Magnetization processes, hysteresis and energy loss

Rudolf SchäferLeibniz Institute for Solid State and Materials Research Dresden, Germany

A substantial part of the energy that is lost in the operation of inductive magnetic devices is connected with hysteresis, i.e. irreversibility and discontinuities in the magnetization process of the soft magnetic cores. Loss reduction and material optimization thus requires knowledge of the magnetic microstructure (domains and domain walls) that is responsible for hysteresis. In this lecture a review is given of magnetic domains and magnetization processes. As representative material class emphasize is on electrical steel, oriented and non-oriented as used in transformers and rotating electrical machines, respectively. Especially for transformer material dramatic and economically important improvements in terms of energy loss were achieved over decades by targeted domain engineering. In the review we will also touch aspects of magnetization reversal in magnetic films as well as amorphous and nanocrystalline material to complete the picture. Excluded from the discussion will be small particle hysteresis, which is fully covered in a tutorial.

Magnetic domains and hysteresis. The magnetization vector field in a sufficiently extended magnetic material prefers to be subdivided in magnetic domains, i.e. regions of homogenous magnetization that are polarized along different directions. They are formed to avoid or reduce stray field energy, which would arise if the magnet would be in the saturated, single-domain state. The domain character is governed by a balance between stray-field-, anisotropy-, domain wall- , and possibly magnetoelastic energy. Application of a magnetic field adds Zeeman energy which leads to domain reorganization by domain wall motion and rotational processes. For extended, homogeneous and soft magnetic bodies these processes are theoretically classified within the framework of phase theory: Here all individual domains of the body, which are magnetized in the same direction, are gathered in a phase that is characterized by its total volume and magnetization direction. By determining the possible phases at a given external field by energy minimization and plotting the average magnetization as a function of field, the vectorial magnetization curve is obtained. Different modes of magnetization processes are distinguished in phase theory: Processes that occur by shifting the domain phases (i.e. the walls separating the domains) without changing the internal magnetic field, are classified as belonging to mode I. These processes are connected with a jump in the magnetization curve M(Hinternal). Processes employing coplanar magnetization phases (i.e. states for which the tips of the magnetization vectors of three or more equilibrium phases lie in a plane) are classified as belonging to mode II. Wall motion and magnetization rotation processes occur simultaneously in this mode. The segments of the magnetization curve, that are obtained with two-phase states, are defined to belong to mode III. Mode IV processes are finally based on single-phase states. With increasing field a sample passes in general through a sequence of magnetization modes: mode I using multiphase field-free states, mode II using three-phase states, mode III with the two-phase states, and mode IV based on single-phase states till saturation is finally reached. Depending on field direction and crystal symmetry some modes may be absent, as in magnetically uniaxial crystals where only modes III and IV can occur. The magnetization curve obtained form phase theory agrees with the “idealized” anhysteretic magnetization curve as it can be experimentally obtained by superimposing decreasing alternating fields during the measurement, thus removing the hysteretic, irreversible contributions to the curve. This idealized magnetization curve then acts as a reference on which domain-wall-related irreversible magnetization phenomena (i.e. hysteresis) are superimposed.

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An example of hysteretic magnetization processes and some phase-theoretical results are displayed in the figure. Shown is the magnetization process of a square-shaped permalloy element of 207 nm thickness and 57 µm edge l e n g t h i n a d i a g o n a l magnetic field pointing along „north-east“. The second row shows the evo lu t ion o f domains s ta r t ing f rom the ac-demagnetized zero-field state, which is a 4-domain flux-closed pattern. With increasing field (given in reduced units), the two domains with components in field direction grow on expense of the other two and the vortex is pushed against the corner. There are t w o c r i t i c a l e v e n t s t r i g g e r i n g h y s t e r e t i c behavior: The first one is the expulsion of parts of the domain walls from the interior of the sample, occurring at a moderate field strength around h = 0.9, the second one is the expulsion of the vortex in the upper left corner in fields stronger than h = 1.3. If the field is released before the first critical point is reached, the magnetization process is completely reversible. Releasing the field after the

walls are partly expelled (third row), the initial 4-domain state is finally recovered, but there is some intermediate hysteresis in the magnetization patterns that has only small traces on the magnetization curve. If the vortex is expelled beyond h = 1.3, the hysteretic phenomena upon reduction of the field are much more dramatic than before (fourth row, see also the displayed magnetization curve). The remanent state is no longer the initial 4-domain state but rather a 7-domain state, so the memory of the 4 domain state has been lost. The blue lines in the first row are the calculated level curves of the potential of the magnetic field that penetrates into the element in a field stronger than 0.85. It is obvious that in the areas of field penetration the magnetization is uniquely determined and there is no domain

hysteresis observed. In all other areas, where the internal field is zero (i.e. where the external field is expelled) hysteresis is observed, leading to different domain patterns for increasing and decreasing field.

Domain engineering in grain-oriented electrical steel. Most technical applications of inductive devices are based on the high permeabilities available from domain wall displacement processes. The irregularities connected with domain wall pinning and domain annihilation and creation processes lead to energy losses in electrical machines, and to noise in communication and sensor devices. If the character of the magnetic microstructure can be improved in the sense of a more regular domain structure, a better performance of inductive devices can be achieved. This is

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ac-dem. 0.48 0.55 0.73 0.85 1.06

0.85

hext = 0.30

0.730.550.480.300

field up

field down

1.41

0 0.13 0.51 0.850.730.55 1.06field down

Sample field-free:hysteresis

Field penetration:hysteresis only in field-free areas

Theory*:

0.85 1.06 1.41

* R.S. and A. deSimone: Hysteresis in soft ferromagnetic films: experimental observation and micromagnetic analysis. IEEE Trans. Magn. 38-5, 2391-2393 (2002)

Theory Experiment

0 1 20

0.5

1

1 hext

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hcrit hcrit*

regions offield

penetrationhave merged

twodisconnected

regions offield

penetration

expulsionof ext. field

vortexdisappears

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edge

Magnetization curves

demonstrated here for grain-oriented FeSi (iron with 3 wt% of silicon) electrical steel sheets (thickness 0.3 mm) with [001](110) Goss-texture that is used as core material for transformers. In the transformer, the magnetic flux alternates along only one, preferred axis of the material which is the [001] direction.

The most important quality number of electrical steels is the loss per cycle, usually given in watts per kilogram for a given frequency and a given induction amplitude. Core losses belong to the extrinsic material properties. They depend strongly on the crystal and magnetic microstructure. With the introduction of coarse-grained, Goss-textured material in the 1930ies, losses were halved and since then the material has been steadily improved. These dramatic and economically important improvements were achieved always in full view of the magnetic microstructure, differing in this aspect from so many other magnetic materials where improvements were developed by trial and error methods, only to be understood microstructurally afterwards. The losses in electrical steels can be separated by frequency-dependent measurements. There are two main contributions: (i) Hysteresis losses that are connected with the pinning of domain walls on defects and surface imperfections. Supplementary domains, which are superimposed on the basic domains for a small misorientation of the [001] axis relative to the surface, contribute decisively to hysteresis losses because they can be attached to the basic walls, impeding their motion, and because they must be annihilated and regenerated every time a basic wall sweeps through. (ii) Equally important in transformer material are anomalous eddy current losses. They are connected with domain-wall related eddy current effects and become important if the basic domain width is larger than the sheet thickness. In general, there is a further important loss mechanism, that of domain rearrangement in the course of magnetization processes. This loss mechanism is largely absent in transformer steel with its well-ordered domain structure. Domain rearrangement losses appear if part of a transformer yoke is not used along the favored axis as sometimes done in small transformers.

The following procedures led to the present excellent level of loss control. (i) Better process technologies reduced the mean misorientation and thus hysteresis losses. It would be possible to suppress supplementary domains completely if a misorientation of better than one degree could be achieved. Such a quasi-single-crystalline material, however, would tend to develop very wide basic domains with correspondingly large anomalous eddy current losses and would therefore be less than optimal. (ii) For a given, moderate misorientation, supplementary domains can be suppressed by mechanical stresses. Practically this is achieved by using a stress-effective insulation coating. The planar stress exerted by the coating is for this texture equivalent to a uniaxial stress and will thus suppress supplementary domains for magnetostrictive reasons. When the supplementary domains are suppressed, the basic domain spacing is decreased because otherwise the overall stray field energy would rise. This is demonstrated in Figs. (a) and (b). Here the a.c. demagnetized state of the same material is shown once without and once with tensile stress along the vertical axis. Without stress, well-oriented grains tend to develop very wide domains as shown in (a). Tensile stress suppresses supplementary

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With tensile stressWithout tensile stress After laser scribingWithout artificial domain refinement

a) b) c) d)

domains to a large degree (b), and, in addition, improves flux continuity along the grains so that even ideally oriented grains assume a small domain width if they are coupled to less well oriented grains. (iii) The basic domain width can be artificially reduced by scratching or by laser scribing as shown in (c) and (d). The stress introduced locally in this way interrupts the basic domains, acting somehow like an artificial grain boundary. With artificial domain refinement even ideally oriented material can be favorably used, in contrast to the conclusion in (i). The stress pattern introduced by laser treatment causes some hysteresis losses and contributes to magnetostrictive noise. (iv) Pinning sites are important as a source of hysteresis and eddy current losses. Pinning centres can be impurity precipitations in the volume, surface irregularities connected with the formation of the insulation layer, and small-angle boundaries within large grains. Domain wall pinning by the defects leads to irregular domain wall motion. A given flux change must be carried by the unpinned walls alone if others are immobilized by pinning. If all available walls would contribute equally to the flux change, the anomalous eddy current losses assume a minimum value, otherwise they are enhanced.

Most challenging: non-oriented material. Much less is known about the magnetization processes of non-oriented silicon iron material commonly used in rotating electrical machines. The domain patterns of such material are of a heavily branched character for most grains, and only the fact that the branched surface structures are confined to a limited near-surface zone makes a high permeability conceivable, which may rely on the underlying basic domains. The latter may be considered as folded bands that can be described as

b a s i c “ q u a s i -d o m a i n s ” . T h e s e bands would in fact be able to carry the flux along the working direction. Certainly the permanent rearrangement of the branched closure pattern causes a kind of friction for the displacement of the basic domain walls and leads to unavoidable hysteresis losses in non-

oriented materials. An interesting feature of non-oriented material is its low remanence that is usually not larger than 50% of saturation. Averaging over independent grains would lead to a remanence beyond 80%. The strongly reduced value of the remanence is due to magnetostrictive interactions between the grains. If magnetostriction along the easy axes is not zero, elastic interactions between the grains lead to additional conditions for the allowed phase volumes in each grain. Altogether, the presented considerations may explain why acceptable loss values are reached at all. But even in the best non-oriented materials the losses are much larger than in grain oriented material. If for an induction amplitude of 1.5 T at 50 Hz the best available textured materials have losses below 0.6 W/kg, the same value for non-oriented material lies even in the best qualities above 2W/kg. The reasons are clearly the complex domain reorientation processes, which especially occur in the presence of rotating magnetic fields.

For reading: A. Hubert and R. Schäfer: Magnetic Domains - The Analysis of Magnetic Microstructure. Springer Verlag (1998)

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