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Time inversion symmetry in the Dirac and Schrödinger-Pauli theories

The Schrödinger-Pauli theory is generally believed to give a faithful representation of the nonrelativistic and weakly relativistic limit of the Dirac theory. However, the Schrödinger-Pauli theory is fundamentally incomplete in its account of broken time inversion symmetry, e.g., in magnetically ordered systems. Here, in the Dirac theory of the electron, magnetic order breaks time inversion symmetry even in the nonrelativistic limit, whereas time inversion symmetry is effectively preserved in the Schrödinger-Pauli theory in the absence of spin-orbit coupling. In the Dirac theory, the Berry curvature $1/(2m^2 c^2)$ is thus an intrinsic property of nonrelativistic electrons similar to the well-known spin magnetic moment $e\hbar/(2m)$, while this result is missed by the nonrelativistic or weakly relativistic Schrödinger-Pauli equation. In ferromagnetically ordered systems, the intrinsic Berry curvature yields a contribution to the anomalous Hall conductivity independent of spin-orbit coupling.

Winkler, R. [Northern Illinois Univ., DeKalb, IL (↗

Two-Dimensional van der Waals Nanoplatelets with Robust Ferromagnetism

We have synthesized unique colloidal nanoplatelets of the two-dimensional (2D) van der Waals ferromagnet CrI3 and have characterized these nanoplatelets structurally, magnetically, and by magnetic circular dichroism spectroscopy. The CrI3 nanoplatelets have lateral dimensions of ~25 nm and thicknesses of only ~4 nm, corresponding to just a few CrI3 monolayers. Magnetic and magneto-optical measurements demonstrate robust 2D ferromagnetic ordering with Curie temperatures similar to bulk CrI3, despite their small size. These data also show magnetization steps akin to those observed in micron-sized few-layer 2D sheets associated with concerted spin-reversal of individual CrI3 layers within few-layer van der Waals stacks. Similar data have also been obtained for CrBr3 and anion-alloyed Cr(I1–xBrx)3 nanoplatelets. These results represent the first example of lateral nanostructures of 2D van der Waals ferromagnets of any composition. The demonstration of robust ferromagnetism at nanometer lateral dimensions opens new doors for miniaturization in spintronics devices based on van der Waals ferromagnets.

De Siena, Michael C.↗

Two-dimensional ferromagnetic superlattices

Mechanically exfoliated two-dimensional ferromagnetic materials (2D FMs) possess long-range ferromagnetic order and topologically nontrivial skyrmions in few layers. However, because of the dimensionality effect, such few-layer systems usually exhibit much lower Curie temperature (T C ) compared to their bulk counterparts. It is therefore of great interest to explore effective approaches to enhance their T C , particularly in wafer-scale for practical applications. Here, we report an interfacial proximity-induced high-T C 2D FM Fe 3 GeTe 2 (FGT) via A-type antiferromagnetic material CrSb (CS) which strongly couples to FGT. A superlattice structure of (FGT/CS) n , where n stands for the period of FGT/CS heterostructure, has been successfully produced with sharp interfaces by molecular-beam epitaxy on 2-inch wafers. By performing elemental specific X-ray magnetic circular dichroism (XMCD) measurements, we have unequivocally discovered that T C of 4-layer Fe 3 GeTe 2 can be significantly enhanced from 140 K to 230 K because of the interfacial ferromagnetic coupling. Meanwhile, an inverse proximity effect occurs in the FGT/CS interface, driving the interfacial antiferromagnetic CrSb into a ferrimagnetic state as evidenced by double-switching behavior in hysteresis loops and the XMCD spectra. Density functional theory calculations show that the Fe-Te/Cr-Sb interface is strongly FM coupled and doping of the spin-polarized electrons by the interfacial Cr layer gives rise to the T C enhancement of the Fe 3 GeTe 2 films, in accordance with our XMCD measurements. Strikingly, by introducing rich Fe in a 4-layer FGT/CS superlattice, T C can be further enhanced to near room temperature. Our results provide a feasible approach for enhancing the magnetic order of few-layer 2D FMs in wafer-scale and render opportunities for realizing realistic ultra-thin spintronic devices.

(Fe3GeTe2/CrSb)n superlattice↗

Prediction of room-temperature multiferroicity in strained MoCr 2 S 6 monolayer

The contrasting d-orbital occupation required for ferroelectricity vs ferromagnetism makes it difficult for their coexistence in two-dimensional materials, especially at high temperature. To resolve this intrinsic contradiction, we propose a layered MoCr 2 S 6 multiferroics by alloying magnetic Cr element into the ferroelectric 1T phase of the MoS 2 matrix. First-principles calculations disclose that a spontaneous symmetry breaking, depending on the Mo atom displacement, leads to a robust ferroelectricity, which coexists with a ferromagnetic order originated from two neighboring Cr atoms. The effect can be further enhanced by tensile strain to bring about a room-temperature multiferroicity. Our results shed new light on the fundamental understanding of multiferroics and display promising applications in spintronics and multistate data storage.

2D materials↗

Pressure-induced suppression of ferromagnetism in the itinerant ferromagnet LaCrSb 3

We have performed an extensive pressure-dependent structural, spectroscopic, and electrical transport study of LaCrSb 3 . The ferromagnetic phase (TC=120 K at p = 0 GPa) is fully suppressed by p = 26.5 GPa and the Cr moment decreases steadily with increasing pressure. The unit-cell volume decreases smoothly up to p = 55 GPa. We find that the bulk modulus and suppression of the magnetism are in good agreement with theoretical predictions, but the Cr moment decreases smoothly with pressure, in contrast to steplike drops predicted by theory. The ferromagnetic ordering temperature appears to be driven by the Cr moment.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

High-temperature ferromagnetism in Cr 1+x Pt 5-x P

In this work, we present the growth and basic magnetic and transport properties of Cr 1+x Pt 5-x P. We show that single crystals can readily be grown from a high-temperature solution created by adding dilute quantities of Cr to Pt-P based melts. Like other 1-5-1 compounds, Cr 1+x Pt 5-x P adopts a tetragonal P4/mmm, structure composed facesharing CrPts like slabs that are broken up along the c-axis by sheets of P atoms. EDS and X-ray diffraction measurements both suggest Cr 1+x Pt 5-x P has mixed occupancy between Cr and Pt atoms, similar to what is found in the closely related compound CrPtg, giving real compositions of Cr 1.5 Pt 4.5 P (x = 0.5). We report that Cr 1.5 Pt 4.5 P orders ferromagnetically at T c = 464.5 K with a saturated moment of ≈ 2.1 μs/Cr at 1.8 K. Likely owing to the strong spin-orbit coupling associated with the large quantity of high Z, Pt atoms, Cr 1.5 Pt 4.5 P has exceptionally strong planar anisotropy with estimated anisotropy fields of 345 kOe and 220 kOe at 1.8 K and 300 K respectively. The resistance of Cr 1.5 Pt 4.5 P has a metallic temperature dependence with relatively weak magnetoresistance. Electronic band structure calculations show that CrPt 5 P has a large peak in the density of states near the Fermi level which is split into spin majority and minority bands in the ferromagnetic state. Furthermore, the calculations suggest substantial hybridization between Cr-3d and Pt-5d states near the Fermi level, in agreement with the experimentally measured anisotropy.

36 MATERIALS SCIENCE↗

Crystal structure, magnetic properties and bonding analysis of M 3 Pt 23 Ge 11 (M=Ca, Sr, Ba and Eu)

The properties of Pt-based materials can be intriguing due to the importance of spin-orbit coupling for Pt. Herein, we report four new phases with formulas M 3 Pt 23 Ge 11 (M ​= ​Ca, Sr, Ba and Eu), which adopt the same structure type as Ce3Pt23Si11. Magnetic susceptibility measurements indicate that none of the phases is superconducting above 1.8 ​K, while for Eu 3 Pt 23 Ge 11 ferromagnetic ordering is observed at ~ 3 ​K. The low Curie temperature for that material compared to that of Eu 3 Pt 23 Si 11 may be due to its larger Eu–Eu distance. One potential factor that destabilizes the structure of other rare-earth based M 3 Pt 23 Ge 11 is demonstrated through COHP calculations.

36 MATERIALS SCIENCE↗

Anisotropic magnetocaloric effect and critical behavior in CrSbSe3

In this work, we report anisotropic magnetocaloric effect and critical behavior in a quasi-one-dimensional ferromagnetic CrSbSe 3 single crystal. The maximum magnetic entropy change - Δ S M max is 2.16 J kg - 1 K - 1 for the easy a axis (2.03 J kg - 1 K - 1 for the hard b axis) and the relative cooling power RCP is 163.1 J kg - 1 for the easy a axis (142.1 J kg - 1 for the hard b axis) near T c with a magnetic field change of 50 kOe. The magnetocrystalline anisotropy constant K u is estimated to be 148.5 kJ m - 3 at 10 K, decreasing to 39.4 kJ m - 3 at 70 K. The rescaled Δ S M ( T , H ) curves along all three axes collapse onto a universal curve, respectively, confirming the second-order ferromagnetic transition. Further critical behavior analysis around T c ~ 70 K gives that the critical exponents β = 0.26 ( 1 ) , γ = 1.32 ( 2 ) , and δ = 6.17 ( 9 ) for H ∥ a , while β = 0.28 ( 2 ) , γ = 1.02 ( 1 ) , and δ = 4.14 ( 16 ) for H ∥ b . The determined critical exponents suggest that the anisotropic magnetic coupling in CrSbSe 3 is strongly dependent on orientations of the applied magnetic field.

2-dimensional systems↗

Discovery of a Ferromagnetic Nickel Chalcogenide Nanocluster Ni 3 S 3 H(PEt 3 ) 5

Atomically precise ligated nanoclusters (NC) are promising cluster-based materials with novel molecular architectures and tunable magnetic properties. Herein, the synthesis and characterization of a nickel sulfide NC Ni 3 S 3 H(PEt 3 ) 5 (PEt 3 = triethylphosphine) with distinct magnetic properties are reported. Magnetization measurements reveal its magnetic moment of 1.5 µ B in the solid phase, consistent with the existence of one unpaired electron predicted by density functional theory (DFT) calculations. Additionally, experimental measurements indicate the presence of ferromagnetic ordering within each Ni 3 S 3 H(PEt 3 ) 5 NC and strong coercivity at temperatures below 20 K. Ion mobility-mass spectrometry is employed in conjunction with DFT calculations and collision cross-section simulations to investigate the structure of the isolated Ni 3 S 3 H(PEt 3 ) 5 . Theoretical studies show that [Ni 3 S 3 H(PEt 3 ) 5 ] + has a planar Ni 3 S 3 core where three Ni atoms are arranged in a triangle with three bridging S atoms residing in the same plane. This structure is preserved in both solution and solid phases, which is confirmed by spectroscopic studies of Ni 3 S 3 H(PEt 3 ) 5 . Additionally, DFT calculations indicate that all spins at the Ni sites are aligned parallel, confirming the presence of ferromagnetic coupling. Overall, this study provides key insights into the structure and magnetic properties of Ni 3 S 3 H(PEt 3 ) 5 , which will facilitate the design of new NC-based magnetic materials.

Nickel sulfide nanocluster↗

The 2022 magneto-optics roadmap

Abstract Magneto-optical (MO) effects, viz. magnetically induced changes in light intensity or polarization upon reflection from or transmission through a magnetic sample, were discovered over a century and a half ago. Initially they played a crucially relevant role in unveiling the fundamentals of electromagnetism and quantum mechanics. A more broad-based relevance and wide-spread use of MO methods, however, remained quite limited until the 1960s due to a lack of suitable, reliable and easy-to-operate light sources. The advent of Laser technology and the availability of other novel light sources led to an enormous expansion of MO measurement techniques and applications that continues to this day (see section 1). The here-assembled roadmap article is intended to provide a meaningful survey over many of the most relevant recent developments, advances, and emerging research directions in a rather condensed form, so that readers can easily access a significant overview about this very dynamic research field. While light source technology and other experimental developments were crucial in the establishment of today’s magneto-optics, progress also relies on an ever-increasing theoretical understanding of MO effects from a quantum mechanical perspective (see section 2), as well as using electromagnetic theory and modelling approaches (see section 3) to enable quantitatively reliable predictions for ever more complex materials, metamaterials, and device geometries. The latest advances in established MO methodologies and especially the utilization of the MO Kerr effect (MOKE) are presented in sections 4 (MOKE spectroscopy), 5 (higher order MOKE effects), 6 (MOKE microscopy), 8 (high sensitivity MOKE), 9 (generalized MO ellipsometry), and 20 (Cotton–Mouton effect in two-dimensional materials). In addition, MO effects are now being investigated and utilized in spectral ranges, to which they originally seemed completely foreign, as those of synchrotron radiation x-rays (see section 14 on three-dimensional magnetic characterization and section 16 on light beams carrying orbital angular momentum) and, very recently, the terahertz (THz) regime (see section 18 on THz MOKE and section 19 on THz ellipsometry for electron paramagnetic resonance detection). Magneto-optics also demonstrates its strength in a unique way when combined with femtosecond laser pulses (see section 10 on ultrafast MOKE and section 15 on magneto-optics using x-ray free electron lasers), facilitating the very active field of time-resolved MO spectroscopy that enables investigations of phenomena like spin relaxation of non-equilibrium photoexcited carriers, transient modifications of ferromagnetic order, and photo-induced dynamic phase transitions, to name a few. Recent progress in nanoscience and nanotechnology, which is intimately linked to the achieved impressive ability to reliably fabricate materials and functional structures at the nanoscale, now enables the exploitation of strongly enhanced MO effects induced by light–matter interaction at the nanoscale (see section 12 on magnetoplasmonics and section 13 on MO metasurfaces). MO effects are also at the very heart of powerful magnetic characterization techniques like Brillouin light scattering and time-resolved pump-probe measurements for the study of spin waves (see section 7), their interactions with acoustic waves (see section 11), and ultra-sensitive magnetic field sensing applications based on nitrogen-vacancy centres in diamond (see section 17). Despite our best attempt to represent the field of magneto-optics accurately and do justice to all its novel developments and its diversity, the research area is so extensive and active that there remains great latitude in deciding what to include in an article of this sort, which in turn means that some areas might not be adequately represented here. However, we feel that the 20 sections that form this 2022 magneto-optics roadmap article, each written by experts in the field and addressing a specific subject on only two pages, provide an accurate snapshot of where this research field stands today. Correspondingly, it should act as a valuable reference point and guideline for emerging research directions in modern magneto-optics, as well as illustrate the directions this research field might take in the foreseeable future.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Driving rapid atomic order in MnAl via low-magnitude magnetic field annealing

Application of a mild (60 mT), uniform magnetic field during short-term thermal treatment of kinetically retained, atomically disordered (paramagnetic) ε-MnAl was found to deliver a significant ~50 % increase in the formation of L1 0 atomically ordered (ferromagnetic) τ-MnAl product phase, compared to that produced by conventional (i.e., zero-field) annealing under identical thermal conditions. The magnetic field, applied in a passive closed-circuit configuration during annealing, induced significant changes in the structural, magnetic, and phase evolution of the material. Computational results based on electronic structure calculations demonstrate that the effective magnetic susceptibility of τ-MnAl is sensitive to the orientation, rather than the magnitude, of an applied magnetic field in the vicinity of the Curie temperature. The uniaxial magnetocrystalline anisotropy of the L1 0 structure is proposed to act as a filter for selective propagation of the population of τ-MnAl variants that are favorably aligned with the applied field. In this manner, crystallographic “gridlock” is alleviated that would otherwise arise from the coexistence of multiple, energetically equivalent τ-phase variants within the parent ε-phase matrix. These results confirm that static, low-magnitude magnetic field annealing is able to accelerate L1 0 atomic ordering in the MnAl system and likely can exert similar influences in relevant magnetic systems, facilitating efficient tailoring of structure-sensitive magnetic properties for the manufacture of magnetic materials.

36 MATERIALS SCIENCE↗

Weyl semimetal in the rare-earth hexaboride family supporting a pseudonodal surface and a giant anomalous Hall effect

Rare-earth hexaborides offer a rich tapestry for exploring the interplay of topological orders, magnetism, and electron-correlation effects associated with protected quantum phenomena. Using first-principles modeling, we identify in cerium hexaboride (CeB 6 ) a topological state that harbors a pseudonodal surface (PNS) along with double-Weyl fermions. An analysis of the electronic states in the vicinity of the Fermi level reveals the presence of M z -mirror-symmetry-protected band crossings that involve itinerant (d) and localized (f) states of Ce. These band crossings are found to remain nearly gapless as one goes away from the mirror plane, driving the formation of PNS states. We also demonstrate the presence of coexisting double-Weyl fermions with chiral charges of ±2 on the C 4z rotational axis. By analyzing the Berry curvature field associated with the topological states, we predict that CeB 6 supports a giant anomalous Hall conductivity of -1840Ω -1 cm -1 in the slightly electron-doped regime, which would be larger than the values reported to date in magnetic Weyl semimetals. Our study thus indicates that CeB 6 , which combines ferromagnetic order with topological physics in a heavy-fermion matrix, would provide a promising playground for investigating topological magnetic states with giant anomalous Hall responses.

36 MATERIALS SCIENCE↗

Ferroic phase transitions and magnetoelectric coupling in cobalt doped BaTiO 3

Magnetoelectric (ME) materials exhibit interesting physics with cross coupling between ferroelectric and magnetic order parameters and thus strong potential to be utilized in memory, spintronics and other multifunctional electronic/magnetic devices. Doping of suitable transition metals in ferroelectrics can induce magnetism and ME coupling and modify the physical properties. Here, we report the structural, electronic, magnetic and ME coupling of 3.5, 5 and 7.5 mol% cobalt doped BaTiO 3 (BTO) ceramics. X-ray diffraction and Raman spectroscopy indicate that the samples are single phase having a tetragonal crystal structure with P4mm symmetry. The tetragonality ratio is found to decrease with increasing cobalt content. We observed a Fano-like asymmetric peak in the [A 1 (LO 1 )] Raman mode at ~173 cm -1 in all the cobalt doped BTO samples. The cobalt dopants are shown to be uniformly distributed throughout the surface of the samples. We observed a lowering of the ferroelectric transition temperature and increasing diffusivity parameter with increasing cobalt concentration. The electrical properties of all the samples have been investigated in detail by impedance spectroscopy and ac conductivity studies before and after the ferroelectric phase transitions. All the samples show hysteretic ferroelectric behavior with a clear saturation state that decreases with increasing cobalt content. The observed ferroelectricity in these samples is intrinsic in nature. The 3.5% cobalt doped BTO sample exhibits paramagnetic behavior whereas the 5 and 7.5% cobalt doped BTO samples show ferromagnetic ordering below 43 K. The 7.5% cobalt doped BTO samples show significant ME coupling.

36 MATERIALS SCIENCE↗

Spin–Phonon Coupling in Ferromagnetic Monolayer Chromium Tribromide

Novel 2D magnets exhibit intrinsic electrically tunable magnetism down to the monolayer limit, which has significant value for nonvolatile memory and emerging computing device applications. In these compounds, spin–phonon coupling (SPC) typically plays a crucial role in magnetic fluctuations, magnon dissipation, and ultimately establishing long-range ferromagnetic order. However, a systematic understanding of SPC in 2D magnets that combines theory and experiment is still lacking. Here in this work, monolayer chromium tribromide is studied to investigate SPC in 2D magnets via Raman spectroscopy and first principle calculations. The experimental Curie temperature and phonon shifts are found to be in good agreement with the numerical simulations. Specifically, it is demonstrated how magnetic exchange interactions affect phonon vibrations, which helps establish design fundamentals for 2D magnetic materials and other related devices.

36 MATERIALS SCIENCE↗

Intrinsically Honeycomb-Patterned Hydrogenated Graphene

Since the advent of graphene ushered the era of 2D materials, many forms of hydrogenated graphene have been reported, exhibiting diverse properties ranging from a tunable bandgap to ferromagnetic ordering. Patterned hydrogenated graphene with micron-scale patterns has been fabricated by lithographic means. We report successful millimeter-scale synthesis of an intrinsically honeycomb-patterned form of hydrogenated graphene on Ru(0001) by epitaxial growth followed by hydrogenation is reported. Combining scanning tunneling microscopy observations with density-functional-theory (DFT) calculations, it is revealed that an atomic-hydrogen layer intercalates between graphene and Ru(0001). The result is a hydrogen honeycomb structure that serves as a template for the final hydrogenation, which converts the graphene into graphane only over the template, yielding honeycomb-patterned hydrogenated graphene (HPHG). In effect, HPHG is a form of patterned graphane. DFT calculations find that the unhydrogenated graphene regions embedded in the patterned graphane exhibit spin-polarized edge states. This type of growth mechanism provides a new pathway for the fabrication of intrinsically patterned graphene-based materials.

2D material↗

Electrochemical Intercalation and Exfoliation of CrSBr into Ferromagnetic Fibers and Nanoribbons

Abstract Recent studies dedicated to layered van der Waals crystals have attracted significant attention to magnetic atomically thin crystals offering unprecedented opportunities for applications in innovative magnetoelectric, magneto‐optic, and spintronic devices. The active search for original platforms for the low‐dimensional magnetism study has emphasized the entirely new magnetic properties of two dimensional (2D) semiconductor CrSBr. Herein, for the first time, the electrochemical exfoliation of bulk CrSBr in a non‐aqueous environment is demonstrated. Notably, crystal cleavage governed by the structural anisotropy occurred along two directions forming atomically thin and few‐layered nanoribbons. The exfoliated material possesses an orthorhombic crystalline structure and strong optical anisotropy, showing the polarization dependencies of Raman signals. The antiferromagnetism exhibited by multilayered CrSBr gives precedence to ferromagnetic ordering in the revealed CrSBr nanostructures. Furthermore, the potential application of CrSBr nanoribbons is pioneered for electrochemical photodetector fabrication and demonstrates its responsivity up to 30 µA cm −2 in the visible spectrum. Moreover, the CrSBr‐based anode for lithium‐ion batteries exhibited high performance and self‐improving abilities. This anticipates that the results will pave the way toward the future study of CrSBr and practical applications in magneto‐ and optoelectronics.

Chemistry↗

The Ce-Fe-Ti System: Phase Equilibria in the Fe-rich Corner at 1000 °C

The rare earth–iron–transition metal systems are of increasing interest in the search for novel permanent magnet phases. This work reports on the solidification behavior, phase equilibria and stability range of solid phases in the ternary Ce-Fe-Ti system, focusing on the iron-rich region (> 65 at.% Fe) of the isothermal section at 1000 °C. Further, two ternary phases Ce 1.03 Fe 12-x Ti x (x = 0.87–1.02) with ThMn 12 structure type and Ce 3.06 Fe 27.6 Ti 1.4 with Nd 3 Fe 29 structure type were observed. Magnetic measurements of Ce 1.03 Fe 12-x Ti x and Ce 3.06 Fe 27.6 Ti 1.4 revealed ferromagnetic ordering with Curie temperatures of 550 K and 327 K, respectively.

36 MATERIALS SCIENCE↗

Tailoring microstructures with mild magnetic-field processing: A case study of CuNiFe alloys

Combined experimental and computational investigations of the CuNiFe spinodal system confirm that application of a mild magnetic field during thermal treatment alters elemental redistribution and the resulting microstructure, relative to that obtained from zero-field annealing. Spinodal decomposition of a Cu 40 Ni 42 Fe 18 alloy was initiated during thermal treatment at 773 K, conducted either under zero field or modest (60 mT) magnetic f ield conditions for up to 200 h. Periodic (~10 nm) chemical modulations into Cu-rich and NiFe-rich regions were observed under both conditions, with the amplitude and wavelength of the segregated regions increasing with treatment time. However, magnetic field annealing resulted in a more than twofold increase in the amplitude of elemental modulations relative to zero-field conditions – consistent with enhanced diffusional f luxes during spinodal decomposition – while the modulation wavelength remained largely unaffected. These microstructural differences are reflected in various extrinsic magnetic properties. In parallel, first-principles DFT calculations indicate that long-range ferromagnetic order, as induced by an applied magnetic field, substantially alters the strength and nature of atomic interactions, enhancing the thermodynamic instability of the CuNiFe solid solution. Collectively, these results suggest that incorporating a mild (millitesla-level) magnetic field – distinct from the strong (tesla-level) fields commonly used in prior studies – during thermal processing has the potential to deliver enhanced control of microstructures for targeted engineering outcomes.

36 MATERIALS SCIENCE↗