We stated in the last topic that different types of magnetism exist, and that they are characterized by the magnitude and the sign of the susceptibility (see Table 14.1). Since various materials respond so differently in a magnetic field, we suspect that several fundamentally different mechanisms must be responsible for the magnetic properties.
Ampere postulated more than one hundred years ago that molecular currents are responsible for the magnetism in a solid. It has been observed that superconducting materials (Section 7.6) expel the magnetic flux lines when in the superconducting state (Meissner effect).
Paramagnetism in solids is attributed, to a large extent, to a magnetic moment that results from electrons which spin around their own axes, Fig. Free atoms (dilute gases) as well as rare earth elements and their salts and oxides possess an additional source of paramagnetism. Without an external magnetic field, these magnetic moments are randomly oriented and thus they mutually cancel one another.
Metals, with a few exceptions, do not obey the Curie-Weiss law, as we shall see in topic 16. It is now possible to make some general statements about whether para- or diamagnetism might be expected in certain materials.
One word of caution should be added about applying the above general principles too rigidly. We turn now to ferromagnetics and commence with the experimentally found magnetization curve for these materials.
Finally, M levels off and reaches a constant value, called the saturation magnetization, Ms. The inverse of piezomagnetism is called magnetostriction, an effect which describes a change in dimensions when a ferromagnetic substance is exposed to a magnetic field. This way, north and south poles are closer together and the external magnetic field is confined to a smaller area (Fig.
A further reduction in magnetostatic energy can be obtained if the magnetic flux follows a completely closed path within a crystal so that no exterior poles are formed. It is the ideal host for x-ray phosphors because it produces the densest known white material, lutetium tantalate (LuTaO4). It is utilized as a dopant in matching lattice parameters of certain substrate garnet crystals, such as indium-gallium-garnet (IGG) crystals due its lack of a magnetic moment. Oxides are available in forms including powders and dense pellets for such uses as optical coating and thin film applications. A temperature dependence of the magnetic susceptibility [?(T)] of rare-earth borates RAl3(BO3)4 (R = Tb, Er, or Ho) is measured by the Faraday method at temperatures in the interval 20–850°С. JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser.
The research group led by Benjamin Lev, assistant professor of physics, has achieved the world's first magneto-optical trapping (MOT) of both the bosonic and fermionic isotopes of dysprosium, a rare-earth (lanthanide) element possessing the largest magnetic moment, 10 Bohr magnetons. Experiments are underway to increase the size of the cloud to 100 million constituent atoms and to capture them in an optical tweezer. The group hopes to achieve temperatures in the 100-nanoK range in the next 18 months, at which point the Dy atoms should form a dipolar BEC, or quantum ferrofluid, when the bosonic isotopes are trapped, or a novel quantum liquid crystal when fermionic isotopes are trapped. Ultracold Dy atoms obtained from these MOTs may be used to investigate poorly understood, though technologically relevant, materials that do not obey standard Fermi liquid theory.
Joining Lev in this pioneering work are graduate students Seo Ho Youn, Mingwu Lu, and Ushnish Ray. This work is supported by the Air Force Office of Scientific Research and the National Science Foundation. Lutetium is one of those rare earth elements that are rare enough, and reactive enough, that they are darned tough to find. Lutetium is so hard to find, in fact, that even the cleverest humans with very large books didn't figure it out until 1907. Lutetium is the densest and hardest of the rare earths, lacks a magnetic moment, and has the highest melting point of the rare earths.
I was just worrying about impurities in my Ytterbium the other day, but I didn't let it get to me. Eh, I tend to worry about impurities in my Ytterbium, slack on the literature review, and rediscover Lutetium.
As the internet's preeminent site for interactive, democratic art appreciation, Infinite Art Tournament frees great art from the straitjackets of chronology and categorical conventions in order to put it in a new straitjacket of its own devising. Magnetic circuits, comprised of permanent magnets and ferromagnetic return paths, can be designed with a wide variety of air gaps and magnetic flux density levels.
The total flux of any closed region within a magnetic circuit must always be conserved; meaning the total flux leaving this region must equal the total flux entering this region. AmpA?re's circuital law relates the integrated magnetic field around a closed loop to the electric current passing through the loop.
The following is a very simple magnetic circuit consisting of one rectangular permanent magnet with two steel components on each side. Magnetic flux from the magnet will travel from one steel pole piece and pass through the air gap to reach the other steel pole piece.
Where Bm is the average magnetic flux density in the magnet, Bg is the average magnetic flux density in the air gap, Am is the cross sectional area of the magnet, Ag is the cross sectional area of the air gap, κ1 is leakage coefficient which has a typical value slightly over unity. Where Lm is the length of the magnet, Hm is the average magnetizing force from the magnet, Lg is the length of the air gap, Bg is the air gap flux density, and κ2 is a loss factor.
The above equation is a first order estimation of the permeance coefficient, which helps us choose the right grade of permanent magnets, reduce the possibility of demagnetization, and minimize the required volume of permanent magnets in the system. In the first part of this topic we shall attempt to unfold the multiplicity of the magnetic behavior of materials by describing some pertinent experimental findings and giving some brief interpretations.

He compared the molecular currents to an electric current in a loop-shaped piece of wire, which is known to cause a magnetic moment. It was found by Lenz that a current is induced in a wire loop whenever a bar magnet is moved toward (or from) this loop.
A more accurate and quantitative explanation of diamagnetism replaces the induced currents by precessions of the electron orbits about the magnetic field direction (Larmor precession, see Fig. In other words, a superconductor behaves in an external magnetic field as if B is zero inside the superconductor (Fig. This is believed to be due to the fact that in crystals the electron orbits are essentially coupled to the lattice, which prevents the orbital magnetic moments from turning into the field direction. Schematic representation of the spin alignment in a d-band which is partially filled with eight electrons (Hund’s rule).
We mention as examples for filled bands intrinsic semiconductors, insulators, and ionic crystals such as NaCl.
A newly cast piece of iron (often called virgin iron) is inserted into a ring-shaped solenoid (Fig.
When H is reduced to zero, the magnetization retains a positive value, called the remanent magnetization, or remanence, Mr. Saturation Magnetization at 0 K and Curie Temperature (TC) for Some Ferromagnetic Materials.
Schematic representation of the effect of tensile and compressive stresses on the magnetization behavior of (a) nickel and (b) iron. To answer this, let us assume for a moment that all electron spins in a crystal are indeed aligned in parallel, Fig.
Again, the above-mentioned exchange energy, which supports a parallel spin alignment, hinders a spontaneous flip-over. The most common method, devised by Bitter in 1931, utilizes an aqueous suspension of very finely dispersed Fe3O4 particles which is applied to the polished surface of a test material. Further, cold work decreases the permeability and causes a clockwise rotation of the hysteresis curve. Nanoparticles (See also Nanotechnology Information and Quantum Dots) also produce very high surface areas.
Like X-rays, the gamma rays emitted by the source pass through soft tissues of the body, but are blocked by bones and other dense materials. Nonlinear anomalies caused by structural transitions are observed in the dependences ?–1(T).
These attributes may be due to the property of lanthanide contraction, which gives it the smallest atomic radius of the rare earths. If the steel pole pieces have sufficiently high permeability and are not saturated, the term HpLp is then very small and can be replaced with a loss factor κ2. One can determine the required magnet using first order estimation from equation (6), (7) and (8), which provides a good starting point without doing finite element analysis. Department of State, Directorate of Defense Trade Controls (DDTC) in accordance with section 122.1 (a) of the International Traffic in Arms Regulations (ITAR).
In the sections to follow, we shall treat the atomistic theory of magnetism in more detail.
The current thus induced causes, in turn, a magnetic moment which is opposite to the one of the bar magnet (Fig. We have already introduced the electron spin in Section 6.4 and mentioned there that, because of the Pauli principle, no two electrons having the same energy can have the same value and sign for the spin moment.
However, when an external field is applied, the individual magnetic vectors tend to turn into the field direction.
Thus, the orbital magnetic moments of thef-electrons may turn into the external field direction and contribute to electron-orbit paramagnetism. For example, in an atom with eight valence d-electrons, five of the spins align, say, up, and three spins point down, which results in a net total of two spins up (Fig.
Moreover, terbium-disprosium-iron displays magnetostriction which is about 3 orders of magnitude larger than in iron and iron-nickel alloys. Further divisions into still smaller and smaller domains with concomitant reductions in magnetostatic energies lead, however, eventually to an optimal domain size. Instead, a gradual rotation over several hundred atomic distances is energetically more favorable. These particles are attracted to the domain wall endings and can then be observed as fine lines under an optical microscope. This is known as the Barkhausen effect, which utilizes an induction coil wound around a ferromagnetic rod. Thus, small 169Yb samples act like tiny X-ray machines useful for radiography of small objects. Fluorides are another insoluble form for uses in which oxygen is undesirable such as metallurgy, chemical and physical vapor deposition and in some optical coatings. It is established that the dependences ?–1(T) for each phase obey the linear Curie–Weiss law. The current in the loop causes a magnetic field that is directed opposite to the magnetic field of the bar magnet (Lenz’s law). This leads to a second contribution to the diamagnetic moment; specifically, the circulating free electrons cause a magnetic moment, similarly as described above. Thus, with (14.5), we obtain which means that the magnetization is equal and opposite to the external magnetic field strength. In other words, each electron state can be occupied by two electrons only; one with positive spin and one with negative spin, or, as is often said, one with spin up and one with spin down.
For example, copper, which has one s-electron in its valence band, should be paramagnetic according to our considerations brought forward so far.

Note, that a current can flow in the secondary circuit only if the current (and therefore the magnetic flux) in the primary winding changes with time. The remanent magnetization can be removed by reversing the magnetic field strength to a value Hc, called the coercive field. As an example, a compressive stress increases the magnetization for nickel, while a tensile stress reduces M and therefore m.
The region between individual domains in which the spins rotate from one direction into the next is called a domain wall or a Bloch wall. Another method exploits the rotation of the plane of polarization of reflected light from differently magnetized areas (Kerr effect). The Curie temperatures and the magnetic moments corresponding to the chemical formula of the compounds have been found. An external magnetic field tries to turn the unfavorably oriented spin moments in the direction of the external field.
Solids that have both orbital as well as spin paramagnetism are clearly paramagnetic since the sum of both paramagnetic components is commonly larger than the diamagnetism. Solids having a large combination of Mr and Hc are called hard magnetic materials (in contrast to soft magnetic materials for which the area inside the loop of Fig. For ferromagnetics the Curie temperature, TC, and the constant 9 in the Curie-Weiss law are nearly identical. This effect is just the opposite in certain nickel-iron alloys (permalloy, see Table 17.1) where a tensile stress increases M or m. The spin direction in each domain is, however, different, so that the individual magnetic moments for the material as a whole cancel each other and the net magnetization is zero.
This would be energetically unfavorable because it would be the source of a large external magnetic field. The energy involved for the latter has been found to be the quantum mechanical exchange energy. In other words, the responses of the orbiting electrons counteract the external field (Fig.
Precession is the motion which arises as a result of external torque acting on a spinning body (such as a spinning top) or, as here, on an orbiting electron.
We will talk about the quantum mechanical aspect of spin paramagnetism in more detail in topic 16. A small difference exists, however, because the transition from ferromagnetism to paramagnetism is gradual, as can be seen in Fig. An external magnetic field causes those domains whose spins are parallel or nearly parallel to the external field to grow at the expense of the unfavorably aligned domains. The magnetostatic energy of this field can be approximately halved if the crystal contains two domains that are magnetized in opposite directions. As we will learn in Section 16.2, this exchange energy causes adjacent spins to align parallel to each other. The wall motions may be impeded by imperfections in the crystal, such as by particles of a second phase, oxides, holes, or cracks. At low fields, iron behaves like permalloy, whereas at high fields it behaves similar to nickel.
It is this interplay between exchange energy, which demands parallel spin alignment, and magnetostatic energy, which supports antiparallel spins, that leads eventually to an energetically most favorable domain size (which is about 1-100 mm).
It is utilized as a dopant in matching lattice parameters of certain substrate garnet crystals, such as indium-gallium-garnet crystals due its lack of a magnetic moment. It is in general very weak and is observed in some metals and in salts of the transition elements. The possible presence of a net spin-paramagnetic moment depends upon whether or not the magnetic moments of the individual spins cancel each other. It should be noted that a second type of hysteresis curve is often used, in which B (instead of M) is plotted versus H. More specifically, if a solid has completely filled electron bands, we anticipate (because of the Pauli principle) the same number of electrons with spins up as well as with spins down. Nevertheless, if the external magnetic field is further increased a small, additional rise in M is observed. For example, a completely filled d-band contains 5N electrons with spins up and 5N electrons with spins down. This is caused by the forced alignment of those spins which precess about the field direction due to thermal activation. This results in a cancellation of the spin moments and no net spin paramagnetism is expected.
15.7(b)) is believed to be due to the fact that, slightly above TC, small clusters of spins are still aligned parallel to each other, a phenomenon which is called magnetic short-range order. Irgashev, in: Optoacoustic, Electric, and Magnetic Investigations of Condensed Media [in Russian], Publishing House of Samarkand State University, Samarkand (1982), pp. Volkov, Magnetic and magnetoelastic properties of rare-earth ferroborates RFe3(BO3)4 (R = Nd, Tb, Dy), Author’s Abstract Cand. Kharlamova, Synthesis, structure, and magnetic and optical properties of rare-earth halo- ferroborates with xantite structure, Author’s Abstract Cand.

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