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# Magnetic anisotropy

About: Magnetic anisotropy is a(n) research topic. Over the lifetime, 36978 publication(s) have been published within this topic receiving 686556 citation(s).

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04 May 1948-Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences

Abstract: The Becker-Kersten treatment of domain boundary movements is widely applicable in the interpretation of magnetization curves, but it does not account satisfactorily for the higher coercivities obtained, for example, in permanent magnet alloys. It is suggested that in many ferromagnetic materials there may occur ‘particles’ (this term including atomic segregates or ‘islands’ in alloys), distinct in magnetic character from the general matrix, and below the critical size, depending on shape, for which domain boundary formation is energetically possible. For such single-domain particles, change of magnetization can take place only by rotation of the magnetization vector, I O . As the field changes continuously, the resolved magnetization, I H , may change discontinuously at critical values, H O , of the field. The character of the magnetization curves depends on the degree of magnetic anisotropy of the particle, and on the orientation of ‘easy axes’ with respect to the field. The magnetic anisotropy may arise from the shape of the particle, from magneto-crystalline effects, and from strain. A detailed quantitative treatment is given of the effect of shape anisotropy when the particles have the form of ellipsoids of revolution (§§ 2, 3, 4), and a less detailed treatment for the general ellipsoidal form (§ 5). For the first it is convenient to use the non-dimensional parameter such that h = H /(| N a - N b |) I O , N a and N b being the demagnetization coefficients along the polar and equatorial axes. The results are presented in tables and diagrams giving the variation with h of I H / I O . For the special limiting form of the oblate spheroid there is no hysteresis. For the prolate spheroid, as the orientation angle, θ , varies from 0 to 90°, the cyclic magnetization curves change from a rectangular form with | h O | = 1, to a linear non-hysteretic form, with an interesting sequence of intermediate forms. Exact expressions are obtained for the dependence of h θ on θ , and curves for random distribution are computed. All the numerical results are applicable when the anisotropy is due to longitudinal stress, when h = HI 0 /3λδ, where λ is the saturation magnetostriction coefficient, and δ the stress. The results also apply to magneto-crystalline anisotropy in the important and representative case in which there is a unique axis of easy magnetization as for hexagonal cobalt. Estimates are made of the magnitude of the effect of the various types of anisotropy. For iron the maximum coercivities, for the most favourable orientation, due to the magneto-crystalline and strain effects are about 400 and 600 respectively. These values are exceeded by those due to the shape effect in prolate spheroids if the dimensional ratio, m , is greater than 1·1; for m = 10, the corresponding value would be about 10,000 (§7). A fairly precise estimate is made of the lower limit for the equatorial diameter of a particle in the form of a prolate spheroid below which boundary formation cannot occur. As m varies from 1 (the sphere) to 10, this varies from 1·5 to 6·1 x 10 -6 for iron, and from 6·2 to 25 x 10 -6 for nickel (§ 6). A discussion is given (§ 7) of the application of these results to ( a ) non-ferromagnetic metals and alloys containing ferromagnetic ‘impurities’, ( b ) powder magnets, ( e ) high coeravity alloys of the dispersion hardening type. In connexion with ( c ) the possible bearing on the effects of cooling in a magnetic field is indicated.

4,108 citations

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TL;DR: Inter interfacial perpendicular anisotropy between the ferromagnetic electrodes and the tunnel barrier of the MTJ is used by employing the material combination of CoFeB-MgO, a system widely adopted to produce a giant tunnel magnetoresistance ratio in MTJs with in-plane an isotropy.

Abstract: Magnetic tunnel junctions (MTJs) with ferromagnetic electrodes possessing a perpendicular magnetic easy axis are of great interest as they have a potential for realizing next-generation high-density non-volatile memory and logic chips with high thermal stability and low critical current for current-induced magnetization switching. To attain perpendicular anisotropy, a number of material systems have been explored as electrodes, which include rare-earth/transition-metal alloys, L1(0)-ordered (Co, Fe)-Pt alloys and Co/(Pd, Pt) multilayers. However, none of them so far satisfy high thermal stability at reduced dimension, low-current current-induced magnetization switching and high tunnel magnetoresistance ratio all at the same time. Here, we use interfacial perpendicular anisotropy between the ferromagnetic electrodes and the tunnel barrier of the MTJ by employing the material combination of CoFeB-MgO, a system widely adopted to produce a giant tunnel magnetoresistance ratio in MTJs with in-plane anisotropy. This approach requires no material other than those used in conventional in-plane-anisotropy MTJs. The perpendicular MTJs consisting of Ta/CoFeB/MgO/CoFeB/Ta show a high tunnel magnetoresistance ratio, over 120%, high thermal stability at dimension as low as 40 nm diameter and a low switching current of 49 microA.

2,754 citations

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Abstract: Magneto-optical Kerr effect microscopy is used to show that monolayer chromium triiodide is an Ising ferromagnet with out-of-plane spin orientation. The question of what happens to the properties of a material when it is thinned down to atomic-scale thickness has for a long time been a largely hypothetical one. In the past decade, new experimental methods have made it possible to isolate and measure a range of two-dimensional structures, enabling many theoretical predictions to be tested. But it has been a particular challenge to observe intrinsic magnetic effects, which could shed light on the longstanding fundamental question of whether intrinsic long-range magnetic order can robustly exist in two dimensions. In this issue of Nature, two groups address this challenge and report ferromagnetism in atomically thin crystals. Xiang Zhang and colleagues measured atomic layers of Cr2Ge2Te6 and observed ferromagnetic ordering with a transition temperature that, unusually, can be controlled using small magnetic fields. Xiaodong Xu and colleagues measured atomic layers of CrI3 and observed ferromagnetic ordering that, remarkably, was suppressed in double layers of CrI3, but restored in triple layers. The two studies demonstrate a platform with which to test fundamental properties of purely two-dimensional magnets. Since the discovery of graphene1, the family of two-dimensional materials has grown, displaying a broad range of electronic properties. Recent additions include semiconductors with spin–valley coupling2, Ising superconductors3,4,5 that can be tuned into a quantum metal6, possible Mott insulators with tunable charge-density waves7, and topological semimetals with edge transport8,9. However, no two-dimensional crystal with intrinsic magnetism has yet been discovered10,11,12,13,14; such a crystal would be useful in many technologies from sensing to data storage15. Theoretically, magnetic order is prohibited in the two-dimensional isotropic Heisenberg model at finite temperatures by the Mermin–Wagner theorem16. Magnetic anisotropy removes this restriction, however, and enables, for instance, the occurrence of two-dimensional Ising ferromagnetism. Here we use magneto-optical Kerr effect microscopy to demonstrate that monolayer chromium triiodide (CrI3) is an Ising ferromagnet with out-of-plane spin orientation. Its Curie temperature of 45 kelvin is only slightly lower than that of the bulk crystal, 61 kelvin, which is consistent with a weak interlayer coupling. Moreover, our studies suggest a layer-dependent magnetic phase, highlighting thickness-dependent physical properties typical of van der Waals crystals17,18,19. Remarkably, bilayer CrI3 displays suppressed magnetization with a metamagnetic effect20, whereas in trilayer CrI3 the interlayer ferromagnetism observed in the bulk crystal is restored. This work creates opportunities for studying magnetism by harnessing the unusual features of atomically thin materials, such as electrical control for realizing magnetoelectronics12, and van der Waals engineering to produce interface phenomena15.

2,376 citations

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General Electric

^{1}Abstract: A new type of magnetic anisotropy has been discovered which is best described as an exchange anisotropy. This anisotropy is the result of an interaction between an antiferromagnetic material and a ferromagnetic material. The material that exhibits this exchange anisotropy is a compact of fine particles of cobalt with a cobaltous oxide shell. The effect occurs only below the N\'eel temperature of the antiferromagnetic material, which is essentially room temperature for the cobaltous oxide. An exchange torque is inferred to exist between the metal and oxide which has a maximum value at 77\ifmmode^\circ\else\textdegree\fi{}K of \ensuremath{\sim}2 dyne-cm/${\mathrm{cm}}^{2}$ of interface.

1,838 citations

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Abstract: A mathematical model of the hysteresis mechanisms in ferromagnets is presented. This is based on existing ideas of domain wall motion including both bending and translation. The anhysteretic magnetization curve is derived using a mean field approach in which the magnetization of any domain is coupled to the magnetic field H and the bulk magnetization M . The anhysteretic emerges as the magnetization which would be achieved in the absence of domain wall pinning. Hysteresis is then included by considering the effects of pinning of magnetic domain walls on defect sites. This gives rise to a frictional force opposing the movement of domain walls. The impedance to motion is expressed via a single parameter k , leading to a simple model equation of state. This exhibits all of the main features of hysteresis such as the initial magnetization curve, saturation of magnetization, coercivity, remanence, and hysteresis loss.

1,814 citations