Magnetic Properties of Thin Films

FERROMAGNETISM

The remainder of this chapter is devoted to some of the ferromagnetic properties of thin films (Refs. 26, 27). We start with the idea that magnetic phenomena have quantum mechanical origins stemming from the quantized angular momentum of orbiting and spinning atomic electrons. These circulat-ing charges effectively establish the equivalent of microscopic bar magnets or magnetic moments. When neighboring moments due to spin spontaneously and cooperatively order ín parallel alígnment over macroscopic dimensions in a material to yield a large moment of magnetization (M), then we speak of ferromagnetism. The quantity M is clearly a vector with a magnitude equal to the vector sum of magnetic moments per unit volume. In an external magnetic field (H) the interaction with M yields a field energy density (E_H) given by

E_H= -H • M.                                    (10-37)

However, no external field need be applied to induce the ferromagnetic state. The phenomenon of ferromagnetism has a number of characteristics and properties worth noting at the outset.

1. Elements (e.g., Fe, Ni, Co), alloys (e.g., Fe-Ni, Co-Ni), oxide insula-tors (e.g., nickel-zinc ferrite, strontium ferrite) and ionic compounds (e.g., CrBr₃,   EuS,  Eul₂)  all  exhibit ferromagnetism.   Not only  are  all  cristal structures and bonding mechanisms represented, but amorphous ferromagnets have also been synthesized (e.g., melt-quenched Fe₈₀B₂₀ ribbons and vapor-deposited Co-Gd films).

2.  Quantum mechanical exchange interactions cause the parallel spin align-

ments that result in ferromagnetism. It requires an increase in system energy to

disorient spin pairings and cause deviations from the parallel alignment direc-

tion. This energy, known as the exchange energy (E_ex), is given by

E_ex = A_x(V<t>)²                                 (10-38)

and is a measure of the "stiffness" of M or how strongly neighboring spins are coupled. The exchange constant A_x is a property of the material and equal to ~ 10~⁶ ergs/cm in Ni-Fe. Avoidance of sharp gradients in <t>, the angle between M and the easy axis of magnetization, leads to small valúes of E_ex.

3.       Absorbed thermal energy serves to randomize the orientation of the spin moments (i_s. At the Curie temperature (7"_c) the collective alignment collapses, and the ferromagnetism is destroyed. By equating the thermal energy absorbed to the internal field energy (n_sH¡), i.e., kT_c = ti_sH¡, valúes of H¡ can be estimated. The internal field H¡ permeating the matrix is established by exchange interactions. Typically, H_i is predicted to be in excess of 10⁶ Oe, an extremely high field.

4.       Magnetic anisotropy phenomena play a dominant role in determining the magnetic properties of ferromagnetic films. By anisotropy we mean the tendency of M to lie along certain directions in a material rather than be isotropically distributed. In single crystals, M prefers to lie in the so-called easy direction, say [100] in Fe and [111] in Ni. To turn M into other orientations, or harder directions, requires energy (i.e., magnetocrystalline anisotropy energy (E_K)). Consider now a fine-grained polycrystalline ferro­magnetic film of Permalloy (~ 80 Ni-20 Fe). Surprisingly, it also exhibits anisotropy with M lying in the film plañe. In such a case E_K is a function of the orientation of M with respect to film coordinates. For uniaxial anisotropy

E_K = Á>in²0,                                 (10-39)

where K_u is a constant with units of energy/volume, and 6 is the angle between the in-plane saturation magnetization and the easy axis. The source of the anisotropy is not due to crystallographic geometry but rather to the anisotropy arising from shape effects (i.e., shape anisotropy).

When ferromagnetic bodies are magnetized, magnetic poles are created on the surface. These poles establish a demagnetizing field (H_d) proportional and antiparallel to M, i.e., H_d = -NM, where N is known as the demagnetizing factor and depends on the shape of the body. For a thin film, N « 4x in the direction normal to the film plañe. Therefore, H_d = -4irM. In evaporated Permalloy films H_d can be as large as ~ 10⁴ Oe. However, in the film plañe H_d is much smaller so that M prefers to lie in this plañe. There are other magnetic films of great technological importance—garnets for magnetic bubble devices (Section 10.8.4) and Co-Cr for perpendicular magnetic recording applications (Section 14.4.3)—where M is perpendicular to the film plañe. Associated with H_d is magnetostatic energy (E_M) of amount

E_M=(l/2)H_dM                                (10-40)

per unit volume. The 1/2 arises because self-energy is involved, Le., H_d is created from the distribution of M in the film. In the hard direction the energy densiry is therefore

E_M = 2irM².                                   (10-41)

The origins of anisotropy are complex and apparently involve directional ordering of magnetic atom pairs, e.g., Fe-Fe. Film anisotropy is affected by film deposition method and variables, impingement angle of the incident vapor flux, applied magnetic fields during deposition, composition, internal stress, and columnar grain morphology, in not readily understood ways. Even amor-phous ferromagnetic films exhibit magnetic anisotropy.

Magnetic Film Size Effects — M_s vs. Thíckness and Temperature

Theory

Magnetic property size effects are expected simply because the electrón spin in an atom on the surface of a uniformly magnetized ferromagnetic film is less tightly constrained than spins on interior atoms. Fewer exchange coupling bonds on the surface than in the interior is the reason. Therefore, the question has been raised of how thin films can be and still retain ferromagnetic properties. At least four decades of both theoretical and experimental research have been conducted on the many aspects of this fundamental issue and related ones. The two theoretical approaches—spin wave and molecular field—both predict that a two-dimensional network of atoms of ferromagnetic elements should not be ferromagnetic but rather paramagnetic at absolute zero. At low temperatures a ferromagnet has very nearly its máximum magnetization. The deviation from complete saturation (AM₅) is due to waves of reversed spin propagating through the material. By summing the spin waves according to the rules of quantum statistical mechanics, we obtain the magnitude of the devia-tion at any temperature (AM_S(T)) relative to absolute zero M_s(0). In bulk materials it is generally accepted that

AM_s{T)/M_s(0) = BT^3/2,                            (10-42)

where B is the spin wave parameter. Its valué at the surface has been calculated to be twice that in the bulk. In thin films, theoretical treatments of magnetic size effects are a subject of controversy. Early calculations show a relative decrease in M vs. T for films of varying thickness as indicated in Fig. 10-17. For films thinner than four atomic layers M_s varíes linearly over a wide temperature range.

The molecular field approach replaces the exchange interaction between neighboring spins around a particular atom by an effective molecular field. A statistical accounting of the number of interactions between an atom in the j\h layer of a film with other atoms in the same as well as y - 1 and j + 1 layers is the approach taken. Such calculations typically reveal that M begins to decrease below the valué in bulk when the film thickness is less than some number of lattice spacings (e.g., 10), corresponding to a film thickness of perhaps 30 A.

In recent years, quantum calculations of ferromagnetic films have achieved a high level of sophistication. Spin densities in the ground state of Fe and Ni films consisting of a few atomic layers have, interestingly, been predicted to lead to an enhancement of the magnetic moment per atom in the outermost layer (e.g., by 20% in (001)Ni and 34% in (001)Fe compared to the bulk valué found four layers away). Such surprising results rule out the existence of magnetically "dead" layers reported in the literature.

Importantly, none of the aforementioned theories explicitly takes into ac-count such surface effects as lattice relaxation or distortion, surface reconstruc-tion, and pseudomorphic growth at real surfaces and interfaces. Rather, perfectly planar surfaces are assumed.

Experiment

Many experimental methods have evolved to yield direct or indirect evidence of ferromagnetic order in thin films. They broadly fall into three categories, depending on whether the

1.       spin polarization of electrons,

2.       net magnetic moment of the sample, or

3.       internal magnetic (hyperfine) field

is measured. The first relies on extracting electrons from the conduction bands of ferromagnetic solids by photoelectron emission and analyzing their energies by methods similar to those employed in Auger spectroscopy. Assuming no spin flips occur during emission, the number of majority and minority spins relative to the direction of magnetization of the surface can be determined. For example, the net surface magnetization of Fe^Ni^B^, an amorphous ferro-magnet (T_c = 700 K), was measured by detecting elastically backscattered spin polarized electrons (Ref. 33). The results are depicted in Fig. 10-17b for 90 eV electrons which are estimated to probé only the topmost one or two atomic layers (—2.5 A). Method 2 relies on very sensitive magnetometers to directly yield macroscopic M vs. H behavior. Although relatively free from interpretation problems associated with indirect methods 1 and 3, the measure-ments are not surface selective. In the third method the hyperfine magnetic field H_efí, which is to a good approximation proportionaJ to the local atomic moment, is measured. Nuclear physics techniques such as nuclear magnetic resonance and Móssbauer effect are used; only the latter will be discussed here at any length.

The Móssbauer effect is based on the spectroscopy of specific low-energy nuclear 7-rays that are emitted (without recoil) from excited radioactive atoms embedded in a source. These 7-rays are absorbed by similar nonradioactive ground state atoms contained within an absorber matrix. In the most famous Móssbauer transition, ⁵⁷Co nuclei emit 14.4-keV 7-rays and decay to the ⁵⁷Fe ground state. An absorber containing ⁵⁷Fe, an isotope present in natural Fe with an atomic abundance of 2.2%, can absorb the 7-ray if its nuclear levéis are very precisely tuned to this exact energy. Otherwise there is no absorption, and the 7-ray will simply pass through the absorber and be counted by a 7-ray detector. This is usually the case because differences in the local electromag-netic environment of Fe⁵⁷ in both the source and absorber alter the 14.4-keV level slightly, destroying the resonance. Fortunately very small, easily pro-duced Doppler effect energy shifts, caused by relative source-absorber veloci-ties of only ~ ± 1 cm/sec, can increase or decrease the energy sufficiently to restore the resonance. Móssbauer spectra thus reveal relative energy differ­ences in 7-ray transitions of Fe as they are affected by atomic surroundings. In a ferromagnetic absorber the Fe nucleus is immersed in the internal magnetic field that splits the nuclear levéis, an effect that is the counterpart to Zeeman splitting of atomic electrón levéis. Six transitions can now be accessed by using an appropriate (unsplit) source.

Móssbauer spectra of Fe film absorbers of varying thickness grown epitaxi-ally on Ag are shown in Fig. 10-18. The detection of 7-ray-induced conversión electrons plus the use of enriched ⁵⁷Fe layers provide the necessary sensitivity to probé ultrathin films. The six spectral lines characteristic of ferromagnetic behavior are clearly discernible at film thicknesses of 5 A. In the 620-A film the velocity or energy span between outer lines is essentially equivalent to the bulk H_eff of 330 kOe. Peak broadening plus a decreased span in the very thinnest films signify a distribution of somewhat reduced field strengths.

Magnetic Thin Films for Memory Applications

Interest in magnetic films aróse primarily because of their potential as com-puter memory elements. Although semiconductor memory is firmly established today, a quarter of a century ago small bulk ferromagnetic ferrite cores were employed for this purpose. Even earlier it was discovered that magnetic films deposited in the presence of a magnetic field exhibited square hysteresis loops. This meant that magnetic films could be used as a bistable element capable of switching from one state to another (e.g. from 0 to 1). Switching times were about 10~⁹ sec, a factor of 100 shorter than that for ferrite cores. The promise of higher-speed computer memory and new devices fueled a huge research and development effort focused primarily on Permalloy films. Despite initial enthusiasm it was found that careful control of magnetic properties produced formidable difficulties. The metallurgical nightmare of film impurities, imper-fections, and stress was among the reasons that actual performance of these films fell short of originally anticipated standards (Ref. 34).

In the mid-1960s an entirely new concept for computer memory and data storage applications was introduced by investigators at Bell Laboratories (Ref. 35). It employed special magnetic thin films (e.g., garnets) possessing cylindri-cal domains known as bubbles. Unlike the switching of M in Permalloy films, information is processed through the generation, translation, and detection of these bubbles (Section 10.8.4). Domain behavior is critical to both approaches, and we therefore turn our attention to this subject now.

Ronellys Flores---CRF---libro 

the materials science of thin films

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