Exchange constants in molecule-based magnets derived from density functional methods

Cu(pyz)(NO3)2 is a quasi-one-dimensional molecular antiferromagnet that exhibits three-dimensional long-range magnetic order below T N = 110 mK due to the presence of weak interchain exchange couplings. Here, we compare calculations of the three largest exchange coupling constants in this system using two techniques based on plane-wave basis-set density functional theory: (i) a dimer fragment approach and (ii) an approach using periodic boundary conditions. The calculated values of the large intrachain coupling constant are found to be consistent with experiment, showing the expected level of variation between different techniques and implementations. However, the interchain coupling constants are found to be smaller than the current limits on the resolution of the calculations. This is due to the computational limitations on convergence of absolute energy differences with respect to basis set, which are larger than the interchain couplings themselves. Our results imply that errors resulting from such limitations are inherent in the evaluation of small exchange constants in systems of this sort, and that many previously reported results should therefore be treated with caution

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

Robustness of superconductivity to structural disorder in Sr0.3(NH2)y(NH3)1−yFe2Se2

The superconducting properties of a recently discovered high-Tc superconductor, Sr/ammonia-intercalated FeSe, have been measured using pulsed magnetic fields down to 4.2 K and muon spin spectroscopy down to 1.5 K. This compound exhibits intrinsic disorder resulting from random stacking of the FeSe layers along the c axis that is not present in other intercalates of the same family. This arises because the coordination requirements of the intercalated Sr and ammonia moieties imply that the interlayer stacking (along c) involves a translation of either a/2 or b/2 that locally breaks tetragonal symmetry. The result of this stacking arrangement is that the Fe ions in this compound describe a body-centered-tetragonal lattice in contrast to the primitive arrangement of Fe ions described in all other Fe-based superconductors. In pulsed magnetic fields, the upper critical field Hc2 was found to increase on cooling with an upward curvature that is commonly seen in type-II superconductors of a multiband nature. Fitting the data to a two-band model and extrapolation to absolute zero gave a maximum upper critical field μ0Hc2(0) of 33(2)T. A clear superconducting transition with a diamagnetic shift was also observed in transverse-field muon measurements at Tc≈36.3(2)K. These results demonstrate that robust superconductivity in these intercalated FeSe systems does not rely on perfect structural coherence along the c axis

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

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

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

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

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

Local magnetism and spin dynamics of the frustrated honeycomb rhodate Li2RhO3

We reportmagnetization, heat capacity, 7Li nuclear magnetic resonance (NMR), and muon-spin rotation (μSR) measurements on the honeycomb 4d5 spin liquid candidate Li2RhO3. The magnetization in small magnetic fields provides evidence of the partial spin-freezing of a small fraction of Rh4+ moments at 6 K, whereas the Curie-Weiss behavior above 100 K suggests a pseudo-spin-1/2 paramagnet with a moment of about 2.2μB. The magnetic specific heat (Cm) exhibits no field dependence and demonstrates the absence of long-range magnetic order down to 0.35 K. Cm/T passes through a broad maximum at about 10 K and Cm ∝ T 2 at low temperatures. Measurements of the spin-lattice relaxation rate (1/T1) reveal a gapless slowing-down of spin fluctuations upon cooling with 1/T1 ∼ T 2.2. The results from NMR and μSR are consistent with a scenario in which a minority of Rh4+ moments are in a short-range correlated frozen state and coexist with a majority of moments in a liquid-like state that continue to fluctuate at low temperatures