Frustrated Exchange Interactions Research Articles

Single crystal synthesis, structure, and magnetism of Pb10−xCux(PO4)6O

The recent claim of superconductivity above room temperature in Pb10−xCux(PO4)6O with 0.9 < x < 1 (referred to as LK-99) has sparked considerable interest. To minimize the influence of structural defects and impurity phases on the physical properties, we have synthesized phase-pure single crystals with a copper doping level of x ∼ 1. We find that the crystals are highly insulating and optically transparent. X-ray analysis reveals an uneven distribution of the substituted Cu throughout the sample. Temperature (T) dependent magnetic susceptibility measurements for 2 ≤ T ≤ 800 K reveal the diamagnetic response characteristic of a non-magnetic insulator, as well as a small ferromagnetic component, possibly originating from frustrated exchange interactions in Cu-rich clusters in the Pb10−xCux(PO4)6O structure. No anomalies indicative of phase transitions are observed. We, therefore, rule out the presence of superconductivity in Pb9Cu(PO4)6O crystals and provide some considerations on the origin of anomalies previously reported in experiments on polycrystalline specimens.

Modulating saturation magnetization and topological Hall resistivity of flexible ferrimagnetic Mn4N films by bending strains

The ferrimagnetic rare-earth-free Mn4N films are considered as a good candidate in spintronics due to its low saturation magnetization (MS) and high Néel temperature. Here, Mn4N films are directly deposited on flexible mica to investigate strain-related magnetic and electronic transport properties. The MS variation of 11.0 nm Mn4N film reaches 453% at tensile strain of radius of curvature (ROC) = 2 mm. Bending strains cannot affect anomalous Hall resistivity and magnetoresistance. However, the topological Hall resistivity of 147.0 nm Mn4N film increases by 58% at tensile strain of ROC = 5 mm due to frustrated exchange interactions. The flexible Mn4N films have great potential applications in flexible magnetic sensor and strain gauge due to strain modulated MS, resistance, and stable magnetoresistance.

Magnetic field-induced nontrivial spin chirality and large topological Hall effect in kagome magnet ScMn6Sn6

RMn6Sn6 (R = rare earth element) kagome magnets have attracted much attention owing to their potential for realizing the emerging topological properties in both reciprocal and real spaces. One of the RMn6Sn6 members, ScMn6Sn6, is predicted to possess room temperature-stabilized chiral spin textures arising from frustrated exchange interactions, but further experimental evidence has not been well established yet. In this work, we fabricate high-quality ScMn6Sn6 single crystals and systematically study their magnetoelectric transport properties. A large topological Hall effect is observed within the temperature range from 100 to 320 K with the magnetic field applied along the parallel direction of the kagome plane. This observation suggests that the spin textures in ScMn6Sn6 have a nonzero scalar spin chirality over a wide temperature range. Our results identify ScMn6Sn6 as a promising member of the rare earth element kagome magnets that hosts chiral spin textures at room temperature.

Frustrated Magnetic Interactions and Quenched Spin Fluctuations in CrAs

The discovery of pressure-induced superconductivity in helimagnets (CrAs, MnP) has attracted considerable interest in understanding the relationship between complex magnetism and unconventional superconductivity. However, the nature of the magnetism and magnetic interactions that drive the unusual double-helical magnetic order in these materials remains unclear. Here, we report neutron scattering measurements of magnetic excitations in CrAs single crystals at ambient pressure. Our experiments reveal well defined spin wave excitations up to about 150 meV with a pseudogap below 7 meV, which can be effectively described by the Heisenberg model with nearest neighbor exchange interactions. Most surprisingly, the spin excitations are largely quenched above the Néel temperature, in contrast to cuprates and iron pnictides where the spectral weight is mostly preserved in the paramagnetic state. Our results suggest that the helimagnetic order is driven by strongly frustrated exchange interactions, and that CrAs is at the verge of itinerant and correlation-induced localized states, which is therefore highly pressure-tunable and favorable for superconductivity.

Nano-scale collinear multi-Q states driven by higher-order interactions

Complex magnetic order arises due to the competition of different interactions between the magnetic moments. Recently, there has been an increased interest in such states not only to unravel the fundamental physics involved, but also with regards to applications exploiting their unique interplay with moving electrons. Whereas it is the Dzyaloshinskii-Moriya interaction (DMI) that has attracted much attention because of its nature to induce non-collinear magnetic order including magnetic-field stabilized skyrmions, it is the frustration of exchange interactions that can drive magnetic order down to the nano-scale. On top of that, interactions between multiple spins can stabilize two-dimensional magnetic textures as zero-field ground states, known as multi-Q states. Here, we introduce a two-dimensional itinerant magnet with various competing atomic-scale magnetic phases. Using spin-polarized scanning tunneling microscopy we observe several zero-field uniaxial or hexagonal nano-scale magnetic states. First-principles calculations together with an atomistic spin model reveal that these states are stabilized by the interplay of frustrated exchange and higher-order interactions while the DMI is weak. Unexpectedly, it is found that not only non-collinear magnetic states arise, but that higher-order interactions can also lead to collinear nano-scale multi-Q states.

Magnetization Compensation Temperature and Frustration-Induced Topological Defects in Ferrimagnetic Antiperovskite Mn_{4}N.

First-principles-based simulations are conducted to investigate magnetic properties and topological spintextures in the antiperovskite Mn_{4}N ferrimagnet. A magnetization compensation temperature, resulting from a competition between different Mn sublattices, is found in this system, when under thermal equilibrium. Striking metastable topological states are also discovered, including nanometric hedgehog-antihedgehog pairs that originate from frustrated exchange interactions rather than the usual Dzyaloshinskii-Moriya interaction.

A frustrated bimeronium: Static structure and dynamics

We show a topological spin texture called “bimeronium” in magnets with in-plane magnetization. It is a topological counterpart of skyrmionium in perpendicularly magnetized magnets and can be seen as a combination of two bimerons with opposite topological charges. We report the static structure and spin-orbit-torque-induced dynamics of an isolated bimeronium in a magnetic monolayer with frustrated exchange interactions. We study the anisotropy and magnetic field dependences of a static bimeronium. We also explore the bimeronium dynamics driven by the damping-like spin-orbit torque. We find that the bimeronium shows steady rotation when the spin polarization direction is parallel to the easy axis. Moreover, we demonstrate the annihilation of the bimeronium when the spin polarization direction is perpendicular to the easy axis. Our results are useful for understanding the fundamental properties of bimeronium structures and may offer an approach to build bimeronium-based spintronic devices.

Featureless quantum paramagnet with frustrated criticality and competing spiral magnetism on spin-1 honeycomb lattice magnet

We study the spin-1 honeycomb lattice magnets with frustrated exchange interactions. The proposed microscopic spin model contains first and second neighbor Heisenberg interactions as well as the single-ion anisotropy. We establish a rich phase diagram that includes a featureless quantum paramagnet and various spin spiral states induced by the mechanism of order by quantum disorder. Although the quantum paramagnet is dubbed featureless, it is shown that, the magnetic excitations develop a contour degeneracy in the reciprocal space at the band minima. These contour degenerate excitations are responsible for the frustrated criticality from the quantum paramagnet to the ordered phases. This work illustrates the effects of magnetic frustration on both magnetic orderings and the magnetic excitations. We discuss the experimental relevance to various Ni-based honeycomb lattice magnets.

Tailoring magnetic interactions in atomic bilayers of Rh and Fe on Re(0001)

Using density functional theory, we investigate the interplay between the stacking order and sequence of bilayers composed of an Fe and a Rh layer on the Re(0001) and their magnetic properties. We find that fcc/ffc stacked bilayers are energetically very unfavorable, while all other combinations of hcp and fcc stacking are energetically close. The magnetic interactions are evaluated by mapping the DFT total energies onto a spin model, which contains Heisenberg exchange, Dzyaloshinskii-Moriya interaction, the magnetocrystalline anisotropy energy, and higher-order exchange interactions. We find that the stacking sequence of the bilayer significantly modifies the magnetic interactions. As a result, we find a DMI driven cycloidal spin spiral ground state with a period of 11~nm for hcp-Fe/hcp-Rh. For fcc-Fe/hcp-Rh and hcp-Fe/fcc-Rh, we obtain a ferromagnetic ground state. The spin spiral energy dispersion of hcp-Fe/hcp-Rh including spin-orbit coupling suggests that isolated skyrmions can be stabilized in the field-polarized ferromagnetic background at external magnetic fields. If the Fe layer is sandwiched between the Rh overlayer and the Re(0001) substrate, there is a competition between the ferromagnetic coupling preferred by the Rh-Fe hybridization and the antiferromagnetic coupling induced by the Fe-Re hybridization. Due to the Fe/Re interface the DMI can become very large. For fcc-Rh/hcp-Fe, we obtain a cycloidal spin spiral with a period of 1.7~nm which is induced by frustration of exchange interactions and further stabilized by the DMI. For hcp-Rh/hcp-Fe, we find a DMI driven cycloidal spin spiral with a period of 4~nm and locally nearly antiparallel magnetic moments due to antiferromagnetic nearest-neighbor exchange. The higher-order exchange constants can be significant in the considered films, however, they do not stabilize multi-$Q$ states.

Scaling theory of magnetism in frustrated Kondo lattices

A scaling theory of the Kondo lattices with frustrated exchange interactions is developed, criterium of antiferromagnetic ordering and quantum-disordered state being investigated. The calculations taking into account magnon and incoherent spin dynamics are performed. Depending on the bare model parameters, one or two quantum phase transitions into non-magnetic spin-liquid and Kondo Fermi-liquid ground states can occur with increasing the bare coupling constant. Whereas the renormalization of the magnetic moment in the ordered phase can reach orders of magnitude, spin fluctuation frequency and coupling constant are moderately renormalized in the spin-liquid phase. This justifies application of the scaling approach. Possibility of a non-Fermi-liquid behavior is treated.

Spin nematics in frustrated spin-dimer systems with bilayer structure

We study frustrated spin-1/2 dimer systems in two dimensions with a bilayer structure, where spins are ferromagnetically coupled in dimers. Our model includes frustrated two-spin exchange interactions as well as four-spin interaction. We pay particular attention to the spin nematic phase, which does not exhibit any magnetic (spin-dipole) order but has a spin-quadrupolar long-range order. Employing a perturbation calculation, a mean-field approximation, and a numerical many-variable variational Monte Carlo method, we determine ground-state phase diagrams on various two-dimensional lattices. It is found that the model exhibits the spin nematic phase with ferro-quadrupolar order in a wide parameter region, in addition to conventional magnetically-ordered phases. In particular, it is shown that even when the four-spin interactions are absent, frustrated two-spin exchange interactions can realize the spin nematic phase as a result of strong interdimer correlations. It is also found that the phase transitions between the spin nematic phase and antiferromagnetic phases can be continuous. Furthermore, we present some exact arguments that various phases including the spin nematic phase and the vector chiral (p-type nematic) phase emerge from an SU(4) symmetric point in the model by the addition of appropriate perturbative interactions. The spin nematic phase generated from the SU(4) point is connected with the spin nematic phase found numerically in the system with only two-spin interactions.

On the scaling theory of antiferromagnetic ordering in frustrated Kondo lattices

A scaling theory of the Kondo lattices with frustrated exchange interactions is developed, criterium of antiferromagnetic ordering being investigated. Depending on the bare model parameters, one or two quantum phase transitions into non-magnetic spin-liquid and Kondo Fermi-liquid ground states can occur with increasing the bare coupling constant. Whereas the renormalization of the magnetic moment in the ordered phase can reach orders of magnitude, spin fluctuation frequency and coupling constant are moderately renormalized in the spin-liquid phase. This justifies application of the scaling approach.

Realizing an Isotropically Coercive Magnetic Layer for Memristive Applications by Analogy to Dry Friction

We investigate the possibility of realizing a spintronic memristive device based on the dependence of the tunnel conductance on the relative angle between the magnetization of the two magnetic electrodes in in-plane magnetized tunnel junctions. For this, it is necessary to design a free layer whose magnetization can be stabilized along several or even any in-plane direction between the parallel and the antiparallel magnetic configurations. We experimentally show that this can be achieved by exploiting antiferromagnet-ferromagnet exchange interactions in a regime where the antiferromagnet is thin enough to induce enhanced coercivity and no exchange bias. The frustration of exchange interactions at the interfaces due to competing ferro- and antiferromagnetic interactions is at the origin of an isotropic dissipation mechanism yielding isotropic coercivity. From a modeling point of view, it is shown that this isotropic dissipation can be described by a dry friction term in the Landau-Lifshitz-Gilbert equation. The influence of this dry friction term on the magnetization dynamics of an in-plane magnetized layer submitted to a rotating in-plane field is investigated both analytically and numerically. The possibility to control the free layer magnetization orientation in an in-plane magnetized magnetic tunnel junction by using the spin transfer torque from an additional perpendicular polarizer is also investigated through macrospin simulation. It is shown that the memristor function can be achieved by the injection of current pulses through the stack in the presence of an in-plane static field transverse to the reference layer magnetization, the aim of which is to limit the magnetization rotation between 0{\deg} and 180{\deg}.

Skyrmion instabilities and distorted spiral states in a frustrated chiral magnet

Magnetic skyrmions are particle-like topological excitations that recently generated much interest as candidates for future spintronic devices based on skyrmion small size, enhanced topological stability, and/or mutual interaction. Here we examine the properties of isolated skyrmions in a frustrated chiral magnet with competing Dzyaloshinskii-Moriya and frustrated exchange interactions. We show that the skyrmion size drastically decreases even for small values of competing stabilization mechanisms. Skyrmion mutual interaction remains attracting as is inherent for frustrated skyrmions, but the value of the Dzyaloshinskii constant regulates the number of minima in the interaction potentials. Moreover, the constructed phase diagrams for a chiral helimagnet contain a distorted spiral state that can be considered as a buffer between the helicoidal and conical one-dimensional modulations. The formulated concepts may further enhance the functionalities of spintronic devices. In particular, the controlled instability of skyrmions with respect to the conical state allows to obtain bimeron-like structures. Moreover, our results provide physical insight into the chiral states in the magnetic systems, e.g., in MnSi$_{1-x}$Ge$_x$.

B–T phase diagram of Pd/Fe/Ir(111) computed with parallel tempering Monte Carlo

We use an atomistic spin model derived from density functional theory calculations for the ultra-thin film Pd/Fe/Ir(111) to show that temperature induces coexisting non-zero skyrmion and antiskyrmion densities. We apply the parallel tempering Monte Carlo method in order to reliably compute thermodynamical quantities and the B–T phase diagram in the presence of frustrated exchange interactions. We evaluate the critical temperatures using the topological susceptibility. We show that the critical temperatures depend on the magnetic field in contrast to previous work. In total, we identify five phases: spin spiral, skyrmion lattice, ferromagnetic phase, intermediate region with finite topological charge and paramagnetic phase. To explore the effect of frustrated exchange interactions, we calculate the B–T phase diagram, when only effective exchange parameters are taken into account.

The extended Bloch's law in yttrium iron garnet doped with Zn, Ni and Co

The empirical extended Bloch's law about the saturation magnetization behavior as a function of temperature was checked in nanoparticles of yttrium iron garnet doped with zinc, nickel and cobalt. The exponent values from fitting extended Bloch's law with experimental results vary from 1.42 to 9.68, and are different from these expected values; 9/2, 2, 3/2, 3 and 5/2. The discrepancy was associated to the existence of structural defects and moments with frustrated exchange interaction, due to the nanoparticles size and thermal treatment conditions. Other adjustment attempt was performed with a linear term combined to the traditional Bloch's law T3/2 motivated by the nanometric particles size. This other attempt was unsuccessful showing discrepancy with the experimental results and attributed to the atomic disorder and magnetic frustrations.

Competition of Dzyaloshinskii-Moriya and Higher-Order Exchange Interactions in Rh/Fe Atomic Bilayers on Ir(111).

Using spin-polarized scanning tunneling microscopy and density functional theory we demonstrate the occurrence of a novel type of noncollinear spin structure in Rh/Fe atomic bilayers on Ir(111). We find that higher-order exchange interactions depend sensitively on the stacking sequence. For fcc-Rh/Fe/Ir(111), frustrated exchange interactions are dominant and lead to the formation of a spin spiral ground state with a period of about 1.5nm. For hcp-Rh/Fe/Ir(111), higher-order exchange interactions favor an up-up-down-down (↑↑↓↓) state. However, the Dzyaloshinskii-Moriya interaction at the Fe/Ir interface leads to a small angle of about 4° between adjacent magnetic moments resulting in a canted ↑↑↓↓ ground state.

Synthesis, Crystal and Electronic Structure of the Titanium Bismuthides Sr5Ti12Bi19+x, Ba5Ti12Bi19+x, and Sr5–δEuδTi12Bi19+x (x ≈ 0.5–1.0; δ ≈ 2.4, 4.0)

Crystals of the new ternary bismuthides AE5Ti12Bi19+x (AE = Sr, Ba) and Sr5–δEuδTi12Bi19+x (δ ≈ 2.4, 4.0; x ≤ 1.0) were grown using an excess of molten Bi as a flux. The title compounds crystallize in the cubic non‐centrosymmetric space group P43m and are structurally related to the antimonides Ba5M12Sb19+x (M = Ti, V, Nb). The crystal structure features Ti atoms stuffed in the γ‐brass‐like sub‐lattice made of AE (AE = Sr, Ba, Eu) and Bi atoms. The arrangement of the AE atoms, on its own, represents a framework consisting of interconnected regular tetrahedra and octahedra. Another notable attribute of the AE5Ti12Bi19+x structure is the disordered Bi moiety located at the center of the unit cell and showing homoatomic Bi–Bi bonding. Electronic structure calculations and electrical resistivity measurements indicate metallic behavior of the new bismuthides. Magnetization measurements on samples of Sr5–δEuδTi12Bi19+x show paramagnetic behavior consistent with the 2+ ground state for Eu. The measurements also confirm no magnetic ordering down to 3 K, stemming from the geometrically frustrated exchange interactions of the Eu2+ cations.

Spin model for nontrivial types of magnetic order in inverse-perovskite antiferromagnets

Nontrivial magnetic orders in the inverse-perovskite manganese nitrides are theoretically studied by constructing a classical spin model describing the magnetic anisotropy and frustrated exchange interactions inherent in specific crystal and electronic structures of these materials. With a replica-exchange Monte-Carlo technique, a theoretical analysis of this model reproduces the experimentally observed triangular \Gamma^{5g} and \Gamma^{4g} spin ordered patterns and the systematic evolution of magnetic orders. Our work solves a 40-year-old problem of nontrivial magnetism for the inverse-perovskite manganese nitrides and provides a firm basis for clarifying the magnetism-driven negative thermal expansion phenomenon discovered in this class of materials.

Supersolid magnetic phase in the two-dimensional Ising-like antiferromagnet with strong single-ion anisotropy

The Ising model with the frustrated exchange interaction for strongly anisotropic antiferromagnetic ultrathin film is investigated in the mean field approximation at low temperatures. It is shown that a spatially inhomogeneous state can be accomplished in the system at a certain relation of material constants values, along with homogeneous states: ferromagnetic, quadrupolar or supersolid magnetic phases. The phase diagram of the system is built on the basis of stability lines analysis.