Reversible transition between perpendicular and in-plane magnetization in ultrathin films

Temperature Induced Reversible Switching of the Magnetic Anisotropy in a Neodymium Complex Adsorbed on Graphite

Controlling the magnetic anisotropy of molecular layers assembled on a surface is one of the challenges that needs to be addressed to create the next-generation spintronic devices. Recently, metal complexes that show a reversible solid-state switch of their magnetic anisotropy in response to physical stimuli, such as temperature and magnetic field, have been discovered. The complex Nd(trensal) (H3trensal = 2,2',2''-tris(salicylideneimino)triethylamine) is predicted to exhibit such property. An ultra-thin film of Nd(trensal) is deposited on highly ordered pyrolytic graphite as a proof-of-concept system to show that this property can be retained at the nanoscale on a layered material. By combining single crystal magnetometric measurements and synchrotron X-ray-based absorption techniques, supported by multiplet ligand field simulations based on the trigonal crystal field surrounding the lanthanide centre, it is demonstrated that changing the temperature reverses the magnetic anisotropy of an ordered film of Nd(trensal), thus opening significant perspectives for the realization of a novel family of temperature-controlled molecular spintronic devices.

Stacking influence on the in-plane magnetic anisotropy in a 2D magnetic system

The magnetization patterns on three atomic layers thick islands of Co on Ru(0001) are studied by spin-polarized low-energy electron microscopy (SPLEEM). In-plane magnetized micrometer wide triangular Co islands are grown on Ru(0001). They present two different orientations correlated with two different stacking sequences which differ only in the last layer position. The stacking sequence determines the type of magnetization pattern observed: the hcp islands present very wide domain walls, while the fcc islands present domains separated by much narrower domain walls. The former is an extremely low in-plane anisotropy system. We estimate the in-plane magnetic anisotropy of the fcc regions to be 1.96 × 10⁴ J m^-3 and of the hcp ones to be 2.5 × 10² J m^-3.

Near Degeneracy of Magnetic Phases in Two-Dimensional Chromium Telluride with Enhanced Perpendicular Magnetic Anisotropy

The discovery of atomically thin van der Waals magnets (e.g., CrI₃ and Cr₂Ge₂Te₆) has triggered a renaissance in the study of two-dimensional (2D) magnetism. Most of the 2D magnetic compounds discovered so far host only one single magnetic phase unless the system is at a phase boundary. In this work, we report the near degeneracy of magnetic phases in ultrathin chromium telluride (Cr₂Te₃) layers with strong perpendicular magnetic anisotropy highly desired for stabilizing 2D magnetic order. Single-crystalline Cr₂Te₃ nanoplates with a trigonal structure (space group P3̅1c) were grown by chemical vapor deposition. The bulk magnetization measurements suggest a ferromagnetic (FM) order with an enhanced perpendicular magnetic anisotropy, as evidenced by a coercive field as large as ∼14 kOe when the field is applied perpendicular to the basal plane of the thin nanoplates. Magneto-optical Kerr effect studies confirm the intrinsic ferromagnetism and characterize the magnetic ordering temperature of individual nanoplates. First-principles density functional theory calculations suggest the near degeneracy of magnetic orderings with a continuously varying canting from the c-axis FM due to their comparable energy scales, explaining the zero-field kink observed in the magnetic hysteresis loops. Our work highlights Cr₂Te₃ as a promising 2D Ising system to study magnetic phase coexistence and switches for ultracompact information storage and processing.

Evidence of Kosterlitz-Thouless phase transitions in the Ising model with dipolar interactions

The ferromagnetic bidimensional Ising model with dipolar interactions has been proposed to model ultrathin films with strong out-of-plane anisotropy. The phase diagram presents a rich phenomenology that includes low-temperature phases characterized by stripes of width n (h_{n}) and a high-temperature phase with domains of stripes with mutually perpendicular orientations, named tetragonal liquid (TL). The latter phase can be reached by two possible ways. One of them is the direct transition h_{n} to TL, and the other one is through an intermediate phase with orientational order but short-range positional disorder, named nematic phase (NM). The regions of the phase diagram where these transitions occur, as well as their character, remain an open question and are the object of the present work. In order to clarify this topic, intensive Monte Carlo simulations were performed by employing short-time dynamics as the main tool for studying the phase transition behavior. The dynamic evolution of the orientational order parameter and its moments are measured for selected values of the ratio between the ferromagnetic exchange and dipolar constants, called δ. The obtained results indicate that the intermediate NM phase is present for δ≥2 in narrow ranges of temperatures. Also, the results suggest that both transitions, i.e., h_{n}-NM and NM-TL, have a Kosterlitz-Thouless character. This type of topological transition is observed in continuous bidimensional models and have been proposed for discrete ones, as in the case of the present work.

Broadband spectroscopy of thermodynamic magnetization fluctuations through a ferromagnetic spin-reorientation transition

We use scanning optical magnetometry to study the broadband frequency spectra of spontaneous magnetization fluctuations, or "magnetization noise", in an archetypal ferromagnetic film that can be smoothly tuned through a spin reorientation transition (SRT). The SRT is achieved by laterally varying the magnetic anisotropy across an ultrathin Pt/Co/Pt trilayer, from the perpendicular to in-plane direction, via graded Ar⁺ irradiation. In regions exhibiting perpendicular anisotropy, the power spectrum of the magnetization noise, S(ν), exhibits a remarkably robust ν ^-3/2 power law over frequencies ν from 1 kHz to 1 MHz. As the SRT region is traversed, however, S(ν) spectra develop a steadily-increasing critical frequency, ν ₀, below which the noise power is spectrally flat, indicating an evolving low-frequency cutoff for magnetization fluctuations. The magnetization noise depends strongly on applied in- and out-of-plane magnetic fields, revealing local anisotropies and also a field-induced emergence of fluctuations in otherwise stable ferromagnetic films. Finally, we demonstrate that higher-order correlators can be computed from the noise. These results highlight broadband spectroscopy of thermodynamic fluctuations as a powerful tool to characterize the interplay between thermal and magnetic energy scales, and as a means of characterizing phase transitions in ferromagnets.

Modeling magnetization curves in magnetic thin films with striped patterns

In this work, we study magnetic thin films presenting magnetic stripe patterns. A fingerprint of such domains is a linear behavior of the in-plane magnetization curves below a given saturation field. We present free energy models for the in-plane magnetization curves which permit us to extract key geometrical information about the stripe patterns, such as the maximum canted angle of the magnetization and the domain wall width. As an example, we discuss in this work magnetization curves for Fe(1-x)Ga(x) magnetic films which present a stripe pattern with a period of 160 nm and we found a typical maximum canted angle of 85° and a domain wall width around 30 nm.

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.

Tailoring the magnetic anisotropy of Py/Ni bilayer films using well aligned atomic steps on Cu(001)

Tailoring the spin orientation at the atomic scale has been a key task in spintronics technology. While controlling the out-of-plane to in-plane spin orientation has been achieved by a precise control of the perpendicular magnetic anisotropy at atomic layer thickness level, a design and control of the in-plane magnetic anisotropy has not yet been well developed. On well aligned atomic steps of a 6° vicinal Cu(001) surface with steps parallel to the [110] axis, we grow Py/Ni overlayer films epitaxially to permit a systematic exploration of the step-induced in-plane magnetic anisotropy as a function of both the Py and the Ni film thicknesses. We found that the atomic steps from the vicinal Cu(001) induce an in-plane uniaxial magnetic anisotropy that favors both Py and Ni magnetizations perpendicular to the steps, opposite to the behavior of Co on vicinal Cu(001). In addition, thickness-dependent study shows that the Ni films exhibit different magnetic anisotropy below and above ~6 ML Ni thickness.

Re-orientation transition in molecular thin films: Potts model with dipolar interaction

We study the low-temperature behavior and the phase transition of a thin film by Monte Carlo simulation. The thin film has a simple cubic lattice structure where each site is occupied by a Potts parameter which indicates the molecular orientation of the site. We take only three molecular orientations in this paper, which correspond to the three-state Potts model. The Hamiltonian of the system includes (i) the exchange interaction J(ij) between nearest-neighbor sites i and j, (ii) the long-range dipolar interaction of amplitude D truncated at a cutoff distance r(c), and (iii) a single-ion perpendicular anisotropy of amplitude A. We allow J(ij) = J(s) between surface spins, and J(ij) = J otherwise. We show that the ground state depends on the ratio D/A and r(c). For a single layer, for a given A, there is a critical value D(c) below (above) which the ground-state (GS) configuration of molecular axes is perpendicular (parallel) to the film surface. When the temperature T is increased, a re-orientation transition occurs near D(c): the low-T in-plane ordering undergoes a transition to the perpendicular ordering at a finite T, below the transition to the paramagnetic phase. The same phenomenon is observed in the case of a film with a thickness. Comparison with the Fe/Gd experiment is given. We show that the surface phase transition can occur below or above the bulk transition depending on the ratio J(s)/J. Surface and bulk order parameters as well as other physical quantities are shown and discussed.

Noncollinear spin reorientation transition in S = 1 ferromagnetic thin films

An in-plane spin reorientation transition in thin ferromagnetic films is discussed in terms of the thermodynamics of inhomogeneous low-dimensional systems based on a Néel sublattices concept while using a spin 1 Heisenberg Hamiltonian. The model allows us to investigate in a straightforward manner the layer-dependent phenomena. In this context, we propose a model of noncollinear magnetization structure based on the appropriate distribution of the anisotropy parameters inside the Fe films on W(110). The spin reorientation transition originates at the Fe/W(110) interface and proceeds via noncollinear magnetization structure toward the surface with increasing film thickness in accordance with the experimental findings. The temperature-driven spin reorientation transition in freestanding Fe films and in Fe/W(110) systems is also discussed in detail.

Canted Magnetic Moments at the Gd (0001) Surface

With spin polarized electron spectroscopies, we have investigated ordered Gd (0001) films deposited on W (110). The photoemission features of the gadolinium 5d surface state, the 4f levels, and the background exhibit considerable spin polarization along the same direction in the plane of the film, indicative of ferromagnetic coupling between the surface and the bulk. The 4f spin polarized photoemission data provides strong evidence that the surface 4f polarization differs from the bulk 4f polarization for Gd (000l). Our temperature dependent measurements with spin polarized secondary electron spectroscopy conclusively establishes that the surface of clean Gd (0001) possesses a perpendicular polarization component which persists to an enhanced surface Curie temperature. SMall amounts of contamination at the surface result in the disappearance of the perpendicular component and, therefore, a more perfect ferromagnetic coupling between the surface and the bulk.

Studies of nanomagnetism using synchrotron-based x-ray photoemission electron microscopy (X-PEEM)

As interest in magnetic devices has increased over the last 20 years, research into nanomagnetism has experienced a corresponding growth. Device applications from magnetic storage to magnetic logic have compelled interest in the influence of geometry and finite size on magnetism and magnetic excitations, in particular where the smallest dimensions reach the important magnetic interaction length scales. The dynamical behavior of nanoscale magnets is an especially important subset of research, as these phenomena are both critical for device physics and profoundly influenced by finite size. At the same time, nanoscale systems offer unique geometries to promote and study model systems, such as magnetic vortices, leading to new fundamental insights into magnetization dynamics. A wide array of experimental and computational techniques have been applied to these problems. Among these, imaging techniques that provide real-space information on the magnetic order are particularly useful. X-ray microscopy offers several advantages over scanning probe or optical techniques, such as high spatial resolution, element specificity and the possibility for high time resolution. Here, we review recent contributions using static and time-resolved x-ray photoemission electron microscopy to nanomagnetism research.

Effects of a perpendicular magnetic field in the dipolar Heisenberg model with dominant exchange interaction

The effects of a uniform magnetic field on the phase diagram of the dipolar Heisenberg model with a dominant antiferromagnetic exchange interaction have been investigated. The model consists of a square lattice of classical spin vectors, where the spins interact through an antiferromagnetic exchange interaction of strength J and a dipole-dipole interaction of strength g. The spins couple to a magnetic surface anisotropy of strength κ and to an applied external magnetic field of strength H. The external field is applied perpendicular to the plane of the lattice. From extensive Monte Carlo simulations, representative magnetic phase diagrams have been determined as a function of the ratios κ/g and T/g, where T is temperature, and at three different ratios of H/g (H/g = 10, 20, 27). These results are compared to the previously investigated case of H/g = 0 and to analytic calculations for the ground state energies. The nature of the equilibrium phases and order of the phase boundaries separating them are considered and changes due to the strength of the applied field are highlighted.

SY. Photoelectron Diffraction of Magnetic Ultrathin Films: Fe/Cu(001)

The preliminary results of an ongoing investigation of Fe/Cu(001) are presented here. Energy dependent photoelectron diffraction, including the spin-dependent variant using the multiplet split Fe 3s state, is being used to investigate the nanoscale structures formed by near-monolayer deposits of Fe onto Cu(001). Core-level photoemission from the Fe3p and Fe3s states has been generated using synchrotron radiation as the tunable excitation source. Tentatively, a comparison of the experimental Fe3p cross section measurements with multiple scattering calculations indicates that the Fe is in a fourfold hollow site with a spacing of 3.6Å between it and the atom directly beneath it, in the third layer. This is consistent with an FCC structure. The possibility of utilizing spin-dleendent photoelectron diffraction to investigate magnetic ultrathin films will be demonstrated, using our preliminary spectra of the multiplet-split Fe3s of near-monolayer Fe/Cu(001).

Instability of the collinear phase in a two-dimensional ferromagnet in a strong in-plane magnetic field

It is well-known that in a thin ferromagnetic film with a net magnetization perpendicular to the film the collinear arrangement of spins is unstable in an in-plane field H smaller than its saturation value H(c). The existence of a stripe phase was proposed with elongated domains of alternating direction of the magnetization component perpendicular to the film. We consider in the present paper the strong-field regime H<H(c) and discuss the minimal microscopic model describing this phenomenon, a two-dimensional Heisenberg ferromagnet with strong easy-axis anisotropy and dipolar forces. The noncollinear (stripe) phase is discussed using the technique of Bose-Einstein condensation of magnons. Some previously unknown results are observed concerning the stripe phase. Evolution of the spin arrangement in the noncollinear phase is established upon field rotation within the plane. We find a rapid decrease of the period of the stripe structure as the field decreases. We demonstrate that spin components perpendicular to the film form a sinusoid in the noncollinear phase at H≈H(c) that transforms to a step-like profile with decreasing field so that the domain wall density decreases from unity to a value much smaller than unity. The spin-wave spectrum in the noncollinear phase is discussed.

Universal window for two-dimensional critical exponents

Two-dimensional condensed matter is realized in increasingly diverse forms that are accessible to experiment and of potential technological value. The properties of these systems are influenced by many length scales and reflect both generic physics and chemical detail. To unify their physical description is therefore a complex and important challenge. Here we investigate the distribution of experimentally estimated critical exponents, β, that characterize the evolution of the order parameter through the ordering transition. The distribution is found to be bimodal and bounded within a window ∼0.1≤β≤0.25, facts that are only in partial agreement with the established theory of critical phenomena. In particular, the bounded nature of the distribution is impossible to reconcile with the existing theory for one of the major universality classes of two-dimensional behaviour-the XY model with four-fold crystal field-which predicts a spectrum of non-universal exponents bounded only from below. Through a combination of numerical and renormalization group arguments we resolve the contradiction between theory and experiment and demonstrate how the 'universal window' for critical exponents observed in experiment arises from a competition between marginal operators.

Magnetic bubble domain phase at the spin reorientation transition of ultrathin Fe/Ni/Cu(001) film

Magnetic domain phases of ultrathin Fe/Ni/Cu(001) are studied using photoemission electron microscopy at the spin reorientation transition (SRT). We observe a new magnetic phase of bubble domains within a narrow SRT region after applying a nearly in-plane magnetic field pulse to the sample. By applying the magnetic field pulse along different directions, we find that the bubble domain phase exists only if the magnetic field direction is less than approximately 10 degrees relative to the sample surface. A temperature dependent measurement shows that the bubble domain phase becomes unstable above 370 K.

Energy- and momentum-resolved exchange and spin-orbit interaction in cobalt film by spin-polarized two-electron spectroscopy

Spontaneous ordering of electronic spins in ferromagnetic materials is one of the best known and most studied examples of quantum correlations. Exchange correlations are responsible for long range spin order and the spin-orbit interaction (SOI) can create preferred crystalline directions for the spins, i.e., magnetic anisotropy. Presented experimental data illustrate how novel spin-polarized two-electron spectroscopy in-reflection mode allows observation of the localization of spin-dependent interactions in energy-momentum space. Comparison of spin-orbit asymmetries in spectra of Co film and clean W(110) may indicate the presence of interface specific proximity effects providing important clues to the formation of preferred orientations for the magnetic moment of the Co film. These results may help to understand the microscopic origin of interface magnetic anisotropy.

Magnetic stripe domains in coupled magnetic sandwiches

Magnetic stripe domains in the spin reorientation transition region are investigated in (Fe/Ni)/Cu(001) and Co/Cu/(Fe/Ni)/Cu(001) using photoemission electron microscopy. For (Fe/Ni)/Cu(001), the stripe domain width decreases exponentially as the Fe/Ni film approaches the spin reorientation transition point. For Co/Cu/(Fe/Ni)/Cu(001), the Fe/Ni stripe orientation is aligned with the Co in-plane magnetization, and the stripe domain width decreases exponentially with increasing the interlayer coupling between the Fe/Ni and Co films. By considering magnetic stripes within an in-plane magnetic field, we reveal a universal dependence of the stripe domain width on the magnetic anisotropy and on the interlayer coupling.

Magnetic microstructure of the spin reorientation transition: a computer experiment

The scenario of the spin reorientation in two-dimensional films within first-order anisotropy approximation is theoretically studied by means of Monte Carlo simulations. The magnetic microstructure is investigated as a function of the ratio of the perpendicular anisotropy energy to the dipolar one. If the anisotropy dominates, out-of-plane domains will be found while in-plane vortices appear for a vanishing anisotropy. In the range of comparable anisotropy and dipolar energies a complex domain pattern evolves yielding a continuous transition between the two structures. The structure with equally distributed magnetic moment orientations is stable at the point where anisotropy and dipolar energies cancel each other.

Theoretical calculation of magnetic properties of ultrathin Fe films on Cu(100)

The temperature dependence of the magnetization in fcc Fe on Cu(100) is calculated using a self-consistent local mean-field theory. The model reproduces an experimental magnetization oscillation as a function of film thickness and supports a picture where the top two layers are ferromagnetically coupled, and the remaining layers are antiferromagnetically coupled. The origin of the puzzling linear temperature dependence in oscillation amplitude is understood as a "surface phenomena" of the antiferromagnetic layer at the Fe/Cu interface. Proximity effects between a thin antiferromagnet with a low Neel temperature and a neighboring ferromagnet with a higher Curie temperature are discussed.