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Self-consistently renormalized spin-wave theory of layered ferromagnets on the honeycomb lattice
We develop a self-consistently renormalized spin-wave theory, within a mean-field approximation, for the two-dimensional Heisenberg ferromagnet with perpendicular easy-axis anisotropy on the honeycomb lattice, as well as its few-layer and bulk extensions. In this method, the magnetization dependence on temperature is found as the solution of the self-consistency equation. Furthermore, we account for the physical difference of surface and bulk layers by treating the layers as separate sublattices. Thus the method can be readily generalized to study various magnetic phenomena in a broad range of systems, including those comprising magnetically inequivalent sublattices. Using our theory, we calculate the temperature-dependent magnetization for two chromium-based layered van der Waals insulating magnets, Cr 2 Ge 2 Te 6 and CrI 3 , employing various sets of Heisenberg exchange and single-ion anisotropy values reported for these materials in the existing literature. As expected, we observe a strong dimensionality effect where the ordering temperature is reduced and its sensitivity on the anisotropy is enhanced with the decrease of dimensionality.
Layer Hall effect in a 2D topological axion antiferromagnet
While ferromagnets have been known and exploited for millennia, antiferromagnets (AFMs) were only discovered in the 1930s. The elusive nature indicates AFMs' unique properties: At large scale, due to the absence of global magnetization, AFMs may appear to behave like any non-magnetic material; However, such a seemingly mundane macroscopic magnetic property is highly nontrivial at microscopic level, where opposite spin alignment within the AFM unit cell forms a rich internal structure. In topological AFMs, such an internal structure leads to a new possibility, where topology and Berry phase can acquire distinct spatial textures. Here, we study this exciting possibility in an AFM Axion insulator, even-layered MnBi 2 Te 4 flakes, where spatial degrees of freedom correspond to different layers. Remarkably, we report the observation of a new type of Hall effect, the layer Hall effect, where electrons from the top and bottom layers spontaneously deflect in opposite directions. Specifically, under no net electric field, even-layered MnBi 2 Te 4 shows no anomalous Hall effect (AHE); However, applying an electric field isolates the response from one layer and leads to the surprising emergence of a large layer-polarized AHE (~50e 2 /h). Such a layer Hall effect uncovers a highly rare layer-locked Berry curvature, which serves as a unique character of the space-time PT-symmetric AFM topological insulator state. Moreover, we found that the layer-locked Berry curvature can be manipulated by the Axion field, E∙B, which drives the system between the opposite AFM states. Our results achieve previously unavailable pathways to detect and manipulate the rich internal spatial structure of fully-compensated topological AFMs. The layer-locked Berry curvature represents a first step towards spatial engineering of Berry phase, such as through layer-specific moiré potential.
Universal Conductance Fluctuations in a MnBi 2 Te 4 Thin Film
Quantum coherence of electrons can produce striking behaviors in mesoscopic conductors, including weak localization and the Aharonov-Bohm effect. Although magnetic order can also strongly affect transport, the combination of coherence and magnetic order has been largely unexplored. Here, we examine quantum coherence-driven universal conductance fluctuations in the antiferromagnetic, canted antiferromagnetic, and ferromagnetic phases of a thin film of the topological material MnBi 2 Te 4 . In each magnetic phase we extract a charge carrier phase coherence length of about 100 nm. The conductance magnetofingerprint is repeatable when sweeping applied magnetic field within one magnetic phase, but changes when the applied magnetic field crosses the antiferromagnetic/canted antiferromagnetic magnetic phase boundary. Surprisingly, in the antiferromagnetic and canted antiferromagnetic phase, but not in the ferromagnetic phase, the magnetofingerprint depends on the direction of the field sweep. Finally, to explain these observations, we suggest that conductance fluctuation measurements are sensitive to the motion and nucleation of magnetic domain walls in MnBi 2 Te 4 .
Magnetic properties of the double trillium lattice antiferromagnet KBaCr 2 (PO 4 ) 3
Trillium lattices formed by corner-shared triangular units are the platform for magnetic frustration in three dimensions. Herein, we report structural and magnetic properties of the Cr-based (S = 3/2) double trillium lattice material KBaCr 2 (PO 4 ) 3 studied by x-ray diffraction, dc and ac magnetization, heat capacity, thermal conductivity, and 31 P nuclear magnetic resonance (NMR) measurements complemented by density-functional band-structure calculations. Magnetization, heat capacity, and 31 P NMR measurements reveal the magnetic transition at T N1 ≃ 12.5 K in zero field followed by another transition (T N2 ) at low temperatures in weak applied fields. The 31 P spin-lattice relaxation rate in the ordered state follows the T 3 behavior indicative of the two-magnon Raman process. Finally, the spin lattice of KBaCr 2 (PO 4 ) 3 comprises two crystallographically nonequivalent ferromagnetic sublattices that are coupled antiferromagnetically, thus eliminating frustration in this trillium network and leading to weak ferromagnetism in the vicinity of T N1 .
Direct Visualization of Surface Spin-Flip Transition in MnBi 4 Te 7
Here, we report direct visualization of spin-flip transition of the surface layer in antiferromagnet MnBi 4 Te 7 , a natural superlattice of alternating MnBi 2 Te 4 and Bi 2 Te 3 layers, using cryogenic magnetic force microscopy (MFM). The observation of magnetic contrast across domain walls and step edges confirms that the antiferromagnetic order persists to the surface layers. The magnetic field dependence of the MFM images reveals that the surface magnetic layer undergoes a first-order spin-flip transition at a magnetic field that is lower than the bulk transition, in excellent agreement with a revised Mills model. Our analysis suggests no reduction of the order parameter in the surface magnetic layer, implying robust ferromagnetism in the single-layer limit. The direct visualization of surface spin-flip transition not only opens up exploration of surface metamagnetic transitions in layered antiferromagnets, but also provides experimental support for realizing quantized transport in ultrathin films of MnBi 4 Te 7 and other natural superlattice topological magnets.
Nanoscale imaging of Gilbert damping using signal amplitude mapping
Ferromagnetic resonance force microscopy (FMRFM) is a powerful scanned probe technique that uses sub-micrometer-scale, spatially localized standing spin wave modes (LMs) to perform local ferromagnetic resonance (FMR) measurements. In this work, we show the spatially resolved imaging of Gilbert damping in a ferromagnetic material (FM) using FMRFM. Typically damping is measured from the FMR linewidth. We demonstrate an approach to image the spatial variation of Gilbert damping utilizing the LM resonance peak height to measure the LM resonance cone angle. This approach enables determination of damping through field-swept FMRFM at a single excitation frequency. The extreme force sensitivity of similar to 2 fN at room temperature can resolve changes of Gilbert damping as small as ~2 x 10 -4 at 2GHz, corresponding to ~0.16Oe in FMR linewidth resolution. This high sensitivity, high spatial resolution, and single frequency imaging of Gilbert damping creates the opportunity to study spin interactions at the interface between an insulating FM and a small volume of nonmagnetic material such as atomically thin two-dimensional materials.
Proximity enhanced magnetism at NiFe 2 O 4 /Graphene interface
Here, we explore the change in effective magnetic anisotropy of the ferrimagnetic (FM) insulator nickel ferrite (NFO) thin film due to the inclusion of monolayer graphene (MLG) grown on top of the NFO layer. This was done by performing radio frequency (RF) transverse susceptibility (TS) measurements on bare NFO and NFO/MLG bilayer samples for both in-plane (IP) and out-of-plane (OOP) configurations utilizing a tunnel diode oscillator technique. Our magnetometry measurements indicated an enhancement in the overall saturation magnetization of the NFO/MLG bilayer with respect to the bare NFO film. The TS measurements reveal that the inclusion of MLG reduces the effective magnetic anisotropy for both IP and OOP configurations drastically, by up to a factor of 2 over the temperature range 40 K ≤ T ≤ 280 K. Since NFO is a magnetic substrate, it is possible that NFO could induce magnetic ordering in MLG at the NFO/MLG interface via the magnetic proximity effect. Furthermore, since NFO is insulating and MLG is a semimetal, there likely exists a large conductivity difference at the interface, making charge transfer plausible. These two effects could modify the interfacial magnetism leading to a change in the effective magnetic anisotropy. These results highlight the importance of understanding the interfacial magnetism of FM/MLG heterostructures.
Structural, magneto transport and magnetic properties of Ruddlesden–Popper La 2-2x Sr 1+2x Mn 2 O 7 (0.42≤x≤0.52) layered manganites
The magneto transport of Ruddlesden–Popper, La 2-2x Sr 1+2x Mn 2 O 7 (0.42≤x≤0.52), 2-dimensional bilayered manganites have been investigated in a broad temperature range. The samples have been synthesized using the solid-state reaction method. Rietveld refinement of the X-ray diffraction data indicates the tetragonal structure formation with I4/mmm space group. The resistivity curves of the samples present a general characteristic of metal-insulator (MI) transition at certain temperature (T MI ). Besides, for samples with x = 0.48, 0.50, and 0.52, at a certain temperature (T CO ) well below T MI the charge ordering is also evident. Furthermore, the samples display a shallow upturn in resistivity below T min due to the Kondo like spin scattering effect, weak localization and electron-phonon interaction. The high temperature semiconducting (T>T MI ) region, the resistivity curve follows the 3D Mott’s variable hopping transport mechanism. The overall suppression of resistivity accounts for a substantial magnetoresistance by applying a magnetic field and the characteristic change in T MI , T CO , and T min are discussed. Temperature-dependent magnetization demonstrates the suppression of ferromagnetism and evident of antiferromagnetic nature with an apparent charge ordering with increasing concentration of Sr 2+ .
Ferrimagnetic 120 ° magnetic structure in Cu 2 OSO 4
We report magnetic properties of a 3d 9 (Cu 2+ ) magnetic insulator Cu 2 OSO 4 measured on both powder and single crystal. The magnetic atoms of this compound form layers whose geometry can be described either as a system of chains coupled through dimers or as a kagome lattice where every third spin is replaced by a dimer. Specific heat and DC susceptibility show a magnetic transition at 20 K, which is also confirmed by neutron scattering. Magnetic entropy extracted from the specific heat data is consistent with an S=1/2 degree of freedom per Cu 2+ , and so is the effective moment extracted from DC susceptibility. The ground state has been identified by means of neutron diffraction on both powder and single crystal and corresponds to an ~120° spin structure in which ferromagnetic intradimer alignment results in a net ferrimagnetic moment. No evidence is found for a change in lattice symmetry down to 2 K. Finally, our results suggest that Cu 2 OSO 4 represents a type of model lattice with frustrated interactions where interplay between magnetic order, thermal and quantum fluctuations can be explored.
$A$-type antiferromagnetic order and magnetic phase diagram of the trigonal Eu spin-$\frac{7}{2}$ triangular-lattice compound $\mathrm{EuSn_2As_2}$
The trigonal compound EuSn 2 As 2 was recently discovered to host Dirac surface states within the bulk band gap and orders antiferromagnetically below the N´eel temperature T N = 23.5(2) K from neutron-diffraction measurements. Here the magnetic ground state of single-crystal EuSn 2 As 2 and the evolution of its properties versus temperature T and applied magnetic field H are reported. Included are the zero-field single-crystal neutron diffraction measurements versus T, magnetization M(H, T), magnetic susceptibility χ(H, T) = M(H,T)/H, heat capacity C p (H, T), and electrical resistivity ρ(H, T) measurements. The neutron-diffraction and χ(T) measurements both indicate a collinear A-type antiferromagnetic (AFM) structure below T N , where the Eu 2+ spins S = 7/2 in a triangular ab-plane layer (hexagonal unit cell) are aligned ferromagnetically in the ab plane whereas the spins in adjacent Eu planes along the c axis are aligned antiferromagnetically. The χ(H ab , T) and χ(Hc, T) data together indicate a smooth crossover between the collinear AFM alignment and an unknown magnetic structure at H ≈ 0.12 T. Dynamic spin fluctuations up to 60 K are evident in the χ(T), Cp(T) and ρ(H, T) measurements, a temperature that is more than twice T N . The ρ(H, T) is consistent with a low-carrier-density metal with strong magnetic scattering and does not reflect a contribution of the topological state of the material as reported earlier by ARPES measurements. This observation is consistent with previous ones for other topological insulators where the chemical potential is above the Dirac point so that ARPES readily detects the surface states, whereas resistivity measurements do not. Finally, the magnetic phase diagrams for both H ∥ c and H ∥ ab in the H-T plane are constructed from the T N (H), χ(H, T), Cp(H, T), and ρ(H, T) data.
Dynamical vertex approximation for many-electron systems with spontaneously broken SU(2) symmetry
We generalize the formalism of the dynamical vertex approximation (DΓA)—a diagrammatic extension of the dynamical mean-field theory (DMFT)—to treat magnetically ordered phases. To this aim, we start by concisely illustrating the many-electron formalism for performing ladder resummations of Feynman diagrams in systems with broken SU(2) symmetry associated to ferromagnetic (FM) or antiferromagnetic (AF) order. We then analyze the algorithmic simplifications introduced by taking the local approximation of the two-particle irreducible vertex functions in the Bethe-Salpeter equations, which defines the ladder implementation of DΓA for magnetic systems. The relation of this assumption with the DMFT limit of large coordination-number/high dimensions is explicitly discussed. As a last step, we derive the expression for the ladder DΓA self-energy in the FM- and AF-ordered phases of the Hubbard model. The physics emerging in the AF-ordered case is explicitly illustrated by means of approximated calculations based on a static mean-field input for DΓA equations. The results obtained capture fundamental aspects of both metallic and insulating ground states of two-dimensional antiferromagnets, providing a reliable compass for future, more extensive applications of our approach. Furthermore, possible routes to further develop diagrammatic-based treatments of magnetic phases in correlated electron systems are briefly outlined in the Conclusions.
Reinvestigation of crystal symmetry and fluctuations in La 2 CuO 4
New surprises continue to be revealed about La 2 CuO 4 , the parent compound of the original cuprate superconductor. In this study we present neutron scattering evidence that the structural symmetry is lower than commonly assumed. The static distortion results in anisotropic Cu-O bonds within the CuO 2 planes; such anisotropy is relevant to pinning charge stripes in hole-doped samples. Associated with the extra structural modulation is a soft phonon mode. If this phonon were to soften completely, the resulting change in CuO 6 octahedral tilts would lead to weak ferromagnetism. Hence, we suggest that this mode may be the “chiral” phonon inferred from recent studies of the thermal Hall effect. We also note the absence of interaction between the antiferromagnetic spin waves and low-energy optical phonons, in contrast to what is observed in hole-doped samples.
Direct evidence of ferromagnetism in MnSb 2 Te 4
We report the magnetic imaging of ferromagnetic domains in the van der Waals single crystal MnSb 2 Te 4 from two different sources using cryogenic magnetic force microscopy. The magnetic field dependence of the domains reveals very weak pinning of domain walls in MnSb 2 Te 4 , resulting in a negligibly small magnetic hysteresis loop. Furthermore, the temperature dependence of the domain contrast reveals a mean field like behavior, in good agreement with that of bulk magnetization measurements.
Designed metal-insulator transition in low-symmetry magnetic intermetallics
Compounds exhibiting half-metallic character and metal-insulator transitions draw considerable attention in condensed-matter and materials physics due to their potential use in spintronics. Here we show that specific electron doping plays a crucial role in tailoring thermodynamic, structural, electronic, and magnetic properties of materials derived from low-symmetry magnetic intermetallics, exemplified on triclinic Mn 4 Al 11 . Upon chemical doping of Al by Ge, we predict improved phase stability and adherence to a generalized “18-n rule” governing closed-shell configurations in intermetallic with narrow bandgaps. Validating experiments include measurements of phase stability and electronic transport properties of electron-doped Mn 4 Al 10 Ge that crystallizes in the Mn 4 Al 11 -type structure, confirming the bandgap opening as predicted by chemical analysis and density-functional theory. Here we also demonstrate theoretically that hydrostatic pressure enhances the predicted half-metallic gap in the up-spin channel, which leads to a ferrimagnetic-to-ferromagnetic transition driven by Mn-Mn charge ordering in the Mn 4 Al 11 parent. We have also discussed the generality of our approach in predicting the design of other classes of intermetallics including half and full Heusler compounds.
Reconfigurable Magnetotransport in MnBi 2 Te 4 via Gate and Magnetic Field Tuning
The intrinsic magnetic topological insulator MnBi 2 Te 4 is a promising platform for exploring quantum phases with nontrivial band topology and for enabling electrical control over coupled magnetic and electronic phase transitions. In-plane magnetic fields, in particular, offer a distinct means of tuning these properties by strengthening quantized Hall effects, enhancing surface energy gaps, and driving spin reorientation transitions. However, a systematic understanding of how such fields affect magnetotransport is limited. Here, the magnetotransport behavior of few-layer MnBi 2 Te 4 as a function of gate voltage, temperature, and magnetic field angle, with a primary focus on in-plane field effects, are investigated. A gate-tunable crossover in magnetoresistance is observed from positive to negative values under in-plane magnetic fields as the gate voltage is swept below the charge neutrality point at temperatures below the Néel temperature. The in-plane field drives a transition from the antiferromagnetic ground state to a ferromagnetic configuration with spins aligned in-plane, while simultaneously altering the electronic structure, as revealed by gate-dependent transport features. The angle-dependent measurements reveal strongly gate-tunable magnetotransport anisotropy. These results establish in-plane magnetic fields as an effective tuning parameter for modulating spin and charge transport in MnBi 2 Te 4 , advancing prospects for reconfigurable spintronic and topological devices.
Variational study of the Kitaev-Heisenberg-Gamma model
Here we compute the low-energy excitation spectrum and the dynamical spin structure factor of the Kitaev-Heisenberg-Gamma model through a variational approach based on the exact fractionalized excitations of the pure Kitaev honeycomb model. This novel approach reveals the physical reason for the asymmetric stability of the Kitaev spin liquid phases around the ferromagnetic and antiferromagnetic Kitaev limits. Moreover, we demonstrate that the fractionalized excitations form bound states in specific regions of each Kitaev spin liquid phase and that certain phase transitions induced by Heisenberg and Gamma interactions are driven by the condensation of such a bound state. Remarkably, this bound state appears as a sharp mode in the dynamical spin structure factor, while its condensation patterns at the appropriate phase transitions provide a simple explanation for the magnetically ordered phases surrounding each Kitaev spin liquid phase.
Tunable anomalous Hall conductivity through volume-wise magnetic competition in a topological kagome magnet
Magnetic topological phases of quantum matter are an emerging frontier in physics and material science. Along these lines, several kagome magnets have appeared as the most promising platforms. Here, we explore magnetic correlations in the kagome magnet Co 3 Sn 2 S 2 . Using muon spin-rotation, we present evidence for competing magnetic orders in the kagome lattice of this compound. Our results show that while the sample exhibits an out-of-plane ferromagnetic ground state, an in-plane antiferromagnetic state appears at temperatures above 90 K, eventually attaining a volume fraction of 80% around 170 K, before reaching a non-magnetic state. Strikingly, the reduction of the anomalous Hall conductivity (AHC) above 90 K linearly follows the disappearance of the volume fraction of the ferromagnetic state. We further show that the competition of these magnetic phases is tunable through applying either an external magnetic field or hydrostatic pressure. Our results taken together suggest the thermal and quantum tuning of Berry curvature induced AHC via external tuning of magnetic order.