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We present zero-field {mu}SR measurements for LiY$_{1-x}$Ho$_{x}$F$_{4}$ samples with x = 0.0017, 0.0085, 0.0406, and 0.0855. We characterize the dynamics associated with the formation of the (F-{mu}-F)$^{-1}$ complex by comparing our data to Monte Carlo simulations to determine the concentration range over which the spin dynamics are determined primarily by the Ho$^{3+}$-{mu} interaction rather than the F-{mu} interaction. Simulations show that F-{mu}-F oscillations should evolve into a Lorentzian Kubo-Toyabe decay for an increasing static magnetic field distribution {Gamma} (i.e., increasing x), but the data do not show this behavior, consistent with the recently reported existence of strong magnetic fluctuations in this system at low temperatures. Anisotropy in the field distribution is shown to cause small errors of order 10% from behavior predicted for an isotropic distribution. Finally, numerical calculations show that values of {Gamma} calculated in the single ion limit greatly exceed the values extracted from curve fits, suggesting that strong correlations play an important role in this system.
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We use complementary optical spectroscopy methods to directly measure the lowest crystal-field energies of the rare-earth quantum magnet LiY$_{1-x}$Ho$_{x}$F$_{4}$, including their hyperfine splittings, with more than 10 times higher resolution than previous work. We are able to observe energy level splittings due to the $^6mathrm{Li}$ and $^7mathrm{Li}$ isotopes, as well as non-equidistantly spaced hyperfine transitions originating from dipolar and quadrupolar hyperfine interactions. We provide refined crystal field parameters and extract the dipolar and quadrupolar hyperfine constants ${A_J=0.02703pm0.00003}$ $textrm{cm}^{-1}$ and ${B= 0.04 pm0.01}$ $textrm{cm}^{-1}$, respectively. Thereupon we determine all crystal-field energy levels and magnetic moments of the $^5I_8$ ground state manifold, including the (non-linear) hyperfine corrections. The latter match the measurement-based estimates. The scale of the non-linear hyperfine corrections sets an upper bound for the inhomogeneous line widths that would still allow for unique addressing of a selected hyperfine transition. e.g. for quantum information applications. Additionally, we establish the far-infrared, low-temperature refractive index of LiY$_{1-x}$Ho$_{x}$F$_{4}$.
We present measurements of magnetic field and frequency dependences of the low temperature (T = 1.8 K) AC-susceptibility, and temperature and field dependences of the longitudinal field positive muon spin relaxation ({mu}SR) for LiY$_{1-x}$Ho$_x$F$_4$ with x = 0.0017, 0.0085, 0.0408, and 0.0855. The fits of numerical simulations to the susceptibility data for the x = 0.0017, 0.0085 and 0.0408 show that Ho-Ho cross-relaxation processes become more important at higher concentrations, signaling the crossover from single-ion to correlated behavior. We simulate the muon spin depolarization using the parameters extracted from the susceptibility, and the simulations agree well with our data for samples with x = 0.0017 and 0.0085. The {mu}SR data for samples with x = 0.0408 and 0.0855 at low temperatures (T < 10 K) cannot be described within a single-ion picture of magnetic field fluctuations and give evidence for additional mechanisms of depolarization due to Ho$^{3+}$ correlations. We also observe an unusual peak in the magnetic field dependence of the muon relaxation rate in the temperature interval 10 - 20 K that we ascribe to a modification of the Ho$^{3+}$ fluctuation rate due to a field induced shift of the energy gap between the ground and the first excited doublet crystal field states relative to a peak in the phonon density of states centered near 63 cm$^{-1}$.
A new pyrochlore compound, NaCaNi$_2$F$_7$, was recently synthesized and has a single magnetic site with spin-1 Ni$^{2+}$. We present zero field (ZF) and longitudinal field (LF) muon spin rotation ($mu$SR) measurements on this pyrochlore. Density functional theory (DFT) calculations show that the most likely muon site is located between two fluorine ions, but off-centre. A characteristic F-$mu$-F muon spin polarization function is observed at high temperatures where Ni spin fluctuations are sufficiently rapid. The Ni$^{2+}$ spins undergo spin freezing into a disordered ground state below 4~K, with a characteristic internal field strength of 140~G. Persistent Ni spin dynamics are present to our lowest temperatures (75~mK), a feature characteristic of many geometrically frustrated magnetic systems.
$LiHo_xY_{1-x}F_4$ is an insulating system where the magnetic Ho$^{3+}$ ions have an Ising character, and interact mainly through magnetic dipolar fields. We used the muon spin relaxation technique to study the nature of the ground state for samples with x=0.25, 0.12, 0.08, 0.045 and 0.018. In contrast with some previous works, we have not found any signature of canonical spin glass behavior down to $approx$15mK. Instead, below $approx$300mK we observed dynamic magnetism characterized by a single correlation time with a temperature independent fluctuation rate. We observed that this low temperature fluctuation rate increases with x up to 0.08, above which it levels off. The 300mK energy scale corresponds to the Ho3+ hyperfine interaction strength, suggesting that the hyperfine interaction may be intimately involved with the spin dynamics in this system.
We report a detailed investigation of GdO$_{1-x}$F$_{x}$FeAs (x = 0, 0.07 and 0.14) samples by means of high-field/high-frequency electron spin resonance (HF-ESR) together with measurements of thermodynamic and transport properties. The parent GdOFeAs compound exhibits Fe long-range magnetic order below 128 K, whereas both doped samples do not show such order and are superconducting with T$_c$ = 20 K (x = 0.07) and T$_c$ = 45 K (x = 0.14). The Gd$^{3+}$ HF-ESR reveals an appreciable exchange coupling between Gd and Fe moments, through which the static magnetic order is clearly seen in the parent compound. Owing to this coupling, HF-ESR can probe sensitively the evolution of the magnetism in the FeAs planes upon F doping. It is found that in both superconducting samples, where the Fe long-range order is absent, there are short-range, static on the ESR time scale magnetic correlations between Fe spins. Their occurrence on a large doping scale may be indicative of the ground states coexistence.
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