Another Dimension: investigations of molecular magnetism using muon-spin relaxation

We review examples of muon–spin relaxation measurements on molecule-based magnetic coordination polymers, classified by their magnetic dimensionality. These include the one-dimensional s = 1/2 spin chain Cu(pyz)(NO3)2 and the two-dimensional s = 1/2 layered material [Cu(HF2)(pyz)2]BF4. We also describe some of the more exotic ground states that may become accessible in the future given the ability to tune the interaction strengths of our materials through crystal engineering

Muon sites in PbF2 and YF3: Decohering environments and the role of anion Frenkel defects

Muons implanted into ionic fluorides often lead to a so-called F– μ –F state, in which the time evolution of the muon spin contains information about the geometry and nature of the muon site. Nuclei more distant from the muon than the two nearest-neighbor fluorine ions result in decoherence of the F– μ –F system, and this can yield additional quantitative information about the state of the muon. We demonstrate how this idea can be applied to the determination of muon sites within the ionic fluorides α − PbF 2 and YF 3 , which contain fluoride ions in different crystallographic environments. Our results can be used to distinguish between different crystal phases and provide strong evidence for the existence of anion Frenkel defects in α − PbF 2

Low-Temperature Spin Diffusion in a Highly Ideal S= Heisenberg Antiferromagnetic Chain Studied by Muon Spin Relaxation

The organic radical-ion salt DEOCC-TCNQF4 contains linear chains of stacked molecules with significant Heisenberg antiferromagnet interactions along the chain and extremely weak interactions between the chains. Zero-field µSR has confirmed the absence of long-range magnetic order down to 20 mK and field-dependent µSR is found to be consistent with diffusive motion of the spin excitations. The anisotropic spin dynamics and the upper boundary for magnetic ordering temperature both indicate interchain magnetic coupling |J|<7 mK. As the intrachain coupling J is 110 K, |J/J| is significantly less than 10-4. This system therefore provides one of the most ideal examples of the one-dimensional S=1/2 Heisenberg antiferromagnet yet discovered

Persistent dynamics in the S = 1/2 quasi-one-dimensional chain compound Rb4Cu(MoO4)3 probed with muon-spin relaxation

We report the results of muon-spin relaxation measurements on the low-dimensional antiferromagnet Rb4Cu(MoO4)3. No long-range magnetic order is observed down to 50 mK implying a ratio TN/J < 0.005 (where J is the principal exchange strength along the spin chains) and an effective ratio of interchain to intrachain exchange of |J⊥/J | < 2 × 10−3, making the material an excellent realization of a one-dimensional quantum Heisenberg antiferromagnet. We probe the persistent spin excitations at low temperatures and find that ballistic spin transport dominates the excitations detected below 0.3 K

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

Magnetic transition and spin dynamics in the triangular Heisenberg antiferromagnet α-KCrO2

We present the results of muon-spin relaxation measurements on the triangular lattice Heisenberg antiferromagnet α -KCrO 2 . We observe sharp changes in behavior at an ordering temperature of T c =23 K, with an additional broad feature in the muon-spin relaxation rate evident at T=13 K, both of which correspond to features in the magnetic contribution to the heat capacity. This behavior is distinct from both the Li- and Na-containing members of the series. These data may be qualitatively described with the established theoretical predictions for the underlying spin system

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 fluctuations and spin freezing in nonsuperconducting LiFeAs derivatives

We present detailed magnetometry and muon-spin rotation data on polycrystalline samples of overdoped, nonsuperconducting LiFe1−xNixAs (x = 0.1,0.2) and Li1−yFe1+yAs (0 y 0.04) as well as superconducting LiFeAs.While LiFe1−xNixAs exhibits weak antiferromagnetic fluctuations down to 1.5 K,Li1−yFe1+yAs samples, which have a much smaller deviation from the 1 : 1 : 1 stoichiometry, show a crossover from ferromagnetic to antiferromagnetic fluctuations on cooling and a freezing of dynamically fluctuating moments at low temperatures. We do not find any signatures of time-reversal symmetry breaking in stoichiometric LiFeAs that would support recent predictions of triplet pairing

Spin diffusion in the low-dimensional molecular quantum Heisenberg antiferromagnet Cu(pyz)(NO3)2 detected with implanted muons

We present the results of muon-spin relaxation measurements of spin excitations in the one-dimensional quantum Heisenberg antiferromagnet Cu(pyz)(NO3)2. Using density-functional theory we propose muon sites and assess the degree of perturbation the muon probe causes on the system. We identify a site involving the muon forming a hydroxyl-type bond with an oxygen on the nitrate group that is sensitive to the characteristic spin dynamics of the system. Our measurements of the spin dynamics show that in the temperature range TNJ and that in the related two-dimensional system Cu(pyz)2(ClO4)2

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