Revealing antiferromagnetic order of the Fe monolayer on W(001): spin-polarized scanning tunneling microscopy and first-principles calculations

Investigation of the temperature phase diagram of the 2D semi-classical ferrimagneticJ1-J2model

The temperature phase diagram (ToverJ₂) of the 2D semiclassicalJ1-J2Heisenberg model is discussed. The investigation was carried out using the self-consistent Bloch equation and a quantum statistical description of the magnetization. In addition to the three states of the zero-temperature phase diagram, theJ2-Tphase diagram shows two new phases, the paramagnetic phase and the semi-paramagneticS1-Néel state. The five occurring ground states, as well as the transitions between these states, are discussed. In particular, attention is paid to the interplay between temperature and frustration.

Discovery and characterization of a new type of domain wall in a row-wise antiferromagnet

Antiferromagnets have recently moved into the focus of application-related research, with the perspective to use them in future spintronics devices. At the same time the experimental determination of the detailed spin texture remains challenging. Here we use spin-polarized scanning tunneling microscopy to investigate the spin structure of antiferromagnetic domain walls. Comparison with spin dynamics simulations allows the identification of a new type of domain wall, which is a superposition state of the adjacent domains. We determine the relevant magnetic interactions and derive analytical formulas. Our experiments show a pathway to control the number of domain walls by boundary effects, and demonstrate the possibility to change the position of domain walls by interaction with movable adsorbed atoms. The knowledge about the exact spin structure of the domain walls is crucial for an understanding and theoretical modelling of their properties regarding, for instance, dynamics, response in transport experiments, and manipulation.

Antiferromagnets (AFM) exhibit faster magnetization dynamics, and have immunity to stray fields, making AFMs attractive for spintronic devices. Here, the authors investigate the behaviour of domain walls in AFMs, and find a new type domain wall, a superposition of two adjacent rotational domains.

Persistence of Magnetism in Atomically Thin MnPS3 Crystals

The magnetic state of atomically thin semiconducting layered antiferromagnets such as CrI₃ and CrCl₃ can be probed by forming tunnel barriers and measuring their resistance as a function of magnetic field (H) and temperature (T). This is possible because the spins within each individual layer are ferromagnetically aligned and the tunneling magnetoresistance depends on the relative orientation of the magnetization in adjacent layers. The situation is different for systems that are antiferromagnetic within the layers in which case it is unclear whether magnetoresistance measurements can provide information about the magnetic state. Here, we address this issue by investigating tunnel transport through atomically thin crystals of MnPS₃, a van der Waals semiconductor that in the bulk exhibits easy-axis antiferromagnetic order within the layers. For thick multilayers below T ∼ 78 K, a T-dependent magnetoresistance sets in at μ₀H ∼ 5 T and is found to track the boundary between the antiferromagnetic and the spin-flop phases known from bulk measurements. We show that the magnetoresistance persists as thickness is reduced with nearly unchanged characteristic temperature and magnetic field scales, albeit with a different dependence on H, indicating the persistence of magnetism in the ultimate limit of individual monolayers.

Tunable magnetic ground states of iron monolayer on nonmagnetic metallic substrates by small in-plane strains

The magnetic states of one single atomic layer of iron epitaxially grown on 4d and 5d nonmagnetic metals are studied under strain systematically using first principle calculations. Our results show that, without strain, the iron on top of different 4d and 5d nonmagnetic metals shows distinct antiferromagnetic or ferromagnetic ground states: a parallel antiferromagnetic ground state (p-AFM) on Rh and a central antiferromagnetic ground state (c-AFM) on Ir and ferromagnetic (FM) ground state on Pd, Ag, Pt and Au. However, when introducing in-plane biaxial and uniaxial strain (Δε xx ) on the substrates, the ground state of iron can be manipulated easily. In detail, for biaxial strain, the ground state of iron on an Rh substrate becomes FM when Δε xx < -2.0% and c-AFM when Δε xx > 0.8%, and on an Ir substrate, the ground state of iron becomes FM when Δε xx < -2.8% and c-AFM when Δε xx > -0.8%. However, for the uniaxial strain along the x direction, while using the corresponding Poisson's ratios to determine the strain along the y direction, the ground state of iron on an Rh substrate remains the p-AFM state, but on an Ir substrate, the ground state of iron changes from c-AFM to p-AFM at Δε xx = 0.2% or Δε xx = -0.3% along the x direction respectively.

Indirect chiral magnetic exchange through Dzyaloshinskii-Moriya-enhanced RKKY interactions in manganese oxide chains on Ir(100)

Localized electron spins can couple magnetically via the Ruderman-Kittel-Kasuya-Yosida interaction even if their wave functions lack direct overlap. Theory predicts that spin-orbit scattering leads to a Dzyaloshinskii-Moriya type enhancement of this indirect exchange interaction, giving rise to chiral exchange terms. Here we present a combined spin-polarized scanning tunneling microscopy, angle-resolved photoemission, and density functional theory study of MnO₂ chains on Ir(100). Whereas we find antiferromagnetic Mn-Mn coupling along the chain, the inter-chain coupling across the non-magnetic Ir substrate turns out to be chiral with a 120° rotation between adjacent MnO₂ chains. Calculations reveal that the Dzyaloshinskii-Moriya interaction results in spin spirals with a periodicity in agreement with experiment. Our findings confirm the existence of indirect chiral magnetic exchange, potentially giving rise to exotic phenomena, such as chiral spin-liquid states in spin ice systems or the emergence of new quasiparticles.

Bulk ferromagnetic tips for spin-polarized scanning tunneling microscopy

We characterized the performance of electrochemically etched bulk Fe and Ni tips as a probe of spin-polarized scanning tunneling microscopy (SP-STM). Through the observation of the striped contrast on the conical spin-spiral structure formed in Mn double layers on a W(110) substrate, the capability of both the tips to detect the magnetic signal was clarified. We also confirmed that the magnetized direction of the Fe and Ni tips can be flipped between the two out-of-plane directions by external magnetic fields. Our results demonstrate that the ex-situ prepared tips are reliable in SP-STM for the samples that are not susceptible to a stray magnetic field.

Density functional theory calculations for magnetic properties of Co3W systems

Cheaper permanent magnetic nanostructures with magnetic properties equivalent to those of noble-metal or rare-earth nanomagnets have been experimentally developed for their potential applications in ultrahigh storage densities in magnetic memory. To date, their intrinsic magnetic properties are not well understood under the micro-level of local atomic arrangements and electronic structures. In this work, we performed theoretical investigations on the Co₃W bulk, the clean surface, nanoclusters, and the Co|Co₃W bilayers and superlattices for their geometrical structures, magnetic moments, and magnetic anisotropy energies (MAEs). We found that the Co₃W nanostructures we constructed are stable and have the local minima in the energetic landscape, whose stabilities increase with increasing proportion of W and cluster size. The Co and W atoms in clusters are antiferromagnetically coupled, and their local magnetic moments decrease with increasing proportion of W. The breakdown of the Hund's third rule in W atoms observed in experiment can be interpreted as the competition between the intra-atomic spin-orbit coupling in W atoms and interatomic Co-W hybridizations. The highest MAE of about a few tens of meV is obtained in small cluster sizes, whereas it is an order of magnitude reduction in large cluster sizes. The magnetic systems of Co₃W clean surface, Co|Co₃W bilayer and superlattice can present large MAEs, and their easy-axes of magnetization are perpendicular to the (001) surface. Our calculated MAEs are of the same order of magnitude as that of the experimental measurements, and the electronic origin is revealed through the second-order perturbation method.

Magnetic exchange force microscopy: theoretical analysis of induced magnetization reversals

In magnetic exchange force microscopy a magnetic tip is scanned over the surface of a solid and an image representing the exchange interaction recorded. Sudden changes in the image corresponding to magnetization switching can be monitored as a function of the tip-surface distance thereby giving important information about the lifetime of metastable magnetic states and how it is affected by the exchange interaction. Here, theoretical calculations are carried out to study the tip-surface interaction and determine the mechanism and rate of transitions in a magnetic exchange force microscopy experiment, and comparison made with reported experimental data on an Fe cluster interacting with an antiferromagnetic Fe overlayer on a W(001) surface. The activation energy was determined from calculations of minimum energy paths and the pre-exponential factor in the Arrhenius rate expression evaluated from harmonic transition state theory, extended to account for zero modes. A noncollinear extension of the Alexander-Anderson model was used to describe the magnetic properties of an atomic scale representation of the system. The calculations reveal how the tip size, tip-surface distance and magnetic field affect the lifetime of the magnetic states.

The Bethe-Slater curve revisited; new insights from electronic structure theory

The Bethe-Slater (BS) curve describes the relation between the exchange coupling and interatomic distance. Based on a simple argument of orbital overlaps, it successfully predicts the transition from antiferromagnetism to ferromagnetism, when traversing the 3d series. In a previous article [Phys. Rev. Lett. 116, 217202 (2016)] we reported that the dominant nearestneighbour (NN) interaction for 3d metals in the bcc structure indeed follows the BS curve, but the trends through the series showed a richer underlying physics than was initially assumed. The orbital decomposition of the inter-site exchange couplings revealed that various orbitals contribute to the exchange interactions in a highly non-trivial and sometimes competitive way. In this communication we perform a deeper analysis by comparing 3d metals in the bcc and fcc structures. We find that there is no coupling between the E_g orbitals of one atom and T_2g orbitals of its NNs, for both cubic phases. We demonstrate that these couplings are forbidden by symmetry and formulate a general rule allowing to predict when a similar situation is going to happen. In γ-Fe, as in α-Fe, we find a strong competition in the symmetry-resolved orbital contributions and analyse the differences between the high-spin and low-spin solutions.

Coupling of Coexisting Noncollinear Spin States in the Fe Monolayer on Re(0001)

Spin-polarized scanning tunneling microscopy is used to investigate the magnetic state of the Fe monolayer on Re(0001). Two coexisting atomic-scale noncollinear spin textures are observed with a sharp transition between them on the order of the atomic lattice spacing. A position correlation between the two spin states is observed both in experiments and in Monte Carlo simulations, demonstrating their coupling behavior.

Coexistence of charge and ferromagnetic order in fcc Fe

Phase coexistence phenomena have been intensively studied in strongly correlated materials where several ordered states simultaneously occur or compete. Material properties critically depend on external parameters and boundary conditions, where tiny changes result in qualitatively different ground states. However, up to date, phase coexistence phenomena have exclusively been reported for complex compounds composed of multiple elements. Here we show that charge- and magnetically ordered states coexist in double-layer Fe/Rh(001). Scanning tunnelling microscopy and spectroscopy measurements reveal periodic charge-order stripes below a temperature of 130 K. Close to liquid helium temperature, they are superimposed by ferromagnetic domains as observed by spin-polarized scanning tunnelling microscopy. Temperature-dependent measurements reveal a pronounced cross-talk between charge and spin order at the ferromagnetic ordering temperature about 70 K, which is successfully modelled within an effective Ginzburg-Landau ansatz including sixth-order terms. Our results show that subtle balance between structural modifications can lead to competing ordering phenomena.

Quantum well states and amplified spin-dependent Friedel oscillations in thin films

Electrons mediate many of the interactions between atoms in a solid. Their propagation in a material determines its thermal, electrical, optical, magnetic and transport properties. Therefore, the constant energy contours characterizing the electrons, in particular the Fermi surface, have a prime impact on the behaviour of materials. If anisotropic, the contours induce strong directional dependence at the nanoscale in the Friedel oscillations surrounding impurities. Here we report on giant anisotropic charge density oscillations focused along specific directions with strong spin-filtering after scattering at an oxygen impurity embedded in the surface of a ferromagnetic thin film of Fe grown on W(001). Utilizing density functional theory, we demonstrate that by changing the thickness of the Fe films, we control quantum well states confined to two dimensions that manifest as multiple flat energy contours, impinging and tuning the strength of the induced charge oscillations which allow to detect the oxygen impurity at large distances (≈50 nm).

Interface-induced chiral domain walls, spin spirals and skyrmions revealed by spin-polarized scanning tunneling microscopy

The spin textures of ultra-thin magnetic layers exhibit surprising variety. The loss of inversion symmetry at the interface of the magnetic layer and substrate gives rise to the so-called Dzyaloshinskii-Moriya interaction which favors non-collinear spin arrangements with unique rotational sense. Here we review the application of spin-polarized scanning tunneling microscopy to such systems, which has led to the discovery of interface-induced chiral domain walls and spin spirals. Recently, different interface-driven skyrmion lattices have been found, and the writing as well as the deleting of individual skyrmions based on local spin-polarized current injection has been demonstrated. These interface-induced non-collinear magnetic states offer new exciting possibilities to study fundamental magnetic interactions and to tailor material properties for spintronic applications.

Spin-correlations and magnetic structure in an Fe monolayer on 5d transition metal surfaces

We present a detailed first principles study on the magnetic structure of an Fe monolayer on different surfaces of 5d transition metals. We use the spin-cluster expansion technique to obtain parameters of a spin model, and predict the possible magnetic ground state of the studied systems by employing the mean field approach and, in certain cases, by spin dynamics calculations. We point out that the number of shells considered for the isotropic exchange interactions plays a crucial role in the determination of the magnetic ground state. In the case of Ta substrate we demonstrate that the out-of-plane relaxation of the Fe monolayer causes a transition from ferromagnetic to antiferromagnetic ground state. We examine the relative magnitude of nearest neighbour Dzyaloshinskii-Moriya (D) and isotropic (J) exchange interactions in order to get insight into the nature of magnetic pattern formations. For the Fe/Os(0 0 0 1) system we calculate a very large D/J ratio, correspondingly, a spin spiral ground state. We find that, mainly through the leading isotropic exchange and Dzyaloshinskii-Moriya interactions, the inward layer relaxation substantially influences the magnetic ordering of the Fe monolayer. For the Fe/Re(0 0 0 1) system characterized by large antiferromagnetic interactions we also determine the chirality of the 120° Néel-type ground state.

Magnetic properties of bcc-Fe(001)/C₆₀ interfaces for organic spintronics

The magnetic structure of the interfaces between organic semiconductors and ferromagnetic contacts plays a key role in the spin injection and extraction processes in organic spintronic devices. We present a combined computational (density functional theory) and experimental (X-ray magnetic circular dichroism) study on the magnetic properties of interfaces between bcc-Fe(001) and C(60) molecules. C(60) is an interesting candidate for application in organic spintronics due to the absence of hydrogen atoms and the associated hyperfine fields. Adsorption of C(60) on Fe(001) reduces the magnetic moments on the top Fe layers by ∼6%, while inducing an antiparrallel magnetic moment of ∼-0.2 μ(B) on C(60). Adsorption of C(60) on a model ferromagnetic substrate consisting of three Fe monolayers on W(001) leads to a different structure but to very similar interface magnetic properties.

Magnetic phases of cobalt atomic clusters on tungsten

First-principle calculations are employed to show that the magnetic structure of small atomic clusters of Co, formed on a crystalline W(110) surface and containing 3-12 atoms, strongly deviates from the usual stable ferromagnetism of Co in other systems. The clusters are ferri-, ferro- or non-magnetic, depending on cluster size and geometry. We determine the atomic Co moments and their relative alignment, and show that antiferromagnetic spin alignment in the Co clusters is caused by hybridization with the tungsten substrate and band filling. This is in contrast with the typical strong ferromagnetism of bulk Co alloys, and ferromagnetic coupling in Fe/W(110) clusters.

Quantitative measurement of the magnetic exchange interaction across a vacuum gap

We demonstrate that magnetic exchange force spectroscopy allows for a quantitative determination of the distance-dependent magnetic exchange interaction across a vacuum gap. Experiments were performed on the antiferromagnetic Fe monolayer on W(001) with magnetically sensitive tips and compared to first-principles calculations performed for different cluster tip models. For stable tips, which can be distinguished from unstable tips by analyzing the dissipation signal, very good agreement with theory is observed.

Magnetic surface nanostructures

Recent trends in the emerging field of surface-supported magnetic nanostructures are reviewed. Current strategies for nanostructure synthesis are summarized, followed by a predominantly theoretical description of magnetic phenomena in surface magnetic structures and a review of experimental research in this field. Emphasis is on Fe- or Co-based nanostructures in various low-dimensional geometries, which are studied as model systems to explore the effects of dimensionality, atomic coordination, chemical bonds, alloying and, most importantly, interactions with the supporting substrate on the magnetism. This review also includes a discussion of closely related systems, such as 3d element impurities integrated into organic networks, surface-supported Fe-based molecular magnets, Kondo systems or 4d element nanostructures that exhibit emergent magnetism, thereby bridging the traditional areas of surface science, molecular physics and nanomagnetism.

The Quest for Nanoscale Magnets: The example of [Mn12] Single Molecule Magnets

Recent advances on the organization and characterization of [Mn12] single molecule magnets (SMMs) on a surface or in 3D are reviewed. By using nonconventional techniques such as X-ray magnetic circular dichroism (XMCD) and scanning tunneling microscopy (STM), it is shown that [Mn12]-based SMMs deposited on a surface lose their SMM behavior, even though the molecules seem to be structurally undamaged. A new approach is reported to get high-density information-storage devices, based on the 3D assembling of SMMs in a liquid crystalline phase. The 3D nanostructure exhibits the anisotropic character of the SMMs, thus opening the way to address micrometric volumes by two photon absorption using the pump-probe technique. We present recent developments such as µ-SQUID, magneto-optical Kerr effect (MOKE), or magneto-optical circular dichroism (MOCD), which enable the characterization of SMM nanostructures with exceptional sensitivity. Further, the spin-polarized version of the STM under ultrahigh vacuum is shown to be the key tool for addressing not only single molecule magnets, but also magnetic nano-objects.

Temperature and size dependence of antiferromagnetism in mn nanostructures

We report on variable-temperature STM investigations of the spontaneous long-range magnetic order of Mn monolayer nanostructures epitaxially grown on stepped W(110). The measurements reveal that the onset of the antiferromagnetic order is closely related to the Mn nanostructure width along the [001] direction, with a decreasing Néel temperature as we move from a 2D toward a quasi-1D system. In contrast, lateral confinement along the [110] direction seems to play a less important role. The results are discussed in terms of anisotropic exchange coupling and of boundary effects, both potentially stabilizing long-range magnetic order in nanostructures confined in the [110] direction.

Magnetic phase control in monolayer films by substrate tuning

We propose tailoring exchange interactions in magnetic monolayer films by tuning the adjacent nonmagnetic substrate. As an example, we demonstrate a ferromagnetic-antiferromagnetic phase transition for one monolayer Fe on a Ta(x)W(1-x)(001) surface as a function of the Ta concentration. At the critical Ta concentration, the nearest-neighbor exchange interaction is small and the magnetic phase space is dramatically broadened. Complex magnetic order such as spin spirals, multiple-Q, or even disordered local moment states can occur, offering the possibility of storing information in terms of ferromagnetic dots in an otherwise zero-magnetization state matrix.

Observing spin polarization of individual magnetic adatoms

We have used spin-polarized scanning tunneling spectroscopy to observe the spin polarization state of individual Fe and Cr atoms adsorbed onto Co nanoislands. These magnetic adatoms exhibit stationary out-of-plane spin polarization, but have opposite sign of the exchange coupling between electron states of the adatom and the Co island surface state: Fe adatoms exhibit parallel spin polarization to the Co surface state while Cr adatoms exhibit antiparallel spin polarization. First-principles calculations predict ferromagnetic and antiferromagnetic alignment of the spin moment for individual Fe and Cr adatoms on a Co film, respectively, implying negative spin polarization for Fe and Cr adatoms over the energy range of the Co surface state.

Chiral magnetic order at surfaces driven by inversion asymmetry

Chirality is a fascinating phenomenon that can manifest itself in subtle ways, for example in biochemistry (in the observed single-handedness of biomolecules) and in particle physics (in the charge-parity violation of electroweak interactions). In condensed matter, magnetic materials can also display single-handed, or homochiral, spin structures. This may be caused by the Dzyaloshinskii-Moriya interaction, which arises from spin-orbit scattering of electrons in an inversion-asymmetric crystal field. This effect is typically irrelevant in bulk metals as their crystals are inversion symmetric. However, low-dimensional systems lack structural inversion symmetry, so that homochiral spin structures may occur. Here we report the observation of magnetic order of a specific chirality in a single atomic layer of manganese on a tungsten (110) substrate. Spin-polarized scanning tunnelling microscopy reveals that adjacent spins are not perfectly antiferromagnetic but slightly canted, resulting in a spin spiral structure with a period of about 12 nm. We show by quantitative theory that this chiral order is caused by the Dzyaloshinskii-Moriya interaction and leads to a left-rotating spin cycloid. Our findings confirm the significance of this interaction for magnets in reduced dimensions. Chirality in nanoscale magnets may play a crucial role in spintronic devices, where the spin rather than the charge of an electron is used for data transmission and manipulation. For instance, a spin-polarized current flowing through chiral magnetic structures will exert a spin-torque on the magnetic structure, causing a variety of excitations or manipulations of the magnetization and giving rise to microwave emission, magnetization switching, or magnetic motors.

Asymmetric domain nucleation and unusual magnetization reversal in ultrathin Co films with perpendicular anisotropy

We report unexpected phenomena during magnetization reversal in ultrathin Co films and Co/Pt multilayers with perpendicular anisotropy. Using magneto-optical Kerr microscopy and magnetic force microscopy we have observed asymmetrical nucleation centers where the reversal begins for one direction of the field only and is characterized by an acute asymmetry of domain-wall mobility. We have also observed magnetic domains with a continuously varying average magnetization, which can be explained in terms of the coexistence of three magnetic phases: up, down, and striped.

Magnetic exchange force microscopy with atomic resolution

The ordering of neighbouring atomic magnetic moments (spins) leads to important collective phenomena such as ferromagnetism and antiferromagnetism. A full understanding of magnetism on the nanometre scale therefore calls for information on the arrangement of spins in real space and with atomic resolution. Spin-polarized scanning tunnelling microscopy accomplishes this but can probe only conducting materials. Force microscopy can be used on any sample independent of its conductivity. In particular, magnetic force microscopy is well suited to exploring ferromagnetic domain structures. However, atomic resolution cannot be achieved because data acquisition involves the sensing of long-range magnetostatic forces between tip and sample. Magnetic exchange force microscopy has been proposed for overcoming this limitation: by using an atomic force microscope with a magnetic tip, it should be possible to detect the short-range magnetic exchange force between tip and sample spins. Here we show for a prototypical antiferromagnetic insulator, the (001) surface of nickel oxide, that magnetic exchange force microscopy can indeed reveal the arrangement of both surface atoms and their spins simultaneously. In contrast with previous attempts to implement this method, we use an external magnetic field to align the magnetic polarization at the tip apex so as to optimize the interaction between tip and sample spins. This allows us to observe the direct magnetic exchange coupling between the spins of the tip atom and sample atom that are closest to each other, and thereby demonstrate the potential of magnetic exchange force microscopy for investigations of inter-spin interactions at the atomic level.

Atomic spin structure of antiferromagnetic domain walls

The search for uncompensated magnetic moments on antiferromagnetic surfaces is of great technological importance as they are responsible for the exchange-bias effect that is widely used in state-of-the-art magnetic storage devices. We have studied the atomic spin structure of phase domain walls in the antiferromagnetic Fe monolayer on W(001) by means of spin-polarized scanning tunnelling microscopy and Monte Carlo simulations. The domain wall width only amounts to 6-8 atomic rows. Although walls oriented along <100> directions are found to be fully compensated, detailed analysis of <110>-oriented walls reveals an uncompensated perpendicular magnetic moment. Our result represents a major advance in the field of antiferromagnetism, and may lead to a better understanding of the magnetic interaction between ferromagnetic and antiferromagnetic materials.

Observation of a complex nanoscale magnetic structure in a hexagonal Fe monolayer

We have observed a novel magnetic structure in the pseudomorphic Fe monolayer on Ir(111). Using spin-polarized scanning tunneling microscopy we find a nanometer-sized two-dimensional magnetic unit cell. A collinear magnetic structure is proposed consisting of 15 Fe atoms per unit cell with 7 magnetic moments pointing in one and 8 moments in the opposite direction. First-principles calculations verify that such an unusual magnetic state is indeed lower in energy than all solutions of the classical Heisenberg model. We demonstrate that the complex magnetic structure is induced by the strong Fe-Ir hybridization.