetic substances are paramagnetic at sufficiently high temperature, where the thermal energy (kT) exceeds the interaction energy between spins on neighboring atoms. Below a certain critical temperature, spins can adopt different kinds of ordered arrangements.
Chart describing the different ordering of spins. Description next to arrow illustration. Ferromagnetic has 7 red arrows pointing up. Description: Below T C, spins are aligned parallel in magnetic domains. Antiferromagnetic has 7 red arrows that alternate between up and down. Description: Below T N, spins are aligned antiparallel in magnetic domains. Ferrimagnetic has 7 arrows alternating between red up and blue down. Description: Below T C, spins are aligned antiparallel but do not cancel. Paramagnetic has 7 red arrows with the arrangement up, down, up, up, down, up, down. Description: Spins are randomly oriented (any of the others above T C or T N).
A pictorial description of the ordering of spins in ferromagnetism, antiferromagnetism, ferrimagnetism, and paramagnetism
Let's begin by considering an individual atom in the bcc structure of iron metal. Fe is in group VIIIb of the periodic table, so it has eight valence electrons. The atom is promoted to the 4s13d7 state in order to make bonds. A localized picture of the d-electrons for an individual iron atom might look like this:
D-electron configuration of an iron atom. 5 orbitals, 3 half filled and 2 filled.
Since each unpaired electron has a spin moment of 1/2, the total spin angular momentum, S, for this atom is:
S=312=32 (in units of h/2π)
We can think of each Fe atom in the solid as a little bar magnet with a spin-only moment S of 3/2. The spin moments of neigboring atoms can align in parallel (↑ ↑), antiparallel (↑ ↓), or random fashion. In bcc Fe, the tendency is to align parallel because of the positive sign of the exchange interaction. This results in ferromagnetic ordering, in which all the spins within a magnetic domain (typically hundreds of unit cells in width) have the same orientation, as shown in the figure at the right. Conversely, a negative exchange interaction between neighboring atoms in bcc Cr results in antiferromagnetic ordering. A third arrangement, ferrimagnetic ordering, results from an antiparallel alignment of spins on neighboring atoms when the magnetic moments of the neighbors are unequal. In this case, the spin moments do not cancel and there is a net magnetization. The ordering mechanism is like that of an antiferromagnetic solid, but the magnetic properties resemble those of a ferromagnet. Ferrimagnetic ordering is most common in metal oxides, as we will learn in Chapter 7.
Magnetization and susceptibility
The magnetic susceptibility, χ, of a solid depends on the ordering of spins. Paramagnetic, ferromagnetic, antiferromagnetic, and ferrimagnetic solids all have χ > 0, but the magnitude of their susceptibility varies with the kind of ordering and with temperature. We will see these kinds of magnetic ordering primarily among the 3d and 4f elements and their alloys and compounds. For example, Fe, Co, Ni, Nd2Fe14B, SmCo5, and YCo5 are all ferromagnets, Cr and MnO are antiferromagnets, and Fe3O4 and CoFe2O4 are ferrimagnets. Diamagnetic compounds have a weak negative susceptibility (χ < 0).
Definitions
H = applied magnetic field (units: Henry (H))
B = induced magnetic field in a material (units: Tesla (T))
M = magnetization, which represents the magnetic moments within a material in the presence of an external field H.
Magnetic susceptibility χ = M/H
Usually, χ is given in molar units in the cgs system:
χM = molar susceptibility (units: cm3/mol)
Typical values of χM:
SiO2
Diamagnetic
- 3 x 10-4
Pt metal
Pauli paramagnetic
+ 2 x 10-4
Gd2(SO4)3.8H2O
Paramagnetic
+ 5 x 10-2
Ni-Fe alloy
Ferromagnetic
+ 104 - 106
To correlate χ with the number of unpaired electrons in a compound, we first correct for the small diamagnetic contribution of the core electrons:
χcorr=χobs−χdiamagneticcores(6.8.1)
Susceptibility of paramagnets
For a paramagnetic substance,
χcorrM=CT(6.8.2)
The inverse relationship between the magnetic susceptibility and T, the absolute temperature, is called Curie's Law, and the proportionality constant C is the Curie constant:
C=NA3kBμ2eff(6.8.3)
Note that C is not a "constant" in the usual sense, because it depends on µeff, the effective magnetic moment of the molecule or ion, which in turn depends on its number of unpaired electrons: