Noncollinear Exchange Coupling Research Articles

Photo-induced non-collinear interlayer RKKY coupling in bulk Rashba semiconductors

The interplay between light-matter, spin-orbit, and magnetic interactions allows the investigation of light-induced magnetic phenomena that are otherwise absent without irradiation. We present our analysis of light-driven effects on the interlayer exchange coupling mediated by a bulk Rashba semiconductor in a magnetic multilayer. The collinear magnetic exchange coupling mediated by the photon-dressed spin-orbit coupled electrons of BiTeI develops light-induced oscillation periods and displays new decay power laws, both of which are enhanced with an increasing light-matter coupling. For magnetic layers with non-collinear magnetization, we find a non-collinear magnetic exchange coupling uniquely generated by light-driving of the multilayer. As the non-collinear magnetic exchange coupling mediated by the photon-dressed electrons of BiTeI is unique to the irradiated system and it is enhanced with increasing light-matter coupling, this effect offers a promising platform of investigation of light-driven effects on magnetic phenomena in spin-orbit coupled systems. In this platform, light properties, such as its intensity, can serve as external knobs for inducing non-collinear couplings of the interlayer exchange and for modulating the collinear couplings. Both of these effects signify the photo-generated modification in the spin textures of spin-orbit coupled electrons in BiTeI.

Noncollinear interlayer exchange coupling across IrFe spacer layers

In this paper, we show that IrFe spacer layers enable the control of noncollinear interlayer exchange coupling between ferromagnetic Co layers over a spacer layer composition and thickness range that is larger than any observed before for other spacer layer materials. Moreover, in the studied Co|IrFe|Co structures, the bilinear coupling strength, J1, is above 2mJ/m2 and the biquadratic coupling strength, J2, is above 1mJ/m2 over a wide spacer layer composition and thickness range. Notably, the largest antiferromagnetic bilinear coupling strength ever observed across spacer layers of 0.6nm or thicker is achieved, with J1 peaking at 3.4mJ/m2. After annealing, orthogonal coupling is favoured over a wide spacer layer composition and thickness range, which could be useful for magnetic sensor devices. As the temperature is reduced below room temperature, the coupling parameters of the as-deposited films vary slowly, which could be a desirable feature for applications. Measurements of the saturation magnetization of Co|IrFe|Co structures reveal that IrFe has a magnetic moment in the spacer layer composition range for which noncollinear coupling is observed. This indicates that the origin of noncollinear coupling in Co|IrFe|Co could be attributed to the competition between the antiferromagnetic coupling of magnetic atoms across Ir atoms in the spacer layer and the ferromagnetic coupling of neighbouring magnetic atoms.

Antiferromagnet-induced perpendicular magnetic anisotropy in ferromagnetic Co/Fe films with strong in-plane magnetic anisotropy

Ferromagnetic (FM) films with higher magnetic moment density typically exhibit sizable in-plane magnetic anisotropy as a result of strong dipolar interactions, which hinder their application in state-of-the-art perpendicularly based magnetic devices. This study reports the effects of triggering the perpendicular magnetic anisotropy (PMA) of a Co/Fe film with strong in-plane magnetic anisotropy through nearby antiferromagnetic (AFM) fcc ${\mathrm{Fe}}_{50}{\mathrm{Mn}}_{50}$ and face-centered tetragonal (e-fct) Mn films. Our results demonstrate that fcc ${\mathrm{Fe}}_{50}{\mathrm{Mn}}_{50}$ films with a three-dimensional quadratic AFM spin structure can trigger robust PMA in a Co/Fe film through collinearlike AFM-FM exchange coupling at room temperature. Furthermore, by incorporating a monolayered ${\mathrm{Fe}}_{50}{\mathrm{Mn}}_{50}$ film into the Mn-Co interface or by reducing the temperature, PMA can also be triggered in a Co/Fe film by using e-fct Mn films with an in-plane-oriented AFM spin structure at room or low temperature through noncollinear exchange coupling across the AFM-FM interface. Our results clarify the exchange-coupling mechanisms, characteristic behaviors, and critical conditions for increasing control over antiferromagnet-induced PMA in FM films with high magnetic moment density but strong in-plane magnetic anisotropy, which is helpful for the development of next-generation perpendicularly based spintronic devices.

Flipping magnetization induced by noncollinear ferromagnetic-antiferromagnetic exchange coupling

We present a direct observation of a flipping magnetization of a uniform Fe film/wedged-Mn bilayer induced by a biquadratic-type exchange coupling established at the interface. The element-resolved magnetic imaging shows that the Fe film exhibited a flipping of magnetization between the [$\overline{1}$00] and [010] directions with a periodicity of one monolayer Mn thickness as below a critical temperature. The enhancement of the variation angle with the increase of Mn thickness follows the tendency of the finite-size effect of antiferromagnetism on interface exchange coupling. The flipping magnetization emerging coincidentally with the uncompensated-compensated transition of Mn magnetic surface indicates a frustration-induced biquadratic-type interface exchange coupling, and suggests a layered-like uncompensated AFM ordering for the Mn layer.

Magnetization reversal and domain correlation for a non-collinear and out-of-plane exchange-coupled system

We have investigated the impact of out-of-plane ferromagnetic (FM) anisotropy (which can be coincident with the direction of unidirectional anisotropy), where antiferromagnetic (AF) anisotropy is along the film plane. This provides a platform for non-collinear exchange coupling in an archetypal exchange coupled system in an unconventional way. We probe the in-plane magnetization by the depth-sensitive vector magnetometry technique. The experimental findings reveal a magnetization reversal (i) that is symmetric for both the branches of the hysteresis loop, (ii) that is characterized by vertically correlated domains associated with a strong transverse component of magnetization and (iii) that remains untrained (suppression of trained state) with field cycling. This scenario has been compared with in-plane magnetization reversal for a conventionalin-plane unidirectional anisotropic case in the same system that shows usual asymmetric reversal and training for vertically uncorrelated domains. We explain the above observations for the out-of-plane case in terms of inhomogeneous magnetic states due to competing perpendicular anisotropies that result in non-collinear FM–AF coupling. This study provides direct evidence for the vertical correlation of domains mediated by out-of-plane exchange coupling.

In-plane noncollinear exchange coupling mediated by helical edge states in quantum spin Hall systems

We study the Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction mediated by helical edge states in quantum spin hall system. The helical edge states induce an in-plane noncollinear exchange coupling between two local spins, in contrast to the isotropic coupling induced in normal metal. The angle between the two local spins in the ground state depends on the Fermi level. This property may be used to control the angle of spins by tuning the electric gate.

Spatial trends of noncollinear exchange coupling mediated by itinerant carriers with different Fermi surfaces

We study the exchange coupling mediated by itinerant carriers with spin-orbit interaction by both analytic and numeric approaches. The mediated exchange coupling is noncollinear and its spatial trends depend on the Fermi-surface topology of the itinerant carriers. Taking Rashba interaction as an example, the exchange coupling is similar to the conventional Ruderman-Kittel-Kasuya-Yosida type in weak coupling. On the other hand, in the strong coupling, the spiral interaction dominates. In addition, inclusion of finite spin relaxation always makes the noncollinear spiral exchange interaction dominant. Potential applications of our findings are explained and discussed.

Anomalous exchange bias in Gd/Cr bilayer and Cr/Gd/Cr trilayers

Exchange bias has been observed in Gd/Cr bilayers and Cr/Gd/Cr trilayers systems in which the Curie temperature ( T C) of ferromagnetic Gd is less than the Néel temperature ( T N) of antiferromagnetic Cr. The exchange bias field H E and coercivity H C of the samples exhibit anomalous temperature dependence behavior in comparison with the conventional ferromagnet/antiferromagnet bilayers with T C > T N. As temperature increases, H E increases monotonically until T C, whereas H C drops first and then goes up; finally, it disappears at T C, which is attributed to the noncollinear interfacial exchange coupling between Gd and Cr. The results show that the exchange bias may exist in the AFM/FM bilayers regardless of the condition of T C > T N.

Non-collinear magnetic junction mediated by Rashba interaction

We study the non-collinear exchange coupling across the trilayer magnetic junction composed of an intermediate layer with Rashba interaction and two sandwiching ferromagnetic ones. To compute the mediated exchange coupling between the ferromagnetic layers, one needs to go beyond the single-particle argument and numerically integrates over contributions from the whole Fermi surface. We found interesting competition between the oscillatory Ruderman–Kittel–Kasuya–Yosida and the non-collinear spiral interactions. Surprisingly, the Fermi surface topology determines which type of magnetic interaction becomes dominant. Finally, we also discuss potential applications for the non-collinear exchange coupling across the junction.

Spiral exchange coupling in trilayer magnetic junction mediated by diluted-magnetic-semiconductor thin film

We revisit the noncollinear exchange coupling across the trilayer magnetic junction mediated by the diluted-magnetic-semiconductor thin film. By numerical approaches, we investigate the spiral angle between the ferromagnetic layers extensively in the parameter space. In contrast to previous study, we discovered the important role of spin relaxation, which tends to favor spiral exchange over the oscillatory Ruderman-Kittel-Kasuya-Yosida interaction. Finally, we discuss the physics origins of these two types of magnetic interactions.

Noncollinear exchange coupling in a trilayer magnetic junction and its connection to Fermi surface topology

We investigate the non-collinear exchange coupling across the trilayer magnetic junction composed of an intermediate layer with Rashba interaction and two sandwiching ferromagnetic ones. To compute the mediated exchange coupling, one needs to go beyond the single-particle argument and integrate over the contributions from the whole Fermi surface. Surprisingly, we find that the topology of the Fermi surface plays a crucial role in determining whether the oscillatory RKKY or the spiral interactions would dominate. At the end, we discuss the connection of our numerical results to experiments and potential applications.

Noncollinear interlayer exchange in Fe/Cr/Fe magnetic structures with different interface roughnesses

The interaction of iron layers through a chromium spacer in Fe/Cr/Fe trilayers with different roughnesses of interfaces was studied by the Kerr magnetometry and Mandel’shtam-Brillouin light scattering techniques so as to trace the interlayer exchange coupling of the Fe layers depending on the Cr spacer thickness and the sample temperature. It is established that, in a broad range of these parameters, the interlayer exchange in Fe/Cr/Fe structures with sufficiently smooth interfaces is adequately described using the proximity magnetism and half-angle coupling models taking into account the antiferromagnetic properties of chromium. As the interface roughness increases, the well-known biquadratic exchange model becomes valid. This is evidence for the decisive role of the magnetic stiffness of a Cr spacer and the structure of interfaces on the noncollinear exchange coupling in Fe/Cr/Fe trilayers.

Non-collinear exchange coupling in Fe/Mn/Fe(0 0 1): insight from scanning tunneling microscopy

The film growth and morphology of epitaxial Mn films grown on Fe(0 0 1) single-crystal whiskers measured with scanning tunneling microscopy (STM) provides insight into the mechanism of interlayer exchange coupling in Fe/Mn/Fe(0 0 1) trilayers. The proximity model of Slonczewski for exchange coupling through an antiferromagnet predicts that the coupling angle between the ferromagnetic layers will oscillate around a mean value of 90° with an amplitude that is very sensitive to the width of the thickness distribution of the spacer layer. We measure the thickness distribution with the STM and find that the coupling angle variation predicted by the proximity model is qualitatively consistent with the actual coupling angle variations in Fe/Mn/Fe(0 0 1) measured with scanning electron microscopy with polarization analysis (SEMPA). Going beyond the proximity model and allowing for a non-uniform magnetization of the thin Fe overlayer provides an improved explanation of the results. We contrast the behavior of Fe/Mn/Fe(0 0 1), where the proximity model appears applicable, to coupling through antiferro-magnetic Cr in Fe/Cr/Fe(0 0 1), where it is not, and discuss possible reasons for the difference.

Interlayer exchange coupling in complex magnetic multilayers

We extend the hole confinement model of Edwards et al. to the problem of two kinds of complex magnetic sandwich structures. One is the magnetic sandwich covered on both sides by nonmagnetic films (case 1) and the other is that covered by magnetic films (case 2). The interlayer exchange coupling and the angular dependence of coupling energy in the two cases are investigated systematically. For case 1, our results show that the magnetic and outer nonmagnetic films influence significantly the oscillation behavior of exchange coupling and the appearance of noncollinear exchange coupling is very sensitive to the thickness of magnetic and outer nonmagnetic layers. Our results also show that the nonoscillatory component of the coupling generally varies with the thickness of magnetic (outer nonmagnetic) films and the results in the case where the thickness of both magnetic (outer nonmagnetic) films vary simultaneously are significantly different from that in the case where the thickness of one of the two magnetic (outer nonmagnetic) films is fixed while the other is varied, which is qualitatively in agreement with the experimental measurements. For case 2, the exponential dependence of exchange coupling on the thickness of the intermagnetic layer has been obtained, similar to the Parkin's experimental results for giant magnetoresistance.

Structure of single-molecule single crystals of isotactic polystyrene and their radiation resistance

Based on the one-band tight-binding model, we systematically investigate the interlayer exchange coupling and the angular dependence of the coupling energy in a magnetic sandwich covered on both sides by nonmagnetic films. Our results show that (i) the thickness of magnetic and outer nonmagnetic films influence significantly the oscillatory behavior of exchange coupling, (ii) the appearance of noncollinear exchange coupling is very sensitive to the thickness of magnetic and outer nonmagnetic layers, (iii) the nonoscillatory component of the coupling varies generally with the thickness of magnetic or outer nonmagnetic films, and (iv) the results in the case where the thickness of both magnetic or both outer nonmagnetic films vary simultaneously are significantly different from that in the case where the thickness of one of the two magnetic or outer nonmagnetic films is fixed while the other is varied. These results are qualitatively in agreement with the experimental measurements. (C) 1998 American Institute of Physics. [S0021-8979(98)02302-0].

Interlayer exchange coupling: Effect of magnetic and outer nonmagnetic films

Based on the one-band tight-binding model, we systematically investigate the interlayer exchange coupling and the angular dependence of the coupling energy in a magnetic sandwich covered on both sides by nonmagnetic films. Our results show that (i) the thickness of magnetic and outer nonmagnetic films influence significantly the oscillatory behavior of exchange coupling, (ii) the appearance of noncollinear exchange coupling is very sensitive to the thickness of magnetic and outer nonmagnetic layers, (iii) the nonoscillatory component of the coupling varies generally with the thickness of magnetic or outer nonmagnetic films, and (iv) the results in the case where the thickness of both magnetic or both outer nonmagnetic films vary simultaneously are significantly different from that in the case where the thickness of one of the two magnetic or outer nonmagnetic films is fixed while the other is varied. These results are qualitatively in agreement with the experimental measurements.

Magnetic Structure of Cr in Exchange Coupled Fe/Cr(001) Superlattices

We demonstrate how the noncollinear exchange coupling between the Fe layers in Fe/Cr(001) superlattices is caused by a frustrated spiral modulation of the Cr moments not observed in bulk. The noncollinear coupling vanishes above the N\'eel temperature of this commensurate antiferromagnetic Cr order. This clarifies the essential contribution of Cr ordering to the coupling in the regime of smallest thicknesses where no incommensurate Cr spin density wave can form. For larger Cr thicknesses we observe a predicted incommensurate to commensurate transition with temperature.

Angular Dependence of the Interlayer Exchange Coupling on the Nonmagnetic Cap Layers

Based on the one-band tight-binding model, the angular dependence of interlayer exchange coupling was investigated on the nonmagnetic cap layers in a magnetic sandwich covered on both sides by nonmagnetic films. The results show that (1) the appearance of noncollinear exchange coupling is very sensitive to the cap layers, (2) the nonoscillatory component of the coupling strength varies generally with the thickness of outer nonmagnetic films, and (3) the variation of exchange coupling exhibits distinct features in the cases where the thicknesses of both outer nonmagnetic films vary simultaneously and where the thickness of one of the two outer nonmagnetic films is fixed while the other is varied.

Noncollinear interlayer exchange coupling caused by interface spin-orbit interaction

The interlayer exchange couplings between neighboring ferromagnetic layers in ferromagnetic-nonmagnetic multilayer structures are derived analytically in the frame of the extended Anderson s-d mixing model with spin-orbit interaction. After transforming the extended Anderson mixing model into an s-d exchange model and taking into account the spin frustration at interfaces, the second-order perturbation calculation naturally gives rise to both the noncollinear Dzyaloshinski-Moriya (DM) exchange coupling as well as the usual isotropic Ruderman-Kittel-Kasuya-Yosida exchange coupling between the neighboring ferromagnetic layers. The isotropic and anisotropic exchange couplings have a decaying oscillatory behavior as a function of spacer layer thickness, but they differ by a phase factor of \ensuremath{\pi}/2. While the exact value of the DM coupling depends on the material parameters as well as the interface s-d mixing effect, a rough estimate suggests that it is significant. Thus our result offers an alternative explanation to the noncollinear exchange coupling as was observed in the experiments.

Correlation between non-collinear exchange coupling and interface structure in Fe/Cr(001) superlattices

Using polarized neutron reflectometry with polarization analysis we have studied the non-collinear interlayer exchange coupling in Fe/Cr(0 0 1) superlattices as a function of growth temperature. From diffuse X-ray spectra we find that the occurence of non-collinear spin structures is correlated with long range lateral Cr-thickness fluctuations which, in turn, depend on the growth temperature. This finding leads the way to a better understanding of the origin of non-collinear coupling in Fe/Cr(0 0 1).