Physics: Determination of the temperature of the ferromagnetic-paramagnetic phase transition, Laboratory work. Determination of the ferromagnetic-paramagnetic phase transition temperature Ferromagnetic-paramagnetic phase transition

IZVESTIYA RAS. PHYSICAL SERIES, 2015, volume 79, no. 8, p. 1128-1130

UDC 537.622:538.955

PHASE TRANSITION STUDIES

FERROMAGNETIC-PARAMAGNETIC IN THIN FILMS FePt1- xRhx PHASE L10

FePtRh films with different Rh contents (FePtj _ xRhx) were obtained by magnetron sputtering. The magnetic structure and ferromagnetic-paramagnetic phase transition in thin films of FePtj _xRhx phase L10 were studied depending on the Rh content (0< х < 0.40) в образце. Показано, что при комнатной температуре тонкие пленки FePti _ xRhx при 0 < х < 0.34 находятся в ферромагнитном состоянии с большой энергией магнитокристаллической анизотропии, тогда как при 0.34 < х < 0.4 - в парамагнитном состоянии.

DOI: 10.7868/S0367676515080335

INTRODUCTION

Many studies of magnetic materials related to the creation of thin films are aimed at increasing the density of magnetic recording of information. As a rule, an increase in recording density is achieved by minimizing the size of grains - information carriers in magnetic film and by moving from a longitudinal type of recording to a perpendicular one. However, the reduction in granule size is limited by the occurrence of a superparamagnetic effect, which prevents an increase in the magnetic recording density. Another limitation to increasing recording density is the exchange interaction between beads. To overcome these limitations, various methods are used, one of which is the use of a structured storage medium. In a conventional magnetic medium, the recording layer consists of randomly arranged grains of a ferromagnetic alloy. In the case of a structured information carrier, ferromagnetic granules or nanodots of the same size are created in the film, arranged in an orderly manner in a non-magnetic matrix. In this case, each of the points acts as a bit of information.

1 Federal State Autonomous educational institution higher vocational education Kazan (Volga region) Federal University.

2 Federal State budgetary institution Sciences Institute of Physics and Technology named after A.F. Ioffe Russian Academy Sciences, St. Petersburg.

3 Department of Materials Science and Engineering, Akita Uni-

versity, 1-1 Gakuen-machi, Tegata, Akita 010-8502, Japan.

In the last decade of film BeR! Li0 phases attract close attention of researchers because they have a high energy of magnetocrystalline anisotropy (Ku ~ 7 107 erg cm-3), which makes their use promising as structured information carriers. In this case, for ultra-high-density magnetic recording (UHDM), the easy magnetization axis (c-axis) in them must be oriented along the normal to the film plane.

It is known that controlling the magnetic properties of BeP films! perhaps by introducing additional elements into them. Addition of rhodium (RH) to the BeR alloy! allows you to optimize the magnetic properties of thin films without significantly reducing the energy of magnetocrystalline anisotropy, which makes it possible to use this composition as a structured information carrier.

In this work, the magnetic structure and ferromagnetic-paramagnetic phase transition in thin films of the FeF1 phase L10 were studied depending on the content of NR (0< х < 0.40) в образце.

1. EXPERIMENT

Thin FeP1- films were obtained by magnetron sputtering onto a single-crystal Mg0 (100) substrate. The thickness of the synthesized films was 20 nm (Fig. 1). Magnetic properties were measured at 300 K using a superconducting quantum interferometer

RESEARCH OF THE FERROMAGNETIC-PARAMAGNETIC PHASE TRANSITION

Fe^Pt! - xRhx)5()

Mg0(100) substrate

20 nm 0.5 mm

Rice. 1. Schematic representation of thin samples

(SQUID) and a vibrating magnetometer. The magnetic structure of the synthesized films, namely the orientation of the remanent magnetization, was studied using conversion electron Mössbauer spectroscopy (CEMS). Mössbauer measurements were carried out on a spectrometer in which a source of 57Co gamma rays in a Rh matrix moved with constant acceleration. To register conversion electrons, an electron detector filled with a mixture of He + 5% CH4 gases was used, into which the sample under study was placed. When measuring the Mössbauer effect, gamma radiation from the 57Co(Rh) source was directed perpendicular to the surface of the film under study. The velocity scale of the spectrometer was calibrated using alpha iron foil at room temperature, and for higher accuracy the calibration was carried out using a laser interferometer. The magnitudes of isomeric shifts were determined relative to metallic a-Fe. Mathematical processing of Mössbauer spectra was carried out using a special program that made it possible to determine the positions, amplitudes and widths of spectral lines from experimental Mössbauer spectra. Further, based on the obtained data, effective magnetic fields on the nuclei of iron ions (Hhf), quadrupole splittings (QS) and chemical shifts (CS) were calculated.

2. RESULTS AND THEIR DISCUSSION

In Fig. Figure 2 shows the FEM spectra of the studied FePt1-xRhx samples. In the spectrum of FePtx_xRhx at x = 0, the 2nd and 5th lines of Zeeman splitting in a hyperfine field are absent, which indicates the orientation of the magnetic moments perpendicular to the film surface. This kind of orientation of effective magnetic field allows us to conclude that the easy axis of magnetic crystalline anisotropy is perpendicular to the film surface. Line subtraction

x = 0.30 ■ .. .-w^

6 -4 -2 0 2 4 6 Speed, mm ■ s-1

Rice. 2. Mössbauer spectra of FePtj _ thin films

Zeeman splitting from the spectrum of FeP1 shows that in the region of “zero” velocities there are no lines belonging to iron ions in the paramagnetic phase, this means that all Fe ions in the sample are in a magnetically ordered state.

With an increase in the concentration of NR in the composition of FeP^xRNRx films, a gradual decrease in the effective magnetic fields is observed, and at x = 0.4 the Zeeman splitting lines “collapse” into a singlet. This change in the spectra of the samples with increasing concentration of nuclear radiation is due to the transition of the FeP1Ri system from the ferromagnetic state to the paramagnetic state at room temperature of measurements. This transition occurs due to the replacement of P ions by rhodium ions and the emergence of paramagnetic clusters. With increasing concentration of nuclear radiation, the number of these clusters increases, ultimately leading to the final transition of the sample to the paramagnetic state (Fig. 3). The data from FEM spectra are confirmed by the results of studies of saturation magnetization (M) given

films FePtt _ xRhx.

VALIULLIN et al.

Paramagnetic phase

Ferromagnetic phase

0.05 0.10 0.15 0.20 0.25 0.30

Ms, erg ■ Gs 1500

Rice. 3. The relative content of the ferromagnetic phase (determined by the relative areas of the Mössbauer subspectra of the ferromagnetic and paramagnetic phases) depending on the concentration of nuclear radiation in thin films of Fe50(P1:1 _ xKIx)50.

mi in fig. 4. The figure shows that as x increases, a monotonic decrease in M is observed.

Using the magnetron sputtering method, 20 nm thick FePIR films with different contents of NR (FeP^ _ xRbx) were obtained, where x varies from 0 to 0.4. It has been established that at x = 0 the film is ferromagnetic at room temperature, and the easy axis of magnetocrystalline anisotropy is directed perpendicular to the film surface. Ferromagnetic ordering in FeP^ xRiH at room temperature is preserved in the range of rhodium content x< 0.32 с сохранением большой энергией магнитокристаллической анизотропии и обусловленной ею перпендикулярной ориентацией намагниченности. В изученном интервале 0.34 < х < 0.4 пленка БеР^ _ хКЬх находится в парамагнитном состоянии. Намагниченность насыщения для 0 < х < 0.32 находится в интервале 1000 >M > 500 erg ■ Gs-1 ■ cm-3.

The work was carried out with financial support from the Russian Foundation for Basic Research (grant No. 14-02-91151) and with partial

J_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I

Rice. 4. Saturation magnetization (Ma) measured at a temperature of 300 K in thin films of Fe50(P111 _ xRAIx)50 depending on the concentration of RR.

support of the Program for Improving the Competitiveness of the Kazan Federal University, funded by the Ministry of Education and Science of the Russian Federation.

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2. Yuasa S., Miyajima H., Otani Y. // J. Phys. Soc. Jpn. 1994. V. 63. P. 3129.

3. Hasegawa T., Miyahara J., Narisawa T., Ishio S., Yamane H., Kondo Y., Ariake J., Mitani S., Sakuraba Y., Takanashi K. // J. Appl. Phys. 2009. V. 106. P. 103928.

4. Ivanov O.A., Solina L.V., Demshina V.A., Magat L.M. // FMM. 1973. T. 35. P. 92.

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KARAMAN I., KIREEVA I.V., KRETININA I.V., KUSTOV S.B., PICORNELL K., POBEDERENNAYA Z.V., PONS J., CESARI E., CHUMLYAKOV Y.I. - 2010

Introduction The study of systems consisting of a large number of interacting particles is one of the most important problems of modern physics. The most interesting is the thermodynamic behavior of substances when a certain type of ordering occurs. This ordering occurs at a certain temperature, and the transition occurs in an extremely narrow temperature range and is called a phase transition (the transition of a substance from one phase to another). Phase transitions associated with ordering occur in various physical systems: binary alloys, ferromagnets and antiferromagnets, in dipole moments in ferroelectrics, electrons in superconductors, in helium in a superfluid state, etc. 2

Classification Of particular interest in the behavior of macroscopic (thermodynamic) systems are phase transition points, since at them the properties of the system change abruptly. There are two options: The first case – phase separation – is a first-order phase transition. Since the emergence of a new phase leads to the appearance of surface energy, small-volume nuclei are energetically unfavorable, while sufficiently large ones can arise only due to fluctuations. Examples of this type of transition are phase separation (vapor - liquid, liquid - solid, vapor – solid) In the second case, the appearance of new properties is not associated with surface energy. Such phase transitions are called second-order phase transitions; they are usually accompanied by a change in the symmetry of the state. Examples of this type of transitions: structural rearrangements in crystals at a certain temperature; order–disorder transitions in alloys; ferromagnetic–paramagnetic transitions in spin systems and ferromagnetic metals and alloys; appearance of superconductivity and superfluidity 3

Order parameter For each phase transition, there is the concept of an order parameter, whose non-zero average value in the ordered phase breaks the symmetry of a ferromagnet. The order parameter is the average magnetization. The boundary temperature at which symmetry is spontaneously broken and at which the order parameter becomes zero is called the critical temperature 4

Order parameter If the order parameter smoothly vanishes at T=T c (but with an infinite derivative due to fluctuations), then this is a second-order phase transition. If the dependence of the order parameter near the phase transition region is ambiguous, then phase separation is necessarily observed in the system , and this is a first-order transition. The theory of phase transitions is based on the idea of an ordering field arising due to the interaction of particles. The theory is simplest if this field is assumed to be equal to the average field 5

Magnetic moment The reason for the magnetic properties of substances is the magnetic moment related either to the electron or to the lattice site where the electron is localized, which usually occurs when the electron moves along closed trajectories. The following classification of substances according to their magnetic properties is accepted: 1) paramagnetic materials: >1 magnetic field intensifies inside; 2) diamagnetic materials: 1 the magnetic field inside is strengthened; 2) diamagnetic materials: ">

Weiss approximation Let magnetic moments interact with each other: Field acting on a selected magnetic moment: Effective field: Weiss molecular field approximation consists in the assumption that the true total field in i-th node coincides with the average field and does not depend on the orientation of the i-th spin 9

Exchange interaction The interaction between magnetic moments is purely quantum in nature - this is the so-called exchange interaction. For an ensemble of identical quantum particles, the principle of identity must be satisfied - they must be indistinguishable due to the uncertainty principle. If there are only two particles, then the states of the system, obtained from each other simply by rearranging both particles, must be physically completely equivalent. This means that as a result of such a rearrangement, the wave function of the system can only change by an insignificant phase factor. Therefore, there are only two possibilities: the wave function is either symmetric (this is Bose statistics) or antisymmetric (this is Fermi statistics) 11

Exchange interaction Let us now consider two isolated particles that have quantum statistics and, to a first approximation, do not interact. The complete wave function of the system: Bosons correspond to the + sign, and fermions –, realizing symmetric and antisymmetric situations. System of electrons localized in the field. crystal lattice, taking into account the spin component: The antisymmetric situation – must correspond to a symmetric spin component, and the symmetric situation + must correspond to an antisymmetric spin component 12

Estimation of the exchange integral In the case of J 12 >0, it is advantageous for the spins to line up in parallel if J 12 It is advantageous for 0 spins to line up parallel if J 12 "> 0 it is advantageous for spins to line up parallel if J 12 "> 0 it is advantageous for spins to line up parallel if J 12 " title="Evaluation of the exchange integral In the case of J 12 >0 spins it is advantageous will line up in parallel if J 12"> title="Estimation of the exchange integral In the case of J 12 >0, it is advantageous for the spins to line up in parallel if J 12"> !}

- materials that interact with a magnetic field, expressed in its change, as well as in other physical phenomena- a change in physical dimensions, temperature, conductivity, the emergence of electric potential, etc. In this sense, almost all substances belong to magnets (since none of them has a magnetic susceptibility equal to zero exactly), most of them belong to the class of diamagnetic substances (having a small negative magnetic susceptibility - and somewhat weaken the magnetic field) or paramagnetic materials (having a small positive magnetic susceptibility - and somewhat strengthen the magnetic field); Ferromagnets are more rare (having a greater positive magnetic susceptibility - and greatly enhance the magnetic field), about even rarer classes of substances in relation to the action of a magnetic field on them.

Classification of magnetic materials and requirements for them
Magnetic substances, or magnets, are substances that have magnetic properties. Magnetic properties mean the ability of a substance to acquire a magnetic moment, i.e. become magnetized when exposed to a magnetic field. In this sense, all substances in nature are magnetic, since when exposed to a magnetic field they acquire a certain magnetic moment. This resulting macroscopic magnetic moment M is the sum of the elementary magnetic moments mi - atoms of a given substance.

Elementary magnetic moments can either be induced by a magnetic field or exist in a substance before the application of a magnetic field; in the latter case, the magnetic field causes their preferential orientation.
The magnetic properties of various materials are explained by the movement of electrons in atoms, and also by the fact that electrons and atoms have permanent magnetic moments.
The rotational motion of electrons around atomic nuclei is similar to the action of a certain electric current circuit and creates a magnetic field, which at a sufficient distance appears as the field of a magnetic dipole with a magnetic moment, the value of which is determined by the product of the current and the area of the circuit around which the current flows. The magnetic moment is a vector quantity and is directed from south pole to the north. This magnetic moment is called orbital.

The electron itself has a magnetic moment, which is called the spin magnetic moment.
An atom is a complex magnetic system, the magnetic moment of which is the result of all the magnetic moments of electrons, protons and neutrons. Since the magnetic moments of protons and neutrons are significantly smaller than the magnetic moments of electrons, the magnetic properties of atoms are essentially determined by the magnetic moments of electrons. In materials of technical importance these are primarily spin magnetic moments.
The resulting magnetic moment of the atom is determined by vector sum orbital and spin magnetic moments of individual electrons in the electron shell of atoms. These two types of magnetic moments can be partially or completely mutually compensated.

According to their magnetic properties, materials are divided into the following groups:
a) diamagnetic (diamagnets),
b) paramagnetic (paramagnetic),
c) ferromagnetic (ferromagnets),
d) antiferromagnetic (antiferromagnets),
e) ferrimagnetic (ferrimagnets),
f) metamagnetic (metamagnetic).

A) Diamagnets
Diamagnetism manifests itself in the magnetization of a substance towards the direction of the external magnetic field acting on it.
Diamagnetism is characteristic of all substances. When a body is introduced into a magnetic field, in the electron shell of each of its atoms, due to the law of electromagnetic induction, induced circular currents arise, i.e., additional circular motion of electrons around the direction of the magnetic field. These currents create in each atom an induced magnetic moment, directed, according to Lenz's rule, towards the external magnetic field (regardless of whether the atom initially had its own magnetic moment or not and how it was oriented). In purely diamagnetic substances, the electronic shells of atoms (molecules) do not have a permanent magnetic moment. The magnetic moments created by individual electrons in such atoms are mutually compensated in the absence of an external magnetic field. In particular, this occurs in atoms, ions and molecules with completely filled electronic shells in atoms of inert gases, in molecules of hydrogen and nitrogen.

An elongated sample of a diamagnetic material in a uniform magnetic field is oriented perpendicular to the field lines (field strength vector). It is pushed out of a non-uniform magnetic field in the direction of decreasing field strength.

The induced magnetic moment I, acquired by 1 mole of a diamagnetic substance, is proportional to the external field strength H, i.e. I=χН. The coefficient χ is called the molar diamagnetic susceptibility and has a negative sign (since I and H are directed towards each other). Usually the absolute value of χ is small (~10-6), for example, for 1 mole of helium χ = -1.9·10-6.

Classical diamagnets are the so-called inert gases (He, Ne, Ar, Kr and Xe), the atoms of which have closed outer electron shells.

Diamagnets also include: inert gases in liquid and crystalline states; compounds containing ions similar to atoms of inert gases (Li+, Be2+, Al3+, O2-, etc.); halogens in gaseous, liquid and solid states; some metals (Zn, Au, Hg, etc.). Diamagnets, more precisely superdiamagnets, with χД = - (1/4) ≈ 0.1, are superconductors; in them, the diamagnetic effect (pushing out the external magnetic field) is caused by surface macroscopic currents. Diamagnets include large number organic substances, and for polyatomic compounds, especially cyclic ones (aromatic, etc.), the magnetic susceptibility is anisotropic (Table 6.1).

Table 6.1 - Diamagnetic susceptibility of a number of materials

B) Paramagnets
Paramagnetism is the property of substances (paramagnets) to be magnetized in the direction of an external magnetic field, and, unlike ferro-, ferri- and antiferromagnetism, paramagnetism is not associated with a magnetic atomic structure, and in the absence of an external magnetic field, the magnetization of a paramagnet is zero.

Paramagnetism is caused mainly by the orientation, under the influence of an external magnetic field H, of the intrinsic magnetic moments µ of particles of a paramagnetic substance (atoms, ions, molecules). The nature of these moments can be associated with the orbital motion of electrons, their spin, and also (to a lesser extent) with the spin of atomic nuclei. At µH « kT, where T is the absolute temperature, the magnetization of the paramagnetic M is proportional to the external field: M = χH, where χ is the magnetic susceptibility. In contrast to diamagnetism, for which χ< 0, при парамагнетизме восприимчивость положительна; её типичная величина при комнатной температуре (Т ≈ 293 К) составляет 10-7 – 10-4.

Paramagnetic – a magnet with a predominance of paramagnetism and the absence of magnetic atomic order. The paramagnet is magnetized in the direction of the external magnetic field, i.e. has a positive magnetic susceptibility, which in a weak field at a not very low temperature (i.e., far from magnetic saturation conditions) does not depend on the field strength. Since the free energy of a paramagnetic decreases in a magnetic field, in the presence of a field gradient it is drawn into a region with a higher magnetic field strength. The competition of diamagnetism and the emergence of long-range magnetic order or superconductivity limit the region of existence of matter in a paramagnetic state.

A paramagnetic material contains at least one of the following types of paramagnetic carriers.

A) Atoms, molecules or ions with uncompensated magnetic moments in the ground or excited states with excitation energy Ei<< kТ. Парамагнетики этого типа обладают ориентацией ланжевеновским парамагнетизмом, зависящим от температуры Т по Кюри закону или Кюри – Вейса закону, в них возможно магнитное упорядочение. [Похожий по проявлениям магнетизм неоднородных систем малых ферро- или ферримагнитных однодоменных частиц (кластеров) в жидкостях или твердых матрицах выделен в особый вид – суперпарамагнетизм].

This type of carrier is present in pairs of metals of odd valency (Na, Tl); in a gas of O2 and NO molecules; in some organic molecules with free radicals; in salts, oxides and other dielectric compounds of 3d-, 4f-, and 5f-elements; in most rare earth metals.

B) The same particles having an orbital magnetic moment in an excited state with excitation energy Ei<< kТ. Для таких парамагнетиков характерен не зависящий от температуры поляризационный парамагнетизм.

This type of paramagnetism carriers manifests itself in some compounds of d- and f-elements (Sm and Eu salts, etc.).

B) Collectivized electrons in partially filled energy bands. They are characterized by spin Pauli paramagnetism, which is relatively weakly dependent on temperature and, as a rule, enhanced by electron-electron interactions. In d-bands, spin paramagnetism is accompanied by noticeable Van Vleck paramagnetism.

This type of carriers predominates in alkali and alkaline earth metals, d-metals and their intermetallic compounds, actinides, as well as in highly conductive radical ion organic salts

P/S material from wiki
Paramagnetic substances are substances that are magnetized in an external magnetic field in the direction of the external magnetic field (JH) and have a positive magnetic susceptibility. Paramagnets belong to weakly magnetic substances; the magnetic permeability differs slightly from unity u > ~ 1.
The term “Paramagnetism” was introduced in 1845 by Michael Faraday, who divided all substances (except ferromagnetic) into dia- and paramagnetic.
Atoms (molecules or ions) of a paramagnetic material have their own magnetic moments, which, under the influence of external fields, are oriented along the field and thereby create a resulting field that exceeds the external one. Paramagnetic substances are drawn into a magnetic field. In the absence of an external magnetic field, a paramagnetic material is not magnetized, since due to thermal motion the intrinsic magnetic moments of the atoms are oriented completely randomly.
Paramagnetic materials include aluminum (Al), platinum (Pt), many other metals (alkali and alkaline earth metals, as well as alloys of these metals), oxygen (O2), nitric oxide (NO), manganese oxide (MnO), ferric chloride (FeCl3) and others.
Ferro- and antiferromagnetic substances become paramagnetic at temperatures exceeding, respectively, the Curie or Néel temperature (the temperature of the phase transition to the paramagnetic state).

B) Ferromagnets

Ferromagnets- substances (usually in a solid crystalline or amorphous state) in which, below a certain critical temperature (Curie point), a long-range ferromagnetic order is established in the magnetic moments of atoms or ions (in non-metallic crystals) or the moments of itinerant electrons (in metallic crystals). In other words, a ferromagnet is a substance that (at a temperature below the Curie point) is capable of magnetization in the absence of an external magnetic field.

Properties of ferromagnets
1. The magnetic susceptibility of ferromagnets is positive and significantly greater than unity.
2. At temperatures that are not too high, ferromagnets have spontaneous (spontaneous) magnetization, which changes greatly under the influence of external influences.
3. Ferromagnets are characterized by the phenomenon of hysteresis.
4. Ferromagnets are attracted by a magnet.

Paramagnetic materials include substances in which the magnetic moment of atoms or molecules is non-zero in the absence of an external magnetic field:

Therefore, when paramagnetic substances are introduced into an external magnetic field, they are magnetized in the direction of the field. In the absence of an external magnetic field, the paramagnet is not magnetized, since due to thermal motion all the magnetic moments of the atoms are randomly oriented, and therefore the magnetization is zero (Fig. 2.7 a). When a paramagnetic substance is introduced into an external magnetic field, a preferential orientation of the magnetic moments of atoms along the field is established (Fig. 2.7 b). Complete orientation is prevented by the thermal motion of atoms, which tends to scatter the moments. As a result of this preferential orientation, the paramagnet is magnetized, creating its own magnetic field, which, superimposed on the external one, strengthens it. This effect is called the paramagnetic effect or paramagnetism.

Fig.2.7. Paramagnetic in

absence of field(s) and in

external magnetic field (b)

Paramagnetic materials also exhibit Larmor precession and the diamagnetic effect, as in all substances. But the diamagnetic effect is weaker than the paramagnetic one and is suppressed by it, remaining invisible. For paramagnets, χ is also small, but positive, on the order of ~10 -7 –10 -4 , which means μ is slightly greater than one.

Just as for diamagnetic materials, the dependence of the magnetic susceptibility of paramagnetic materials on the external field is linear ( Fig.5.8).

The preferential orientation of magnetic moments along the field depends on temperature. As the temperature increases, the thermal movement of atoms increases, therefore, orientation in one direction becomes difficult and magnetization decreases. The French physicist P. Curie established the following pattern: where C is the Curie constant, depending on the type of substance. The classical theory of paramagnetism was developed in 1905 by P. Langevin.

2.10 Ferromagnetism. Ferromagnets. Domain structure of ferromagnets.

.7. Ferromagnetism. Ferromagnets. @

Ferromagnets are solid crystalline substances that have spontaneous magnetization in the absence of an external magnetic field. .Atoms (molecules) of such substances have a non-zero magnetic moment. In the absence of an external field, magnetic moments within large regions are oriented in the same way (more on this later). Unlike weakly magnetic dia- and paramagnets, ferromagnets are highly magnetic substances. Their internal magnetic field can be hundreds and thousands of times greater than the external one. For ferromagnets, χ and μ are positive and can reach very large values, on the order of ~10 3 . Only ferromagnets can be permanent magnets.

Why do ferromagnetic bodies exhibit such strong magnetization? Why does thermal motion in them not interfere with the establishment of order in the arrangement of magnetic moments? To answer this question, let's look at some important properties of ferromagnets.

If we depict the main magnetization curve in coordinates (B, H) (Fig. 2.10, curve 0-1), we get a slightly different picture: since , then when the value J us is reached, the magnetic induction continues to grow along with the growth linearly:

= μ 0 + const, const = μ 0 J us.

Ferromagnets are characterized by the phenomenon hysteresis(from the Greek hysteresis – lag, delay).

We will bring the magnetization of the body to saturation, increasing the external field strength (Fig. 2.10, point 1), and then we will decrease H. In this case, the dependence B(H) follows not the original curve 0-1, but the new curve 1-2. When the voltage decreases to zero, the magnetization of the substance and magnetic induction will disappear. At H=0, magnetic induction has a non-zero value B ost, which is called residual induction. The magnetization J ost, corresponding to B ost, is called residual magnetization, and the ferromagnet acquires the properties of a permanent magnet. V ost and J ost become zero only under the influence of a field opposite in direction to the original one. The value of the field strength H c at which the residual magnetization and induction vanish is called coercive force(from Latin coercitio - retention). Continuing to act on the ferromagnet with an alternating magnetic field, we obtain the curve 1-2-3-4-1, called hysteresis loop. In this case, the body’s reaction (B or J) seems to lag behind the causes that cause it (H).

The existence of residual magnetization makes it possible to manufacture permanent magnets, because ferromagnets with Bres ≠ 0 have a constant magnetic moment and create a constant magnetic field in the space surrounding them. Such a magnet retains its properties better, the greater the coercive force of the material from which it is made. Magnetic materials are usually divided according to the value of Hc into magnetically soft(i.e. with low H of the order of 10 -2 A/m and, accordingly, with a narrow hysteresis loop) and magnetically hard(H with ~10 5 A/m and a wide hysteresis loop). Soft magnetic materials are required for the manufacture of transformers, the cores of which are constantly remagnetized by alternating current. If the transformer core has a large hysteresis, it will heat up during magnetization reversal, which will waste energy. Transformers therefore require materials that are as hysteresis-free as possible. Ferromagnets with a narrow hysteresis loop include alloys of iron with nickel or iron with nickel and molybdenum (permalloy and supermalloy).

Magnetically hard materials (including carbon, tungsten, chromium and aluminum-nickel steels) are used to make permanent magnets.

Residual permanent magnetization will exist indefinitely if the ferromagnet is not exposed to strong magnetic fields, high temperatures and deformation. All information recorded on magnetic tapes - from music to video programs - is stored thanks to this physical phenomenon.

An essential feature of ferromagnets is the enormous values of magnetic permeability and magnetic susceptibility. For example, for iron μ max ≈ 5000, for permalloy – 100000, for supermalloy – 900000. For ferromagnets, the values of magnetic susceptibility and magnetic permeability are functions of the magnetic field strength H (Fig. 2.11). With increasing field strength, the value of μ first quickly increases to μ max, and then decreases, approaching the value μ=1 in very strong fields. Therefore, although the formula B = μμ 0 H remains valid for ferromagnetic substances, the linear relationship between B and H is violated.

The second magnetomechanical effect is Villari effect– change and even disappearance of the residual magnetization of a body when it is shaken or deformed (discovered by E. Villari in 1865). It is because of this that permanent magnets should be protected from shock.

Heating acts on ferromagnets in a similar way to deformation. With increasing temperature, the residual magnetization begins to decrease, weakly at first, and then, when a certain sufficiently high temperature is reached, characteristic of each ferromagnet, a sharp decrease in magnetization occurs to zero. The body then becomes paramagnetic. The temperature at which such a change in properties occurs is called Curie point, in honor of P. Curie who discovered it. For iron, the Curie point is 770ºC, for cobalt - 1130ºC, for nickel - 358ºC, for gadolinium - 16ºC. This transition is not accompanied by the release or absorption of heat and is a second-order phase transition. All these phenomena find their explanation when considering the structure of ferromagnets.

According to their magnetic properties, all substances are divided into weakly magnetic and strongly magnetic. In addition, magnets are classified depending on the magnetization mechanism.

Diamagnets

Diamagnets are classified as weakly magnetic substances. In the absence of a magnetic field, they are not magnetized. In such substances, when they are introduced into an external magnetic field, the movement of electrons in molecules and atoms changes so that an oriented circular current is formed. The current is characterized by a magnetic moment ($p_m$):

where $S$ is the area of the coil with current.

The magnetic induction created by this circular current, additional to the external field, is directed against the external field. The value of the additional field can be found as:

Any substance has diamagnetism.

The magnetic permeability of diamagnetic materials differs very slightly from unity. For solids and liquids, the diamagnetic susceptibility is of the order of approximately $(10)^(-5),\ $for gases it is significantly less. The magnetic susceptibility of diamagnetic materials does not depend on temperature, which was discovered experimentally by P. Curie.

Diamagnets are divided into “classical”, “anomalous” and superconductors. Classical diamagnetic materials have a magnetic susceptibility $\varkappa

In weak magnetic fields, the magnetization of diamagnetic materials is proportional to the magnetic field strength ($\overrightarrow(H)$):

where $\varkappa$ is the magnetic susceptibility of the medium (magnet). Figure 1 shows the dependence of the magnetization of a “classical” diamagnetic on the magnetic field strength in weak fields.

Paramagnets

Paramagnetic substances are also classified as weakly magnetic substances. Paramagnetic molecules have a permanent magnetic moment ($\overrightarrow(p_m)$). The energy of the magnetic moment in an external magnetic field is calculated by the formula:

The minimum energy value is achieved when the direction of $\overrightarrow(p_m)$ coincides with $\overrightarrow(B)$. When a paramagnetic substance is introduced into an external magnetic field in accordance with the Boltzmann distribution, a preferential orientation of the magnetic moments of its molecules appears in the direction of the field. Magnetization of the substance appears. The induction of the additional field coincides with the external field and accordingly enhances it. The angle between the direction $\overrightarrow(p_m)$ and $\overrightarrow(B)$ does not change. The reorientation of magnetic moments in accordance with the Boltzmann distribution occurs due to collisions and interactions of atoms with each other. Paramagnetic susceptibility ($\varkappa $) depends on temperature according to Curie’s law:

or the Curie-Weiss law:

where C and C" are the Curie constants, $\triangle $ is a constant that can be greater or less than zero.

The magnetic susceptibility ($\varkappa $) of a paramagnetic is greater than zero, but, like that of a diamagnetic, it is very small.

Paramagnets are divided into normal paramagnets, paramagnetic metals, and antiferromagnets.

For paramagnetic metals, magnetic susceptibility does not depend on temperature. These metals are weakly magnetic $\varkappa \approx (10)^(-6).$

In paramagnetic materials there is a phenomenon called paramagnetic resonance. Let us assume that in a paramagnetic material that is in an external magnetic field, an additional periodic magnetic field is created, the induction vector of this field is perpendicular to the induction vector of a constant field. As a result of the interaction of the magnetic moment of an atom with an additional field, a moment of force ($\overrightarrow(M)$) is created, which tends to change the angle between $\overrightarrow(p_m)$ and $\overrightarrow(B).$ If the frequency of the alternating magnetic field and the frequency the precession of the atomic motion coincides, then the torque created by the alternating magnetic field either constantly increases the angle between $\overrightarrow(p_m)$ and $\overrightarrow(B)$, or decreases. This phenomenon is called paramagnetic resonance.

In weak magnetic fields, magnetization in paramagnetic materials is proportional to the field strength and is expressed by formula (3) (Fig. 2).

Ferromagnets

Ferromagnets are classified as highly magnetic substances. Magnets whose magnetic permeability reaches large values and depends on the external magnetic field and previous history are called ferromagnets. Ferromagnets can have residual magnetization.

The magnetic susceptibility of ferromagnets is a function of the strength of the external magnetic field. The J(H) dependence is shown in Fig. 3. Magnetization has a saturation limit ($J_(nas)$).

The existence of a magnetization saturation limit indicates that the magnetization of ferromagnets is caused by the reorientation of some elementary magnetic moments. In ferromagnets, the phenomenon of hysteresis is observed (Fig. 4).

Ferromagnets, in turn, are divided into:

Soft magnetically. Substances with high magnetic permeability, easily magnetized and demagnetized. They are used in electrical engineering, where they work with alternating fields, for example in transformers.
Magnetically hard. Substances with relatively low magnetic permeability, difficult to magnetize and demagnetize. These substances are used to create permanent magnets.

Example 1

Assignment: The dependence of magnetization for a ferromagnet is shown in Fig. 3. J(H). Draw the B(H) curve. Is there saturation for magnetic induction, why?

Since the magnetic induction vector is related to the magnetization vector by the relation:

\[(\overrightarrow(B)=\overrightarrow(J\ )+\mu )_0\overrightarrow(H)\ \left(1.1\right),\]

then the curve B(H) does not reach saturation. A graph of the dependence of magnetic field induction on the strength of the external magnetic field can be presented as shown in Fig. 5. Such a curve is called a magnetization curve.

Answer: There is no saturation for the induction curve.

Example 2

Assignment: Obtain the formula for paramagnetic susceptibility $(\varkappa)$, knowing that the mechanism of magnetization of a paramagnet is similar to the mechanism of electrification of polar dielectrics. For the average value of the magnetic moment of a molecule in projection onto the Z axis, we can write the formula:

\[\left\langle p_(mz)\right\rangle =p_mL\left(\beta \right)\left(2.1\right),\]

where $L\left(\beta \right)=cth\left(\beta \right)-\frac(1)(\beta )$ is the Langevin function with $\beta =\frac(p_mB)(kT).$

At high temperatures and small fields, we get that:

Therefore, for $\beta \ll 1$ $cth\left(\beta \right)=\frac(1)(\beta )+\frac(\beta )(3)-\frac((\beta )^3 )(45)+\dots $ , restricting the function by a linear term in $\beta $ we obtain:

Substituting the result (2.3) into (2.1), we obtain:

\[\left\langle p_(mz)\right\rangle =p_m\frac(p_mB)(3kT)=\frac((p_m)^2B)(3kT)\ \left(2.4\right).\]

Using the relationship between magnetic field strength and magnetic induction ($\overrightarrow(B)=\mu (\mu )_0\overrightarrow(H)$), taking into account that the magnetic permeability of paramagnetic materials differs little from unity, we can write:

\[\left\langle p_(mz)\right\rangle =\frac((p_m)^2(\mu )_0H)(3kT)\left(2.5\right).\]

Then the magnetization will look like:

Knowing that the relationship between the magnetization modulus and the voltage vector modulus has the form:

For paramagnetic susceptibility we have:

\[\varkappa =\frac((p_m)^2m_0n)(3kT)\ .\]

Answer: $\varkappa =\frac((p_m)^2(\mu )_0n)(3kT)\ .$