Dichotomous dynamics of magnetic monopole fluids.

A recent advance in the study of emergent magnetic monopoles was the discovery that monopole motion is restricted to dynamical fractal trajectories [J. N. Hallén et al., Science 378, 1218 (2022)], thus explaining the characteristics of magnetic monopole noise spectra [R. Dusad et al., Nature 571, 234 (2019); A. M. Samarakoon et al., Proc. Natl. Acad. Sci. U.S.A. 119, e2117453119 (2022)]. Here, we apply this novel theory to explore the dynamics of field-driven monopole currents, finding them composed of two quite distinct transport processes: initially swift fractal rearrangements of local monopole configurations followed by conventional monopole diffusion. This theory also predicts a characteristic frequency dependence of the dissipative loss angle for AC field-driven currents. To explore these novel perspectives on monopole transport, we introduce simultaneous monopole current control and measurement techniques using SQUID-based monopole current sensors. For the canonical material Dy2Ti2O7, we measure [Formula: see text], the time dependence of magnetic flux threading the sample when a net monopole current [Formula: see text] is generated by applying an external magnetic field [Formula: see text] These experiments find a sharp dichotomy of monopole currents, separated by their distinct relaxation time constants before and after t ~[Formula: see text] from monopole current initiation. Application of sinusoidal magnetic fields [Formula: see text] generates oscillating monopole currents whose loss angle [Formula: see text] exhibits a characteristic transition at frequency [Formula: see text] over the same temperature range. Finally, the magnetic noise power is also dichotomic, diminishing sharply after t ~[Formula: see text]. This complex phenomenology represents an unprecedented form of dynamical heterogeneity generated by the interplay of fractionalization and local spin configurational symmetry.

Magnetic monopole noise.

Magnetic monopoles1-3 are hypothetical elementary particles with quantized magnetic charge. In principle, a magnetic monopole can be detected by the quantized jump in magnetic flux that it generates upon passage through a superconducting quantum interference device (SQUID)4. Following the theoretical prediction that emergent magnetic monopoles should exist in several lanthanide pyrochlore magnetic insulators5,6, including Dy2Ti2O7, the SQUID technique has been proposed for their direct detection6. However, this approach has been hindered by the high number density and the generation-recombination fluctuations expected of such thermally generated monopoles. Recently, theoretical advances have enabled the prediction of the spectral density of magnetic-flux noise from monopole generation-recombination fluctuations in these materials7,8. Here we report the development of a SQUID-based flux noise spectrometer and measurements of the frequency and temperature dependence of magnetic-flux noise generated by Dy2Ti2O7 crystals. We detect almost all of the features of magnetic-flux noise predicted for magnetic monopole plasmas7,8, including the existence of intense magnetization noise and its characteristic frequency and temperature dependence. Moreover, comparisons of simulated and measured correlation functions of the magnetic-flux noise indicate that the motions of magnetic charges are strongly correlated. Intriguingly, because the generation-recombination time constant for Dy2Ti2O7 is in the millisecond range, magnetic monopole flux noise amplified by SQUID is audible to humans.

Magnetostriction-Driven Muon Localization in an Antiferromagnetic Oxide.

Magnetostriction results from the coupling between magnetic and elastic degrees of freedom. Though it is associated with a relatively small energy, we show that it plays an important role in determining the site of an implanted muon, so that the energetically favorable site can switch on crossing a magnetic phase transition. This surprising effect is demonstrated in the cubic rocksalt antiferromagnet MnO which undergoes a magnetostriction-driven rhombohedral distortion at the Néel temperature T_{N}=118 K. Above T_{N}, the muon becomes delocalized around a network of equivalent sites, but below T_{N} the distortion lifts the degeneracy between these equivalent sites. Our first-principles simulations based on Hubbard-corrected density-functional theory and molecular dynamics are consistent with the experimental data and help to resolve a long-standing puzzle regarding muon data on MnO, as well as having wider applicability to other magnetic oxides.

Entanglement between Muon and I>1/2 Nuclear Spins as a Probe of Charge Environment.

We report on the first example of quantum coherence between the spins of muons and quadrupolar nuclei. We reveal that these entangled states are highly sensitive to a local charge environment and thus, can be deployed as a functional quantum sensor of that environment. The quantum coherence effect was observed in vanadium intermetallic compounds which adopt the A15 crystal structure, and whose members include all technologically pertinent superconductors. Furthermore, the extreme sensitivity of the entangled states to the local structural and electronic environments emerges through the quadrupolar interaction with the electric field gradient due to the charge distribution at the nuclear (I>1/2) sites. This case study demonstrates that positive muons can be used as a quantum sensing tool to also probe structural and charge-related phenomena in materials, even in the absence of magnetic degrees of freedom.

Exsolution of SrO during the Topochemical Conversion of LaSr3CoRuO8 to the Oxyhydride LaSr3CoRuO4H4.

 Reaction of the n = 1 Ruddlesden-Popper oxide LaSr3CoRuO8 with CaH2 yields the oxyhydride phase LaSr3CoRuO4H4 via a topochemical anion exchange. Close inspection of the X-ray and neutron powder diffraction data in combination with HAADF-STEM images reveals that the nanoparticles of SrO are exsolved from the system during the reaction, with the change in cation stoichiometry accommodated by the inclusion of n > 1 (Co/Ru)nOn+1H2n "perovskite" layers into the Ruddlesden-Popper stacking sequence. This novel pseudotopochemical process offers a new route for the formation of n > 1 Ruddlesden-Popper structured materials. Magnetization data are consistent with a LaSr3Co+Ru2+O4H4 (Co+, d8, S = 1; Ru2+, d6, S = 0) oxidation/spin state combination. Neutron diffraction and µ+SR data show no evidence for long-range magnetic order down to 2 K, suggesting the diamagnetic Ru2+ centers impede the Co-Co magnetic-exchange interactions.

Magnetic order and enhanced exchange in the quasi-one-dimensional molecule-based antiferromagnet Cu(NO3)2(pyz)3.

The quasi-one-dimensional molecule-based Heisenberg antiferromagnet Cu(NO3)2(pyz)3 has an intrachain coupling J = 13.7(1) K () and exhibits a state of long-range magnetic order below TN = 0.105(1) K. The ratio of interchain to intrachain coupling is estimated to be |J'/J| = 3.3 × 10-3, demonstrating a high degree of isolation for the Cu chains.

Extreme Sensitivity of a Topochemical Reaction to Cation Substitution: SrVO2H versus SrV1- xTi xO1.5H1.5.

The anion-ordered oxide-hydride SrVO2H is an antiferromagnetic insulator due to strong correlations between vanadium d electrons. In an attempt to hole-dope SrVO2H into a metallic state, a strategy of first preparing SrV1- xTi xO3 phases and then converting them to the corresponding SrV1- xTi xO2H phases via reaction with CaH2 was followed. This revealed that the solid solution between SrVO3 and SrTiO3 is only stable at high temperature. In addition, reactions between SrV0.95Ti0.05O3 and CaH2 were observed to yield SrV0.95Ti0.05O1.5H1.5 not SrV0.95Ti0.05O2H. This dramatic change in reactivity for a very modest change in initial chemical composition is attributed to an electronic destabilization of SrVO2H on titanium substitution. Density functional theory calculations indicate that the presence of an anion-ordered, tetragonal SrMO2H phase is uniquely associated with a d2 electron count and that titanium substitution leads to an electronic destabilization of SrV1- xTi xO2H phases, which, ultimately, drives further reaction of SrV1- xTi xO2H to SrV1- xTi xO1.5H1.5. The observed sensitivity of the reaction products to the chemical composition of initial phases highlights some of the difficulties associated with electronically doping metastable materials prepared by topochemical reactions.

Doped Sr2FeIrO6-Phase Separation and a Jeff ≠ 0 State for Ir5.

High-resolution synchrotron X-ray and neutron powder diffraction data demonstrate that, in contrast to recent reports, Sr2FeIrO6 adopts an I1̅ symmetry double perovskite structure with an a-b-c- tilting distortion. This distorted structure does not tolerate cation substitution, with low levels of A-site (Ca, Ba, La) or Fe-site (Ga) substitution leading to separation into two phases: a stoichiometric I1̅ phase and a cation-substituted, P21/ n symmetry, a-a-c+ distorted double perovskite phase. Magnetization, neutron diffraction, and 57Fe Mössbauer data show that, in common with Sr2FeIrO6, the cation substituted Sr2- xA xFe1- yGa yIrO6 phases undergo transitions to type-II antiferromagnetically ordered states at TN ∼ 120 K. However, in contrast to stoichiometric Sr2FeIrO6, cation substituted samples exhibit a further magnetic transition at TA ∼ 220 K, which corresponds to the ordering of Jeff ≠ 0 Ir5+ centers in the cation-substituted, P21/ n symmetry, double perovskite phases.

LaSr3 NiRuO4 H4 : A 4d Transition-Metal Oxide-Hydride Containing Metal Hydride Sheets.

The synthesis of the first 4d transition metal oxide-hydride, LaSr3 NiRuO4 H4 , is prepared via topochemical anion exchange. Neutron diffraction data show that the hydride ions occupy the equatorial anion sites in the host lattice and as a result the Ru and Ni cations are located in a plane containing only hydride ligands, a unique structural feature with obvious parallels to the CuO2 sheets present in the superconducting cuprates. DFT calculations confirm the presence of S=1/2 Ni+ and S=0, Ru2+ centers, but neutron diffraction and µSR data show no evidence for long-range magnetic order between the Ni centers down to 1.8 K. The observed weak inter-cation magnetic coupling can be attributed to poor overlap between Ni 3dz2 and H 1s in the super-exchange pathways.

Strong Coupling of Microwave Photons to Antiferromagnetic Fluctuations in an Organic Magnet.

Coupling between a crystal of di(phenyl)-(2,4,6-trinitrophenyl)iminoazanium radicals and a superconducting microwave resonator is investigated in a circuit quantum electrodynamics (circuit QED) architecture. The crystal exhibits paramagnetic behavior above 4 K, with antiferromagnetic correlations appearing below this temperature, and we demonstrate strong coupling at base temperature. The magnetic resonance acquires a field angle dependence as the crystal is cooled down, indicating anisotropy of the exchange interactions. These results show that multispin modes in organic crystals are suitable for circuit QED, offering a platform for their coherent manipulation. They also utilize the circuit QED architecture as a way to probe spin correlations at low temperature.

Quantum Griffiths Phase Inside the Ferromagnetic Phase of Ni_{1-x}V_{x}.

We study by means of bulk and local probes the d-metal alloy Ni_{1-x}V_{x} close to the quantum critical concentration, x_{c}≈11.6%, where the ferromagnetic transition temperature vanishes. The magnetization-field curve in the ferromagnetic phase takes an anomalous power-law form with a nonuniversal exponent that is strongly x dependent and mirrors the behavior in the paramagnetic phase. Muon spin rotation experiments demonstrate inhomogeneous magnetic order and indicate the presence of dynamic fluctuating magnetic clusters. These results provide strong evidence for a quantum Griffiths phase on the ferromagnetic side of the quantum phase transition.

Experimental and Theoretical Electron Density Analysis of Copper Pyrazine Nitrate Quasi-Low-Dimensional Quantum Magnets.

The accurate electron density distribution and magnetic properties of two metal-organic polymeric magnets, the quasi-one-dimensional (1D) Cu(pyz)(NO3)2 and the quasi-two-dimensional (2D) [Cu(pyz)2(NO3)]NO3·H2O, have been investigated by high-resolution single-crystal X-ray diffraction and density functional theory calculations on the whole periodic systems and on selected fragments. Topological analyses, based on quantum theory of atoms in molecules, enabled the characterization of possible magnetic exchange pathways and the establishment of relationships between the electron (charge and spin) densities and the exchange-coupling constants. In both compounds, the experimentally observed antiferromagnetic coupling can be quantitatively explained by the Cu-Cu superexchange pathway mediated by the pyrazine bridging ligands, via a σ-type interaction. From topological analyses of experimental charge-density data, we show for the first time that the pyrazine tilt angle does not play a role in determining the strength of the magnetic interaction. Taken in combination with molecular orbital analysis and spin density calculations, we find a synergistic relationship between spin delocalization and spin polarization mechanisms and that both determine the bulk magnetic behavior of these Cu(II)-pyz coordination polymers.

Studies of a Large Odd-Numbered Odd-Electron Metal Ring: Inelastic Neutron Scattering and Muon Spin Relaxation Spectroscopy of Cr8 Mn.

The spin dynamics of Cr8 Mn, a nine-membered antiferromagnetic (AF) molecular nanomagnet, are investigated. Cr8 Mn is a rare example of a large odd-membered AF ring, and has an odd-number of 3d-electrons present. Odd-membered AF rings are unusual and of interest due to the presence of competing exchange interactions that result in frustrated-spin ground states. The chemical synthesis and structures of two Cr8 Mn variants that differ only in their crystal packing are reported. Evidence of spin frustration is investigated by inelastic neutron scattering (INS) and muon spin relaxation spectroscopy (µSR). From INS studies we accurately determine an appropriate microscopic spin Hamiltonian and we show that µSR is sensitive to the ground-spin-state crossing from S=1/2 to S=3/2 in Cr8 Mn. The estimated width of the muon asymmetry resonance is consistent with the presence of an avoided crossing. The investigation of the internal spin structure of the ground state, through the analysis of spin-pair correlations and scalar-spin chirality, shows a non-collinear spin structure that fluctuates between non-planar states of opposite chiralities.

La2SrCr2O7F2: A Ruddlesden-Popper Oxyfluoride Containing Octahedrally Coordinated Cr(4+) Centers.

The low-temperature fluorination of the n = 2 Ruddlesden-Popper phase La2SrCr2O7 yields La2SrCr2O7F2 via a topochemical fluorine insertion reaction. The structure-conserving nature of the fluorination reaction means that the chromium centers of the initial oxide phase retain an octahedral coordination environment in the fluorinated product, resulting in a material containing an extended array of apex-linked Cr(4+)O6 units. Typically materials containing networks of octahedrally coordinated Cr(4+) centers can only be prepared at high pressure; thus, the preparation of La2SrCr2O7F2 demonstrates that low-temperature topochemical reactions offer an alternative synthesis route to materials of this type. Neutron diffraction, magnetization, and µ(+)SR data indicate that La2SrCr2O7F2 undergoes a transition to an antiferromagnetic state below TN ≈ 140 K. The structure-property relations of this phase and other Cr(4+) oxide phases are discussed.

La2SrCr2O7: Controlling the Tilting Distortions of n = 2 Ruddlesden-Popper Phases through A-Site Cation Order.

Structural characterization by neutron diffraction, supported by magnetic, SHG, and µ(+)SR data, reveals that the n = 2 Ruddlesden-Popper phase La2SrCr2O7 adopts a highly unusual structural configuration in which the cooperative rotations of the CrO6 octahedra are out of phase in all three Cartesian directions (ΦΦΦz/ΦΦΦz; a(-)a(-)c(-)/a(-)a(-)c(-)) as described in space group A2/a. First-principles DFT calculations indicate that this unusual structural arrangement can be attributed to coupling between the La/Sr A-site distribution and the rotations of the CrO6 units, which combine to relieve the local deformations of the chromium-oxygen octahedra. This coupling suggests new chemical "handles" by which the rotational distortions or A-site cation order of Ruddlesden-Popper phases can be directed to optimize physical behavior. Low-temperature neutron diffraction data and µ(+)SR data indicate La2SrCr2O7 adopts a G-type antiferromagnetically ordered state below TN ∼ 260 K.

The Parent Li(OH)FeSe Phase of Lithium Iron Hydroxide Selenide Superconductors.

Lithiation of hydrothermally synthesized Li1-xFex(OH)Fe1-ySe turns on high-temperature superconductivity when iron ions are displaced from the hydroxide layers by reductive lithiation to fill the vacancies in the iron selenide layers. Further lithiation results in reductive iron extrusion from the hydroxide layers, which turns off superconductivity again as the stoichiometric composition Li(OH)FeSe is approached. The results demonstrate the twin requirements of stoichiometric FeSe layers and reduction of Fe below the +2 oxidation state as found in several iron selenide superconductors.

Antiferromagnetism in a Family of S = 1 Square Lattice Coordination Polymers NiX2(pyz)2 (X = Cl, Br, I, NCS; pyz = Pyrazine).

The crystal structures of NiX2(pyz)2 (X = Cl (1), Br (2), I (3), and NCS (4)) were determined by synchrotron X-ray powder diffraction. All four compounds consist of two-dimensional (2D) square arrays self-assembled from octahedral NiN4X2 units that are bridged by pyz ligands. The 2D layered motifs displayed by 1-4 are relevant to bifluoride-bridged [Ni(HF2)(pyz)2]EF6 (E = P, Sb), which also possess the same 2D layers. In contrast, terminal X ligands occupy axial positions in 1-4 and cause a staggered packing of adjacent layers. Long-range antiferromagnetic (AFM) order occurs below 1.5 (Cl), 1.9 (Br and NCS), and 2.5 K (I) as determined by heat capacity and muon-spin relaxation. The single-ion anisotropy and g factor of 2, 3, and 4 were measured by electron-spin resonance with no evidence for zero-field splitting (ZFS) being observed. The magnetism of 1-4 spans the spectrum from quasi-two-dimensional (2D) to three-dimensional (3D) antiferromagnetism. Nearly identical results and thermodynamic features were obtained for 2 and 4 as shown by pulsed-field magnetization, magnetic susceptibility, as well as their Néel temperatures. Magnetization curves for 2 and 4 calculated by quantum Monte Carlo simulation also show excellent agreement with the pulsed-field data. Compound 3 is characterized as a 3D AFM with the interlayer interaction (J⊥) being slightly stronger than the intralayer interaction along Ni-pyz-Ni segments (J(pyz)) within the two-dimensional [Ni(pyz)2](2+) square planes. Regardless of X, J(pyz) is similar for the four compounds and is roughly 1 K.

Soft chemical control of superconductivity in lithium iron selenide hydroxides Li(1-x)Fe(x)(OH)Fe(1-y)Se.

Hydrothermal synthesis is described of layered lithium iron selenide hydroxides Li(1-x)Fe(x)(OH)Fe(1-y)Se (x ∼ 0.2; 0.02 < y < 0.15) with a wide range of iron site vacancy concentrations in the iron selenide layers. This iron vacancy concentration is revealed as the only significant compositional variable and as the key parameter controlling the crystal structure and the electronic properties. Single crystal X-ray diffraction, neutron powder diffraction, and X-ray absorption spectroscopy measurements are used to demonstrate that superconductivity at temperatures as high as 40 K is observed in the hydrothermally synthesized samples when the iron vacancy concentration is low (y < 0.05) and when the iron oxidation state is reduced slightly below +2, while samples with a higher vacancy concentration and a correspondingly higher iron oxidation state are not superconducting. The importance of combining a low iron oxidation state with a low vacancy concentration in the iron selenide layers is emphasized by the demonstration that reductive postsynthetic lithiation of the samples turns on superconductivity with critical temperatures exceeding 40 K by displacing iron atoms from the Li(1-x)Fe(x)(OH) reservoir layer to fill vacancies in the selenide layer.

Enhancement of the superconducting transition temperature of FeSe by intercalation of a molecular spacer layer.

The discovery of high-temperature superconductivity in a layered iron arsenide has led to an intensive search to optimize the superconducting properties of iron-based superconductors by changing the chemical composition of the spacer layer between adjacent anionic iron arsenide layers. Superconductivity has been found in iron arsenides with cationic spacer layers consisting of metal ions (for example, Li(+), Na(+), K(+), Ba(2+)) or PbO- or perovskite-type oxide layers, and also in Fe(1.01)Se (ref. 8) with neutral layers similar in structure to those found in the iron arsenides and no spacer layer. Here we demonstrate the synthesis of Li(x)(NH(2))(y)(NH(3))(1-y)Fe(2)Se(2) (x~0.6; y~0.2), with lithium ions, lithium amide and ammonia acting as the spacer layer between FeSe layers, which exhibits superconductivity at 43(1) K, higher than in any FeSe-derived compound reported so far. We have determined the crystal structure using neutron powder diffraction and used magnetometry and muon-spin rotation data to determine the superconducting properties. This new synthetic route opens up the possibility of further exploitation of related molecular intercalations in this and other systems to greatly optimize the superconducting properties in this family.

Lattice-site-specific spin dynamics in double perovskite Sr2CoOsO6.

Magnetic properties and spin dynamics have been studied for the structurally ordered double perovskite Sr2CoOsO6. Neutron diffraction, muon-spin relaxation, and ac-susceptibility measurements reveal two antiferromagnetic (AFM) phases on cooling from room temperature down to 2 K. In the first AFM phase, with transition temperature TN1=108 K, cobalt (3d7, S=3/2) and osmium (5d2, S=1) moments fluctuate dynamically, while their average effective moments undergo long-range order. In the second AFM phase below TN2=67 K, cobalt moments first become frozen and induce a noncollinear spin-canted AFM state, while dynamically fluctuating osmium moments are later frozen into a randomly canted state at T≈5 K. Ab initio calculations indicate that the effective exchange coupling between cobalt and osmium sites is rather weak, so that cobalt and osmium sublattices exhibit different ground states and spin dynamics, making Sr2CoOsO6 distinct from previously reported double-perovskite compounds.