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At least 55 records · Page 3

Interfacial reconstruction effects in insulating double perovskite Nd2NiMnO6/SrTiO3 and Nd2NiMnO6/NdGaO3 thin films

Ferromagnetic insulating (FMI) double perovskite oxides (DPOs) A2BB′O6 with near-room-temperature Curie temperatures are promising candidates for ambient-temperature spintronics applications. To realize their potential, epitaxial stabilization of DPO films and understanding the effect of multiple broken symmetries across the film/substrate interface are crucial. This study investigates ultrathin films of the FMI Nd2NiMnO6 grown on SrTiO3 (STO) and NdGaO3 (NGO) substrates. By comparing growth on these substrates, we examine the influence of polarity and structural symmetry mismatches, which are absent in the NGO system. The interface exhibits immeasurable resistance in both cases. Using synchrotron x-ray diffraction, we show that films have three octahedral rotational domains because of the structural symmetry mismatch with the STO substrate. Furthermore, our coherent Bragg rod analysis of specular x-ray diffraction reveals a significant modification of the out-of-plane lattice parameter within a few unit cells at the film/substrate interface and the surface. This arises from polarity compensation and surface symmetry breaking, respectively. These structural alterations influence the Mn orbital symmetry, a dependence that we further confirm through x-ray linear dichroism measurements. Since the ferromagnetism in insulating DPOs is mediated by orbital-dependent superexchange interactions [Phys. Rev. Lett. 100, 186402 (2008)0031-900710.1103/PhysRevLett.100.186402], our study provides a framework for understanding the evolution of magnetism in ultrathin geometry.

Bhattacharya, Nandana↗

Magnetic domain engineering in SrRuO3 thin films

Abstract Magnetic domain engineering in ferromagnetic thin films is a very important route toward the rational design of spintronics and memory devices. Although the magnetic domain formation has been extensively studied, artificial control of magnetic domain remains challenging. Here, we present the control of magnetic domain formation in paradigmatic SrRuO 3 /SrTiO 3 heterostructures via structural domain engineering. The formation of structural twin domains in SrRuO 3 films can be well controlled by breaking the SrTiO 3 substrate symmetry through engineering miscut direction. The combination of x-ray diffraction analysis of structural twin domains and magnetic imaging of reversal process demonstrates a one-to-one correspondence between structural domains and magnetic domains, which results in multi-step magnetization switching and anomalous Hall effect in films with twin domains. Our work sheds light on the control of the magnetic domain formation via structural domain engineering, which will pave a path toward desired properties and devices applications.

Materials Science↗

Magnetic field dependence of low-energy magnons, anisotropic heat conduction, and spontaneous relaxation of magnetic domains in the cubic helimagnet ZnCr 2 Se 4

Here, anisotropic low-temperature properties of the cubic spinel helimagnet ZnCr 2 Se 4 in the single-domain spin-spiral state are investigated by a combination of neutron scattering, thermal conductivity, ultrasound velocity, and dilatometry measurements. In an applied magnetic field, neutron spectroscopy shows a complex and nonmonotonic evolution of the spin-wave spectrum across the quantum-critical point that separates the spin-spiral phase from the field-polarized ferromagnetic phase at high fields. A tiny spin gap of the pseudo-Goldstone magnon mode, observed at wave vectors that are structurally equivalent but orthogonal to the propagation vector of the spin helix, vanishes at this quantum critical point, restoring the cubic symmetry in the magnetic subsystem. The anisotropy imposed by the spin helix has only a minor influence on the lattice structure and sound velocity but has a much stronger effect on the heat conductivities measured parallel and perpendicular to the magnetic propagation vector. The thermal transport is anisotropic at T≲ 2K, highly sensitive to an external magnetic field, and likely results directly from magnonic heat conduction. We also report long-time thermal relaxation phenomena, revealed by capacitive dilatometry, which are due to magnetic domain motion related to the destruction of the single-domain magnetic state, initially stabilized in the sample by the application and removal of magnetic field. Our results can be generalized to a broad class of helimagnetic materials in which a discrete lattice symmetry is spontaneously broken by the magnetic order.

36 MATERIALS SCIENCE↗

Anisotropic magnetism and electronic structure of trigonal EuAl 2 Ge 2 single crystals

Understanding the interplay between magnetic and electronic degrees of freedom is of profound recent interest in different Eu-based magnetic topological materials. Here, we studied the magnetic and electronic properties of the layered Zintl-phase compound EuAl 2 Ge 2 crystallizing in the trigonal CaAl 2 Si 2 -type structure. We report zero-field neutron diffraction, temperature T - and magnetic-field H-dependent magnetic susceptibility χ(T, H), isothermal magnetization M(T, H), heat capacity C p (T, H), and electrical resistivity ρ(T, H) measurements, together with T-dependent angle-resolved photoemission spectroscopy (ARPES) measurements complemented with first-principle calculations. EuAl 2 Ge 2 undergoes second-order A-type antiferromagnetic (AFM) ordering below T N = 27.5(5) K, with the Eu moments (Eu 2+ , S = 7/2) aligned ferromagnetically in the ab plane while these layers are stacked antiferromagnetically along the c axis. The critical fields at which all moments become parallel to the field are 37.5(5) and 52.5(5) kOe for H ∥ ab and H ∥ c, respectively. The H = 0 magnetic structure consists of trigonal AFM domains associated with ab-plane magnetic anisotropy and a field-induced reorientation of the Eu spins in the domains is also evident at T = 2 K below the critical field H c1 = 2.5(1) kOe. The ρ(T) measurements reveal metallic behavior transforming into a slight resistivity increase on cooling towards T N . A pronounced loss of spin-disorder scattering is observed below T N . The ARPES results show that EuAl 2 Ge 2 is metallic both above and below T N , and the Fermi surface is anisotropic with two hole pockets at the zone center and one small electron pocket at each M point. In the AFM phase, we directly observe folded bands in ARPES due to the doubling of the magnetic unit cell along the c axis with an enhancement of quasiparticle weight due to the complex change in the coupling between the magnetic moments and itinerant electrons on cooling below T N . The observed electronic structure is well reproduced by first-principle calculations, which also predict the presence of nontrivial electronic states near the Fermi level in the AFM phase with Z 2 topological numbers 1;(000)

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Characterization of Magnetoacoustic Emission Related to Structural Properties of Ferromagnets

An extensive study of magnetoacoustic emission (MAE) properties has been performed over the past several years. As a result, the dependence of the spectral characteristics of MAE on certain microstructural variations and uniaxially applied stress in a particular type of low carbon steel are now well known. The embrittlement-causing concentration of certain atomic species, e. g., tin, sulphur, phosphorous etc., at the grain boundaries of this steel creates strong potential barriers resisting the motion of non-180 domain walls which is the source of MAE. (Since the only type of non-180 domain walls in this material are 90 domain walls, the term 90 domain wall will be used throughout this paper in place of non-180 domain wall.) An MAE burst produced during one-half cycle of a hysteresis loop at a low AC magnetic field frequency (e. g., 0.7 Hz) shows two sub-peaks; the leading peak is usually sharp and short-lived, while the trailing peak is usually smooth and long-lasting. It has been shown that the enhanced domain wall-defect interaction, due to the strengthened potential barriers, causes an increase in the asymmetry of the MAE signal by suppressing the leading sub-peak and amplifying the trailing sub-peak. This phenomena is due to the delayed motion of the 90 domain walls. The effect of a tensile stress applied parallel to the external AC magnetic field is to diminish the MAE. On the other hand, the amplitude of the MAE burst has been shown to be a non-monotonic function of the stress amplitude. Recently, our study has concentrated on obtaining quantitative values for parameters computed from the MAE spectra averaged over a sufficient number of cycles to achieve statistical stability. Nevertheless, certain fundamental elements of the MAE characteristics remain unexplained.

Namkung, M.↗

Nematic Colloidal Micro‐Robots as Physically Intelligent Systems

Abstract Physically intelligent micro‐robotic systems exploit information embedded in micro‐robots, their colloidal cargo, and their milieu to interact, assemble, and form functional structures. Nonlinear anisotropic fluids such as nematic liquid crystals (NLCs) provide untapped opportunities to embed interactions via their topological defects, complex elastic responses, and ability to dramatically restructure in dynamic settings. Here a four‐armed ferromagnetic micro‐robot is designed and fabricated to embed and dynamically reconfigure information in the nematic director field, generating a suite of physical interactions for cargo manipulation. The micro‐robot shape and surface chemistry are designed to generate a nemato‐elastic energy landscape in the domain that defines multiple modes of emergent, bottom‐up interactions with passive colloids. Micro‐robot rotation expands the ability to sculpt interactions; the energy landscape around a rotating micro‐robot is dynamically reconfigured by complex far‐from‐equilibrium dynamics of the micro‐robot's companion topological defect. These defect dynamics allow transient information to be programmed into the domain and exploited. Robust micro‐robotic manipulation strategies are demonstrated that exploit these diverse modes of nemato‐elastic interaction to achieve cargo docking, transport, release, and assembly of complex reconfigurable structures at multi‐stable sites. Such structures are of great interest to future developments of LC‐based advanced optical device and micro‐manufacturing in anisotropic environments.

Yao, Tianyi↗

In situ observation of the magnetization configuration and reversal in cylindrical nanowires

Curvilinear magnetic structures often have unique magnetic behavior compared to their rectilinear counterparts. This is due to the unique curvilinear boundary conditions as well as the curvature induced Dzyaloshinskii–Moriya-like interaction and the curvature induced anisotropy. The effects of a curvilinear geometry are best studied in 3D structures, where the curvature can have a significant spatial extent. Of these 3D structures, the simplest structure to study is the cylindrical nanowire. Here, we have simulated the magnetization reversal in cylindrical NiFe nanowires and present in situ Lorentz TEM images to support the findings of the simulations. We studied the domain formation and reversal of nanowires with two distinct diameters that give rise to a different reversal behavior. We have, thus, found that the zero-field magnetization configuration in these wires can take on a double helix type of configuration. The reversal in these structures then proceeds through the winding and unwinding of these helical configurations rather than through domain wall propagation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Visualizing the Effect of Oxidation on Magnetic Domain Behavior of Nanoscale Fe 3 GeTe 2 for Applications in Spintronics

Magnetic van der Waals (vdW) materials offer an opportunity to design heterostructures that will lead to exotic functionalities that arise from interfacial interaction. In addition to coupling to different vdW materials, the naturally oxidized surface layer of a vdW material also forms a heterostructure with its bulk film, giving rise to intriguing phenomena. Here, we directly observe the impact of oxidation on the magnetic domains, namely, magnetic stripe domain and skyrmions, in a nanoscale Fe 3 GeTe 2 flake using cryo Lorentz transmission electron microscopy. After the Fe 3 GeTe 2 is exposed to ambient conditions, partial oxidation leads to an increase in the density of skyrmions even under zero magnetic field. Complete oxidation leads to a loss of the magnetic domain structure. We observe a gradual change in Fe 3 GeTe 2 from single crystal to amorphous as the oxidation increases. The oxidized Fe 3 GeTe 2 primarily consists of iron oxide, which could be antiferromagnetic in nature. We hypothesize that the interfacial interaction between these surface antiferromagnetic oxides and the bulk ferromagnetic Fe 3 GeTe 2 , as well as the effect of interfacial roughness, leads to the increase in Néel skyrmion creation. Furthermore, this work opens a path to harness controlled oxidation as a build block to create dense skyrmion lattices without the need for an external magnetic field, leading to potential future applications in spintronic devices.

36 MATERIALS SCIENCE↗

Optical control of orbital magnetism in magic angle twisted bilayer graphene

Flat bands in graphene-based moiré structures host a wide range of emerging strongly correlated and topological phenomena. Optically probing and controlling them can reveal important information such as symmetry and dynamics, but have so far been challenging due to the small energy gap compared to optical wavelengths. Here, we report near infrared optical control of orbital magnetism and associated anomalous Hall effects (AHE) in a magic angle twisted bilayer graphene (MATBG) on monolayer WSe$_2$ device. We show that the properties of the AHE, such as hysteresis and amplitude, can be controlled by light near integer moiré fillings, where spontaneous ferromagnetism exists. By modulating the light helicity, we observe periodic modulation of the transverse resistance in a wide range of fillings, indicating light induced orbital magnetization through a large inverse Faraday effect. At the transition between metallic and AHE regimes, we also reveal large and random switching of the Hall resistivity, which are attributed to optical control of percolating cluster of magnetic domains. Our results open the door to optical manipulation of correlation and topology in MATBG and related structures.

FOS: Physical sciences↗

Segregation of Al and its effect on coercivity in Nd-Fe-B

Doping a small amount of Al can effectively enhance coercivity in Nd-Fe-B magnets. Here we investigated the partitioning behavior of Al and its effect on coercivity in Nd-Fe-B using first principles DFT (density functional theory) calculation and micromagnetic simulation. The calculated substitution energies of Fe by Al are negative at the crystallographic sites of 4c and 8j 2 while they are positive values at the other sites in Nd 2 Fe 14 B (2:14:1), implying a small solubility of Al in 2:14:1. Further, Al prefers to segregate at grain boundary (GB) and stabilize the Nd-Fe-Al phase with a Nd 6 Fe 13 Si-type tetragonal structure (6:13:1). The formation of the antiferromagnetic or weak ferrimagnetic 6:13:1-like phase depletes Fe and reduces the amount of ferromagnetic Nd–Fe type grain boundary phase (GBP), which weakens the inter-grain magnetic interaction. Micromagnetic simulations indicate that the 6:13:1-like GBP increases the pinning field of magnetic domain wall at GB and suppresses the nucleation of reversal magnetic domain on the grain surface of 2:14:1 during demagnetization process. The formation of Al-rich shell on 2:14:1 grain surface can further moderately increase the domain pinning field at GB and the nucleation field of 2:14:1 grain. Developing novel processing method to tailor Al segregation and promote formation of 6:13:1-like phase at GB can be a promising approach to improve coercivity in Nd-Fe-B magnet.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Local Inversion Symmetry Breaking and Thermodynamic Evidence for Ferrimagnetism in Fe 3 GaTe 2

The layered compound Fe 3 GaTe 2 is attracting attention due to its high Curie temperature, low dimensionality, and the presence of topological spin textures above room temperature, making Fe 3 GaTe 2 a good candidate for applications in spintronics. Here, in this study, we show, through transmission electron microscopy (TEM) techniques, that Fe 3 GaTe 2 single crystals break local inversion symmetry while maintaining global inversion symmetry according to X-ray diffraction. Coupled to the observation of Néel skyrmions via Lorentz-TEM, our structural analysis provides a convincing explanation for their presence in centrosymmetric materials. Magnetization measurements as a function of the temperature displays a sharp first-order thermodynamic phase-transition leading to a reduction in the magnetic moment. This implies that the ground state of Fe 3 GaTe 2 is globally ferrimagnetic and not a glassy magnetic state composed of ferrimagnetic, and ferromagnetic domains as previously claimed. Neutron diffraction studies indicate that the ferromagnetic to ferrimagnetic transition upon reducing the external magnetic field is associated with a change in the magnetic configuration/coupling between Fe1 and Fe2 moments. We observe a clear correlation between the hysteresis observed in both the skyrmion density and the magnetization of Fe 3 GaTe 2 . This indicates that its topological spin textures are affected by the development of ferrimagnetism upon cooling. Observation, via magnetic force microscopy, of magnetic bubbles at the magnetic phase boundary suggests skyrmions stabilized by the competition among magnetic phases and distinct exchange interactions. Our study provides an explanation for the observation of Néel skyrmions in centrosymmetric systems, while exposing a correlation between the distinct magnetic phases of Fe 3 GaTe 2 and topological spin textures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Enhanced positive and negative exchange bias in FeF 2 /Ni with dusted interfaces

An enhanced exchange bias was found in FeF 2 /Ni interfaces by inserting dusting of Pd and Cu atoms. We have used an ultrathin wedge to investigate systematically the effect of a discontinuous nonmagnetic spacer between the antiferromagnetic and ferromagnetic layers. Negative and positive exchange biases are symmetric and maximized for less than two angstroms of the nonmagnetic layer. Moreover, the dusting reduces the field cooling threshold to switch between the negative and the positive exchange bias. This finding demonstrates that nonmagnetic dusted layers can improve the interfacial exchange energy density in antiferromagnetic/ferromagnetic heterostructures and modify the bulk antiferromagnetic domain structure. Other dusting materials such as Ag, Ti, V, and SiO 2 showed no enhancement in FeF 2 /Ni bilayers, which indicates the atomic sensitivity of this effect.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Novel self-assembled two-dimensional layered oxide structure incorporated with Au nanoinclusions towards multifunctionalities

Two-dimensional (2D) layered oxides have recently attracted wide attention owing to the strong coupling among charges, spins, lattice, and strain, which allows great flexibility and opportunities in structure designs as well as multifunctionality exploration. In parallel, plasmonic hybrid nanostructures exhibit exotic localized surface plasmon resonance (LSPR) providing a broad range of applications in nanophotonic devices and sensors. A hybrid material platform combining the unique multifunctional 2D layered oxides and plasmonic nanostructures brings optical tuning into the new level. Here, a novel self-assembled Bi 2 MoO 6 (BMO) 2D layered oxide incorporated with plasmonic Au nanoinclusions has been demonstrated via one-step pulsed laser deposition (PLD) technique. Comprehensive microstructural characterizations, including scanning transmission electron microscopy (STEM), differential phase contrast imaging (DPC), and STEM tomography, have demonstrated the high epitaxial quality and particle-in-matrix morphology of the BMO-Au nanocomposite film. DPC-STEM imaging clarifies the magnetic domain structures of BMO matrix. Three different BMO structures including layered supercell (LSC) and superlattices have been revealed which is attributed to the variable strain states throughout the BMO-Au film. Owing to the combination of plasmonic Au and layered structure of BMO, the nanocomposite film exhibits a typical LSPR in visible wavelength region and strong anisotropy in terms of its optical and ferromagnetic properties. This study opens a new avenue for developing novel 2D layered complex oxides incorporated with plasmonic metal or semiconductor phases showing great potential for applications in multifunctional nanoelectronics devices.

36 MATERIALS SCIENCE↗

Spin-orbital order and excitons in magnetoresistive HoBi

The magnetism of the rocksalt fcc rare-earth monopnictide HoBi, a candidate topological material with extreme magnetoresistance, is investigated. From the Ho 3+ non-Kramers J=8 spin-orbital multiplet, the cubic crystal electric field yields six nearly degenerate low-energy levels. These constitute an anisotropic magnetic moment with a Jahn-Teller-like coupling to the lattice. In the cubic phase for T>T N =5.72(1)K, the paramagnetic neutron scattering is centered at k=($\frac{1}{2}$$\frac{1}{2}$$\frac{1}{2}$) and was fit to dominant antiferromagnetic interactions between Ho spins separated by {100} and ferromagnetic interactions between spins displaced by {$\frac{1}{2}$ $\frac{1}{2}$ 0}. For T < T N , a type-II AFM long-range order with k=($\frac{1}{2}$$\frac{1}{2}$$\frac{1}{2}$) develops along with a tetragonal lattice distortion. While neutron diffraction from a multidomain sample cannot unambiguously determine the spin orientation within a domain, the bulk magnetization, structural distortion, and our measurements of the magnetic excitations all show the easy axis coincides with the tetragonal axis. Finally, the weakly dispersive excitons for T < T N can be accounted for by a spin Hamiltonian that includes the crystal electric field and exchange interactions within the random phase approximation.

36 MATERIALS SCIENCE↗

Valence instability and collapse of ferromagnetism in EuB 6 at high pressures

Despite the simplicity of their cubic crystal lattice, rare-earth hexaborides display complex physical properties including a (long debated) onset of metallization via magnetic polaron formation at T c1 approximate to 15 K preceding ferromagnetic ordering at T c2 approximate to 12 K. Here, in this work, we used applied pressure to tune the interplay between electronic structure and magnetism in EuB6. We probed the magnetism, valence, and structure of EuB 6 under quasi-hydrostatic pressures up to 30 GPa using X-ray techniques. Our findings show evidence for collapse of ferromagnetism above 20 GPa following a monotonic increase of mean Eu valence. While X-ray diffraction measurements in the paramagnetic state at room temperature show that the lattice retains cubic symmetry, a measurable quadrupole interaction seen by time-domain synchrotron Mössbauer spectroscopy suggests a lowering of symmetry associated with magnetic ordering, becoming more prominent across the magnetic transition. The interplay between conduction band electron count and magnetism observed under applied pressure in EuB 6 opens possibilities for fine-tuning metallization and magnetic properties of similar Eu-based semi-metal systems.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Topological control of magnetic textures

Here, a micromagnetic study is carried out on the role of using topology to stabilize different magnetic textures, such as a vortex or an antivortex state, in a magnetic heterostructure consisting of a permalloy disk coupled to a set of nanomagnetic bars. The topological boundary condition is set by the stray field contributions of the nanomagnet bars and thus by their magnetization configuration, and can be described by a discretized winding number that will be matched by the winding number of the topological state set in the disk. The lowest number of nanomagnets that defines a suitable boundary is 4, and we identify a critical internanomagnet angle of 225 ° between two nanomagnets, at which the boundary fails because the winding number of the nanomagnet configuration no longer controls that of the disk magnetization. The boundary also fails when the disk-nanomagnets separation is >50 nm and for disk diameters >480 nm. Finally, we provide preliminary experimental evidence from magnetic force microscopy studies in which we demonstrate that an energetically unstable, antivortex-like structure can indeed be stabilized in a permalloy disk, provided that the appropriate topological conditions are set.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Spin orbit torque in ferromagnet/topological-quantum-material heterostructures

The main objective of this proposal was to investigate the spin-orbital driven phenomena in topological insulator (TI)/ferromagnet (FM) or transition metal (TM) heterostructures. In particularly, we tried to utilize the spin-momentum locking properties on the surface of TIs to achieve ideal spin-orbit torques (SOTs). In practice, we found that the surface properties have been greatly modified, resulting in much more complicated magneto-transport behaviors than what is expected in SOT-driven magnetotransport. Through systematic and extended investigations, we start to unravel that the nonlinear magnetotransport properties, which was, in the past, mainly attributed to SOT-driven phenomena, can be used to infer the modification of the electronic band structures of TIs and spin textures in FMs which are closely related with charge-spin interconversion phenomena. Regarding the band structures In TIs, we find under electrostatic perturbations imposed by deposition of nonmagnetic TMs, the quantum well states formed on the surface of TIs develop substantial Rashba spin-splitting, which is detected as a bilinear magnetoresistance (BMR). Under magnetic perturbations, the nonlinear planar Hall effect (NPHE) in the topological surface states is greatly enhanced, possibly reflecting the modified surface band structure due to time-reversal symmetry breaking. In a double HM/FM heterostructure where the magnetic anisotropy can be robustly tuned, we observed second-harmonic Hall voltage responses corresponding to domain wall structures with fixed chirality, stabilized by interfacial Dzyaloshinskii–Moriya interaction (DMI). In addition, in the linear transport regime, we utilized inverse-SHE-induced anomalous Hall effect in Pt to probe the exchange bias on the surface of a doped magnetic insulator Tm 3 Fe 5 O 12 .

36 MATERIALS SCIENCE↗

Reciprocity relations in a biologically inspired nanomagnonic system with dipolar coupling

In this study, magnetosome chains in magnetotactic bacteria present ideal nanomagnonic model systems for studying collective resonance modes of dipolar-coupled single domain particles in relation to their spatial arrangement. Using microresonator-based ferromagnetic resonance (FMR) spectroscopy, electron microscopy, and micromagnetic modeling, we here provide insights into the complex magnonic activity within a single magnetosome chain. While the angular dependence of its FMR spectrum is dominated by twofold symmetry features due to the uniaxial anisotropy of linear chain segments, we also observed an unexpected behavior such as interrupted lines and flat bands due to the intricate geometrical details of this particular chain, such as a cross-like structural anomaly where a pair of particles is oriented perpendicular to the main axis of the chain and thus breaks the prevailing axial dipolar coupling symmetry. Such a cross junction formed by four particles exhibits interesting magnonic network properties. Notably, we observe reciprocity in the sense that the spectral response of one particle to an excitation of another one is identical to the response of the latter given an excitation of the former. Furthermore, we have identified that magnonic coupling between A and B can be facilitated via a dark state, as in magnonic stimulated Raman adiabatic passage, and that this dark-state coupling can be made non-reciprocal between A and B by breaking the symmetry of the spatial arrangement of the four particles.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗