Using vortex dynamics tools to explore magnetic configurations in non-superconducting materials [Slides]
A different look at the magnetic properties of the geometrically frustrated spin-chain compound Ca 3 Co 2 O 6
36 MATERIALS SCIENCE↗
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Ubiquity of amplitude-modulated magnetic ordering in the H - T phase diagram of the frustrated non-Fermi-liquid YbAgGe
YbAgGe contains a magnetic geometrically frustrated kagome-like lattice that also features significant local single-ion anisotropy. The electronic state is established by hybridization of 4f and conduction electrons leading to heavy electronic masses. The competition between these various interactions leads to nontrivial behavior under external magnetic field, including a sequence of magnetic phase transitions, non-Fermi-liquid states, and possibly a quantum critical point. We present a series of neutron diffraction experiments performed in the mK temperature range and under magnetic fields up to 8 T in the hexagonal plane, revealing the microscopic nature of the first four subsequent magnetic states of this phase diagram. The magnetic phases are associated with the propagation vectors K 1 =($\frac{1}{3}$ 0 $\frac{1}{3}$) for H < 2 T, K 2 = (0 0 0.32) for 2 T < H < 3 T, K 1 = ($\frac{1}{3}$ 0 $\frac{1}{3}$) for 3 T < H < 4.5 T and k 3 = (0.195 0.195 0.38) for 4.5 T < H < 7 T. Our structural refinements reveal a strong modulation of the magnetic moment amplitude in all phases. We observe that the ordered moments of the three magnetically different Yb sites become increasingly different in field, which complies with the principle local anisotropy directions relative to the field direction. While the ordered moments are aligned predominantly in the hexagonal plane, we also find a significant out-of-plane component and a ferromagnetic contribution above 2 T. Here we discuss possible scenarios that may evolve around the phase boundary at 4.5 T, which is associated with putative quantum criticality as identified by various bulk probes. We propose further steps that are required to better understand the microscopic interactions in this material.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Novel Phases and Dynamics of Multi-orbital Mott Insulators
The goal of this project is to gain theoretical insight into magnetism in the presence of spin-orbit coupling (SOC) for multi-orbital Mott insulators. Inspired by the exact solution of the Kitaev model that harbors a quantum spin liquid with novel excitations and struck by its relevance for materials with anisotropic orbital interactions, the PI will explore various new classes of 4d and 5d transition metal oxides. Starting with all electron Hamiltonians, the PI will derive minimal magnetic models. The aim will be to understand the role played by orbital frustration, even in the absence of any geometric frustration, in creating orbitally ordered as well as spin-orbital liquid phases. Orbital frustration arises primarily from the directional or anisotropic nature of d-orbitals in contrast to the isotropic nature of the spin degree of freedom. These models will be investigated by a variety of theoretical and numerical methods, including exact diagonalization, mean field theories, density matrix renormalization group and quantum Monte Carlo methods. Testable predictions for three experiments: nuclear magnetic resonance (NMR) and resonant x-ray scattering (RXS) to probe orbital ordering and pump-probe experiments to probe quantum dynamics will test the validity of these models for materials.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Fragile 3D Order in V 1 - x Mo x O 2
The metal-to-insulator transition in rutile VO2 has proven uniquely difficult to characterize because of the complex interplay between electron correlations and atomic structure. Here, we report the discovery of the sudden collapse of three-dimensional order in the low-temperature phase of V1-xMoxO2 at x = 0.17 and the emergence of a novel frustrated two-dimensional order at x = 0.19, with only a slight change in electronic properties. Single crystal diffuse x-ray scattering reveals that this transition from the 3D M1 phase to a 2D variant of the M2 phase results in long-range structural correlations along symmetry-equivalent (11L) planes of the tetragonal rutile structure, yet extremely short-range correlations transverse to these planes. These findings suggest that this two dimensionality results from a novel form of geometric frustration that is essentially structural in origin.
36 MATERIALS SCIENCE↗
Frustration- and doping-induced magnetism in a Fermi–Hubbard simulator
Geometrical frustration in strongly correlated systems can give rise to a plethora of novel ordered states and intriguing magnetic phases, such as quantum spin liquids. Promising candidate materials for such phases can be described by the Hubbard model on an anisotropic triangular lattice, a paradigmatic model capturing the interplay between strong correlations and magnetic frustration. However, the fate of frustrated magnetism in the presence of itinerant dopants remains unclear, as well as its connection to the doped phases of the square Hubbard model. Here we investigate the local spin order of a Hubbard model with controllable frustration and doping, using ultracold fermions in anisotropic optical lattices continuously tunable from a square to a triangular geometry. At half-filling and strong interactions U/t ≈ 9, we observe at the single-site level how frustration reduces the range of magnetic correlations and drives a transition from a collinear Néel antiferromagnet to a short-range correlated 120° spiral phase. Away from half-filling, the triangular limit shows enhanced antiferromagnetic correlations on the hole-doped side and a reversal to ferromagnetic correlations at particle dopings above 20%, hinting at the role of kinetic magnetism in frustrated systems. Furthermore, this work paves the way towards exploring possible chiral ordered or superconducting phases in triangular lattices and realizing t–t' square lattice Hubbard models that may be essential to describe superconductivity in cuprate materials.
74 ATOMIC AND MOLECULAR PHYSICS↗
Some exactly solvable and tunable frustrated spin models
In this report we discuss three exactly solvable spin models of geometric frustration. First, we discuss a 1-parameter subfamily of the 16 vertex model, which can be mapped to a planar Ising model and solved via Fisher-Dubedát decorations. We then consider a 1-parameter family generalization of the Villain’s fully frustrated model, which interpolates between Onsager’s 2D Ising model and the Villain one. We then discuss spin ice models on a tree, which can be solved exactly using recursions a lá Bethe.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
ASb 3 Mn 9 O 19 (A = K or Rb): New Mn-Based 2D Magnetoplumbites with Geometric and Magnetic Frustration
Magnetoplumbites are one of the most broadly studied families of hexagonal ferrites, typically with high magnetic ordering temperatures, making them excellent candidates for permanent magnets. However, magnetic frustration is rarely observed in magnetoplumbites. Herein, the discovery, synthesis, and characterization of the first Mn-based magnetoplumbite, as well as the first magnetoplumbite involving pnictogens (Sb), ASb 3 Mn 9 O 19 (A = K or Rb) are reported. The Mn 3+ ( S = 2) cations, further confirmed by DC magnetic susceptibility and X-ray photoelectron spectroscopy, construct three geometrically frustrated sublattices, including Kagome, triangular, and puckered honeycomb lattices. Magnetic properties measurements revealed strong antiferromagnetic spin–spin coupling as well as multiple low-temperature magnetic features. Heat capacity data does not show any prominent λ-anomaly, suggesting minimal associated magnetic entropy. Moreover, neutron powder diffraction (NPD) implied the absence of long-range magnetic ordering in KSb 3 Mn 9 O 19 down to 3 K. However, several magnetic peaks are observed in RbSb 3 Mn 9 O 19 at 3 K, corresponding to an incommensurate magnetic structure. Interestingly, strong diffuse scattering is seen in the NPD patterns of both compounds at low angles and is analyzed by reverse Monte Carlo refinements, indicating short-range spin ordering related to frustrated magnetism as well as 2D magnetic correlations in ASb 3 Mn 9 O 19 (A = K or Rb).
2-D magnetic correlation↗
Spectrally sharp magnetic excitations above the critical temperature in a frustrated Weyl semimetal
The rare-earth α-pyrochlore iridates are a prospective class of conducting frustrated magnets where electronic correlations, large spin-orbit coupling, and geometrical frustration interplay, leading to a rich set of magnetic and electronic phases. Despite their intriguing properties, the magnetic order and excitations in this fundamental class of topological quantum materials remain poorly understood due to challenges in growing large single crystals and insufficient microscopic information on their temperature-dependent phases. Here, by combining state-of-the-art thin-film synthesis, resonant elastic and inelastic X-ray scattering, spin wave analysis, and dynamical spin susceptibility calculations, we unequivocally reveal the presence of spectrally sharp, gapped magnetic excitations in Y 2 Ir 2 O 7 that surprisingly persist well above the Néel transition temperature, signaling the presence of a quasi-universal regime connected to fluctuations on frustrated lattices. This finding implies the existence of a highly unusual cooperative paramagnetic (CP) phase above the ordering temperature and offers an explanation for the puzzling high-temperature magnetic behavior observed across the family of metallic pyrochlore crystals. Understanding such magnetic excitations at technologically relevant temperatures opens up possibilities for novel topological spintronic devices.
36 MATERIALS SCIENCE↗
Anisotropy, frustration, and saddle point in the twisted kagome compound ErPdPb
The kagome lattice, with its inherent geometric frustration, provides a rich platform for exploring intriguing magnetic phenomena and topological electronic structures. In reduced-symmetry structures, such as twisted kagome systems involving rare earth elements, additional anisotropy can arise, enabling intriguing properties including spin-ice states, magnetocaloric effects, noncollinear magnetic ordering, and the anomalous Hall effect. Here, we report the synthesis of single crystals of ErPdPb, which features a twisted kagome lattice net of Er atoms within the hexagonal ZrNiAl-type structure, and we investigate its magnetic, electronic, and thermal properties. The material exhibits a highly anisotropic, correlated magnetic state below 2.7 K, as evidenced by magnetic, transport, and heat capacity measurements. Density functional theory (DFT) calculations indicate strong easy-axis anisotropy, consistent with experiment and crystal-field expectations, as well as quasi-one-dimensional bands and a spin-split saddle point at the zone center. Here, the coexistence of competing magnetic interactions along different crystallographic directions suggests an inherent degree of frustration. ErPdPb thus provides a promising platform for exploring the interplay of frustration, anisotropy, and electronic structure in a twisted kagome lattice.
Antiferromagnets↗
Controlling inversion disorder in a stoichiometric spinel magnet
In the study of frustrated quantum magnets, it is essential to be able to control the nature and degree of site disorder during the growth process, as many measurement techniques are incapable of distinguishing between site disorder and frustration-induced spin disorder. Pyrochlore-structured spinel oxides can serve as model systems of geometrically frustrated three-dimensional quantum magnets; however, the nature of the magnetism in one well-studied spinel, ZnFe 2 O 4 , remains unclear. Here, we demonstrate simultaneous control of both stoichiometry and inversion disorder in the growth of ZnFe 2 O 4 single crystals, directly yielding a revised understanding of both the collective spin behavior and lattice symmetry. Crystals grown in the stoichiometric limit with minimal site inversion disorder contravene all the previously suggested exotic spin phases in ZnFe 2 O 4 . Furthermore, the structure is confirmed on the F$\bar{4}$3m space group with broken inversion symmetry that induces antiferroelectricity. The effective tuning of magnetic behavior by site disorder in the presence of robust antiferroelectricity makes ZnFe 2 O 4 of special interest to multiferroic devices.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Structural and double magnetic transitions in the frustrated spin- 1 2 capped-kagome antiferromagnet ( RbCl ) Cu 5 P 2 O 10
The structural and magnetic properties of the geometrically frustrated spin- 1 2 capped-kagome antiferromagnet (RbCl) Cu 5 P 2 O 10 are investigated via temperature-dependent x-ray diffraction, magnetization, heat capacity, and 31 P NMR experiments on a polycrystalline sample. It undergoes a structural transition at around T t ≃ 310 K from a high-temperature trigonal (P ¯3m1) to a low-temperature monoclinic (C2/c) unit cell, where the low-temperature structure features the capped-kagome geometry of Cu 2+ ions. Interestingly, it shows the onset of two successive magnetic transitions at T N1 ≃ 20 K and T N2 ≃ 7 K. The shape of the 31 P NMR spectra unfolds the possible nature of the transitions below T N1 and T N2 to be of incommensurate and commensurate antiferromagnetic type, respectively. A large value of the Curie-Weiss temperature as compared to T N1 sets the frustration parameter f ≃ 8, ensuring strong magnetic frustration in the compound. From the 31 P NMR spin-lattice relaxation rate, the leading antiferromagnetic exchange coupling is estimated to be J/k B ≃ 117 K. Furthermore, these unusual double magnetic transitions make this compound beguiling for further investigations.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Short-range spin freezing in the double trillium lattice spin-liquid candidate KSrFe 2 (PO 4 ) 3 revealed via 31 P NMR
A comprehensive 31 P nuclear magnetic resonance (NMR) study, combined with thermodynamic measurements and first-principles band-structure calculations, has been conducted to explore the ground state of the 𝑆=5/2 double trillium lattice antiferromagnet KSrFe 2 (PO 4 ) 3 . Our experimental results indicate that the magnetic ground state is neither a conventional three-dimensional (3D) long-range order (LRO) nor a pure gapless spin-liquid state, as conjectured previously [Boya et al., APL Mater. 10, 101103 (2022)]. Specifically, the observation of a nearly field-independent NMR linewidth below 𝑇* = (3.5 ± 0.4) K, and a significant enhancement of spin-spin relaxation rate 1/𝑇 2 below 2𝑇* (where 𝑇* is the characteristic temperature identified from the magnetic susceptibility), indicate a complex magnetic ground state where spin freezing coexists with persistent dynamics. Furthermore, we argue that the lack of magnetic LRO and the persistence of strong magnetic fluctuations in KSrFe 2 (PO 4 ) 3 are unlikely to originate from intersite K/Sr disorder, rather they arise due to intrinsic magnetic frustration. In conclusion, our findings position KSrFe 2 (PO 4 ) 3 into a broader family of geometrically frustrated magnets characterized by coexisting spin freezing and pronounced antiferromagnetic fluctuations, marking it as a promising platform for investigating exotic phenomena in 3D frustrated magnets.
Exotic phases of matter↗
Frustrated Magnetism and Ferroelectricity in a Dy 3+ -Based Triangular Lattice
Triangular lattice magnets have attracted extensive research interest because they are potential hosts for geometrically frustrated magnetism and strong quantum fluctuations. Here, utilizing a laser floating zone technique, we report the first-time successful growth of a DyInO 3 sizable crystal, which contains Dy3+-based triangular layers. The fine-tuning of Indium stoichiometry was found to be the key factor in the stabilization of the desired hexagonal phase. The X-ray diffraction study of the crystal structure reveals a non-centrosymmetric P6 3mc space group. Switchable polarization, i.e., ferroelectricity, and ferroelectric domain configuration are experimentally demonstrated at room temperature. Anisotropic magnetic and thermodynamic measurements unveil antiferromagnetic interactions, the absence of long-range ordering down to 0.1 K, and a possible doublet ground state, indicating a strongly frustrated magnetism. Our findings suggest that the DyInO 3 crystal is an excellent platform for studying emergent phenomena and their interplay with coherent topological defects in the quantum realm.
36 MATERIALS SCIENCE↗
Interleaved bond frustration in a triangular lattice antiferromagnet
Frustration of long-range order via lattice geometry amplifies fluctuations and generates ground states that are highly sensitive to perturbations. Traditionally, geometric frustration is used to engineer unconventional magnetic states; however, the charge degree of freedom and bond order can be similarly frustrated. Finding materials that host both frustrated magnetic and bond networks holds promise for engineering structural and magnetic states with the potential of coupling to one another via either magnetic or strain fields. Here we identify an unusual instance of this coexistence in the triangular lattice antiferromagnets LnCd 3 P 3 (Ln = lanthanides). These compounds feature two-dimensional planes of unique trigonal planar CdP 3 units with an underlying bond instability that is frustrated via emergent kagome ice correlations. This bond instability is interleaved in between layers of frustrated magnetic moments. Furthermore, our results establish LnCd 3 P 3 as a rare materials class in which frustrated magnetism is embedded within a dopable semiconductor with a frustrated bond order instability.
Gomez Alvarado, S. J. [University of California, S↗
Unconventional skyrmions in an interfacial frustrated triangular lattice
Magnetic skyrmions are spin topological textures of potential interest in spintronics-related data storage and processing devices. Here, in this work, we show the emergence of unconventional skyrmions in a geometrically frustrated triangular lattice on an inversion-symmetry-breaking two-dimensional electron gas substrate. Starting with a classical double-exchange mechanism, this generic interface induces exotic skyrmionic and unique noncoplanar magnetic states not observed in the equivalent square lattice interface. We study the model by deriving an effective spin Hamiltonian. Large scale classical Monte Carlo simulations provide a quantitative evidence for the emergence of these exotic magnetic states. We found that these chiral magnetic states exhibit a substantial and nonzero topological Hall conductivity. As potential material candidates, we propose Cr/MoS 2 , Fe/MoS 2 , and Fe/WSe 2 interfaces because they have the requisite underlying triangular lattice structures and large spin-orbit coupling.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Frustration-mediated crossover from long-range to short-range magnetic ordering in Y 1 – x L u x BaC o 4 O 7
The RBaCo 4 O 7 system is a prototype geometrically frustrated magnet in which kagome planes and triangular layers of Co-O tetrahedra interleave. For R=Y, an antiferromagnetic ground state is realized due to a frustration-breaking trigonal-orthorhombic phase transition. For R = Lu, however, a long-range ordered state has rarely, if ever, been reported despite a similar symmetry-breaking transition, albeit at a significantly lower temperature. To explore this dichotomy, we present a comprehensive magnetic and structural phase diagram for Y 1-x Lu x BaCo 4 O 7 , established through complementary neutron diffraction and magnetization measurements. Our results outline the phase evolution of the nuclear structures in response to changes in composition and temperature. Further, the temperature of the trigonal (P31c) to orthorhombic (Pbn2 1 ) transition, T s1 , decreases monotonically with increasing Lu content from 310 K for x = 0.0 to 110 K for x = 1.0. In Lu-rich compositions (0.7 ≤ x ≤ 1.0), first-order structural transitions are observed with coexisting and competing orthorhombic Pbn2 1 and metastable monoclinic Cc phases. For the magnetically ordered Y-rich compositions, T- and x-dependent refinements of the magnetic structure reveal an antiferromagnetic “ribbonlike” arrangement of Co spin pairs in both the triangular and the kagome layers. A gradual suppression of long-range magnetic order is observed with increasing the Lu content, accompanied by the development of short-range magnetic correlations present in all the samples.
36 MATERIALS SCIENCE↗
Topological flat bands in frustrated kagome lattice CoSn
Electronic flat bands in momentum space, arising from strong localization of electrons in real space, are an ideal stage to realize strongly-correlated phenomena. Theoretically, the flat bands can naturally arise in certain geometrically frustrated lattices, often with nontrivial topology if combined with spin-orbit coupling. Here, we report the observation of topological flat bands in frustrated kagome metal CoSn, using angle-resolved photoemission spectroscopy and band structure calculations. Throughout the entire Brillouin zone, the bandwidth of the flat band is suppressed by an order of magnitude compared to the Dirac bands originating from the same orbitals. The frustration-driven nature of the flat band is directly confirmed by the chiral d-orbital texture of the corresponding real-space Wannier functions. Spin-orbit coupling opens a large gap of 80 meV at the quadratic touching point between the Dirac and flat bands, endowing a nonzero Z2 invariant to the flat band. These findings demonstrate that kagome-derived flat bands are a promising platform for novel emergent phases of matter at the confluence of strong correlation and topology.
36 MATERIALS SCIENCE↗
Ferroelectric phase-transition frustration near a tricritical composition point
Phase transition describes a mutational behavior of matter states at a critical transition temperature or external field. Despite the phase-transition orders are well sorted by classic thermodynamic theory, ambiguous situations interposed between the first- and second-order transitions were exposed one after another. Here, we report discovery of phase-transition frustration near a tricritical composition point in ferroelectric Pb(Zr 1-x Ti x )O 3 . Our multi-scale transmission electron microscopy characterization reveals a number of geometrically frustrated microstructure features such as self-assembled hierarchical domain structure, degeneracy of mesoscale domain tetragonality and decoupled polarization-strain relationship. Associated with deviation from the classic mean-field theory, dielectric critical exponent anomalies and temperature dependent birefringence data unveil that the frustrated transition order stems from intricate competition of short-range polar orders and their decoupling to long-range lattice deformation. With supports from effective Hamiltonian Monte Carlo simulations, our findings point out a potentially universal mechanism to comprehend the abnormal critical phenomena occurring in phase-transition materials.
42 ENGINEERING↗