Properties magnetic

Magnetic properties, especially the effects of spin paramagnetism, are sensitive indicators of the state of valence electrons in solids and fluids. 

Our concern here goes beyond the limiting cases, of course, because of the wide range of temperatures and densities encountered between 

To deal with the general situation of interacting electrons and to connect the theory of the magnetic susceptibility to various magnetic measurements, it is useful to introduce the generalized spin susceptibility This complex function describes the response of the electron spin system to a time- and spatially-varying magnetic field whose Fourier components are H Q, oj). The ordinary, static spin susceptibility (x in Eqs. (3.1)-(3.3)) is the real part of x(Q o) at o = 0 and Q = 0, that is, 

In an actual static susceptibility experiment one measures the total susceptibility including the diamagnetic contributions. 

Alternatively, the spin susceptibility can be measured directly from the integrated intensity of the valence electron spin resonance (ESR). The ESR intensity is the integral of the imaginary part x (Qy ) over all Q and a and is equal to 0). However, technical difficulties and large linewidths due to strong spin-orbit interactions have restricted ESR measurements to the simplest liquid metals, lithium and sodium, at temperatures close to their melting points (Enderby, Titman, and Wignall, 1964 Devine and Dupree, 1970). 

The presence of a magnetic field-external, or from a nuclear spin-can be incorporated by minimal substitution for the electron momentum operator. 

As it has been shown previously [21 ], at the ZORA level the magnetic perturbation operators are the same no matter if the minimal substitution is made in the Dirac Hamiltonian before 

There are electron spin-independent and spin-dependent paramagnetic terms (linear in the vector potential), and a diamagnetic spin-independent term that (quadratic in the vector potential). By substituting (12.12a) or (12.12b) in the spin-free linear terms, one obtains the ZORA form of the Orbital Zeeman (OZ) operator 

In the last two equations, curly braces indicate that derivatives are only taken in the operator, not of a function to its right. For completeness, we also give the ZORA expressions 

When a substance is placed in a magnetic field H, it develops a certain amount of magnetization (magnetic moment per unit volume) M given by M = yH, where y is the magnetic susceptibility. The magnetic induction B is defined as 

Magnetic properties are due to the orbital and spin motions of electrons in atoms. The relation between the magnetic dipole moment p and the angular momentum J of an electron of charge e and mass m can be expressed as 

The angular momentum is quantized in units of h/2n and the lowest nonzero value of p is the Bohr magneton, P 

The orbital motion of the electron about the nucleus in an atom gives rise to a magnetic moment which is related to the magnitude of the orbital angular momentum L by the expression 

The total magnetic moment can be added up if the populations of the various sublevels are known. Assuming that the spacing of the multiplet levels is large compared to the splitting of the levels of a given J, the mean magnetization can be expressed as 

In sufficiently small ferro- or ferrimagnetic particles with an effective uniaxial anisotropy per unit volume Ka the relaxation of the magnetization will vary exponentially with the temperature following a Neel-Brown process characterized by a relaxation time given by 

14 (a) Magnetization curves for maghemite-PVP samples containing particles with specific surface 1.50 (1), 0.87 (2), 0.65 (3), 0.36 (4). (b) Magnetization curves for goethite-PVP samples containing particles with specific surface 0.27 (1),0.14 (2), 0.13 (3). 

75 In-phase ac magnetic susceptibility of several maghemite-PVP samples with different particlesizesin a range from 4 nm (1) to 16nm (9) (the curves are rescaled). 

In the presence of an oscillating magnetic field, superparamagnetic nanoparticles can absorb energy by two resonance mechanisms  

There are two main areas of development for magnetic nanocomposites. One of them is dealing with applications in biomedicine, and the other with the development of methods for the fabrication of nano-organized sfructures and their applications in recording media, sensors and devices. These are very current in the main nanotechnology initiatives in the and Europe. In 

The loss of coercivity with size, i.e., the superparamagnetic nature of nanoparticles, has been well studied. The discussion earlier deals with the behavior below the blocking temperature. Neel s theory suggests an exponential behavior for the temperature induced relaxation (t)  

By measuring Tb using Mossbauer spectroscopy and magnetic measurements, one obtains estimates of the particle size as well as the magnetic anisotropic properties. 

A layer of uncompensated spins at the surface is responsible for the ferromagnetic interactions observed at low temperatures in normally antiferromagnetic oxides such as MnO, NiO, and CoO [44,45,805,806]. Evidence for such a behavior can be seen from Fig. 1.10. In this study, the blocking temperature was shown to increase with increase in size for NiO and show the opposite trend for MnO nanoparticles. Nanoparticles of ReOs also turn ferromagnetic, exhibiting hysteresis at low temperatures (see Fig. 4.26) [250]. The 

It has been found recently that nanoparticles of all metal oxides, including those which are normally nonmagnetic such as AI2O3, Sn02, and Ti02, show ferromagnetic features in terms of magnetic hysteresis at room temperature due to surface effects [807]. 

In the previous chapter we have defined several electric properties as derivatives of the energy of a charge distribution p(r in the presence of an electric field or field gradient. Some of these properties were alternatively also defined as derivatives of the electric moments. Furthermore, quantum mechanical expressions were derived for all these properties using perturbation theory or static response theory as outlined in Chapter 3. 

Analogously to the electrostatic force in an electric field, the magnetic force, Fm, is expressed in the form 

For both diamagnetic materials and paramagnetic materials, p,r is about unity. For ferromagnetic materials, p,r ranges from 104 to 105. Typical ferromagnetic materials include iron, nickel, cobalt, and six rare-earth elements, and their alloys. 

Expressions for the calculation of magnetic properties at the relativistic level of theory can be derived by replacing the momentum operator p in the Dirac equation (1) with the generalized momentum operator n 

In equation (58), e is the electron charge, c is the speed of light,. / A- (r) is the vector potential describing the magnetic interactions, and denotes the strength parameter of the vector potential. Differentiation of the Dirac energy 

In order to derive expressions which can be used for calculating magnetic properties at the quasi-relativistic level of theory, we analogously replace p in equations (13)-(18) by the corresponding generalized momentum %. The expressions are inserted into equation (20) and one proceeds as described in Section 3. The total quasi-relativistic energy as a function of the perturbation strength parameter then becomes 

The operator in equation (59) consists the nonrelativistic kinetic operator which depends on the vector potential, and the po- 

The equations for the calculation of the first-order magnetic properties can be obtained by differentiation of the quasi-relativistic energy expression (59) with respect to the strength of the magnetic perturbation 

The absorption features of zeolites (mordenite, ZSM-5, NaY, Beta) have been studied by performing magnetic measurements on iron oxide in a composite to produce a magnetic adsorbent [05P1]. These magnetic composites can be used as adsorbents for water contaminants and srrbsequent removal from the medium by the magnetic process. 

Our discussion of electric properties showed that at least for time-independent fields the operators derived for the relativistic case were just the four-component analogs of the nonrelativistic operators. For magnetic relativistic property operators we do not expect the connection to be so simple due to the fact that the field appears in different forms in the two versions of the Hamiltonian. For the relativistic case, we again write the Hamiltonian as 

For the nonrelativistic case we may use the spin Hamiltonian discussed in chapter 4, 

We see that the vector potentials appear to different order in the two Hamiltonians. The form of any property operator derived as a response to changes in the vector potential (or the induction) is therefore likely to depend on which Hamiltonian is used as a starting point. 

We will demonstrate this for the magnetic dipole moment, m, and for simplicity we assume that we have a uniform field, that is, (13.24) holds. For the relativistic case, this yields the Hamiltonian 

We define the magnetic dipole moment m via the first-order response to changes in the magnetic induction 

Ferroelasticity is the mechanical analogon to ferroelectricity. A crystal is ferroelastic if it exhibits two (or more) differently oriented states in the absence of mechanical strain, and if one of these states can be shifted to the other one by mechanical strain. CaCl2 offers an example (Fig. 4.1, p. 33). During the phase transition from the rutile type to the CaCl2 type, the octahedra can be rotated in one or the other direction. If either rotation takes place in different regions of the crystal, the crystal will consist of domains having the one or the other orientation. By exerting pressure all domains can be forced to adopt only one orientation. 

An unpaired electron executes a spin about its own axis. The mechanical spin momentum is related to a spin vector which specifies the direction of the rotation axis and the magnitude of the momentum. The spin vector s of an electron has an exactly defined magnitude  

The spin quantum number s is used to characterize the spin. It can have only the one numerical value of x = h = 6.6262 10—34 J s = Planck s constant. 

The magnetic moment of an isolated electron has a definite values of 

An electron orbiting in an atom is a circular electric current that is surrounded by a magnetic field. This also can adopt only certain orientations in an external magnetic field according to quantum mechanics. The state of an electron in an atom is characterized by four quantum numbers  

The distribution of diffusing atoms represented by the Gaussian distribution curve  

Pg is termed the Bohr magneton. Magnetic moments are given as multiples of pg. 

The calculated /reff and observed values from experiments are listed in Table 18.1.4 and shown in Fig. 18.1.2. There is good agreement in all cases except for Sm3+ and Eu3+, both of which have low-lying excited states (6 3i/2 for Sm3+, and1 F and11 2 for Eu3+) which are appreciably populated at room temperature. 

Measured and calculated effective magnetic moments (/ne[[) of Ln3+ ions at 300 K (broken lines represents the calculated values). 

2 Coran A Y, Ignatz-Hoover F, Smakula P C, Chem. TechnoL, 67, No.2, 1994,237-51. 

7 Ogadhoh S O, Papathanasiou T D, Composites Part A Applied Science and Manufacturing, Ilk., No.l, 1996, 57-63. 

14 Jones D W, Rizkalla A S, J. Biomedical Materials Research (Applied Biomaterials), 33, No.2, 1996, 89-100. 

15 Weeling B, Electrical Conductivity in Heterogeneous Polymer Systems. Conductive Polymers, Conference Proceedings, 1992, Bristol, UK. 

16 Itatani K, Yasuda R, Scott Howell F, Kishioka, J. Mater. Sci., 32, 1997, 2977-84. 

Therefore, the reduction in interelectronic repulsion in going from the gaseous Fe ion to [FeFe] is a 19%. 

We begin the discussion of magnetochemistry with the so-called spin-only formula, an approximation that has limited, but useful, applications. 

Paramagnetism arises from unpaired electrons. Each electron has a magnetic moment with one component associated with the spin angular momentum of the electron and (except when the quantum number / = 0) a second component associated with the orbital angular momentum. For many complexes of first row J-block metal ions we can 

The effective magnetic moment, can be obtained from the experimentally measured molar magnetic susceptibility, Xm, and is expressed in Bohr magnetons p ) where l B = eh/Attm = 9.27 x 10 JT . Equation 20.12 gives the relationship between and Xml using SI units for the constants, this expression reduces to equation 20.13 in which Xm is in cm moU. In the laboratory, the continued use of Gaussian units in magnetochemistry means that irrational susceptibility is the measured quantity and equation 20.14 is therefore usually applied.  

As seen from eq. (10.21), the first-order property is given as an expectation value of operators linear in the perturbation. The second-order property contains two contributions, an expectation value over quadratic (or bilinear) operators and a sum over products of matrix elements involving linear operators connecting the ground and excited states. 

The first-order property with respect to an external field is the magnetic dipole moment m (eq. (10.10)). When field-independent basis functions are used, the HF magnetic dipole moment is given as the expectation value of the V2LG and S (total electron spin) operators over the unperturbed wave function, eqs (10.21) and (10.24). Since the Lg operator is imaginary it can only yield a non-zero result for spatially degenerate wave functions and the expectation value of S is only non-zero for non-singlet states. 

Origin Operator Equation Name Perturbation order Bex, I C  

Note that the spin-Zeeman term involves the total electron spin S. 

The second-order term, the magnetizability has two components. The derivative expression (10.34) is given by eq. (10.85). 

The effective magnetic moment, can be obtained from the experimentally measured molar magnetic susceptibility, Xm (see Box 21.5), and is expressed in Bohr magnetons ( b) where lpB = eh/Anm = 9.27 x 10 JT. Equation 

17 gives the relationship between p ff and Xm using SI units for the constants, this expression reduces to equation 

18 in which Xm is in cm mol . In the laboratory, the continued use of Gaussian units in magnetochemistry means that irrational susceptibility is the measured quantity and equation 21.19 is therefore usually apphed.  

CHEMICAL AND THEORETICAL BACKGROUND Box 21.6 A paramagnetic, tetrahedral Pd(ll) complex 

For complexes with a common metal ion, it is found that the nephelauxetic effect of ligands varies according to a series independent of metal ion  

A nephelauxetic series for metal ions (independent of ligands) is as follows  

The nephelauxetic effect can be parameterized and the values shown in Table 20.10 used to estimate the reduction in electron-electron repulsion upon complex formation. In eq. 20.14, the interelectronic repulsion in the complex is the Racah parameter B-, is the interelectronic repulsion in the gaseous M ion. 

The worked example and exercises below illustrate how to apply eq. 20.14. 

Iron oxide silica aerogel composites have been prepared by the sol-gel method followed by supercritical drying [6] and are found to be two or three orders of magnitude more reactive than the conventional iron oxide. The increase in reactivity was attributed to the large surface area of iron oxide nanoparticles supported on the silica aerogel. 

To better understand the relative contributions of the component rings to the observed chemical shifts in the phenylenes, recourse was taken to nucleus-independent chemical shift (NICS) [118] calculations, which provide such data (in ppm) for a point nucleus at any given position in a molecule. For cyclic polyenes 

The angular mode of fusion in 15 further reduces the diatropism of the center (NICS = —3.3 3 = 6.18 ppm), in conjunction with decreased paratropism of the cyclobutadienes (NICS = 3.1). As a consequence, the termini are more diatropic than in biphenylene (NICS = —9.5 vs. 8.0) [120]. In the remainder of the angular series, the arguments advanced previously for the rationalization of the trends in bond-localizations are clearly augmented by the magnetic data. Thus, 19, as an example, shows the alternation of diatropism of the six-membered rings NICS = 

In the branched 21b, the central six-membered ring becomes essentially atropic (NICS = —1.1), as do the adjacent cyclobutadienes (NICS = —0.4), allowing for 

The high positive value of Ega,2 makes the formation of gaseous Cr seem very unlikely. The ion can exist, however, in ionic compounds, such as MgO(s), where formation of the ion is accompanied by other energetically favorable processes. 

On the blank periodic table in the margin locate the group expected to have 

Manganese has a paramagnetism corresponding to five unpaired electrons, which is consistent with the electron configuration 

When a manganese atom loses two electrons, it becomes the ion Mn, which is paramagnetic, and the strength of its paramagnetism corresponds to five unpaired electrons. 

When a third electron is lost to produce Mn, the ion has a paramagnetism corresponding to four unpaired electrons. The third electron lost is one of the unpaired 3d electrons. 

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EXAMINATION OF THE KINETICS OF MAGNETIC PROPERTIES IN TEMPERING STRUCTURAL STEELS WITH SPECIAL REFERENCE TO ACTIVE INSPECTION OF THEIR QUALITY by E.S. Gorkunov and I.n. Batuklitina, Vol. 23, No.3, pp. 177-183... 

To be easily attracted by the poles created perpendicularly to the defect, particles must satisfy precise conditions concerning dimensions, shape, density and magnetic property. 

Small metal clusters are also of interest because of their importance in catalysis. Despite the fact that small clusters should consist of mostly surface atoms, measurement of the photon ionization threshold for Hg clusters suggest that a transition from van der Waals to metallic properties occurs in the range of 20-70 atoms per cluster [88] and near-bulk magnetic properties are expected for Ni, Pd, and Pt clusters of only 13 atoms [89] Theoretical calculations on Sin and other semiconductors predict that the stmcture reflects the bulk lattice for 1000 atoms but the bulk electronic wave functions are not obtained [90]. Bartell and co-workers [91] study beams of molecular clusters with electron dirfraction and molecular dynamics simulations and find new phases not observed in the bulk. Bulk models appear to be valid for their clusters of several thousand atoms (see Section IX-3). 

Chartler A, D Arco P, DovesI R and Saunders V R 1999 Ab initio Flartree-Fock Investigation of the structural, electronic, and magnetic properties of MOjO Pbys. Rev. B 60 14 042-8, and references therein... 

Wu R and Freeman A J 1994 Magnetism at metal-ceramic interfaces effects of a Au overlayer on the magnetic properties of Fe/MgO(001) J. Magn. Magn. Mater. 137 127-33... 

One of tire interesting aspects of transition-metal clusters is tlieir novel magnetic properties [91, 92, 93 and 94l]. ... 

Pastor G M, Dorantes-Davila J and Bennemann K H 1989 Size and structural dependence of the magnetic properties of small 3d-transition metal clusters Phys. Rev. B 40 7642... 

Bucher J P, Douglass D C and Bloomfield L A 1991 Magnetic properties of free cobalt clusters Phys. Rev. Lett. 66 3052... 

Also, novel magnetic properties have been reported in mixed fullerene composites, in which the fullerene is limited... 

It should be noted that the magnetic properties of iron are dependent on purity of the iron and the nature of any impurities.)... 

Evidence other than that of ion-exchange favours the view of the new elements as an inner transition series. The magnetic properties of their ions are very similar to those of the lanthanides whatever range of oxidation states the actinides display, they always have -1-3 as one of them. Moreover, in the lanthanides, the element gado-... 

Within the periodic Hartree-Fock approach it is possible to incorporate many of the variants that we have discussed, such as LFHF or RHF. Density functional theory can also be used. I his makes it possible to compare the results obtained from these variants. Whilst density functional theory is more widely used for solid-state applications, there are certain types of problem that are currently more amenable to the Hartree-Fock method. Of particular ii. Icvance here are systems containing unpaired electrons, two recent examples being the clci tronic and magnetic properties of nickel oxide and alkaline earth oxides doped with alkali metal ions (Li in CaO) [Dovesi et al. 2000]. 

L. magnes, magnet, from magnetic properties of pyrolusite It. manganese, corrupt form of magnesia)... 

Platinum-cobalt alloys have magnetic properties. One such alloy made of 76.7% Pt and 23.3%... 

Pure holmium has a metallic to bright silver luster. It is relatively soft and malleable, and is stable in dry air at room temperature, but rapidly oxidizes in moist air and at elevated temperatures. The metal has unusual magnetic properties. Few uses have yet been found for the element. The element, as with other rare earths, seems to have a low acute toxic rating. 

Spinel ferrites, isostmctural with the mineral spinel [1302-67-6] MgAl204, combine interesting soft magnetic properties with a relatively high electrical resistivity. The latter permits low eddy current losses in a-c appHcations, and based on this feature spinel ferrites have largely replaced the iron-based core materials in the r-f range. The main representatives are MnZn-ferrites (frequencies up to about 1 MH2) and NiZn-ferrites (frequencies 1 MHz). 

Substitution for Fe has a drastic effect on intrinsic magnetic properties. Partial substitution by or decreases J) without affecting seriously, resulting in larger and values. Substitution by Ti and Co causes a considerable decrease in K , the uniaxial anisotropy (if j > 0) may even change into planar anisotropy (if < 0). Intermediate magnetic stmctures are also possible. For example, preferred directions on a conical surface around the i -axis are observed for substitution (72). For a few substitutions the value is increased whereas the J) value is hardly affected, eg, substitution of Fe byRu (73) or by Fe compensated by at Ba-sites (65). 

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