Session F58: Pyrochlore Lattices

Controlling spin Dynamics in permalloy nanodisks arranged on honeycomb lattices

There has been significant interest in studies of spin dynamics in artificial spin ice (ASI) systems due to their potential applications in magnonic devices. Here, we present experimental and theoretical studies of spin dynamics in artificial spin ice arrays¹, which consist of contacting and non-contacting honeycomb lattices made of ferromagnetic nanodisks². The nanodisks are patterned on a co-planar waveguide using nanofabrication by electron-beam lithography, electron-beam evaporation of permalloy (NiFe), and lift-off. We employ broadband ferromagnetic resonance to experimentally determine the spin-wave spectra, which are found to be in good agreement with micromagnetic simulations using Mumax³. We demonstrate that the complex spin dynamics of the ASI systems can be controlled by the excitation frequency. Our study opens up new opportunities for designing specific applications in the emerging field of magnonics.   

Topological Kinetics in a Vertex-Frustrated Artificial Spin Ice Nanomagnet Array

We have experimentally investigated and imaged how the topology of a frustrated artificial spin ice nanomagnet array can affect and constrain its kinetics. Studying vertex-frustrated Santa Fe artificial spin ice, in which magnetic excitations are correlated in thermally active one-dimensional emergent strings, we imaged the thermally-driven motion of these emergent string excitations in real time. At high temperatures, the string kinetics include topologically complex changes, which are highly constrained at lower temperatures. This system provides an unusually accessible venue in which to study the effects of topology on ergodicity through direct measurement of the thermal kinetics.

    

Noise Detection of Mobile Magnetic Excitations in a Vertex-Frustrated Artificial Spin Ice

Direct detection of equilibrium spin fluctuations, or "magnetization noise", is emerging as a powerful means of revealing and studying topologically-protected magnetic excitations in both natural and artificial frustrated magnets. Depending on the lattice geometry and nature of the frustration, these excitations can often be described as quasiparticles that behave as mobile magnetic charges. Here, using ultrasensitive optical detection of spontaneous magnetization noise in a thermally active system, supported by additional insight from Monte Carlo simulations, we reveal new regimes of mobile magnetic excitations in the vertex-frustrated artificial spin ice lattices, including tetris and Shakti geometries. A substantial increase of the detected noise for specific directions and ranges of applied in-plane magnetic field heralds the proliferation of these excitations, which can diffuse freely, without any cost in energy, along specific quasi-1D paths in the lattice. As such, those magnetic excitations have no analogous counterpart in naturally-occurring materials and constitute an interesting subject in studies of magnetricity.   

Engineering Artificial Spin Ice with a Frustrated Lattice of Y-shaped Non-Ising Moments

Artificial spin ice (ASI) systems composed of arrays of frustrated interacting nanomagnets offer a valuable platform for designing and exploring collective magnetic phenomena. However, most ASI geometries explored to date employ stadium-shaped magnetic islands with Ising-like character, i.e., the island moments are binary.  We report the study of an artificial spin system based on a new type of artificial moment: a three-fold symmetric Y-shape island. The resulting non-binary nanomagnetic building block effectively behaves as a multipolar magnetic element, giving rise to behavior akin to a Potts-like 6-state clock model. These new magnetic objects enable the exploration of a variety of novel magnetic phases, opening a path to new collective phenomena and kinetics beyond the traditional ASI binary moment systems.

    

Generalized auto-oscillator model for arbitrary artificial spin ices

Artificial spin ices (ASIs) are ensembles of geometrically structured, interacting magnetic nano-elements that exhibit frustration as a result of their design [1] and can be considered magnonic crystals [2]. While the magnon band structures in ASIs is rich, it is time consuming to compute numerically [3] and only a few analytical approaches have been presented [4]. Here, we present a generalized semi-analytical model based on a Holstein-Primakoff transformation [5] to compute the band structure of arbitrary ASIs. The numerical model accounts for arbitrary positioning and rotation of nanoislands and returns the full non-local dipole coupling between elements. While the model currently assumes a two-dimensional dispersion, it can be easily extended to three-dimensional ASIs and their full band structure.

 

[1]    S. H. Skjærvø et al., Nat. Rev. Phys. 2, 13 – 28 (2020)

[2]    S. Gliga, E. Iacocca, and O. G. Heinonen, APL Materials 8, 040911 (2020)

[3]    E. Iacocca, S. Gliga, and O. G. Heinonen, Phys. Rev. Appl. 13, 044047 (2020)

[4]    E. Iacocca et al., Phys. Rev. B 93, 134420 (2016); T. D. Lasnier and G. M. Wysin, Phys. Rev. B 101, 224428 (2020)

[5]    A. Slavin and V. Tiberkevich, IEEE Trans. Magn. 45, 1875 – 1918 (2008)

    

Dynamical fractal and anomalous noise in a clean magnetic crystal

Fractals – objects with non-integer dimensions – occur in manifold settings and length scales in nature, ranging from snowflakes and lightning strikes to natural coastlines. Much effort has been expended to generate fractals for use in many-body physics. Here, we identify an emergent dynamical fractal in a disorder-free, stoichiometric three-dimensional magnetic crystal in thermodynamic equilibrium. The phenomenon is born from constraints on the dynamics of the magnetic monopole excitations in spin ice, which restrict them to move on the fractal. This observation explains the anomalous exponent found in magnetic noise experiments in the spin ice compound Dy₂Ti₂O₇, and it resolves a long-standing puzzle about its rapidly diverging relaxation time. The capacity of spin ice to exhibit such striking phenomena holds promise of further surprising discoveries in the cooperative dynamics of even simple topological many-body systems.   

Symmetry breaking in the S=1/2 and S=1 pyrochlore Heisenberg antiferromagnets

We investigate the ground-state properties of the nearest-neighbor S=1/2 and S=1 pyrochlore Heisenberg antiferromagnet using three complementary numerical methods, density-matrix renormalization group (DMRG),  pseudofermion functional renormalization group (PFFRG) and numerical linked cluster expansion. Within DMRG, we are able to reliably study clusters with up to 128 spins (for S=1/2) and 48 spins (for S=1) by keeping 20 000 SU(2) states. Our most striking finding in the S=1/2 case is a robust spontaneous inversion symmetry breaking, reflected in an energy density difference between the two sublattices of tetrahedra. We also determine the ground-state energy, E₀/N sites=-0.490(6)J, by combining extrapolations of DMRG with those of a numerical linked cluster expansion. In the S=1 case, the investigated 32-site and 48-site clusters both show indications of a robust C₃ rotation symmetry breaking of the ground-state spin correlations and the 48-site cluster additionally features inversion symmetry breaking. Our PFFRG analysis of various symmetry-breaking perturbations corroborates the findings of either C₃ or a combined C₃/inversion symmetry breaking. Moreover, in both methods the symmetry-breaking tendencies appear to be more pronounced than in the S=1/2 system.   

Abundance of hard-hexagon crystals in the quantum pyrochlore Heisenberg antiferromagnet

We propose a simple family of valence-bond crystals as potential ground states of the S=1/2 and S=1 Heisenberg antiferromagnet on the pyrochlore lattice. Exponentially numerous in the linear size of the system, these can be visualized as hard-hexagon coverings, with each hexagon representing a resonating valence-bond ring. This ensemble spontaneously breaks rotation, inversion, and translation symmetries. A simple yet accurate variational wavefunction allows a precise determination of the energy, confirmed by DMRG and numerical linked cluster expansion and extended by an analysis of excited states. The identification of the origin of the stability indicates applicability to a broad class of frustrated lattices, which we demonstrate for the checkerboard and ruby lattices. Our work suggests a perspective on such quantum magnets, in which unfrustrated motifs are effectively uncoupled by the frustration of their interactions.   

Geometrical Frustration and Tunable Lattice Dynamics of Highly Anisotropic Pyrochlore Cuprospinels

Recently there has been a strong research interest in the field of frustrated magnetism in tertragonally distorted spinels (AB₂O₄) because they exhibit peculiar magnetic characteristics such as spin-liquid and reentrant spin-glass behavior. Among the various spinels, CuFe₂O₄ and ZnFe₂O₄ are unique systems in which the former exhibit Jahn-Teller distortion with high temperature ferrimagentic (FiM) ordering (743 K) while the later possesses pyrochlore structure and shows low-temperature antiferromagnetic (T_N ~ 10 K) ordering with high degree of magnetic frustration index (f ≥ 12). In this work, we report magnetic properties and lattice dynamics of few intermediate compositions (0 ≤ x ≤ 1) of the above two systems (Cu_1−xZn_xFe₂O₄) in the form of bulk polycrystals. Analysis of the magnetization data (χ = M/H) for x = 0.1 shows T_FiM ~ 700 K with two additional transitions at 65 K and 250 K, the latter is expected to result from the domain crossover dynamics. Based on the factor group analysis, 10 Raman active modes for tetragonal CuFe₂O₄ and 5 modes for cubic CuFe₂O₄ (A_1g + E_g + 3F_2g) are observed, whereas 18 modes for cubic ZnFe₂O₄ are evident. Our results across the morphotropic phase boundary (0.05 < x_P < 0.1) shows 6 vibrational modes. On the contrary, only one mode is noticed for x = 0.5 at ν = 500 cm⁻¹. A systematic comparative study between the parameters extracted from magnetic and spectroscopic data will be discussed in correlation to the changes occurring in the crystal structure.   

Spin-Spin Correlations in the CuAlCr4S8 Breathing Pyrochlore Lattice

In recent years, the breathing pyrochlore structure has been realized in a number of compounds which display complex spin-spin correlations arising from the many competing interactions that characterize them. Recently, a new breathing pyrochlore, CuAlCr₄S₈, has been synthesized and found to develop magnetic order below 20 K [Phys. Rev. B 106, 024407 (2022)]. In an attempt to theoretically understand the nature of the ordering in this system, superexchange couplings were determined using density-functional theory (DFT), and the resulting spin Hamiltonian was studied using large-N theory, pseudo-fermion functional renormalization group (PFFRG) calculations and classical Monte Carlo (MC) simulations. Interestingly, the DFT-based exchange model suggests that this system, and some other related Cr-based breathing pyrochlore materials, can be mapped onto an effective face-centered cubic (FCC) antiferromagnetic model which displays order-by-disorder, where an accidental degeneracy is lifted by thermal or quantum fluctuations. In this talk, we will present results using PFFRG, large-N and MC simulations that clarify when these breathing pyrochlore systems can be described as an effective FCC antiferromagnet and when they cannot.   

Beyond Single Tetrahedron Physics of Breathing Pyrochlore Compound Ba3Yb2Zn5O11

Recently a new class of quantum magnets, the so-called breathing pyrochlore systems, have attracted much attention due to their potential to host exotic emergent phenomena. Here, we present magnetometry, thermal, muon-spin relaxation, and polarized inelastic neutron scattering measurements performed on high-quality single-crystal samples of breathing pyrochlore compound Ba₃Yb₂Zn₅O₁₁. We interpret these results using a simplified toy model and provide a new insight into the low-energy physics of this system beyond the single-tetrahedron physics proposed previously [1].

 

    

Dynamical Scaling in the intermediate temperature phase of Yb2Ti2O7

The magnetic pyrochlore Yb₂Ti₂O₇ is a prototype 3D frustrated magnetic insulator with behaviors that have defied explanation for decades. In this talk I will present ultra-high-resolution neutron scattering from Yb₂Ti₂O₇ just above its ferromagnetic ordering transition T_c=270 mK. We find that spin correlations exhibit dynamical scaling, analogous to behavior found near to a quantum critical point. We show that the observed scaling collapse can be explained within a phenomenological theory of multiple phase competition. However, the scaling equations show T_rod=0, which classically occurs at the degenerate point between three phases, where a classical spin liquid resides. I discuss the possibility that quantum effects renormalize Yb₂Ti₂O₇ closer to this degenerate point. This perspective may hold the key to finally understanding this enigmatic material.   

Detection of cluster magnetic octupoles in antiferromagnetic Nd2Ir2O7 thin film via planar Hall effect

Antiferromagnetic (AFM) materials are attracting tremendous attention due to their spintronic applications and associated novel topological phenomena. However, detecting and identifying the spin configurations in AFM materials is quite challenging due to the absence of net magnetization. Herein, we report the practicality of utilizing the planar Hall effect (PHE) to detect and distinguish "cluster magnetic multipoles" in AFM Nd2Ir2O7 (NIO-227) fully strained films. By imposing compressive strain on the spin structure of NIO-227, we artificially induced cluster magnetic multipoles, namely dipoles and A2- and T1-octupoles. Importantly, under magnetic field rotation, each magnetic multipole exhibits distinctive harmonics of PHE oscillation. Moreover, the planar Hall conductivity has nonlinear magnetic field dependence, which can be attributed to the magnetic response of the cluster magnetic octupoles. Our work provides a strategy for identifying cluster magnetic multipoles in AFM systems, and it would promote octupole-based AFM spintronics.