Erratum: Equilibrium Magnetization at the Boundary of a Magnetoelectric Antiferromagnet

The Letter [1] should have acknowledged and cited the work by Andreev [2], which was inadvertently overlooked. This latter work introduced a phenomenological surface magnetization and concluded, by analyzing exchange invariants, that it may be finite for all antiferromagnets and that those with unbroken macroscopic time-reversal symmetry can exhibit surface magnetization domains. These arguments are highly relevant to Ref. [1], which I happily acknowledge. The work [1] treats the problem of (otherwise poorly defined) boundary magnetization as a special case of a general, microscopically definable probe functional, explicitly taking into account boundary roughness and allowing for relativistic interactions. It also spells out the implications for electrically controlled magnetism using magnetoelectric and multiferroic materials

Spin density in frustrated magnets under mechanical stress: Mn-based antiperovskites

In this paper we present results of our calculations of the non-collinear spin density distribution in the systems with frustrated triangular magnetic structure (Mn-based antiperovskite compounds, Mn_{3}AN (A=Ga, Zn)) in the ground state and under external mechanical strain. We show that the spin density in the (111)-plane of the unit cell forms a "domain" structure around each atomic site but it has a more complex structure than the uniform distribution of the rigid spin model, i.e. Mn atoms in the (111)-plane form non-uniform "spin clouds", with the shape and size of these "domains" being function of strain. We show that both magnitude and direction of the spin density change under compressive and tensile strains, and the orientation of "spin domains" correlates with the reversal of the strain, i.e. switching compressive to tensile strain (and vice versa) results in "reversal" of the domains. We present analysis for the intra-atomic spin-exchange interaction and the way it affects the spin density distribution. In particular, we show that the spin density inside the atomic sphere in the system under mechanical stress depends on the degree of localization of electronic states

Interfacial contributions to spin-orbit torque and magnetoresistance in ferromagnet/heavy-metal bilayers

The thickness dependence of spin-orbit torque and magnetoresistance in ferromagnet/heavy-metal bilayers is studied using the first-principles nonequilibrium Green’s function formalism combined with the Anderson disorder model. A systematic expansion in orthogonal vector spherical harmonics is used for the angular dependence of the torque. The dampinglike torque in Co/Pt and Co/Au bilayers can be described as a sum of the spin-Hall contribution, which increases with thickness in agreement with the spin-diffusion model, and a comparable interfacial contribution. The magnetoconductance in the plane perpendicular to the current in Co/Pt bilayers is of the order of a conductance quantum per interfacial atom, exceeding the prediction of the spin-Hall model by more than an order of magnitude. This suggests that the “spin-Hall magnetoresistance,” similarly to the dampinglike torque, has a large interfacial contribution unrelated to the spin-Hall effect

Spin-fluctuation mechanism of anomalous temperature dependence of magnetocrystalline anisotropy in itinerant magnets

The origins of the anomalous temperature dependence of magnetocrystalline anisotropy in (Fe$_{1-x}$Co$_{x}$)$_{2}$B alloys are elucidated using first-principles calculations within the disordered local moment model. Excellent agreement with experimental data is obtained. The anomalies are associated with the changes in band occupations due to Stoner-like band shifts and with the selective suppression of spin-orbit "hot spots" by thermal spin fluctuations. Under certain conditions, the anisotropy can increase, rather than decrease, with decreasing magnetization due to these peculiar electronic mechanisms, which contrast starkly with those assumed in existing models.Comment: 9 pages, 10 figures (including supplemental material

Influence of strain and chemical substitution on the magnetic anisotropy of antiferromagnetic Cr\u3csub\u3e2\u3c/sub\u3eO\u3csub\u3e3\u3c/sub\u3e: An \u3ci\u3eab-initio\u3c/i\u3e study

The influence of the mechanical strain and chemical substitution on the magnetic anisotropy energy (MAE) of Cr2O3 is studied using first-principles calculations. Dzyaloshinskii-Moriya interaction contributes substantially to MAE by inducing spin canting when the antiferromagnetic order parameter is not aligned with the hexagonal axis. Nearly cubic crystal field results in a very small MAE in pure Cr2O3 at zero strain, which is incorrectly predicted to be negative (in-plane) on account of spin canting. The MAE is strongly modified by epitaxial strain, which tunes the crystal-field splitting of the t2g triplet. The contribution from magnetic dipolar interaction is very small at any strain. The effects of cation (Al, Ti, V, Co, Fe, Nb, Zr, Mo) and anion (B) substitutions on MAE are examined. Al increases MAE thanks to the local lattice deformation. In contrast, the electronic configuration of V and Nb strongly promotes easy-plane anisotropy, while other transition-metal dopants have only a moderate effect on MAE. Substitution of oxygen by boron, which has been reported to increase the Néel temperature, has a weak effect on MAE, whose sign depends on the charge state of B. The electric field applied along the (0001) axis has a weak second-order effect on the MAE

Proximitized Materials

Advances in scaling down heterostructures and having an improved interface quality together with atomically-thin two-dimensional materials suggest a novel approach to systematically design materials. A given material can be transformed through proximity effects whereby it acquires properties of its neighbors, for example, becoming superconducting, magnetic, topologically nontrivial, or with an enhanced spin-orbit coupling. Such proximity effects not only complement the conventional methods of designing materials by doping or functionalization, but can also overcome their various limitations. In proximitized materials it is possible to realize properties that are not present in any constituent region of the considered heterostructure. While the focus is on magnetic and spin-orbit proximity effects with their applications in spintronics, the outlined principles provide also a broader framework for employing other proximity effects to tailor materials and realize novel phenomena.Comment: Invited Review to appear in Materials Today, 28 pages, 22 figure

Effective gating and tunable magnetic proximity effects in two-dimensional heterostructures

Electrostatic gating enables key functionality in modern electronic devices by altering the properties of materials. While classical electrostatics is usually sufficient to understand the effects of gating in extended systems, the inherent quantum properties of gating in nanostructures offer unexplored opportunities for materials and devices. Using first-principles calculations for Co/bilayer graphene, Co/BN/graphene, and Co/BN/benzene, as well as a simple physical model, we show that heterostructures with two-dimensional materials yield tunable magnetic proximity effects. van der Waals bonding is identified as a requirement for large electronic structure changes by gating, enabling both the magnitude and sign change of spin polarization in physisorbed graphene. The ability to electrically reverse the spin polarization of an electrode provides an alternative to using the applied magnetic field or spin transfer torque in spintronic devices, thus transforming a spin valve into a spin transistor

Interfacial contributions to spin-orbit torque and magnetoresistance in ferromagnet/heavy-metal bilayers

The thickness dependence of spin-orbit torque and magnetoresistance in ferromagnet/heavy-metal bilayers is studied using the first-principles nonequilibrium Green’s function formalism combined with the Anderson disorder model. A systematic expansion in orthogonal vector spherical harmonics is used for the angular dependence of the torque. The dampinglike torque in Co/Pt and Co/Au bilayers can be described as a sum of the spin-Hall contribution, which increases with thickness in agreement with the spin-diffusion model, and a comparable interfacial contribution. The magnetoconductance in the plane perpendicular to the current in Co/Pt bilayers is of the order of a conductance quantum per interfacial atom, exceeding the prediction of the spin-Hall model by more than an order of magnitude. This suggests that the “spin-Hall magnetoresistance,” similarly to the dampinglike torque, has a large interfacial contribution unrelated to the spin-Hall effect

Theory of Spin Loss at Metallic Interfaces

Interfacial spin-flip scattering plays an important role in magnetoelectronic devices. Spin loss at metallic interfaces is usually quantified by matching the magnetoresistance data for multilayers to the Valet-Fert model, while treating each interface as a fictitious bulk layer whose thickness is δ times the spin-diffusion length. By employing the properly generalized circuit theory and the scattering matrix approaches, we derive the relation of the parameter δ to the spin-flip transmission and reflection probabilities at an individual interface. It is found that δ is proportional to the square root of the probability of spin-flip scattering. We calculate the spin-flip scattering probabilities for flat and rough Cu/Pd interfaces using the Landauer-Büttiker method based on the first-principles electronic structure and find δ to be in reasonable agreement with experiment

Theory of Spin Loss at Metallic Interfaces

Interfacial spin-flip scattering plays an important role in magnetoelectronic devices. Spin loss at metallic interfaces is usually quantified by matching the magnetoresistance data for multilayers to the Valet-Fert model, while treating each interface as a fictitious bulk layer whose thickness is δ times the spin-diffusion length. By employing the properly generalized circuit theory and the scattering matrix approaches, we derive the relation of the parameter δ to the spin-flip transmission and reflection probabilities at an individual interface. It is found that δ is proportional to the square root of the probability of spin-flip scattering. We calculate the spin-flip scattering probabilities for flat and rough Cu/Pd interfaces using the Landauer-Büttiker method based on the first-principles electronic structure and find δ to be in reasonable agreement with experiment