In this paper, we review some of the key concepts in ultrathin film magnetism which underpin nanomagnetism. We survey the results of recent experimental and theoretical studies of well characterized epitaxial structures based on Fe, Co and Ni to illustrate how intrinsic fundamental properties such as the magnetic exchange interactions, magnetic moment and magnetic anisotropies change markedly in ultrathin films as compared with their bulk counterparts, and to emphasize the role of atomic scale structure, strain and crystallinity in determining the magnetic properties. After introducing the key length scales in magnetism, we describe the 2D magnetic phase transition and survey studies of the thickness dependent Curie temperature and the critical exponents which characterize the paramagnetic–ferromagnetic phase transition. We next discuss recent experimental and theoretical results on the determination of the exchange constant, followed by an overview of measurements of the magnetic moment in the elemental 3d transition metal thin films in the various crystal phases that have been successfully stabilized, thereby illustrating the sensitivity of the magnetic moment to the local symmetry and to the atomic environment. Finally, we discuss briefly the magnetic anisotropies of Fe, Co and Ni in the fcc crystalline phase, to emphasize the role of structure and the details of the interface in influencing the magnetic properties. The dramatic effect that adsorbates can have on the magnetic anisotropies of thin magnetic films is also discussed. Our survey demonstrates that the fundamental properties, namely, the magnetic moment and magnetic anisotropies of ultrathin films have dramatically different behaviour compared with those of the bulk while the comparable size of the structural and magnetic contributions to the total energy of ultrathin structures results in an exquisitely sensitive dependence of the magnetic properties on the film structure.

https://iopscience.iop.org/article/10.1088/0034-4885/71/5/056501/pdf

Magnetism in ultrathin film structures

We review some recent conceptual improvements of the Korringa–Kohn–Rostoker (KKR) Green function method for electronic structure calculations. After an introduction into the KKR–Green function method we present an extension of this method into an accurate full-potential scheme, which allows calculation of forces and lattice relaxations. The additional numerical effort compared to the atomic sphere approximation scales only linear with the number of atoms. In addition, we discuss the recently developed screened KKR method which represents a reformulation of the multiple scattering theory with exponentially decreasing structure constants. This method, which has the same accuracy as the standard KKR method, exhibits strong advantages for two-dimensional systems like multilayers or surfaces, since the numerical effort scales linearly with the number of layers. The strength of both methods is illustrated in typical applications.

/pdf/conceptual-improvements-of-the-kkr-method-4zimwe52ob.pdf

Conceptual improvements of the KKR method

https://www.physics.uci.edu/wugroup/publication/JMMM.200.498.1999.pdf

Spin}orbit induced magnetic phenomena in bulk metals and their surfaces and interfaces

In order to study spin-wave excitations of itinerant ferromagnets a relativistic first-principles method based on the adiabatic approach is presented. The derivatives of the free energy up to second order with respect of the polar and azimuthal angles are derived within the framework of the magnetic force theorem and the fully relativistic Korringa-Kohn-Rostoker method. Exchange and spin-orbit coupling are thus incorporated on equal footing in the Hamiltonian. Furthermore, a detailed comparison to classical spin Hamiltonians is given and it is shown that the magnetocrystalline anisotropy energy contains contributions from both the on-site anisotropy and the off-site exchange coupling terms. The method is applied to an Fe monolayer on Cu(001) and Au(001) surfaces and for a Co monolayer on Cu(001). The calculations provide with the gap at zero wave number due to the spin-orbit coupling and uniaxial anisotropy energies in good agreement with the results of the band energy difference method. It is pointed out that the terms in the spin-wave Hamiltonian related to the mixed partial derivatives of the free energy, absent within a nonrelativistic description, introduce an asymmetry in the magnon spectrum with respect to two in-plane easy axes. Moreover, in the case of an in-plane magnetized system the long-wavelength magnons are elliptically polarized due to the difference of the second-order uniaxial and fourth-order in-plane magnetic anisotropy.

First-principles relativistic study of spin waves in thin magnetic films

The creation of large magnetic fields is a necessary component in many technologies, ranging from magnetic resonance imaging, electric motors and generators, and magnetic hard disk drives in information storage. This is typically done by inserting a ferromagnetic pole piece with a large magnetisation density MS in a solenoid. In addition to large MS, it is usually required or desired that the ferromagnet is magnetically soft and has a Curie temperature well above the operating temperature of the device. A variety of ferromagnetic materials are currently in use, ranging from FeCo alloys in, for example, hard disk drives, to rare earth metals operating at cryogenic temperatures in superconducting solenoids. These latter can exceed the limit on MS for transition metal alloys given by the Slater-Pauling curve. This article reviews different materials and concepts in use or proposed for technological applications that require a large MS, with an emphasis on nanoscale material systems, such as thin and ultra-thin films. Attention is also paid to other requirements or properties, such as the Curie temperature and magnetic softness. In a final summary, we evaluate the actual applicability of the discussed materials for use as pole tips in electromagnets, in particular, in nanoscale magnetic hard disk drive read-write heads; the technological advancement of the latter has been a very strong driving force in the development of the field of nanomagnetism.

/pdf/a-review-of-high-magnetic-moment-thin-films-for-microscale-mhfn2l7x2f.pdf

A review of high magnetic moment thin films for microscale and nanotechnology applications

The oscillatory behavior of the magnetic-anisotropy energy in different types of ${\mathrm{Co}}_{n}$ multilayers on a Cu(100) substrate, including free surfaces, capped surfaces, and Co/Cu spacer systems, is shown in terms of ab initio\char21{}like calculations using the self-consistent fully relativistic spin-polarized screened Korringa-Kohn-Rostoker method. Deduced from direct representations and discrete (linear) Fourier transformations with respect to the number of Co layers, a period of two monolayers seems to be characteristic for these oscillations, whereas for a given number of Co layers and viewed with respect to the number of Cu-spacer layers they rapidly approach the value of the magnetic anisotropy energy for the corresponding ${\mathrm{Co}}_{n}$ multilayer on Cu(100) with a semi-infinite Cu cap, the so-called biased value. By excluding the so-called preasymptotic regime a short and a long period of 2.5 and 5.5 monolayers, respectively, can be traced for the oscillations with respect to the number of Cu-spacer layers. All types of oscillations, namely, either with respect to the number of Co layers or with respect to the number of Cu-spacer layers, are analyzed in terms of layer-resolved band-energy contributions to the magnetic-anisotropy energy. Such a layerwise distribution of the magnetic-anisotropy energy allows one not only to characterize different regimes of thicknesses, but also to discuss the effect of the actual interface on the absolute values of the magnetic-anisotropy energy, shown in particular by considering a system with Co/Au interfaces.

/pdf/oscillatory-behavior-of-the-magnetic-anisotropy-energy-in-cu-4e10u0vp06.pdf

Oscillatory behavior of the magnetic anisotropy energy in Cu(100)/Con multilayer systems

The magnetic properties of ${\mathrm{Co}}_{n}/\mathrm{Pt}(100),$ ${\mathrm{Co}}_{n}/\mathrm{Pt}(111),$ $({\mathrm{Co}}_{0.5}{\mathrm{Pt}}_{0.5}{)}_{n}/\mathrm{Pt}(100),$ $(\mathrm{CoPt}{)}_{n}/\mathrm{Pt}(100)$, and $(\mathrm{CoPt}{)}_{n}/\mathrm{Pt}(111),$ $nl~15$, are investigated using the relativistic spin-polarized screened Korringa-Kohn-Rostoker method. It is found that only the artificial superstructures $(\mathrm{CoPt}{)}_{n}/\mathrm{Pt}(100)$ and $(\mathrm{CoPt}{)}_{n}/\mathrm{Pt}(111)$ show a perpendicular magnetic anisotropy beyond $n=10$. For the free surfaces of Co on Pt in the case of the (100) orientation, a multiple reorientation transition below $n=7$ is found, while along (111) such a transition is predicted at about four layers of Co. For the homogeneous, statistically disordered alloy ${\mathrm{Co}}_{0.5}{\mathrm{Pt}}_{0.5}$ on Pt(100) the orientation of the magnetization remains in-plane for all n investigated. A comparison to experiment yields interesting insight into aspects of order and disorder, surface segregation, and phase separation frequently encountered in experimental studies of perpendicular magnetism in the Co/Pt system.

Magnetic properties of thin films of Co and of (CoPt) superstructures on Pt(100) and Pt(111)

An extensive study of the magnetic moment and of the magnetic anisotropy of a Co monolayer on a Cu(100) substrate capped by an additional $3d$, $4d,$ or $5d$ monolayer is presented in terms of first-principles calculations. While for the magnetic moment of the Co and the cap layer systematic trends can be traced that seem to be consistent with the Stoner model, the dependence of the magnetic anisotropy energy on the type of overlayer is found to be less straightforward. However, in some selected cases a correlation of the magnetic anisotropy with the specific features in the electronic structure of the Co and the cap layer can be pinpointed.

Overlayer-dependent magnetic moment and anisotropy of a Co monolayer on Cu(100)

Magnetic anisotropy of FexCo1-x multilayers on Cu(001): Reorientation transition of magnetic moments due to different interlayer coupling

The problem of superlattice symmetry, i.e., the question of periodicity along the growth direction ~surface normal! in magnetic multilayer systems, is discussed using discrete Fourier transformations for the anisotropy energy, as well as, for the antiparallel and perpendicular interface exchange coupling. We analyze the system Cu~100!/~Cu 3Ni 3) n , where n is the number of repetitions, for the case of free surfaces and surfaces capped semi-infinitely by Cu~100!. It will be shown that for some magnetic properties, and only in certain situations, ~almost! periodic behavior with respect to n applies, while for other properties an oscillatory behavior is characteristic. Also discussed are implications with respect to typical experimental situations and with respect to traditional supercell approaches. @S0163-1829~98!00313-0#

/pdf/superlattice-symmetry-in-magnetic-multilayer-systems-yd8o06obql.pdf

U. Pustogowa

Papers

Oscillatory behavior of the magnetic anisotropy energy in Cu(100)/Con multilayer systems

Magnetic properties of thin films of Co and of (CoPt) superstructures on Pt(100) and Pt(111)

Overlayer-dependent magnetic moment and anisotropy of a Co monolayer on Cu(100)

Magnetic anisotropy of FexCo1-x multilayers on Cu(001): Reorientation transition of magnetic moments due to different interlayer coupling

Superlattice symmetry in magnetic multilayer systems