Physics Commons^™

Ferroelectric Polarization Dependent Interface Effects, Xiaohui Liu

Department of Physics and Astronomy: Dissertations, Theses, and Student Research

Utilization of the switchable spontaneous polarization of nanometer scale ferroelectric materials offers a promising avenue for future nanoelectronic devices. In this dissertation, we use density-functional calculations and phenomenological modeling to explore the effects of interface termination on thin-film heterostructures, the effects of electron doping in bulk ferroelectric materials on ferroelectric stability, and the effects of ferroelectric polarization switching on the electronic and transport properties of interfaces.

For SrRuO₃/BaTiO₃/SrRuO₃ epitaxial heterostructures grown on SrTiO₃, we find that the built-in dipole at the BaO/RuO₂ terminated interface leads to a strong preference for one polarization. …

Ferroelectric Tunnel Junctions With Graphene Electrodes, Haidong Lu, Alexey Lipatov, Sangjin Ryu, D. J. Kim, H. Lee, M. Ye. Zhuravlev, Chang-Beom Eom, Evgeny Y. Tsymbal, Alexander Sinitskii, Alexei Gruverman

Evgeny Tsymbal Publications

Polarization-driven resistive switching in ferroelectric tunnel junctions (FTJs)—structures composed of two electrodes separated by an ultrathin ferroelectric barrier—offers new physics and materials functionalities, as well as exciting opportunities for the next generation of non-volatile memories and logic devices. Performance of FTJs is highly sensitive to the electrical boundary conditions, which can be controlled by electrode material and/or interface engineering. Here, we demonstrate the use of graphene as electrodes in FTJs that allows control of interface properties for significant enhancement of device performance. Ferroelectric polarization stability and resistive switching are strongly affected by a molecular layer at the graphene/BaTiO₃ interface. …

Nonlinear Dichroism In Back-To-Back Double Ionization Of He By An Intense Elliptically Polarized Few-Cycle Extreme Ultraviolet Pulse, Jean Marcel Ngoko Djiokap, N. L. Manakov, A. V. Meremianin, S. X. Hu, L. B. Madsen, Anthony F. Starace

Anthony F. Starace Publications

Control of double ionization of He by means of the polarization and carrier-envelope phase (CEP) of an intense, few-cycle extreme ultraviolet (XUV) pulse is demonstrated numerically by solving the six-dimensional two-electron, time-dependent Schrödinger equation for He interacting with an elliptically polarized XUV pulse. Guided by perturbation theory (PT), we predict the existence of a nonlinear dichroic effect (∝ I^3/2) that is sensitive to the CEP, ellipticity, peak intensity I, and temporal duration of the pulse. This dichroic effect (i.e., the difference of the two-electron angular distributions for opposite helicities of the ionizing XUV pulse) originates from interference of …

Control Of Majorana Edge Modes By A G-Factor Engineered Nanowire Spin Transistor, Amrit De, Alexey Kovalev

Department of Physics and Astronomy: Faculty Publications

We propose the manipulation of Majorana edge states via hybridization and spin currents in a nanowire spin transistor. The spin transistor is based on a heterostructure nanowire comprising of semiconductors with large and small g-factors that form the topological and non-topological regions respectively. The hybridization of bound edge states results in spin currents and 4π-periodic torques, as a function of the relative magnetic field angle – an effect which is dual to the fractional Josephson effect. We establish relation between torques and spin-currents in the non-topological region where the magnetic field is almost zero and spin is …

Complex Band Structure Of Topologically Protected Edge States, Xiaoqian Dang, John D. Burton, Alan Kalitsov, Julian P. Velev, Evgeny Y. Tsymbal

Evgeny Tsymbal Publications

One of the great successes of modern condensed matter physics is the discovery of topological insulators (TIs). A thorough investigation of their properties could bring such materials from fundamental research to potential applications. Here, we report on theoretical investigations of the complex band structure (CBS) of two-dimensional (2D) TIs. We utilize the tight-binding form of the Bernevig, Hughes, and Zhang model as a prototype for a generic 2D TI. Based on this model, we outline the conditions that the CBS must satisfy in order to guarantee the presence of topologically protected edge states. Furthermore, we use the Green’s function technique …

Emergent Vortices At A Ferromagnetic Superconducting Oxide Interface, Alexander Paul Petrović, A. Paré, Tula R. Paudel, K. Lee, S. Holmes, Crispin H.W. Barnes, A. David, T. Wu, Evgeny Y. Tsymbal, C. Panagopoulos

Evgeny Tsymbal Publications

Understanding the cohabitation arrangements of ferromagnetism and superconductivity at the LaAlO₃/SrTiO₃ interface remains an open challenge. Probing this coexistence with sub-Kelvin magnetotransport experiments, we demonstrate that a hysteretic in-plane magnetoresistance develops below the superconducting transition for H < 0.15 T, independently of the carrier density or oxygen annealing. This hysteresis is argued to arise from vortex depinning within a thin (< 20 nm) superconducting layer, mediated by discrete ferromagnetic dipoles located solely above the layer. The pinning strength may be modified by varying the superconducting channel thickness via electric field-effect doping. No evidence is found for bulk magnetism or finite-momentum pairing, and we conclude that ferromagnetism is strictly confined to the interface, where it competes with superconductivity. Our work indicates that oxide interfaces are ideal candidate materials for the growth and analysis of nanoscale superconductor/ferromagnet hybrids.

Effect Of Thermal Annealing On Ferroelectric Domain Structures In Poly(Vinylidene-Fluoride-Trifluorethylene) Langmuir-Blodgett Thin Films, Zhiyong Xiao, J. Hamblin, Shashi Poddar, Stephen Ducharme, P. Paruch, Xia Hong

Stephen Ducharme Publications

We report a piezo-response force microscopy study of the effect of thermal annealing on ferroelectric domain structures in 6 to 20 monolayer (11 to 36 nm) polycrystalline poly(vinylidene-fluoridetrifluorethylene) thin films prepared using the Langmuir-Blodgett approach. Stripe-shape domains have been created at room temperature and subjected to thermal annealing at progressively higher temperatures up to the ferroelectric Curie temperature T_C of approximately 110 °C. The static configuration of the domain walls exhibits no appreciable temperature dependence after thermal annealing, with the domain-wall roughness exponent ζ ranging from 0.4 to 0.5. Above 80 °C, we observed spontaneous polarization reversal at randomly …

Chemically Induced Jahn–Teller Ordering On Manganite Surfaces, Zheng Gai, Wenzhi Lin, John D. Burton, K. Fuchigami, Paul C. Snijders, T. Z. Ward, Evgeny Y. Tsymbal, J. Shen, Stephen Jesse, Sergei V. Kalinin, Arthur P. Baddorf

Evgeny Tsymbal Publications

Physical and electrochemical phenomena at the surfaces of transition metal oxides and their coupling to local functionality remains one of the enigmas of condensed matter physics. Understanding the emergent physical phenomena at surfaces requires the capability to probe the local composition, map order parameter fields and establish their coupling to electronic properties. Here we demonstrate that measuring the sub-30-pm displacements of atoms from high-symmetry positions in the atomically resolved scanning tunnelling microscopy allows the physical order parameter fields to be visualized in real space on the single-atom level. Here, this local crystallographic analysis is applied to the in-situ-grown manganite surfaces. …

Nonlinear Transport In Nanoscale Phase Separated Colossal Magnetoresistive Oxide Thin Films, V. R. Singh, L. Zhang, Anil Rajapitamahuni, N. Devries, Xia Hong

Materials Research Science and Engineering Center: Faculty Publications

We report a study of the I-V characteristics of 2.5–5.4 nm epitaxial La_1xSr_xMnO₃ (x = 0.33 and 0.5) and La_0.7Ca_0.3MnO₃ thin films. While La_0.67Sr_0.33MnO₃ films exhibit linear conduction over the entire temperature and magnetic field ranges investigated, we observe a strong correlation between the linearity of the I-V relation and the metal-insulator transition in highly phase separated La_0.5Sr_0.5MnO₃ and La_0.7Ca_0.3MnO₃ films. Linear I-V behavior has been observed in the high temperature paramagnetic insulating phase, and …

Below Gap Optical Absorption In Gaas Driven By Intense, Single-Cycle Coherent Transition Radiation, J. Goodfellow, Matthias Fuchs, D. Daranciang, S. Ghimire, F. Chen, H. Loos, D. A. Reis, A. S. Fisher, A. M. Lindenberg

Matthias Fuchs Publications

Single-cycle terahertz fields generated by coherent transition radiation from a relativistic electron beam are used to study the high field optical response of single crystal GaAs. Large amplitude changes in the sub-band-gap optical absorption are induced and probed dynamically by measuring the absorption of a broad-band optical beam generated by transition radiation from the same electron bunch, providing an absolutely synchronized pump and probe geometry. This modification of the optical properties is consistent with strong-field-induced electroabsorption. These processes are pertinent to a wide range of nonlinear terahertz-driven lightmatter interactions anticipated at accelerator-based sources.

Investigation Of Ferroelectric Domains In Thin Films Of Vinylidene Fluoride Oligomers, Pankaj Sharma, Shashi Poddar, Rafal Korlacki, Stephen Ducharme, Alexei Gruverman

Stephen Ducharme Publications

High-resolution vector piezoresponse force microscopy (PFM) has been used to investigate ferroelectric domains in thin vinylidene fluoride oligomer films fabricated by the Langmuir-Blodgett deposition technique. Molecular chains are found to be preferentially oriented normal to the substrate, and PFM imaging shows that the films are in ferroelectric β-phase with a predominantly in-plane polarization, in agreement with infrared spectroscopic ellipsometry and X-ray diffraction measurements. The fractal analysis of domain structure has yielded the Hausdorff dimension (D) in the range of ~1.3–1.5 indicating a random-bond nature of the disorder potential, with domain size exhibiting Landau-Lifshitz-Kittel scaling.

Long-Range Electronic Reconstruction To A Dxz,Yz-Dominated Fermi Surface Below The Laalo3/Srtio3 Interface, Alexander Paul Petrović, A. Pare, Tula R. Paudel, K. Lee, S. Holmes, Crispin H.W. Barnes, A. David, T. Wu, Evgeny Y. Tsymbal, C. Panagopoulos

Evgeny Tsymbal Publications

Low dimensionality, broken symmetry and easily-modulated carrier concentrations provoke novel electronic phase emergence at oxide interfaces. However, the spatial extent of such reconstructions - i.e. the interfacial ‘‘depth’’ - remains unclear. Examining LaAlO₃/SrTiO₃ heterostructures at previously unexplored carrier densities n_2D 14 cm^-2 , we observe a Shubnikov-de Haas effect for small in-plane fields, characteristic of an anisotropic 3D Fermi surface with preferential d_xz,yz orbital occupancy extending over at least 100 nm perpendicular to the interface. Quantum oscillations from the 3D Fermi surface of bulk doped SrTiO₃ emerge simultaneously at higher n_2D. …

Polarization Imaging In Ferroelectric Polymer Thin Film Capacitors By Pyroelectric Scanning Microscopy, Jingfeng Song, Haidong Lu, Alexei Gruverman, Stephen Ducharme

Stephen Ducharme Publications

A Pyroelectric Scanning Microscopy system, which uses laser-induced thermal modulation for mapping the pyroelectric response, has been used to image a bipolar domain pattern in a ferroelectric polymer thin film capacitor. This system has achieved a resolution of 660±28 nm by using a violet laser and high f-number microscope objective to reduce the optical spot size, and by operating at high modulation frequencies to reduce the thermal diffusion length. The results agree well with a thermal model implemented numerically using finite element analysis.

Electron Matter Interferometry And The Electron Double-Slit Experiment, Roger Bach

Department of Physics and Astronomy: Dissertations, Theses, and Student Research

Quantum mechanics has fundamentally changed the way scientists think about the world. Quantum mechanical theory has found it's way into our everyday lives through advances in technology. In this dissertation a fundamental quantum mechanical demonstration and the technological development of a new quantum mechanical device are presented.

Double-slit diffraction is a corner stone of quantum mechanics. It illustrates key features of quantum mechanics: interference and the particle-wave duality of matter. Here we demonstrate the full realization of Richard Feynman's famous thought experiment. By placing a movable mask in front of a double-slit to control the transmission through the individuals slits. …

X-Ray Second Harmonic Generation, S. Shwartz, Matthias Fuchs, J. B. Hastings, Y. Inubushi, T. Ishikawa, T. Katayama, D. A. Reis, T. Sato, K. Tono, M. Yabashi, S. Yudovich, S. E. Harris

Matthias Fuchs Publications

We report clear experimental evidence for second harmonic generation at hard x-ray wavelengths. Using a 1.7 Å pumping beam generated by a free electron laser, we observe second harmonic generation in diamond. The generated second harmonic is of order 10 times the background radiation, scales quadratically with pump pulse energy, and is generated over a narrow phase-matching condition. Of importance for future experiments, our results indicate that it is possible to observe nonlinear x-ray processes in crystals at pump intensities exceeding 10¹⁶ W/cm².

Magnetic Properties Of Fe-Doped Mnal, Priyanka Manchanda, Arti Kashyap, Jeffrey E. Shield, L. H. Lewis, Ralph Skomski

Ralph Skomski Publications

Electronic and magnetic properties of L1₀-ordered Fe_xMn_1−xAl alloys (x = 0, 0.0625, 0.125, 0.1875, 0.5) are investigated by first-principle supercell calculations. Pristine MnAl exhibits robust ferromagnetism involving the dense-packed Mn atoms in (001) planes of the tetragonal structure. Iron substitution for Mn significantly deteriorates the magnetiza­tion of the alloy. The reduction is a dilution effect, caused by the relatively small Fe moment of about 1.9 μ_B per atom, as compared to the Mn moment, which exceeds 2.4 μ_B. By contrast, 50% Fe substituted for Mn (x = 0.5) …

Spin Transfer Of Quantum Information Between Majorana Modes And A Resonator, Alexey Kovalev, Amrit De, Kirill Shtengel

Department of Physics and Astronomy: Faculty Publications

We show that resonant coupling and entanglement between a mechanical resonator and Majorana bound states can be achieved via spin currents in a 1D quantum wire with strong spin-orbit interactions. The bound states induced by vibrating and stationary magnets can hybridize, thus resulting in spin-current induced 4π-periodic torques, as a function of the relative field angle, acting on the resonator. We study the feasibility of detecting and manipulating Majorana bound states with the use of magnetic resonance force microscopy techniques.

A Low-Power Optical Electron Switch, Wayne Cheng-Wei Huang, Roger Bach, Peter Beierle, Herman Batelaan

Department of Physics and Astronomy: Faculty Publications

An electron beam is deflected when it passes over a silicon-nitride surface, if the surface is illuminated by a low-power continuous-wave diode laser. A deflection angle of up to 1.2 mrad is achieved for an electron beam of 29 μrad divergence. A mechanical beam-stop is used to demonstrate that the effect can act as an optical electron switch with a rise and fall time of 6 μs. Such a switch provides an alternative means to control electron beams, which may be useful in electron lithography and microscopy.

Large-Scale Solution Synthesis Of Narrow Graphene Nanoribbons, Timothy H. Vo, Mikhail Shekhirev, Donna A. Kunkel, Martha D. Morton, Eric Berglund, Lingmei Kong, Peter M. Wilson, Peter A. Dowben, Axel Enders, Alexander Sinitskii

Nebraska Center for Materials and Nanoscience: Faculty Publications

According to theoretical studies, narrow graphene nanoribbons with atomically precise armchair edges and widths of(1.1 eV), which makes them potentially promising for logic applications. Different top–down fabrication approaches typically yield ribbons with width >10nm and have limited control over their edge structure. Here we demonstrate a novel bottom–up approach that yields gram quantities of high-aspect-ratio graphene nanoribbons, which are only ~1 nm wide and have atomically smooth armchair edges. These ribbons are shown to have a large electronic bandgap of ~1.3 eV, which is significantly higher than any value reported so far in experimental studies of graphene nanoribbons prepared by …

Resonant Electron-Atom Bremsstrahlung In An Intense Laser Field, A. N. Zheltukhin, A. V. Flegel, M. V. Frolov, N. L. Manakov, Anthony F. Starace

Anthony F. Starace Publications

We analyze a resonant mechanism for spontaneous laser-assisted electron bremsstrahlung (BrS) involving the resonant transition (via either laser-assisted electron-ion recombination or electron-atom attachment) into a laser-dressed intermediate quasibound state (corresponding, respectively, to either a field-free neutral atom or a negative-ion bound state) accompanied by ionization or detachment of this state by the laser field. This mechanism leads to resonant enhancement (by orders of magnitude) of the BrS spectral density for emitted photon energies corresponding to those for laser-assisted recombination or attachment. We present an accurate parametrization of the resonant BrS amplitude in terms of the amplitudes for nonresonant BrS, for …

Nonlinear Transport In Nanoscale Phase Separated Colossal Magnetoresistive Oxide Thin Films, V. R. Singh, L. Zhang, A. K. Rajapitamahuni, N. Devires, X. Hong

Xia Hong Publications

We report a study of the I-V characteristics of 2.5–5.4 nm epitaxial La_1-xSr_xMnO₃ (x=0.33 and 0.5) and La_0.7Ca_0.3MnO₃ thin films. While La_0.67Sr_0.33MnO₃ films exhibit linear conduction over the entire temperature and magnetic field ranges investigated, we observe a strong correlation between the linearity of the I-V relation and the metal-insulator transition in highly phase separated La_0.5Sr_0.5MnO₃ and La_0.7Ca_0.3MnO₃ films. Linear I-V behavior has been observed in the high temperature …

Spin Density Waves In Periodically Strained Graphene Nanoribbons, Nabil M. Al-Aqtash, Renat F. Sabirianov

Nebraska Center for Materials and Nanoscience: Faculty Publications

Zigzag graphene nanoribbons (ZGNRs) are antiferromagnetic in the ground state with zero net magnetization due to the compensation of contributions from opposite edges. Uniform deformations (both shear and axial) do not produce magnetization due to symmetry restrictions. However, we report the results of first-principles calculations that predict the induction of spin density waves (SDWs) in ZGNRs under non-uniform periodic strain. Using the density functional theory (DFT) method, we show that a sinusoidal magnetization variation along the axis of the ribbon occurs under a sinusoidal transversal shear strain. SDWs appear due to the presence of a strain gradient that induced asymmetry …

Phase Composition And Nanostructure Of Zr2Co11-Based Alloys, Y.L. Jin, Wenyong Zhang, Ralph A. Skomski, Shah R. Valloppilly, Jeffrey E. Shield, David J. Sellmyer

David Sellmyer Publications

The effect of Mo addition on phase composition and nanostructure of nanocrystalline Zr₁₆Co_84-xMo_x (x=0–2.0) melt spun at 55 m/s has been investigated. All the ribbons consist mainly of a hard magnetic Zr₂Co₁₁ phase with rhombohedral crystal structure but also contain minor amounts of soft-magnetic phases. The increase in cell volume on alloying suggests that Mo mainly enters the rhombohedral Zr₂Co₁₁ structure and occupies the Co site. Mo addition promotes the formation of the hard magnetic phase and increases its volume fraction. The mean grain size of the hard magnetic …

Structural, Magnetic, And Electron Transport Properties Of Mn3-XPtXSn (X = 0, 0.5, 1) Nanomaterials, A Nelson, Yung Huh, Parashu Kharel, Shah R. Valloppilly, Ralph A. Skomski, David J. Sellmyer

David Sellmyer Publications

The structural, magnetic, and electron-transport properties of Mn_3-xPt_xSn (x=0, 0.5, 1) nanomaterials prepared by arc-melting, melt-spinning, and annealing were investigated. It was found that the hexagonal structure is the most stable structure for Mn³Sn and the samples show an antiferromagnetic spin order at room temperature. The Pt-containing samples are mainly tetragonal but contain a small amount of other impurity phases, including hexagonal Mn³Sn and Mn₂Sn. At room temperature, the Pt-containing samples show ferri- or ferromagnetic spin order with a Curie temperature of about 370 K. The measured high-field magnetization and …

Magnetic Nanostructuring And Overcoming Brown’S Paradox To Realize Extraordinary High-Temperature Energy Products, Balamurugan Balasubramanian, Pinaki Mukherjee, Ralph A. Skomski, Priyanka Manchanda, Bhaskar Das, David J. Sellmyer

David Sellmyer Publications

Nanoscience has been one of the outstanding driving forces in technology recently, arguably more so in magnetism than in any other branch of science and technology. Due to nanoscale bit size, a single computer hard disk is now able to store the text of 3,000,000 average-size books, and today’s high-performance permanent magnets—found in hybrid cars, wind turbines, and disk drives—are nanostructured to a large degree. The nanostructures ideally are designed from Co- and Fe-rich building blocks without critical rare-earth elements, and often are required to exhibit high coercivity and magnetization at elevated temperatures of typically up to 180 °C for …

Size-Induced Chemical And Magnetic Ordering In Individual Fe–Au Nanoparticles, Pinaki Mukherjee, Priyanka Manchanda, Pankaj Kumar, Lin Zhou, Matthew J. Kramer, Arti Kashyap, Ralph Skomski, David J. Sellmyer, Jeffrey E. Shield

David Sellmyer Publications

Formation of chemically ordered compounds of Fe and Au is inhibited in bulk materials due to their limited mutual solubility. However, here we report the formation of chemically ordered L12-type Fe₃Au and FeAu₃ compounds in Fe–Au sub-10 nm nanoparticles, suggesting that they are equilib-rium structures in size-constrained systems. The stability of these L12-ordered Fe₃Au and FeAu₃ com-pounds along with a previously discovered L10-ordered FeAu has been explained by a size-dependent equilibrium thermodynamic model. Furthermore, the spin ordering of these three com-pounds has been computed using ab initio first-principle calculations. All ordered compounds exhibit a …

Magneto-Electric Control Of Surface Anisotropy And Nucleation Modes In L10-Copt Thin Films, Priyanka Manchanda, Pankaj Kumar, Hans Fangohr, David J. Sellmyer, Arti Kashyap, Ralph Skomski

David Sellmyer Publications

The interplay between electric field-controlled surface magnetic anisotropy and micromagnetic nu-cleation modes for L1₀-CoPt thin films is investigated with density-functional and micromagnetic model calculations. The electric field redistributes electron states near the Fermi level, which has a fairly strong effect on the surface anisotropy, but due to inversion symmetry, the net anisotropy of the films with odd numbers of layers remains unchanged. By contrast, the micromagnetic nucleation mode is spatially asymmetric even for symmetric thin films with odd numbers of layers. This leads to a reduction of the nucleation field (coercivity) and—for suitably chosen nanostructures—to sub-stantial changes in …

Kondorski Reversal In Magnetic Nanowires, Ralph A. Skomski, Eva Schubert, Axel Enders, David J. Sellmyer

David Sellmyer Publications

Magnetization reversal in nanowire systems, such as alnico-type permanent magnets, slanted columns produced by glancing-angle deposition, and nanowires embedded in alumina templates, is investigated by model calculations. The angular dependence of the domain-wall propagation is Kondorski-like, reminiscent of Kondorski pinning in bulk materials but with a somewhat different physics and consistent with Kerr hysteresis-loop measurements. Criss-cross patterning of alnicos improves the coercivity but reduces the remanence, with virtually zero net effect on energy product. Finally, we briefly discuss the wire-radius dependence of the coercivity in the context of "shape anisotropy" and the occurrence of interaction domains in alnico.

Magnetic Silicon Nanoparticles, Priyanka Manchanda, Pankaj Kumar, Balamurugan Balasubramanian, Pinaki Mukherjee, Arti Kashyap, David J. Sellmyer, Ralph Skomski

David Sellmyer Publications

Prospects for diamond-structured magnetic Si are investigated experimentally, by model calcula-tions, and numerically. Our theoretical analysis, using bond-orbital, Vienna ab-initio simulation pack-age, and SIESTA calculations, suggest that some diamond-Si imperfection may carry a magnetic moment. In particular, for tetrahedral Si₅ clusters, we calculate a magnetic moment of 4 μB per cluster. These moments are more likely to be observed in nanoparticles, as compared with thin films, due to the larger surface-to-volume ratios of the former and to their more versatile atomic surface structure. Experimentally, we have prepared Si nanoparticles by cluster deposition and found a small magnet-ization of 2.9 …

Effect Of Annealing On Nanostructure And Magnetic Properties Of Zr2Co11 Material, Wenyong Zhang, Xingzhong Li, Shah R. Valloppilly, Ralph A. Skomski, David J. Sellmyer

David Sellmyer Publications

Single-phaseZr₂Co₁₁ nanomagnetic materials with high coercivity have been fabricated by melt spin-ning with subsequent annealing under Ar, N₂, and vacuum. Annealing coarsens the grains and de-creases the density of defects, leading to intergrain decoupling action and the enhancement of the magnetocrystalline anisotropy field of the hard magnetic phase. Therefore, coercivity increases 44.7% from 6.7 kOe for the as-spun to 9.7 kOe for the annealed, which is the highest among Zr–Co alloys so far. The results show that the magnetic-hardening mechanism is primarily dominated by domain-wall pinning. In addition, annealing clearly increases the saturation magnetization. The …