Exchange bias

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As exchange bias (EB) is called a unidirectional anisotropy (hence unidirectional exchange anisotropy called) by the coupling between a ferrous and antiferromagnets is created. The exchange bias causes a preferred direction of magnetization in the ferromagnet, which is expressed in the experiment as a shift in the measured hysteresis curves along the magnetic field axis. By preferring a certain direction, the effect differs significantly from the usual ferromagnetic anisotropy , in which the alignment of the spins parallel and antiparallel to the preferred direction (easy direction) are energetically equivalent.

The effect is based on an exchange interaction (hence the name) of the ferromagnet (FM) with the antiferromagnet, and not just on a magnetostatic coupling. Since the antiferromagnet (AF) has no magnetization on average, the effect must be based on the magnetic fine structure of the AF (e.g. defects or the formation of domains) near the interface to the ferromagnet, which has long been difficult to determine experimentally. The effect itself (coupling through an exchange interaction between FM and AF with preferential direction in the FM) was discovered in 1956 by WH Meiklejohn and CP Bean. Theoretically the effect has not yet been explained satisfactorily.

The exchange bias is z. B. used for magnetic sensors in hard drives, in which the magnetic orientation in a ferromagnetic layer, which serves as a reference, is kept constant by this effect. Research at EB was also strongly promoted through the discovery of the GMR effect in the 1980s with its potential for hard disk development.

discovery

In 1956 WH Meiklejohn and CP Bean discovered a unidirectional anisotropy, which is caused by the coupling between a ferromagnetic (FM) and an antiferromagnetic (AFM) material. While ferromagnetic cobalt particles with oxidized , antiferromagnetic surfaces were investigated in the first work on this effect , many other material systems are now known that show the same effect. Most often, thin-film systems consisting of a ferromagnet and an antiferromagnet are examined, as this allows the interface and the crystallinity of the layers to be well controlled. In addition, most of the applications are based on thin-film technology .

Basics

Exchange Bias Graph Schematic representation of the exchange bias. If a ferromagnetic (FM) film is coupled with an antiferromagnetic (AFM) film, the hysteresis curve shifts by HEB along the magnetic field axis, and the coercive field HC can increase.

Magnetic anisotropies are often caused by the influence of crystal symmetries on the atomic magnetic moments. Such magnetic anisotropies lead to energetically favorable (light) and unfavorable (heavy) directions of magnetization in relation to the crystal lattice . Without magnetic anisotropies, a compass needle, for example, would not align itself with the magnetic moments in it.

Depending on the respective crystal lattice, one can find, for example, uniaxial anisotropies, in which the easy directions differ by 180 °, or four-fold, in which the energetically favorable directions are separated by 90 °.

The exchange bias, on the other hand, represents a unidirectional anisotropy, i.e. an anisotropy that preferably orients the magnetization in only one specific spatial direction. It occurs in systems in which the order temperature of the antiferromagnet ( Néel temperature ) is below the order temperature of the ferromagnet ( Curie temperature ) when the system is cooled in an external magnetic field or in the case of magnetized ferromagnets.

In simplified terms, one can imagine the phenomenon as such that when cooling below the Néel temperature, a magnetic field is frozen in the system. Accordingly, many effects related to exchange bias can be compared with the influence of an external magnetic field on a ferromagnet. A less easily explainable exchange bias is found in FeMn / CuNi, in which the order temperature of the ferromagnet is higher than that of the antiferromagnet.

While the hysteresis curve of a ferromagnet is symmetrical to the external magnetic field as well as to the magnetization , if the external magnetic field is traversed from sufficiently large positive to negative fields and back, there is a shift in the hysteresis curve in exchange bias systems. For positive cooling fields, the hysteresis curve is usually shifted towards negative magnetic fields; In addition, some measurements show a vertical shift of the curve along the M axis. The shift of the hysteresis curve along the magnetic field axis is referred to as the exchange bias field HEB.

If one compares an exchange bias system of ferromagnet and antiferromagnet with a ferromagnetic film of the same thickness, one also often finds a greatly increased coercive field . The increase in the coercive field occurs particularly below the Néel temperature ; it is strongly temperature-dependent. Some systems also have a maximum of the coercive field near the Néel temperature, e.g. B. Fe / FeF2 (with the ferromagnet iron and the antiferromagnet iron difluoride) in the crystal orientation (110).

In addition to other effects that only occur in exchange bias systems, the often found strong asymmetry of the hysteresis curve should be mentioned - for example, in some Fe / MnF2 samples (consisting of iron and the antiferromagnetic manganese difluoride) one side of the hysteresis can be mentioned have a pronounced step while the other side shows no such phenomenon.

Properties of Exchange Bias Systems

Exchange bias systems show various properties that can be found in almost all samples:

  • Temperature dependency: Starting from low temperatures, the exchange bias field usually decreases with increasing temperature until it disappears below the Néel temperature of the antiferromagnet - depending on whether the system under investigation has a thin antiferromagnetic layer or a relatively thick antiferromagnetic layer Single crystal contains well below or very close to the Néel temperature. The disorder in the antiferromagnet and the nature of the interface also influence the temperature at which the exchange bias becomes zero.
  • Layer thickness dependency: The exchange bias in the investigated systems is inversely proportional to the layer thickness of the ferromagnet, which suggests that the exchange bias is an interface effect. Deviations can be found for very thick or very thin layers. There are two different observations for the dependence of the exchange bias on the layer thickness of the antiferromagnet: The exchange bias initially increases with increasing layer thickness and either falls again after reaching a maximum or remains at a constant value. Which behavior occurs depends on the material system used and the preparation conditions.
  • Cooling field dependency: The exchange bias can be varied by changing the cooling field in which the system is cooled below the Néel temperature of the antiferromagnet. The dependency of the exchange bias on the cooling field is different for different systems: In some cases there is a reduction or even a change in sign of the exchange bias with high fields; In other investigations one sees an exchange bias that initially increases with increasing cooling field, while it no longer changes with high magnetic fields.
  • Dependence on the interface roughness: If you couple a single-crystalline antiferromagnetic substrate (e.g. FeF2) with a very smooth surface to a ferromagnet, the resulting system shows only a slight exchange bias. Roughening the substrate surface before applying the ferromagnet increases the exchange bias considerably. While in most thin-film systems, such as Fe / FeF2, the exchange bias is large with a smooth boundary layer and decreases with increasing roughness of the interface, the exchange bias in Fe / MnF2 thin-layer systems initially also decreases with increasing roughness, but then increases again . If you take NiO as the antiferromagnet , you can see no dependence of the exchange bias on the standard deviation of the layer thickness of the antiferromagnet (roughness). In contrast, the exchange bias in this system is increased when the mean slope of the interface profile increases.
  • Dependence on the nature of the antiferromagnet: The exchange bias does not only depend on the interface roughness, but also on the crystal quality of the antiferromagnet. For example, systems made of Fe and twinned FeF2 films, which consist of two sublattices that are rotated relative to one another, show a higher exchange bias than corresponding systems on monocrystalline substrates. The same behavior can be found for thin CoO layers and substrates with Co as the ferromagnet. In polycrystalline films one usually sees an exchange bias that increases with the smaller crystallite size, but sometimes exactly the opposite behavior. The crystallite size can be determined by choosing different temperatures, growth rates or pressures during the preparation. These preparation parameters presumably also influence other variables, which also have an impact on the exchange bias, which can explain the different observations.
  • Dependence on the orientation of the interface: If you cut a crystal in different directions, the magnetic moments on the surface can be oriented antiparallel or parallel to each other, which is called “compensated” or “uncompensated” surfaces. Contrary to the intuitive idea, all previous studies have also found an exchange bias on compensated surfaces, which in some cases is even greater than on uncompensated surfaces. In addition, the magnetic moments in some crystal orientations are not parallel to the surface. For FeF2, for example, in the (110) -orientation they lie in the plane, in the (001) -orientation perpendicular to the interface, and in the (101) -orientation they enclose a mean angle with the surface. The maximum exchange bias is found for the (110) -orientation, at FeF2 (001) the exchange bias disappears, and in the (101) -orientation one obtains about half of the maximum exchange bias.

Theoretical models

Despite a wide range of technical applications, the microscopic origin of the exchange bias is not yet fully understood. Some models can explain partial aspects, but quantitative predictions usually differ by orders of magnitude from the experimental data.

The simplest models for the exchange bias assume perfectly compensated or uncompensated surfaces. In addition, an infinite anisotropy is assumed in the antiferromagnet, that is, the spins can only align themselves parallel or anti-parallel ( Ising model ). Such intuitive models result, for example, for CoO (111) exchange bias fields that are one to three orders of magnitude higher than the measured ones.

Exchange bias models
Representation of compensated and uncompensated surfaces, smooth and rough as well as under the assumption that domain walls perpendicular to the interface are allowed. The energetically favorable (+) and unfavorable (-) orientations of the magnetic moments apply under the assumption of a ferromagnetic interface coupling; in the case of an antiferromagnetic coupling, these signs are reversed. In the case of a rough interface, the energetically favorable and unfavorable orientations cancel each other out on average; If the formation of domain walls is permitted, this can result in a further reduction in energy, which can lead to net magnetization in the antiferromagnet and thus to an exchange bias.

Malozemoff's random field model allows domain walls to be formed in the antiferromagnet perpendicular to the interface. This allows the antiferromagnet to form domains which all have a small excess of magnetization in the direction of the magnetization of the ferromagnet. This net magnetization is frozen at low temperatures and causes the exchange bias. Shortly after their discovery of exchange bias, Meiklejohn and Bean developed a model to describe this unidirectional anisotropy, which is based on torque measurements. This model also results in an exchange bias that is orders of magnitude too high.

In contrast to the models described so far, Mauri's model also allows the non-parallel alignment of the spins in the antiferromagnet. Within a plane parallel to the interface, all spins are aligned parallel, but spins in different planes can be rotated against each other. In contrast to the random field model, this means the possible formation of domains parallel to the interface, which is assumed here to be uncompensated. Depending on the strength of the coupling at the interface, results similar to those in the two models described above are obtained.

The model by Schulthess and Butler, on the other hand, represents a micromagnetic simulation of a three-dimensional Heisenberg model . The calculation is limited to single crystals as ferro- and antiferromagnets with a smooth interface in a single-domain state. If you introduce defects at the perfectly smooth interface by replacing individual ferromagnetic moments with antiferromagnetic ones, this excess leads to a preferred direction for the magnetization in the ferromagnet. For an excess of about 1%, which has also been determined experimentally, realistic values ​​for the exchange bias are obtained. The model by Schulthess and Butler thus clarifies the importance of interface defects, but cannot derive them theoretically.

The model by Stiles and McMichael is the only one described here based on the assumption of a polycrystalline antiferromagnet. In the individual crystallites, a partial domain wall parallel to the interface, caused by the influence of the ferromagnet, is possible; the ferromagnet is again assumed to be one-domain. The magnetic moments in the antiferromagnet can rotate freely in all spatial directions (Heisenberg model). The result is similar to that of the Mauri model.

The domain state model also introduces non-magnetic defects into the antiferromagnetic layer. In contrast to Malozemoff's model, defects in the volume of the antiferromagnet (not only at the interface with the ferromagnet) play a role here, which was confirmed by Monte Carlo simulations . This suggests that the antiferromagnet is breaking up into domains, caused by local random fields. The resulting net magnetization causes the exchange bias. This model can u. a. explain the frequently observed vertical shift in the hysteresis curve as the magnetization of the antiferromagnet. The dependence of the exchange bias on the number of defects in the antiferromagnet (with a maximum exchange bias at an “ideal dilution”) is observed in the experiment and simulation alike. The domain-state model can also explain the temperature and cooling field dependency as well as other experimentally observed effects and thus represents a useful approach to understanding exchange bias.

Applications

Is technologically interesting the exchange bias as it was in spin valves (Engl. Spin valves) plays an important role. These systems contain two ferromagnets, one of which can be freely reversed while the other is held as a reference. This “pinning” takes place through the coupling to an antiferromagnet, i.e. through the exchange bias. Depending on the separating layer between the two ferromagnets, two different systems are obtained:

  • The GMR effect was discovered in 1988. GMR systems consist of two ferromagnetic layers that are separated by a non-magnetic metal. The electrical resistance parallel to the layer plane in such a system depends strongly on the orientation of the two magnetizations of the ferromagnets to one another. GMR elements are used, for example, in hard disk read heads.
  • In Tunneling Magneto Resistance Elements (TMR), two ferromagnetic layers are separated by a non-magnetic insulator . Here the tunnel current perpendicular to the layer plane is strongly dependent on the relative orientation of the two magnetizations to one another. By means of the TMR effect, magnetic memory modules can be produced, e.g. B. MRAMs ( Magnetoresistive Random Access Memory ).

Measurement method

The longitudinal magnetization component (along the external field) can be measured, for example, using a SQUID (Superconducting Quantum Interference Device), and PNR measurements (Polarized Neutron Reflectometry) can provide information about a transverse magnetization component (perpendicular to the external field). Alternatively, the samples can be examined magneto-optically by e.g. B. the change in polarization of a linearly polarized laser beam s is detected. This interaction of electromagnetic radiation with a magnetic material was described by Faraday in 1845 and by Kerr in 1876 . The static measurement of the longitudinal magnetization component can be realized much faster in this way than with a SQUID. The transverse magnetization component can also be measured magneto-optically more easily and quickly than with PNR. In addition, the sign of the transverse signal provides information about the direction of rotation of the magnetic moments in the sample, which PNR measurements do not allow. Last but not least, time-resolved magneto-optical measurements make it possible to study magnetization dynamics on the picosecond scale. The precession frequency of the magnetic moments in the sample measured in this way is directly related to the anisotropies, so - similar to what can be determined by BLS measurements ( Brillouin Light Scattering ).

The magneto-optical Kerr effect (MOKE) is also used in current technology. Magneto-optical storage media combine magnetic (hard drives, floppy disks, tape drives) and optical media (CD-ROM). The reading of the data is made possible by MOKE.

Current developments

Due to the great technological relevance, in addition to various effects that only occur in exchange bias systems, in particular magnetic reversal processes by different groups have been investigated using different methods. In all of these time-resolved measurements, a change in the anisotropy field causes a precession of the magnetic moments in the sample, which is mostly detected optically. This local change in the anisotropies can be induced by thermal excitation by means of a laser pulse, by a field pulse or by a spin-selective excitation.

In order to generate a field pulse at the location of the sample, it can be attached to a micro-stripline through which a current pulse that is phase- coupled with the laser is sent. While a static magnetic field parallel to this micro-stripline aligns the magnetic moments in the sample before the excitation, the direction of the effective field is deflected from the original direction by the magnetic field pulse occurring perpendicular to it. Similarly, a conductor loop can be placed around a very small magnetic area. Hiebert et al. Magnetic oscillations detected in a Permalloy disk. Freeman et al. have shown that the response of the magnetization to a field pulse of around 10 nanoseconds duration in small permalloy structures depends on the shape of the sample.

A stronger field pulse can cause the magnetization to rotate by 180 °, known as “precessional switching”. Schumacher et al. have shown that the precession of the magnetization alternately leads to a reversal of magnetization and a return to the original position of the magnetization, depending on the pulse duration. Mayergoyz, et al. calculate the strength and shape of a field pulse that induces a magnetic reversal. Precessional switching is also possible without a second pulse that stops the rotation of the magnetization after half a precession period. On the other hand, measurements by Hiebert et al. on particles with a side length of 7 × 20  μm shows that the magnetization does not behave homogeneously within the entire sample even in these relatively large structures. Since the magnetization is more strongly pinned at the edges of the sample, the original direction of magnetization remains there and, after switching off the external field, leads to the previously magnetized center of the sample also returning to its original state. With regard to an application of precessional switching in the even smaller MRAMs and other components, this effect can lead to problems.

Instead of a laser, Silva et al. Pick-up coils to inductively measure the change in magnetization caused by a field pulse or a field step. In the case of an excitation by a field stage, two different frequencies and amplitudes appear, which can be simulated by assuming a time-dependent damping. In permalloy structures with side lengths in the μm range, which can be classified between nano-particles and extended layers, Koch et al. Depending on the size of the field pulse, very different magnetization reversal times between 10 nanoseconds and 500 picoseconds were found, which they assign to a transition from domain wall mechanisms to coherent rotation of the magnetization. In this experiment, the investigated layers represent the upper electrode of a tunnel contact, so that the rotation of the magnetization can be detected via the tunnel resistance.

Freeman et al. use an improved Kerr microscope to study the magnetization dynamics in thin permalloy films not only with time but also with spatial resolution (with an accuracy of less than 1 micrometer). In addition to the experiments described so far, in which the local anisotropies in a sample are changed by means of a field pulse, thermal excitation using a laser pump pulse is also possible. With this method, for example, Ju et al. Time-resolved measurements carried out on NiFe / NiO layer systems, which have basically shown that such photo-induced changes in the effective magnetic field are possible.

Koopmans et al. examined nickel samples that were tilted with respect to the external field and found in them not only the precession of the magnetic moments but also non-magnetic contributions to the time-resolved signal, which must be taken into account in this type of measurement. Van Kampen et al. have to microstructured Permalloy the excitation of spin waves detected whose samples dispersion can be examined with such a time-resolved experiments.

Other current topics are, for example, basic investigations into the asymmetry of the hysteresis curves, the magneto-electrical switching of the exchange bias and the behavior of exchange bias micro and nano systems in various forms.

literature

  • J. Stöhr, H. Ch. Siegmann: Magnetism - From Fundamentals to Nanoscale Dynamics . Springer Series in Solid-State Sciences Vol. 152, 2006, ISBN 978-3-540-30282-7 (Section 13.4.3, pp. 617ff)
  • L. Guhr: Exchange bias effect in magnetic films on particle monolayers . Shaker Verlag , Aachen 2008, ISBN 978-3-8322-7196-1
  • WD Brewer: Modern Methods for Investigating Magnetism . In: AV Narlikar (Ed.): Frontiers in Magnetic Materials . Springer-Verlag, Heidelberg / Berlin 2005, ISBN 978-3-540-24512-4 , pp. 1-42

Web links

Individual evidence

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