Broadband magnetic resonance spectroscopy in MnSc[Formula: see text]S[Formula: see text].

Recent neutron scattering experiments suggested that frustrated magnetic interactions give rise to antiferromagnetic spiral and fractional skyrmion lattice phases in MnSc[Formula: see text]S[Formula: see text] . Here, to trace the signatures of these modulated phases, we studied the spin excitations of MnSc[Formula: see text]S[Formula: see text] by THz spectroscopy at 300 mK and in magnetic fields up to 12 T and by broadband microwave spectroscopy at various temperatures up to 50 GHz. We found a single magnetic resonance with frequency linearly increasing in field. The small deviation of the Mn[Formula: see text] ion g-factor from 2, g = 1.96, and the absence of other resonances imply very weak anisotropies and negligible contribution of higher harmonics to the spiral state. The significant difference between the dc magnetic susceptibility and the lowest-frequency ac susceptibility in our experiment implies the existence of mode(s) outside of the measured frequency windows. The combination of THz and microwave experiments suggests a spin gap opening below the ordering temperature between 50 GHz and 100 GHz.

Gapped magnetic ground state in quantum spin liquid candidate κ-(BEDT-TTF)2Cu2(CN)3.

Geometrical frustration, quantum entanglement, and disorder may prevent long-range ordering of localized spins with strong exchange interactions, resulting in an exotic state of matter. κ-(BEDT-TTF)2Cu2(CN)3 is considered the prime candidate for this elusive quantum spin liquid state, but its ground-state properties remain puzzling. We present a multifrequency electron spin resonance (ESR) study down to millikelvin temperatures, revealing a rapid drop of the spin susceptibility at 6 kelvin. This opening of a spin gap, accompanied by structural modifications, is consistent with the formation of a valence bond solid ground state. We identify an impurity contribution to the ESR response that becomes dominant when the intrinsic spins form singlets. Probing the electrons directly manifests the pivotal role of defects for the low-energy properties of quantum spin systems without magnetic order.

Microwave probing of bulk dielectrics using superconducting coplanar resonators in distant-flip-chip geometry.

Dielectric measurements on insulating materials at cryogenic temperatures can be challenging, depending on the frequency and temperature ranges of interest. We present a technique to study the dielectric properties of bulk dielectrics at GHz frequencies. A superconducting coplanar Nb resonator is deposited directly on the material of interest, and this resonator is then probed in distant-flip-chip geometry with a microwave feedline on a separate chip. Evaluating several harmonics of the resonator gives access to various probing frequencies in the present studies up to 20 GHz. We demonstrate the technique on three different materials (MgO, LaAlO3, and TiO2), at temperatures between 1.4 K and 7 K.

Cryogenic frequency-domain electron spin resonance spectrometer based on coplanar waveguides and field modulation.

We present an instrument to perform frequency-domain electron spin resonance experiments that is based on coplanar waveguides and field modulation. A large parameter space in frequency (up to 25 GHz), magnetic field (up to 8 T), and temperature (down to 1.6 K) is accessible. We performed experiments on DPPH (2,2-diphenyl-1-picrylhydrazyl) as a standard to calibrate the field modulation as well as on a carbon fiber sample to estimate the overall sensitivity of the instruments. Spectra of a ruby sample in a broad frequency and field range at cryogenic temperatures are recorded with and without field modulation. The comparison reveals the improved signal-to-noise ratio achieved by field modulation.

Characterizing dielectric properties of ultra-thin films using superconducting coplanar microwave resonators.

We present an experimental approach for cryogenic dielectric measurements on ultrathin insulating films. Based on a coplanar microwave waveguide design, we implement superconducting quarter-wave resonators with inductive coupling, which allows us to determine the real part ε1 of the dielectric function at gigahertz frequencies and sample thicknesses down to a few nanometers. We perform simulations to optimize resonator coupling and sensitivity, and we demonstrate the possibility to quantify ε1 with a conformal mapping technique in a wide sample-thickness and ε1-regime. Experimentally, we determine ε1 for various thin-film samples (photoresist, MgF2, and SiO2) in the thickness regime of nanometer up to micrometer. We find good correspondence with nominative values, and we identify the precision of the film thickness as our predominant error source. Additionally, we present a temperature-dependent measurement for a SrTiO3 bulk sample, using an in situ reference method to compensate for the temperature dependence of the superconducting resonator properties.

Role of non-linear effects and standing waves in microwave spectroscopy: Corbino measurements on superconductors and VO2.

Broadband microwave spectroscopy can probe material properties in wide spectral and temperature ranges. The quality of such measurements crucially depends on the calibration, which also removes from the obtained spectra signatures of standing waves. Here we consider cryogenic Corbino-type reflection measurements on superconductors close to the critical temperature. We show that the non-linear sample response, which relates to sample heating, can lead to strong signatures of standing waves even in a well-calibrated Corbino spectrometer. We demonstrate our findings with microwave measurements as a function of frequency, power, and temperature and for different lengths of the microwave transmission line. Finally, we note such non-linear effects beyond the case of superconductors by probing a VO2 thin film at the insulator-metal transition.

New insights into MagPI: a promising tool to determine the adhesive capacity of biofilm on the mesoscale.

The adhesiveness and stability of ubiquitously distributed biofilms is a significant issue in many areas such as ecology, biotechnology and medicine. The magnetic particle induction (MagPI) system allows precise determinations of biofilm adhesiveness at high temporal and spatial resolution on the mesoscale. This paper concerns several technical aspects to further improve the performance of this powerful experimental approach and enhance the range of MagPI applications. First, several electromagnets were built to demonstrate the influence of material and geometry with special regard to core remanence and magnetic strength. Secondly, the driving force to lift up the particles was evaluated and it was shown that both the magnetic field strength and the magnetic field gradient are decisive in the physics of the MagPI approach. The intricate combination of these two quantities was demonstrated with separate experiments that add permanent magnets to the MagPI system.

Single-Gap Superconductivity and Dome of Superfluid Density in Nb-Doped SrTiO_{3}.

SrTiO_{3} exhibits a superconducting dome upon doping with Nb, with a maximum critical temperature T_{c}≈0.4 K. Using microwave stripline resonators at frequencies from 2 to 23 GHz and temperatures down to 0.02 K, we probe the low-energy optical response of superconducting SrTiO_{3} with a charge carrier concentration from 0.3 to 2.2×10^{20} cm^{-3}, covering the majority of the superconducting dome. We find single-gap electrodynamics even though several electronic bands are superconducting. This is explained by a single energy gap 2Δ due to gap homogenization over the Fermi surface consistent with the low level of defect scattering in Nb-doped SrTiO_{3}. Furthermore, we determine T_{c}, 2Δ, and the superfluid density as a function of charge carrier concentration, and all three quantities exhibit the characteristic dome shape.

Single spin optically detected magnetic resonance with 60-90 GHz (E-band) microwave resonators.

Magnetic resonance with ensembles of electron spins is commonly performed around 10 GHz, but also at frequencies above 240 GHz and in corresponding magnetic fields of over 9 T. However, experiments with single electron and nuclear spins so far only reach into frequency ranges of several 10 GHz, where existing coplanar waveguide structures for microwave (MW) delivery are compatible with single spin readout techniques (e.g., electrical or optical readout). Here, we explore the frequency range up to 90 GHz, with magnetic fields of up to ≈3 T for single spin magnetic resonance in conjunction with optical spin readout. To this end, we develop MW resonators with optical single spin access. In our case, rectangular 60-90 GHz (E-band) waveguides guarantee low-loss supply of microwaves to the resonators. Three dimensional cavities, as well as coplanar waveguide resonators, enhance MW fields by spatial and spectral confinement with a MW efficiency of 1.36 mT/√W. We utilize single nitrogen vacancy (NV) centers as hosts for optically accessible spins and show that their properties regarding optical spin readout known from smaller fields (<0.65 T) are retained up to fields of 3 T. In addition, we demonstrate coherent control of single nuclear spins under these conditions. Furthermore, our results extend the applicable magnetic field range of a single spin magnetic field sensor. Regarding spin based quantum registers, high fields lead to a purer product basis of electron and nuclear spins, which promises improved spin lifetimes. For example, during continuous single-shot readout, the (14)N nuclear spin shows second-long longitudinal relaxation times.

Surface-resistance measurements using superconducting stripline resonators.

We present a method to measure the absolute surface resistance of conductive samples at a set of GHz frequencies with superconducting lead stripline resonators at temperatures 1-6 K. The stripline structure can easily be applied for bulk samples and allows direct calculation of the surface resistance without the requirement of additional calibration measurements or sample reference points. We further describe a correction method to reduce experimental background on high-Q resonance modes by exploiting TEM-properties of the external cabling. We then show applications of this method to the reference materials gold, tantalum, and tin, which include the anomalous skin effect and conventional superconductivity. Furthermore, we extract the complex optical conductivity for an all-lead stripline resonator to find a coherence peak and the superconducting gap of lead.

Microwave resonances in dielectric samples probed in Corbino geometry: simulation and experiment.

The Corbino approach, where the sample of interest terminates a coaxial cable, is a well-established method for microwave spectroscopy. If the sample is dielectric and if the probe geometry basically forms a conductive cavity, this combination can sustain well-defined microwave resonances that are detrimental for broadband measurements. Here, we present detailed simulations and measurements to investigate the resonance frequencies as a function of sample and probe size and of sample permittivity. This allows a quantitative optimization to increase the frequency of the lowest-lying resonance.

Broadband microwave spectroscopy in Corbino geometry at 3He temperatures.

A broadband microwave spectrometer has been constructed to determine the complex conductivity of thin metal films at frequencies from 45 MHz to 20 GHz working in the temperature range from 0.45 K to 2 K (in a (3)He cryostat). The setup follows the Corbino approach: a vector network analyzer measures the complex reflection coefficient of a microwave signal hitting the sample as termination of a coaxial transmission line. As the calibration of the setup limits the achievable resolution, we discuss the sources of error hampering different types of calibration. Test measurements of the complex conductivity of a heavy-fermion material demonstrate the applicability of the calibration procedures.

Fabry-Perot resonances in birefringent YAlO3 analyzed at terahertz frequencies.

We present transmission and phase measurements on a birefringent YAlO(3) crystal that is illuminated with linearly polarized terahertz radiation in a broad frequency range (10 cm(-1) to 16 cm(-1)). The spectra exhibit pronounced and complex Fabry-Perot resonances that depend on the polarization orientation of the incoming light. We present a theoretical description to analyze these data and to obtain the optical constants of the crystal in the terahertz range.

Strip-shaped samples in a microwave Corbino spectrometer.

The Corbino geometry, where a flat sample is pressed against an open end of a coaxial cable, is an established probe layout for broadband microwave spectroscopy. Here we show that besides the conventional case of the sample covering the complete Corbino probe, also strip-shaped samples can be studied with a Corbino spectrometer. This increases the sensitivity for highly conductive samples and furthermore opens the route for the study of anisotropic materials.

Extremely slow Drude relaxation of correlated electrons.

The electrical conduction of metals is governed by how freely mobile electrons can move throughout the material. This movement is hampered by scattering with other electrons, as well as with impurities or thermal excitations (phonons). Experimentally, the scattering processes of single electrons are not observed, but rather the overall response of all mobile charge carriers within a sample. The ensemble dynamics can be described by the relaxation rates, which express how fast the system approaches equilibrium after an external perturbation. Here we measure the frequency-dependent microwave conductivity of the heavy-fermion metal UPd2Al3 (ref. 4), finding that it is accurately described by the prediction for a single relaxation rate (the so-called Drude response). This is notable, as UPd2Al3 has strong interactions among the electrons that might be expected to lead to more complex behaviour. Furthermore, the relaxation rate of just a few gigahertz is extremely low--this is several orders of magnitude below those of conventional metals (which are typically around 10 THz), and at least one order of magnitude lower than previous estimates for comparable metals. These observations are directly related to the high effective mass of the charge carriers in this material and reveal the dynamics of interacting electrons.