μSR investigation of magnetism in κ−(ET)2X : Antiferromagnetism

We study magnetism in the κ-(ET)2X family of charge-transfer salts using implanted muon spectroscopy in conjunction with detailed ab initio electronic structure calculations using density functional theory (DFT). ET stands for the electron donor molecule bis(ethylendithio)tetrathiafulvalene and X is an anion. The DFT calculations are used to establish molecular spin distributions, muon stopping sites, and dipolar field parameters, that allow us to make a quantitative interpretation of the experimental results. Materials in the κ-(ET)2X family with X = Ag2(CN)3 and X = Cu2 (CN)3 have attracted particular interest, as they have the attributes of quantum spin liquids, showing no magnetic ordering down to 30 mK in zero field μSR and in NMR, despite having exchange couplings of order 200–250 K. In contrast, the material with X = Cu[N(CN)2]Cl has an antiferromagnetic (AF) ordering transition with TN in the region of 23–30 K. In order to better understand the muon spectroscopy signature of magnetism in this whole family of compounds at both low and high magnetic fields, we look in detail at the case X = Cu[N(CN)2]Cl. As the first step in our study, the spin density distribution for the ET dimer is calculated using DFT and used to simulate the 3.7 T 1 H-NMR spectrum of this salt, with the spectrum showing good agreement with that measured previously [K. Miyagawa, A. Kawamoto, Y. Nakazawa, and K. Kanoda, Phys. Rev. Lett. 75, 1174 (1995)]. Best match to the data is found for antiferromagnetic interlayer ordering and an ordered moment per dimer of 0.25 μB. DFT is also used to explore muon stopping sites for this salt, finding one set of sites resulting from muonium addition to C=C double bonds in the ET layer, with muons stopping in the anion layer forming another group of sites. The dipolar fields associated with each of the stopping sites is computed and these are compared with the precession frequencies observed in the ZF-μSR spectrum [M. Ito, T. Uehara, H. Taniguchi, K. Satoh, Y. Ishii, and I. Watanabe, J. Phys. Soc. Jpn. 84, 053703 (2015)]. Best match to the ZF-μSR spectrum is obtained with the mode of interlayer ordering having FM character and an ordered moment per dimer of 0.31 μB for muon sites in the anion layer and 0.36 μB for muonium sites in the ET layer. New measurements of TF-μSR spectra for fields up to 8 T are reported and analyzed to obtain the best estimate of the magnetic order parameter under different measurement conditions, allowing us to observe the variation of TN with applied field and the field-induced transverse canting of the moments

MuFinder: A program to determine and analyse muon stopping sites

Significant progress has recently been made in calculating muon stopping sites using density functional theory. The technique aims to address two of the most common criticisms of the muon-spin spectroscopy (μ+SR) technique, namely, where in the sample does the muon stop, and what is its effect on its local environment. We have designed and developed a program called MuFinder that enables users to carry out these calculations through a simple graphical user interface (GUI). The procedure for calculating muon sites by generating initial muon positions, relaxing the structures, and then clustering and analysing the resulting candidate sites, can be done entirely within the GUI. The local magnetic field at the muon site can also be computed, allowing the connection between the muon sites obtained and experiment to be made. MuFinder will make these computations significantly more accessible to non-experts and help to establish muon site calculations as a routine part of μ+SR experiments

Magnetic order and ballistic spin transport in a sine-Gordon spin chain

We report the results of muon-spin spectroscopy (μ+SR) measurements on the staggered molecular spin chain [pym-Cu(NO3 )2(H2O)2] (pym = pyrimidine), a material previously described using sine-Gordon field theory. Zero-field μ+SR reveals a long range magnetically ordered ground state below a transition temperature TN = 0.23(1) K. Using longitudinal-field (LF) μ+SR we investigate the dynamic response in applied magnetic fields 0 < B < 500 mT and find evidence for ballistic spin transport. Our LF μ+SR measurements on the chiral spin chain [Cu(pym)(H2O)4]SiF6 · H2O instead demonstrate one-dimensional spin diffusion, and the distinct spin transport in these two systems suggests that additional anisotropic interactions play an important role in determining the nature of spin transport in S = 1/2 antiferromagnetic chains

Position-dependent stability and lifetime of the skyrmion state in nickel-substituted Cu2OSeO3

We report spatially resolved small-angle neutron-scattering measurements of the conical and skyrmion states of a bulk single crystal of nickel-substituted Cu2OSeO3, with a nominal concentration of Ni of 14%. We observe a significant spatial dependence of the structure of these magnetic states, characterized by increased disorder and misalignment with respect to the applied field as we approach the edge of the sample. Remarkably, the edge skyrmion state is also characterized by an extended stability towards lower temperatures. Surprisingly, in the same region of the sample, the metastable skyrmion state did not show simple decay. Instead, only a fraction of the scattered intensity appeared to decay, and the intensity therefore did not approach zero during our measurements. We suggest that the increased local disorder and the coexistence of conical and skyrmion states, induced by demagnetization effects at the edge of the sample, are responsible for the increased stability of this skyrmion state. We also infer that the unclear metastable behavior of the skyrmion lattice at the edge of the sample is due to the local geometry of the sample, which induces coexistence of different skyrmion states whose lifetimes are superimposed and difficult to separate in the data

Megahertz dynamics in skyrmion systems probed with muon-spin relaxation

We present longitudinal-field muon-spin relaxation (LF μ SR ) measurements on two systems that stabilize a skyrmion lattice (SkL): Cu 2 OSeO 3 , and Co x Zn y Mn 20 − x − y for ( x , y ) = ( 10 , 10 ) , (8, 9), and (8, 8). We find that the SkL phase of Cu 2 OSeO 3 exhibits emergent dynamic behavior at megahertz frequencies, likely due to collective excitations, allowing the SkL to be identified from the μ SR response. From measurements following different cooling protocols and calculations of the muon stopping site, we suggest that the metastable SkL is not the majority phase throughout the bulk of this material at the fields and temperatures where it is often observed. The dynamics of bulk Co 8 Zn 9 Mn 3 are well described by ≃ 2 GHz excitations that reduce in frequency near the critical temperature, while in Co 8 Zn 8 Mn 4 we observe similar behavior over a wide range of temperatures, implying that dynamics of this kind persist beyond the SkL phase

Magnetic order and disorder in a quasi-two-dimensional quantum Heisenberg antiferromagnet with randomized exchange

We present an investigation of the effect of randomizing exchange coupling strengths in the S = 1/2 square lattice quasi-two-dimensional quantum Heisenberg antiferromagnet (QHAF) (QuinH)2Cu(ClxBr1−x )4 · 2H2O (QuinH = Quinolinium, C9H8N+), with 0 x 1. Pulsed-field magnetization measurements allow us to estimate an effective in-plane exchange strength J in a regime where exchange fosters short-range order, while the temperature TN at which long-range order (LRO) occurs is found using muon-spin relaxation, allowing us to construct a phase diagram for the series. We evaluate the effectiveness of disorder in suppressing TN and the ordered moment size, and we find an extended disordered phase in the region 0.4 x 0.8 where no magnetic order occurs. The observed critical substitution levels are accounted for by an energetics-based competition between different local magnetic orders. Furthermore, we demonstrate experimentally that the ground-state disorder is driven by quantum effects of the exchange randomness, which is a feature that has been predicted theoretically and has implications for other disordered quasi-two-dimensional QHAFs

Anomalous magnetic exchange in a dimerized quantum magnet composed of unlike spin species

We present here a study of the magnetic properties of the antiferromagnetic dimer material CuVOF 4 ( H 2 O ) 6 ⋅ H 2 O , in which the dimer unit is composed of two different S = 1 / 2 species, Cu(II) and V(IV). An applied magnetic field of μ 0 H c 1 = 13.1 ( 1 ) T is found to close the singlet-triplet energy gap, the magnitude of which is governed by the antiferromagnetic intradimer J 0 ≈ 21 K, and interdimer J ′ ≈ 1 K, exchange energies, determined from magnetometry and electron-spin resonance measurements. The results of density functional theory (DFT) calculations are consistent with the experimental results. The DFT calculations predict antiferromagnetic coupling along all nearest-neighbor bonds, with the magnetic ground state comprising spins of different species aligning antiparallel to one another, while spins of the same species are aligned parallel. The magnetism in this system cannot be accurately described by the overlap between localized V orbitals and magnetic Cu orbitals lying in the Jahn-Teller (JT) plane, with a tight-binding model based on such a set of orbitals incorrectly predicting that interdimer exchange should be dominant. DFT calculations indicate significant spin density on the bridging oxide, suggesting instead an unusual mechanism in which intradimer exchange is mediated through the O atom on the Cu(II) JT axis

Intrinsic nature of spontaneous magnetic fields in superconductors with time-reversal symmetry breaking

We present a systematic investigation of muon-stopping states in superconductors that reportedly exhibit spontaneous magnetic fields below their transition temperatures due to time-reversal symmetry breaking. These materials include elemental rhenium, several intermetallic systems and Sr2RuO4. We demonstrate that the presence of the muon leads to only a limited and relatively localized perturbation to the local crystal structure, while any small changes to the electronic structure occur several electron volts below the Fermi energy leading to only minimal changes in the charge density on ions close to the muon. Our results imply that the muon-induced perturbation alone is unlikely to lead to the observed spontaneous fields in these materials, whose origin is more likely intrinsic to the time-reversal symmetry broken superconducting state

Muon-spin relaxation investigation of magnetic bistability in a crystalline organic radical compound

We present the results of a muon-spin relaxation (+SR) investigation of the crystalline organic radicalcompound 4-(2-benzimidazolyl)-1,2,3,5-dithiadiazolyl (HbimDTDA), in which we demonstrate the hystereticmagnetic switching of the system that takes place at = (274 ± 11) K caused by a structural phase transition.Muon-site analysis using electronic structure calculations suggests a range of candidate muon stopping sites.The sites are numerous and similar in energy but, significantly, differ between the two structural phases of thematerial. Despite the difference in the sites, the muon remains a faithful probe of the transition, revealing adynamically-fluctuating magnetically disordered state in the low-temperature structural phase. In contrast, in the high temperature phase the relaxation is caused by static nuclear moments, with rapid electronic dynamics being motionally narrowed from the muon spectr