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Electrically induced ionic motion offers a new way to realize voltage-controlled magnetism, opening the door to a new generation of logic, sensor, and data storage technologies. Here, we demonstrate an effective approach to magneto-ionically and electrically tune exchange bias in Gd/Ni$_{1-x}$Co$_{x}$O thin films (x=0.50, 0.67), where neither of the layers alone is ferromagnetic at room temperature. The Gd capping layer deposited onto antiferromagnetic Ni$_{1-x}$Co$_{x}$O initiates a solid-state redox reaction that reduces an interfacial region of the oxide to ferromagnetic NiCo. Exchange bias is established after field cooling, which can be enhanced by up to 35% after a voltage conditioning and subsequently reset with a second field cooling. These effects are caused by the presence of an interfacial ferromagnetic NiCo layer, which further alloys with the Gd layer upon field cooling and voltage application, as confirmed by electron microscopy and polarized neutron reflectometry studies. These results highlight the viability of the solid-state magneto-ionic approach to achieve electric control of exchange bias, with potentials for energy-efficient magneto-ionic devices., 25 pages, 5 figures; 8 pages of Supporting Information with 5 figures

Following the success and relevance of the 2014 and 2017 Magnetism Roadmap articles, this 2020 Magnetism Roadmap edition takes yet another timely look at newly relevant and highly active areas in magnetism research. The overall layout of this article is unchanged, given that it has proved the most appropriate way to convey the most relevant aspects of today's magnetism research in a wide variety of sub-fields to a broad readership. A different group of experts has again been selected for this article, representing both the breadth of new research areas, and the desire to incorporate different voices and viewpoints. The latter is especially relevant for thistype of article, in which one's field of expertise has to be accommodated on two printed pages only, so that personal selection preferences are naturally rather more visible than in other types of articles. Most importantly, the very relevant advances in the field of magnetism research in recent years make the publication of yet another Magnetism Roadmap a very sensible and timely endeavour, allowing its authors and readers to take another broad-based, but concise look at the most significant developments in magnetism, their precise status, their challenges, and their anticipated future developments. While many of the contributions in this 2020 Magnetism Roadmap edition have significant associations with different aspects of magnetism, the general layout can nonetheless be classified in terms of three main themes: (i) phenomena, (ii) materials and characterization, and (iii) applications and devices. While these categories are unsurprisingly rather similar to the 2017 Roadmap, the order is different, in that the 2020 Roadmap considers phenomena first, even if their occurrences are naturally very difficult to separate from the materials exhibiting such phenomena. Nonetheless, the specifically selected topics seemed to be best displayed in the order presented here, in particular, because many of the phenomena or geometries discussed in (i) can be found or designed into a large variety of materials, so that the progression of the article embarks from more general concepts to more specific classes of materials in the selected order. Given that applications and devices are based on both phenomena and materials, it seemed most appropriate to close the article with the application and devices section (iii) once again. The 2020 Magnetism Roadmap article contains 14 sections, all of which were written by individual authors and experts, specifically addressing a subject in terms of its status, advances, challenges and perspectives in just two pages. Evidently, this two-page format limits the depth to which each subject can be described. Nonetheless, the most relevant and key aspects of each field are touched upon, which enables the Roadmap as whole to give its readership an initial overview of and outlook into a wide variety of topics and fields in a fairly condensed format. Correspondingly, the Roadmap pursues the goal of giving each reader a brief reference frame of relevant and current topics in modern applied magnetism research, even if not all sub-fields can be represented here. The first block of this 2020 Magnetism Roadmap, which is focussed on (i) phenomena, contains five contributions, which address the areas of interfacial Dzyaloshinskii–Moriya interactions, and two-dimensional and curvilinear magnetism, as well as spin-orbit torque phenomena and all optical magnetization reversal. All of these contributions describe cutting edge aspects of rather fundamental physical processes and properties, associated with new and improved magnetic materials' properties, together with potential developments in terms of future devices and technology. As such, they form part of a widening magnetism 'phenomena reservoir' for utilization in applied magnetism and related device technology. The final block (iii) of this article focuses on such applications and device-related fields in four contributions relating to currently active areas of research, which are of course utilizing magnetic phenomena to enable specific functions. These contributions highlight the role of magnetism or spintronics in the field of neuromorphic and reservoir computing, terahertz technology, and domain wall-based logic. One aspect common to all of these application-related contributions is that they are not yet being utilized in commercially available technology; it is currently still an open question, whether or not such technological applications will be magnetism-based at all in the future, or if other types of materials and phenomena will yet outperform magnetism. This last point is actually a very good indication of the vibrancy of applied magnetism research today, given that it demonstrates that magnetism research is able to venture into novel application fields, based upon its portfolio of phenomena, effects and materials. This materials portfolio in particular defines the central block (ii) of this article, with its five contributions interconnecting phenomena with devices, for which materials and the characterization of their properties is the decisive discriminator between purely academically interesting aspects and the true viability of real-life devices, because only available materials and their associated fabrication and characterization methods permit reliable technological implementation. These five contributions specifically address magnetic films and multiferroic heterostructures for the purpose of spin electronic utilization, multi-scale materials modelling, and magnetic materials design based upon machine-learning, as well as materials characterization via polarized neutron measurements. As such, these contributions illustrate the balanced relevance of research into experimental and modelling magnetic materials, as well the importance of sophisticated characterization methods that allow for an ever-more refined understanding of materials. As a combined and integrated article, this 2020 Magnetism Roadmap is intended to be a reference point for current, novel and emerging research directions in modern magnetism, just as its 2014 and 2017 predecessors have been in previous years., Journal of Physics D: Applied Physics, 53 (45), ISSN:0022-3727, ISSN:1361-6463

Controlling changes in magnetic anisotropy across epitaxial film interfaces is an important prerequisite for many spintronic devices. For the canonical dilute magnetic semiconductor GaMnAs, magnetic anisotropy is highly tunable through strain and doping, making it a fascinating model system for exploration of anisotropy control in a carrier-mediated ferromagnet. Here, we have used transmission electron microscopy and polarized neutron reflectometry to characterize the interface between GaMnAs-based layers designed to have anisotropy vectors oriented at right angles from one another. For a bilayer of ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}{\mathrm{As}}_{1\ensuremath{-}y}{\mathrm{P}}_{y}$ and ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{As}$, we find that the entirety of the ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{As}$ layer exhibits in-plane magnetic anisotropy and that the $majority$ of the ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}{\mathrm{As}}_{1\ensuremath{-}y}{\mathrm{P}}_{y}$ exhibits perpendicular anisotropy. However, near the ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{As}$ interface, we observe a thin Mn-rich region of the nominally perpendicular ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}{\mathrm{As}}_{1\ensuremath{-}y}{\mathrm{P}}_{y}$ that instead exhibits $in\ensuremath{-}plane$ anisotropy. Using first-principles energy considerations, we explain this sublayer as a natural consequence of interfacial carrier migration.

We report on the evolution of the average and depth-dependent magnetic order in thin-film samples of biaxially stressed and electron-doped EuTiO3 for samples across a doping range < 0.1 to 7.8 × 1020 cm-3. Under an applied in-plane magnetic field, the G-type antiferromagnetic ground state undergoes a continuous spin-flop phase transition into in-plane, field-polarized ferromagnetism. The critical field for ferromagnetism slightly decreases with an increasing number of free carriers, yet the field evolution of the spin-flop transition is qualitatively similar across the doping range. Unexpectedly, we observe interfacial ferromagnetism with saturated Eu2+ moments at the substrate interface at low fields preceding ferromagnetic saturation throughout the bulk of the degenerate semiconductor film. We discuss the implications of these findings for the unusual magnetotransport properties of this compound.

Engineering magnetic anisotropy in two-dimensional systems has enormous scientific and technological implications. The uniaxial anisotropy universally exhibited by two-dimensional magnets has only two stable spin directions, demanding 180 degrees spin switching between states. We demonstrate a novel eightfold anisotropy in magnetic SrRuO3 monolayers by inducing a spin reorientation in (SrRuO3)1/(SrTiO3)N superlattices, in which the magnetic easy axis of Ru spins is transformed from uniaxial direction (N = 1 and 2) to eightfold directions (N = 3, 4 and 5). This eightfold anisotropy enables 71 and 109 degrees spin switching in SrRuO3 monolayers, analogous to 71 and 109 degrees polarization switching in ferroelectric BiFeO3. First-principle calculations reveal that increasing the SrTiO3 layer thickness induces an emergent correlation-driven orbital ordering, tuning spin-orbit interactions and reorienting the SrRuO3 monolayer easy axis. Our work demonstrates that correlation effects can be exploited to substantially change spin-orbit interactions, stabilizing unprecedented properties in two-dimensional magnets and opening rich opportunities for low-power, multi-state device applications., 15+13 pages, 5+10 figures, including supplementary materials

Tensile-strained $\mathrm{LaCo}{\mathrm{O}}_{3\ensuremath{-}\ensuremath{\delta}}$ thin films are ferromagnetic, in sharp contrast to the zero-spin bulk, although no clear consensus has emerged as to the origin of this phenomenon. While magnetism has been heavily studied, relatively little attention has been paid to electronic transport, due to the insulating nature of the strain-stabilized ferromagnetic state. Here, structure, magnetism, and transport are studied in epitaxial $\mathrm{LaCo}{\mathrm{O}}_{3\ensuremath{-}\ensuremath{\delta}}$ films (10--22-nm thick) on various substrates (from 1.4% compressive to 2.5% tensile strain), using synchrotron x-ray diffraction, scanning probe and transmission electron microscopy, magnetometry, polarized neutron reflectometry, resistivity, and Hall effect. High quality, smooth films are obtained, exhibiting superstructures associated with both oxygen vacancy ordering and periodic in-plane ferroelastic domains. Consistent with prior work, ferromagnetism with an approximately 80--85 K Curie temperature is observed under tension; polarized neutron reflectometry confirms a relatively uniform magnetization depth profile, albeit with interfacial dead layer formation. Electrical transport is found to have similar semiconducting nature to bulk, but with reduced resistivity and activation energy. Hall effect measurements, however, reveal a striking inversion of the majority carrier type, from $p$-type in the bulk and under compression to n-type under tension. While thus far overlooked, ferromagnetism in epitaxial $\mathrm{LaCo}{\mathrm{O}}_{3\ensuremath{-}\ensuremath{\delta}}$ films is thus directly correlated with $n$-type behavior, providing important insight into the ferromagnetic state in this system. Aided by density functional theory calculations, these results are interpreted in terms of tensile-strain-induced orbital occupation and band structure changes, including a rapid decrease in effective mass at the ${e}_{g}$-derived conduction band minimum, and corresponding increase at the valence band maximum.

Low-dimensional quantum materials that remain strongly ferromagnetic down to mono layer thickness are highly desired for spintronic applications. Although oxide materials are important candidates for next generation of spintronic, ferromagnetism decays severely when the thickness is scaled to the nano meter regime, leading to deterioration of device performance. Here we report a methodology for maintaining strong ferromagnetism in insulating LaCoO3 (LCO) layers down to the thickness of a single unit cell. We find that the magnetic and electronic states of LCO are linked intimately to the structural parameters of adjacent "breathing lattice" SrCuO2 (SCO). As the dimensionality of SCO is reduced, the lattice constant elongates over 10% along the growth direction, leading to a significant distortion of the CoO6 octahedra, and promoting a higher spin state and long-range spin ordering. For atomically thin LCO layers, we observe surprisingly large magnetic moment (0.5 uB/Co) and Curie temperature (75 K), values larger than previously reported for any mono layer oxide. Our results demonstrate a strategy for creating ultra thin ferromagnetic oxides by exploiting atomic hetero interface engineering,confinement-driven structural transformation, and spin-lattice entanglement in strongly correlated materials., 24 pages, 5 figures, 1 supporting information with 13 figures

Superconducting ($S$) thin film superlattices composed of Nb and a normal metal spacer ($N$) have been extensively utilized in Josephson junctions given their favorable surface roughness compared to Nb films of comparable thickness. In this work, we characterize the London penetration depth and Ginzburg-Landau coherence lengths of $S/N$ superlattices using polarized neutron reflectometry and electrical transport. Despite the normal metal spacer layers being only approximately 8% of the total superlattice thickness, we surprisingly find that the introduction of these thin $N$ spacers between $S$ layers leads to a dramatic increase in the measured London penetration depth compared to that of a single Nb film of comparable thickness. Using the measured values for the effective in- and out-of-plane coherence lengths, we quantify the induced anisotropy of the superlattice samples and compare to a single Nb film sample. From these results, we find that that the superlattices behave similarly to layered 2D superconductors., Comment: 9 pages, 3 figures main text and 7 pages, 5 figures supplemental materials

Charge storage and trapping properties of polymer dielectrics govern the charge densities of adjacent semiconductors and greatly influence the on–off switching voltage (threshold voltage, Vth) of o...

Solid state ionic approaches for modifying ion distributions in getter/oxide heterostructures offer exciting potentials to control material properties. Here we report a simple, scalable approach allowing for total control of the superconducting transition in optimally doped YBa$_{2}$Cu$_{3}$O$_{7-{\delta}}$ (YBCO) films via a chemically-driven ionic migration mechanism. Using a thin Gd capping layer of up to 20 nm deposited onto 100 nm thick epitaxial YBCO films, oxygen is found to leach from deep within the YBCO. Progressive reduction of the superconducting transition is observed, with complete suppression possible for a sufficiently thick Gd layer. These effects arise from the combined impact of redox-driven electron doping and modification of the YBCO microstructure due to oxygen migration and depletion. This work demonstrates an effective ionic control of superconductivity in oxides, an interface induced effect that goes well into the quasi-bulk regime, opening up possibilities for electric field manipulation., Comment: 26 pages, 5 figures

We report on the emergent magnetic state of (111)-oriented CoCr2O4 ultrathin films sandwiched between Al2O3 spacer layers in a quantum confined geometry. At the two-dimensional crossover, polarized neutron reflectometry reveals an anomalous enhancement of the total magnetization compared to the bulk value. Synchrotron X-ray magnetic circular dichroism measurements demonstrate the appearance of a long-range ferromagnetic ordering of spins on both Co and Cr sublattices. Brillouin function analyses and ab-initio density functional theory calculations further corroborate that the observed phenomena are due to the strongly altered magnetic frustration invoked by quantum confinement effects, manifested by the onset of a Yafet–Kittel-type ordering as the magnetic ground state in the ultrathin limit, which is unattainable in the bulk.

The coexistence and coupling of ferroelasticity and magnetic ordering in a single material offers a great opportunity to realize novel devices with multiple tuning knobs. Complex oxides are a particularly promising class of materials to find multiferroic interactions as they often possess rich phase diagrams and the interactions are very sensitive to external perturbations. Still, there are very few examples of these systems. Here we report the observation of twinning domains in ferroelastic LaCoO3 epitaxial thin films and their geometric control of structural symmetry that are intimately linked to the material electronic and magnetic states. A unidirectional structural modulation is achieved by selective choice of substrates possessing two-fold rotational symmetry. This modulation perturbs the crystal field splitting energy, leading to unexpected in plane anisotropy of orbital configuration and magnetization. These findings demonstrate the utilization of structural modulation to control multiferroic interactions and may enable a great potential for stimulation of exotic phenomena through artificial domain engineering., 24 pages, 4 figures, and one supporting information (10 figures); accepted for publication in Science Advances

Anderson localization in phonon heat conduction is observed in GaAs/AlAs superlattices with ErAs nanodots., Nondiffusive phonon thermal transport, extensively observed in nanostructures, has largely been attributed to classical size effects, ignoring the wave nature of phonons. We report localization behavior in phonon heat conduction due to multiple scattering and interference events of broadband phonons, by measuring the thermal conductivities of GaAs/AlAs superlattices with ErAs nanodots randomly distributed at the interfaces. With an increasing number of superlattice periods, the measured thermal conductivities near room temperature increased and eventually saturated, indicating a transition from ballistic to diffusive transport. In contrast, at cryogenic temperatures the thermal conductivities first increased but then decreased, signaling phonon wave localization, as supported by atomistic Greenșs function simulations. The discovery of phonon localization suggests a new path forward for engineering phonon thermal transport.

Geometric Hall effect is induced by the emergent gauge field experienced by the carriers adiabatically passing through certain real-space topological spin textures, which is a probe to non-trivial spin textures, such as magnetic skyrmions. We report experimental indications of spin-texture topological charges induced in heterostructures of a topological insulator (Bi,Sb)2Te3 coupled to an antiferromagnet MnTe. Through a seeding effect, the pinned spins at the interface leads to a tunable modification of the averaged real-space topological charge. This effect experimentally manifests as a modification of the field-dependent geometric Hall effect when the system is field-cooled along different directions. This heterostructure represents a platform for manipulating magnetic topological transitions using antiferromagnetic order., Spin-polarized carriers could show an extra Hall component when moving through certain real-space topological spin textures. Here, He et al. report an exchange bias experienced by the topological spin textures living at the interface between a topological insulator and an adjacent antiferromagnet, suggesting a chiral spin texture is induced.

Graded magnetic materials represent a promising new avenue in modern material science from both fundamental and application points of view. Over the course of the last few years, remarkable results have been obtained in (epitaxial) heterostructures based on thin alloy films featuring diverse compositional depth profiles. As a result of the precise tailoring of such profiles, the exchange coupling, and the corresponding effective or local Curie temperatures can be controlled over tens of nm with an excellent precision. This topical review article reports the most recent advances in this emerging research field. Several aspects are covered, but the primary focus lies in the study of compositional gradients being transferred into depth dependent magnetic states in ferromagnets, while also reviewing other experimental attempts to create exchange graded films and materials in general. We account for the remarkable progress achieved in each sample and composition geometry by reporting the recent developments and by discussing the research highlights obtained by several groups. Finally, we conclude the review article with an outlook on future challenges in this field.

Magnetic topological insulators such as Cr-doped (Bi,Sb)2Te3 provide a platform for the realization of versatile time-reversal symmetry-breaking physics. By constructing heterostructures with N\'eel order in an antiferromagnetic CrSb and magnetic topological order in Cr-doped (Bi,Sb)2Te3, we realize emergent interfacial magnetic phenomena which can be tailored through artificial structural engineering. Through deliberate geometrical design of heterostructures and superlattices, we demonstrate the use of antiferromagnetic exchange coupling in manipulating the magnetic properties of the topological surface massive Dirac fermions. This work provides a new framework on integrating topological insulators with antiferromagnetic materials and unveils new avenues towards dissipationless topological antiferromagnetic spintronics., Comment: 25 pages, 4 figures

Phenyl-C71-butyric acid methyl ester (PC71BM) could intercalate between the side-chains of poly(2,5-bis(3-tetradecylthiophen-2-yl)thieno[3,2-b]thiophene (pBTTT) creating a stable co-crystal structure, so optimal solar cell performance was obtained at high PC71BM concentrations promoting phase separated electron conductive pathways. Neutron reflectivity, with the application of magnetic contrast variation, was used to investigate the concentration profile of PC71BM within the active layer. And this profile was found to be homogeneous through the film thickness. Small angle neutron scattering was utilized to find there is amorphous PC71BM even at 50 wt% of fullerene while previously it was believed that all fullerene was consumed to form co-crystals when its concentration is below 75 wt%. These fullerene molecules evolve into approximately 15 nm sized agglomerates to improve the electron transport when their concentration is above 75 wt%. Thermal annealing gives these agglomerates mobility to form micrometer sized crystals causing a decrease of device performance. These findings can therefore correlate the morphology, especially in terms of fullerene agglomerates, vertical concentration profile and percolating structure they formed, with the device performance and provide valuable guidance for optimal morphology design of polymer: fullerene solar cells.

Charge trapping and storage in polymer dielectrics can be harnessed to control semiconductor devices. Organic transistor (OFET) gate insulators affect bias stress and threshold voltage (Vth), and charging them can preset the operating voltages and control bias stress. We describe a chemical design and film fabrication procedure for construction of stacks of polystyrene (PS) layers, each with arbitrary concentrations of potentially chargeable functional groups. Thermal cross-linking of benzocyclobutene subunits ensures layer integrity while keeping the layers free of polar functionality and small molecule byproducts. Neutron reflectivity (NR), scanning electron microscopy, and atomic force microscopy (AFM) showed that individual layer thicknesses varied systematically with polymer concentration in deposition solutions, and interfacial thicknesses ranged from 1.5 to 4 nm, independent of layer thickness, demonstrating formation of distinct layers with minimal roughness or intermixing. The PS-based materials ...

We report on x-ray and neutron scattering studies that reveal the structure of interfaces of C60 layers with adjacent transition metal layers, in this instance, Cu. Such interfaces produce room-temperature long-range spin order that is not described by conventional theories of metallic magnetism. We use a combination of hard x-ray reflectivity and neutron scattering to investigate the interfacial structure of two C60/Cu layered samples: a superlattice with multiple C60/Cu repeats and a simpler tri-layer structure. For both structures, we develop a consistent structural model for the two scattering techniques, which details the critical interfacial roughness between the layers. We find that while x-ray reflectivity provides a strong contrast between the C60 and Cu layers, the similar neutron scattering length density of the two materials severely reduces the neutron scattering contrast. Our results can be used to design material systems that permit studies of the magnetism of the C60/transition metal interfaces with spin-sensitive scattering probes such as polarized neutron reflectometry.

Strain-coupled composite multiferroics, comprised of magnetostrictive and piezoelectric materials, promise tunable control of magnetism in applications such as rf resonators, sensors, and energy harvesters. Using polarized neutron reflectometry, the authors demonstrate that magnetostrictive and weakly magnetostrictive materials in a multilayer can be strain-coupled to an electric field over large length scales that enable designer functionality across a range of device applications.

© 2018 American Physical Society. Control of materials through custom design of ionic distributions represents a powerful new approach to develop future technologies ranging from spintronic logic and memory devices to energy storage. Perovskites have shown particular promise for ionic devices due to their high ion mobility and sensitivity to chemical stoichiometry. In this work, we demonstrate a solid-state approach to control of ionic distributions in (La,Sr)CoO3 thin films. Depositing a Gd capping layer on the perovskite film, oxygen is controllably extracted from the structure, up to 0.5 O/u.c. throughout the entire 36-nm thickness. Commensurate with the oxygen extraction, the Co valence state and saturation magnetization show a smooth continuous variation. In contrast, magnetoresistance measurements show no change in the magnetic anisotropy and a rapid increase in the resistivity over the same range of oxygen stoichiometry. These results suggest significant phase separation, with metallic ferromagnetic regions and oxygen-deficient, insulating, nonferromagnetic regions, forming percolated networks. Indeed, x-ray diffraction identifies oxygen-vacancy ordering, including transformation to a brownmillerite crystal structure. The unexpected transformation to the brownmillerite phase at ambient temperature is further confirmed by high-resolution scanning transmission electron microscopy which shows significant structural - and correspondingly chemical - phase separation. This work demonstrates room-temperature ionic control of magnetism, electrical resistivity, and crystalline structure in a 36-nm-thick film, presenting opportunities for ionic devices that leverage multiple material functionalities.

We demonstrate emergent antiferromagnetic interactions in strained thin films of the mixed valence manganite $(\mathrm{Eu},\mathrm{Sr}){\mathrm{MnO}}_{3}$. Although the composition studied, ${\mathrm{Eu}}_{0.7}{\mathrm{Sr}}_{0.3}{\mathrm{MnO}}_{3}$, will nominally yield a ferromagnetic phase in the bulk, we observe significant suppression of the saturation magnetization in films under both tensile and compressive strain. Despite the magnetization suppression, muon spin rotation spectrometry and polarized neutron reflectometry reveal uniform magnetic ordering in these films. Neutron diffraction and x-ray absorption spectroscopy demonstrate high-temperature G-type antiferromagnetic order in films under tensile strain, in contrast to the A- and C-type orders that are found in the phase diagrams of bulk $(\mathrm{Eu},\mathrm{Sr}){\mathrm{MnO}}_{3}$ and other mixed-valence manganites. These probes also show that compressive strain results in a uniform but suppressed magnetization suggestive of moment canting resulting from competition between ferromagnetism and antiferromagnetism.

Although ferromagnetism is in general a long-range collective phenomenon, it is possible to induce local spatial variations of magnetic properties in ferromagnetic materials. For example, systematic variation of the exchange coupling strength can be used to create systems that behave as if they are composed of virtually independent segments that exhibit ``local'' Curie temperatures. Such localization of thermodynamic behavior leads to boundaries between strongly and weakly magnetized regions that can be controllably moved within the material with temperature. The utility of this interesting functionality is largely dependent on the inherent spatial resolution of magnetic properties, specifically the distance over which the exchange strength and corresponding properties behave locally. To test the degree to which this type of localization can be realized in materials, we have fabricated epitaxial films of ${\mathrm{Co}}_{1\ensuremath{-}x}{\mathrm{Ru}}_{x}$ alloy featuring a nanometer-scale triangular wavelike concentration depth profile. Continuous nanoscale modulation of the local Curie temperature was observed using polarized neutron reflectometry. These results are consistent with mean-field simulations of spin systems that encompass the possibility of delocalized exchange coupling and show that composition grading can be used to localize magnetic properties in films down to the nanometer level. Since this is demonstrated here for an itinerant metal, we assert that for virtually any modulated magnetic material system, collective effects can be suppressed to length scales smaller than about 3 nm, so that magnetic behavior overall can be well described in terms of local material properties.

High carrier density quantum wells embedded within a Mott insulating matrix present a rich arena for exploring unconventional electronic phase behavior ranging from non-Fermi-liquid transport and signatures of quantum criticality to pseudogap formation. Probing the proposed connection between unconventional magnetotransport and incipient electronic order within these quantum wells has however remained an enduring challenge due to the ultra-thin layer thicknesses required. Here we address this challenge by exploring the magnetic properties of high-density SrTiO3 quantum wells embedded within the antiferromagnetic Mott insulator SmTiO3 via muon spin relaxation and polarized neutron reflectometry measurements. The one electron per planar unit cell acquired by the nominal d0 band insulator SrTiO3 when embedded within a d1 Mott SmTiO3 matrix exhibits slow magnetic fluctuations that begin to freeze into a quasistatic spin state below a critical temperature T*. The appearance of this quasistatic well magnetism coincides with the previously reported opening of a pseudogap in the tunneling spectra of high carrier density wells inside this film architecture. Our data suggest a common origin of the pseudogap phase behavior in this quantum critical oxide heterostructure with those observed in bulk Mott materials close to an antiferromagnetic instability. Magnetic correlations may drive ‘pseudogap’ physics in a complex oxide device, suggesting a connection to high-temperature superconductors. The mechanism underlying the so-called pseudogap state, a regime of unconventional electronic behavior, is one of the central mysteries of high-temperature superconductivity in cuprate materials. A team led by Stephen Wilson at the University of California, Santa Barbara studied the magnetic response of another system with a pseudogap, an artificial structure made by combining samarium and strontium titanate thin films. They found that the pseudogap formation coincided with the observation of antiferromagnetic correlations, indicating that short-range magnetic ordering may be the source of the pseudogap. A similar mechanism has been proposed to play a role in the cuprates, suggesting that a more detailed understanding of these oxide heterostructures could yield insights that apply to high-temperature superconductors as well.

In this letter we report a direct observation of a magnetic proximity effect in an amorphous thin film exchange-spring magnet by the use of neutron reflectometry. The exchange-spring magnet is a trilayer consisting of two ferromagnetic layers with high $T_c$'s separated by a ferromagnetic layer, which is engineered to have a significantly lower $T_c$ than the embedding layers. This enables us to measure magnetization depth profiles at which the low $T_c$ material is in a ferromagnetic or paramagnetic state, while the embedding layers are ferromagnetic. A clear proximity effect is observed 7 K above the $T_c$ of the embedded layer, with a range extending 50 $\unicode{xC5}$., Comment: 5 pages, 3 figures

Electrostatic control using electrolytes such as ionic liquids has emerged as an exciting means to induce ultrahigh carrier densities on material surfaces, to the point where electronic phases can be tuned. In materials such as oxides, the gating mechanisms remain controversial, however. Here, $i\phantom{\rule{0}{0ex}}n$ $o\phantom{\rule{0}{0ex}}p\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}d\phantom{\rule{0}{0ex}}o$ x-ray diffraction and neutron reflectometry are used in combination to probe gating mechanisms in ferromagnetic cobaltite films. The results confirm a striking polarity asymmetry, negative gate voltage enabling primarily electrostatic control of magnetism, while positive bias provides electrochemical control via oxygen vacancy formation. Generally, these results highlight the importance of a small number of key factors in determining electrostatic vs. redox response in a given material.

Ferromagnetic alloy materials with designed composition depth profiles provide an efficient route for the control of magnetism at the nanometer length scale. In this regard, cobalt-chromium and cobalt-ruthenium alloys constitute powerful model systems. They exhibit easy-to-tune magnetic properties such as saturation magnetization MS and Curie temperature TC while preserving their crystalline structure over a wide composition range. In order to demonstrate this materials design potential, we have grown a series of graded Co1−xCrx and Co1−wRuw (10 1 ¯ 0) epitaxial thin films, with x and w following predefined concentration profiles. Structural analysis measurements verify the epitaxial nature and crystallographic quality of our entire sample sets, which were designed to exhibit in-plane c-axis orientation and thus a magnetic in-plane easy axis to achieve suppression of magnetostatic domain generation. Temperature and field-dependent magnetic depth profiles have been measured by means of polarized neutron reflectometry. In both investigated structures, TC and MS are found to vary as a function of depth in accordance with the predefined compositional depth profiles. Our Co1−wRuw sample structures, which exhibit very steep material gradients, allow us to determine the localization limit for compositionally graded materials, which we find to be of the order of 1 nm. The Co1−xCrx systems show the expected U-shaped TC and MS depth profiles, for which these specific samples were designed. The corresponding temperature dependent magnetization profile is then utilized to control the coupling along the film depth, which even allows for a sharp onset of decoupling of top and bottom sample parts at elevated temperatures.

Modulation and \ud δ\ud -doping strategies, in which atomically thin layers of charged dopants are precisely deposited within a heterostructure, have played enabling roles in the discovery of new physical behavior in electronic materials. Here, we demonstrate a purely structural “\ud δ\ud -doping” strategy in complex oxide heterostructures, in which atomically thin manganite layers are inserted into an isovalent manganite host, thereby modifying the local rotations of corner-connected \ud MnO\ud 6\ud octahedra. Combining scanning transmission electron microscopy, polarized neutron reflectometry, and density functional theory, we reveal how local magnetic exchange interactions are enhanced within the spatially confined regions of suppressed octahedral rotations. The combined experimental and theoretical results illustrate the potential to utilize noncharge-based approaches to “doping” in order to enhance or suppress functional properties within spatially confined regions of oxide heterostructures.

The magnetic structure of the in-plane skyrmions in epitaxial MnSi/Si(111) thin films is probed in three dimensions by the combination of polarized neutron reflectometry (PNR) and small angle neutron scattering (SANS). We demonstrate that skyrmions exist in a region of the phase diagram above at temperature of 10 K. PNR shows the skyrmions are confined to the middle of the film due to the potential well formed by the surface twists. However, SANS shows that there is considerable disorder within the plane indicating that the magnetic structure is a 2D skyrmion glass.

Preventing stray magnetic interactions is important to improving technology that relies upon manipulating an electron's charge and spin. To this end, the authors investigate a binary intermetallic that has an internal magnetic field, yet does not affect the spin of surrounding components. As-grown epitaxial thin films of Mn${}_{3}$Al on GaAs(001) present the the ideal D0${}_{3}$ Heusler phase. This compound should be quite interesting for optimizing tomorrow's spintronic devices.

et al., The combination of lithography and ion implantation is demonstrated to be a suitable method to prepare lateral multilayers. A laterally, compositionally, and magnetically modulated microscale pattern consisting of alternating Co (1.6 µm wide) and Co-CoO (2.4 µm wide) lines has been obtained by oxygen ion implantation into a lithographically masked Au-sandwiched Co thin film. Magnetoresistance along the lines (i.e., current and applied magnetic field are parallel to the lines) reveals an effective positive giant magnetoresistance (GMR) behavior at room temperature. Conversely, anisotropic magnetoresistance and GMR contributions are distinguished at low temperature (i.e., 10 K) since the O-implanted areas become exchange coupled. This planar GMR is principally ascribed to the spatial modulation of coercivity in a spring-magnet-type configuration, which results in 180° Néel extrinsic domain walls at the Co/Co-CoO interfaces. The versatility, in terms of pattern size, morphology, and composition adjustment, of this method offers a unique route to fabricate planar systems for, among others, spintronic research and applications., This work was financed by the Research Foundation-Flanders (FWO), the Concerted Research ActionGOA/14/007, the 2014-SGR-1015 project of the Generalitat de Catalunya, and the European Commission under the 7th Framework Programme through the “Research Infrastructure” action of the “Capacities” Programme, NMI3-II Grant No. 283883. This work is based upon experiments (Proposal Nos. 5928 and 9384) performed at the MARIA instrument operated by JCNS at Heinz Maier-Leibnitz Zentrum (MLZ), Garching, Germany. The authors would like to thank IMEC for access to its lithography facilities as well as J. Moonens and J. Loo for technical support. ICN2 acknowledges support from the Severo Ochoa Program (MINECO, Grant SEV-2013-0295).

Storing information in magnetic recording technologies requires careful optimization of the recording media’s magnetic properties. For example, heat-assisted magnetic recording (HAMR) relies on a prerecording heating step that momentarily lowers the coercivity of the ferromagnetic recording media, and thereby decreases the energy expenditure for each writing operation. However, this process currently requires local temperature increases of several hundred Kelvins, which in turn can cause heat spreading, damage the write head, and limit recording rates. Here, we describe a general mechanism for dramatically tuning the coercivity of ferromagnetic films over small temperature ranges, by coupling them to an adjacent layer that undergoes a structural phase transition with large volume changes. The method is demonstrated in Ni/FeRh bilayers where the Ni layer was deposited at 300 K and 523 K, above and below the FeRh metamagnetic transition at 370 K. When the Ni layer is grown at high temperatures, the 1% FeRh lattice expansion relative to room temperature alters the Ni’s crystallographic texture during growth and leads to a 500% increase in coercivity upon cooling through the FeRh’s metamagnetic transition. Our analysis suggests this effect is related to domain wall pinning across grain boundaries with different orientations and strain states. This work highlights the promise of thermally tuning the coercivity of ferromagnetic materials through structural coupling to underlying films that could enable simplified heatsink designs and expand the selection of materials compatible with HAMR.

Low-damping magnetic oxide thin films with small thicknesses are essential for efficient insulator spintronic devices, particularly those driven by spin torque effects. Here, we investigate the depth-resolved compositional and magnetic properties of epitaxial spinel MgAl0.5Fe1.5O4 (MAFO), which has recently been reported as a promising low-damping insulator. We find that ≈11 nm films exhibit optimal Gilbert damping, with a typical damping parameter of 0.001. While defects due to strain relaxation in the bulk of the film contribute to increased damping for large film thickness, the damping increase in thinner films is attributed to the presence of a chemically disordered magnetic dead layer at the film/substrate interface. This interfacial dead layer arises from an Fe-deficient MAFO layer. Notably, this layer is only about one-sixth the thickness of that found at the interface between yttrium iron garnet films and gadolinium gallium garnet substrates, making MAFO an ideal thin-film insulator for spin-torque applications.

The depth-dependent magnetization in thin film oxygen stoichiometric and oxygen-deficient La0.7Sr0.3MnO3 is investigated by using polarized neutron reflectivity and DC bulk magnetometry. The polarized neutron reflectivity results reveal that the stoichiometric sample shows enhanced interfacial magnetization relative to the rest of the film. The oxygen-deficient sample exhibits a reduced average magnetization from the optimized recipe. Both films show regions of suppressed magnetization at the surface regardless of the growth pressure. The oxygen stoichiometric film does not show an interfacial dead layer, whereas the oxygen-deficient film exhibits a dead layer whose thickness changes with temperature. At a low applied field, we observe striking differences in the depth dependence of the magnetic ordering, with the oxygen-deficient film exhibiting exchange spring behavior, while the stoichiometric film shows a constant magnetization direction across the film. These results suggest that the incorporation of oxygen vacancies during growth leads to an accumulation of vacancies at the interface, which is enhanced at higher temperature due to increased oxygen mobility, creating a region of reduced magnetism that couples to the rest of the film. These results offer insight into the complex behavior and role of oxygen vacancies in the magnetism of these systems. Additionally, the study reveals further details of the negative magnetization in La0.7Sr0.3MnO3 reported in previous studies, which are discussed here.

We observe an induced switchable magnetic moment of $1.6\ifmmode\pm\else\textpm\fi{}0.40\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}/\mathrm{Fe}$ for the nominally antiferromagnetic $\mathrm{LaFe}{\mathrm{O}}_{3}$ extending two to four interface layers into the non--charge transfer system $\mathrm{L}{\mathrm{a}}_{0.7}\mathrm{S}{\mathrm{r}}_{0.3}\mathrm{Mn}{\mathrm{O}}_{3}\text{/}\mathrm{LaFe}{\mathrm{O}}_{3}\text{/}\mathrm{SrTi}{\mathrm{O}}_{3}(111)$. Simultaneously a mismatch of oxygen octahedra rotations at the interface implies an atomic reconstruction of reduced symmetry at the interface, reaching two to five layers into $\mathrm{LaFe}{\mathrm{O}}_{3}$. Density functional theory of a structure with atomic reconstruction and different correlation strength shows a ferrimagnetic state with a net Fe moment at the interface. Together these results suggest that engineered oxygen octahedra rotations, affecting the local symmetry, affect electron correlations and can be used to promote magnetic properties.

Interfaces between correlated complex oxides are promising avenues to realize new forms of magnetism that arise as a result of charge transfer, proximity effects, and locally broken symmetries. We report on the discovery of a noncollinear magnetic structure in superlattices of the ferromagnetic metallic oxide La_{2/3}Sr_{1/3}MnO_{3} (LSMO) and the correlated metal LaNiO_{3} (LNO). The exchange interaction between LSMO layers is mediated by the intervening LNO, such that the angle between the magnetization of neighboring LSMO layers varies in an oscillatory manner with the thickness of the LNO layer. The magnetic field, temperature, and spacer thickness dependence of the noncollinear structure are inconsistent with the bilinear and biquadratic interactions that are used to model the magnetic structure in conventional metallic multilayers. A model that couples the LSMO layers to a helical spin state within the LNO fits the observed behavior. We propose that the spin-helix results from the interaction between a spatially varying spin susceptibility within the LNO and interfacial charge transfer that creates localized Ni^{2+} states. Our work suggests a new approach to engineering noncollinear spin textures in metallic oxide heterostructures.

Assessing and controlling magnetic interactions in magnetic nanostructures are critical to nanomagnetic and spintronic explorations, such as magnetic recording media, permanent magnets, magnetic memory and logic devices, etc. Here we demonstrate an extremely sensitive magnetic yoking effect and tunable interactions in FePt based hard/soft bilayers mediated by the soft layer. Below the exchange length, a thin soft layer strongly exchange couples to the perpendicular moments of the hard layer; above the exchange length, just a few nanometers thicker, the soft layer moments turn in-plane and act to yoke the dipolar fields from the adjacent hard layer perpendicular domains. The evolution from exchange to dipolar-dominated interactions is experimentally captured by first-order reversal curves, the delta-M method, and polarized neutron reflectometry, and confirmed by micromagnetic simulations. These findings demonstrate an effective yoking approach to design and control magnetic interactions in wide varieties of magnetic nanostructures and devices., Comment: 24 pages, 5 figures, plus 3-page supplementary information

We demonstrate substantial enhancement in the energy product of MnBi-based magnets by forming robust ferromagnetic exchange coupling between a MnBi layer and a thin CoFe layer in a unique perpendicular coupling configuration, which provides increased resistance to magnetization reversal. The measured nominal energy product of $172\phantom{\rule{0.16em}{0ex}}\mathrm{kJ}/{\mathrm{m}}^{3}$ at room temperature is the largest value experimentally attained for permanent magnets free of expensive raw materials. Our finding shows that exchange-coupled MnBi/CoFe magnets are a viable option for pursuing rare-earth-free magnets with energy products approaching those containing rare-earth elements.

The emergence of complex new ground states at interfaces has been identified as one of the most promising routes to highly tunable nanoscale materials. Despite recent progress, isolating and controlling the underlying mechanisms behind these emergent properties remains among the most challenging materials physics problems to date. In particular, generating ferromagnetism localized at the interface of two nonferromagnetic materials is of fundamental and technological interest. Moreover, the ability to turn the ferromagnetism on and off would shed light on the origin of such emergent phenomena and is promising for spintronic applications. We demonstrate that ferromagnetism confined within one unit cell at the interface of CaRuO3 and CaMnO3 can be switched on and off by changing the symmetry of the oxygen octahedra connectivity at the boundary. Interfaces that are symmetry-matched across the boundary exhibit interfacial CaMnO3 ferromagnetism while the ferromagnetism at symmetry-mismatched interfaces is suppressed. We attribute the suppression of ferromagnetic order to a reduction in charge transfer at symmetry-mismatched interfaces, where frustrated bonding weakens the orbital overlap. Thus, interfacial symmetry is a new route to control emergent ferromagnetism in materials such as CaMnO3 that exhibit antiferromagnetism in bulk form.

Electric field control of magnetism provides a promising route towards ultralow power information storage and sensor technologies. The effects of magneto-ionic motion have been prominently featured in the modification of interface characteristics. Here, we demonstrate magnetoelectric coupling moderated by voltage-driven oxygen migration beyond the interface in relatively thick AlOx/GdOx/Co(15 nm) films. Oxygen migration and Co magnetization are quantitatively mapped with polarized neutron reflectometry under electro-thermal conditioning. The depth-resolved profiles uniquely identify interfacial and bulk behaviours and a semi-reversible control of the magnetization. Magnetometry measurements suggest changes in the microstructure which disrupt long-range ferromagnetic ordering, resulting in an additional magnetically soft phase. X-ray spectroscopy confirms changes in the Co oxidation state, but not in the Gd, suggesting that the GdOx transmits oxygen but does not source or sink it. These results together provide crucial insight into controlling magnetism via magneto-ionic motion, both at interfaces and throughout the bulk of the films., Mechanisms allowing electrical manipulation of magnetic material possess potential applications in low power memory and sensor technologies. Here, the authors demonstrate the control of magnetic characteristics via voltage-driven migration of oxygen across a GdOx/Co interface, well into the bulk of the cobalt.

Here we present polarized neutron reflectometry measurements exploring thin film heterostructures comprised of a strongly correlated Mott state, GdTiO$_3$, embedded with SrTiO$_3$ quantum wells. Our results reveal that the net ferromagnetism inherent to the Mott GdTiO$_3$ matrix propagates into the nominally nonmagnetic SrTiO$_3$ quantum wells and tracks the magnetic order parameter of the host Mott insulating matrix. Beyond a well thickness of 5 SrO layers, the magnetic moment within the wells is dramatically suppressed, suggesting that quenched well magnetism comprises the likely origin of quantum critical magnetotransport in this thin film architecture. Our data demonstrate that the interplay between proximate exchange fields and polarity induced carrier densities can stabilize extended magnetic states within SrTiO$_3$ quantum wells., Comment: 5 pages, 4 figures

Ferromagnetism in topological insulators (TIs) opens a topologically non-trivial exchange band gap, providing an exciting platform to manipulate the topological order through an external magnetic field. Here, we experimentally show that the surface of an antiferromagnetic thin film can independently control the topological order of the top and the bottom surface states of a TI thin film through proximity couplings. During the magnetization reversal in a field scan, two intermediate spin configurations stem from unsynchronized magnetic switchings of the top and the bottom AFM/TI interfaces. These magnetic configurations are shown to result in new topological phases with non-zero Chern numbers for each surface, introducing two counter-propagating chiral edge modes inside the exchange gap. This change in the number of transport channels, as the result of the topological transitions, induces antisymmetric magneto-resistance spikes during the magnetization reversal. With the high Neel ordering temperature provided by the antiferromagnetic layers, the signature of the induced topological transition persists in transport measurements up to a temperature of around 90 K, a factor of three over the Curie temperature in a typical magnetically doped TI thin film.

Pulsed laser deposition films from Ba2FeMoO6 (BFMO) targets onto SrTiO3[001] (STO) substrates have been reported previously to have non-zero magnetism at 300 K, a majority of magnetic ordering at 240 K that is less than the 370 K ordering temperature of polycrystalline BFMO, and suppressed saturation magnetization compared to polycrystalline BFMO. To interrogate these previously reported observations of BFMO on STO, we have used a combination of x-ray diffraction, atomic force microscopy, x-ray and neutron reflectivity, and x-ray photoelectron spectroscopy that shows inhomogeneities. The present results show off-stoichiometry on the A-site by incorporation of Sr from the substrate and on the B-site to have %Fe/%Mo > 1 by evolution of BaMoO4. There is an enhanced ordering temperature and magnetic response nearer to the SrTiO3 interface compared to the air interface. Depth dependent strain and microstructure are needed to explain the magnetic response. Holistic considerations and implications are also discussed.Pulsed laser deposition films from Ba2FeMoO6 (BFMO) targets onto SrTiO3[001] (STO) substrates have been reported previously to have non-zero magnetism at 300 K, a majority of magnetic ordering at 240 K that is less than the 370 K ordering temperature of polycrystalline BFMO, and suppressed saturation magnetization compared to polycrystalline BFMO. To interrogate these previously reported observations of BFMO on STO, we have used a combination of x-ray diffraction, atomic force microscopy, x-ray and neutron reflectivity, and x-ray photoelectron spectroscopy that shows inhomogeneities. The present results show off-stoichiometry on the A-site by incorporation of Sr from the substrate and on the B-site to have %Fe/%Mo > 1 by evolution of BaMoO4. There is an enhanced ordering temperature and magnetic response nearer to the SrTiO3 interface compared to the air interface. Depth dependent strain and microstructure are needed to explain the magnetic response. Holistic considerations and implications are also discu...

Magnetic compensation in ferrimagnets plays an important role in spintronic and magnetic recording devices. Experimental results have demonstrated a thickness dependence of the compensation temperature (Tcomp) in amorphous TbFeCo thin films. It was speculated that this thickness dependence originated from a variation in the short-range order. In this work, we have investigated the depth-resolved compositional and magnetization profiles using polarized neutron reflectometry. We find that although the composition is uniform across the film thickness, near the substrate interface, the magnetization exhibits a different temperature dependence from that of the rest of the sample. Monte Carlo simulations show that it is this difference in interfacial magnetization that causes the aforementioned thickness dependence of the compensation. These results demonstrate the critical role of the substrate interface in determining the magnetic properties of amorphous ferrimagnetic thin films for spintronic applications.

We studied the depth dependent magnetization profile of the magnetostrictive Co thin film layer in a (PbMg0.33Nb0.67)1-x:(PbTiO3)x (PMN-PT) (011)/Ta/Co/Ta structure under both zero and nonzero applied electric field using polarized neutron reflectometry. Application of an electric field across the PMN-PT substrate generates a strain, which rotates the magnetization of the Co layer consistent with the Villari effect. At low magnetic fields (near remanence and coercive field conditions), we find that the depth dependent magnetization profile is non-uniform, under both zero and nonzero applied electric fields. These variations are attributable to the depth dependent strain profile in the Co film, as determined by finite element analysis simulations.

Polarized neutron reflectometry measurements are presented exploring the evolution of ferrimagnetism in GdTiO$_3$ films as they are confined between SrTiO$_3$ layers of variable thicknesses. As GdTiO$_3$ films approach the thin layer limit and are confined within a substantially thicker SrTiO$_3$ matrix, the TiO$_6$ octahedral tilts endemic to GdTiO$_3$ coherently relax toward the undistorted, cubic phase of SrTiO$_3$. Our measurements reveal that the ferrimagnetic state within the GdTiO$_3$ layers survives as the TiO$_6$ octahedral tilts in the GdTiO$_3$ layers are suppressed. Furthermore, our data suggest that a magnetic dead layer develops within the GdTiO$_3$ layer at each GdTiO$_3$/ SrTiO$_3$ interface. The ferrimagnetic moment inherent to the core GdTiO$_3$ layers is negligibly (in models with dead layers) or only weakly (in models without dead layers) impacted as the octahedral tilt angles are suppressed by more than 50$\%$ and the $t_{2g}$ bandwidth is dramatically renormalized., 5 pages, 4 figures

A procedure is described for polarized neutron reflectometry when the Zeeman corrections are significant, which occurs when both the magnetic anisotropy and the applied magnetic field are significant. Calculations and a recommended procedure for an example system are provided., The presence of a large applied magnetic field removes the degeneracy of the vacuum energy states for spin-up and spin-down neutrons. For polarized neutron reflectometry, this must be included in the reference potential energy of the Schrödinger equation that is used to calculate the expected scattering from a magnetic layered structure. For samples with magnetization that is purely parallel or antiparallel to the applied field which defines the quantization axis, there is no mixing of the spin states (no spin-flip scattering) and so this additional potential is constant throughout the scattering region. When there is non-collinear magnetization in the sample, however, there will be significant scattering from one spin state into the other, and the reference potentials will differ between the incoming and outgoing wavefunctions, changing the angle and intensities of the scattering. The theory of the scattering and recommended experimental practices for this type of measurement are presented, as well as an example measurement.