Open Access Article

This Open Access Article is licensed under a Creative Commons Attribution-Non Commercial 3.0 Unported Licence

Ushnish Chaudhuri and
R. Mahendiran*

Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore-117551, Republic of Singapore. E-mail: phyrm@nus.edu.sg

Received
12th April 2020
, Accepted 27th April 2020

First published on 5th May 2020

Detection of electron paramagnetic resonance (EPR) using a microwave cavity resonating at a fixed frequency (between 9 and 10 GHz) remains the most popular method to date. Here, we report a cavity-less technique which makes use of only an impedance analyzer and a copper strip coil to detect L-band EPR (f = 1–3 GHz) in the standard EPR marker 2,2-diphenyl-1-picrylhydrazyl (DPPH). Our method relies on measuring the magnetoimpedance (MI) response of DPPH through a copper strip coil that encloses DPPH. In contrast to commercial EPR which measures only the field derivative of power absorption, our method enables us to deduce both absorption and dispersion. Changes in resistance (R) and reactance (X) of the copper strip while sweeping an external dc magnetic field, were measured for different frequencies (f = 0.9 to 2.5 GHz) of radio frequency current in the coil. R exhibits a sharp peak at a critical value of the dc magnetic field, which is identified as the resonance field and X shows a dispersion at the same frequency. The data were analyzed to obtain line width and resonance field parameters. The resonance field increased linearly with frequency and the obtained Landé g factor of 1.999 ± 0.0197 is close to the accepted value of 2.0036, measured in the X-band. The simplicity of this technique can be exploited to study paramagnetic centers in catalysis and other materials.

In this article, we present a simple method to detect EPR in the L-band frequency region, which makes use of only an impedance analyzer and a copper strip coil. In a closely related work, Kitagawa studied EPR of DPPH placed above a 50 ohm impedance matched microinductor fabricated with CMOS-25 nanotechnology and used a vector network analyzer to extract EPR signal in frequency sweep mode.^{21} A vector network analyzer measures the ratio of a transmitted or reflected power to the incident power from a device under test. Impedance is calculated from scattering parameter S_{12} and S_{11}.^{21} In contrast, the instrument used in the current work (Agilent E4991 RF impedance analyzer) measures impedance of a copper strip based on the radio frequency current–voltage technique and does not require 50 ohm impedance matching or CMOS technology. The copper strip is prepared manually by cutting and folding a copper foil to desired shape. Our method is compact, requires very less instrumentation and does not require multistep device fabrication therefore, it can be easily incorporated in teaching and research laboratories. Our technique provides additional information pertaining to the absorptive and dispersive components of the high frequency magnetic susceptibility whereas conventional EPR spectrometers are designed to provide information about the field derivative of the power absorbed by the sample. Using our simple setup, we demonstrate the detection of EPR due to free radicals in a standard sample of 2,2-diphenyl-1-picrylhydrazyl (DPPH). As a stable and well-characterized solid radical source, DPPH is the most popular reference sample with Landé g-factor of 2.0036.^{22} The intensity of EPR signals depends on the number of radicals for a freshly prepared sample and can be determined by weighing the DPPH sample. DPPH exhibits a single response line in X-band with a small linewidth ∼1.5–4.7 Oe due to the presence of only one unpaired spin per 41 atoms.

Our technique involves using a copper strip coil as an antenna and a radio frequency impedance analyzer (Agilent model E4991A) as a microwave signal source and detector. DPPH powder obtained from Sigma-Aldrich™ was pressed into a disc shaped pellet at room temperature using a hydraulic press (pressure 5 ton per in^{2}). Then, the disc was cut into a rectangular bar of dimension (4.5 mm × 3.5 mm × 0.5 mm). A 0.2 mm thick copper strip was folded in the shape of a cuboidal coil of the same dimension as that of the sample. The sample was tightly fixed inside the coil whose inner surface was covered with a Kapton tape to electrically insulate the sample from the copper strip. One end of the copper strip coil was soldered to the signal line while the other end was soldered to the ground of a subminiature A type (SMA) coaxial connector. The radio frequency (rf) current from the impedance analyzer flows through the strip coil and terminates at the ground of the SMA connector creating an rf magnetic field in the interior of the strip coil along the axial direction as shown in Fig. 1. Hence, the DPPH sample experiences an rf axial magnetic field. An electromagnet is used to apply dc magnetic field perpendicular to the axial rf field. The resistance (R) and reactive (X) components of the electrical impedance of the copper strip were simultaneous measured at different frequencies of rf current while sweeping the dc magnetic field. The electrical impedance of the copper strip is where ϕ is the rf magnetic flux passing through the strip coil given by ϕ = μ_{0}μ_{r}H_{rf}A. Here, H_{rf} is the magnetic field inside the strip-coil and A is the cross-sectional area of the strip coil. Since the high frequency permeability is μ = μ′ − iμ′′ where μ′ is the in-phase and μ′′ is the out-of phase of the permeability which describe dispersion and absorption or loss in the sample, respectively. By substituting the complex permeability, we obtain and where G is a constant depending on the geometry of the strip coil. Since the high frequency permeability of the paramagnetic DPPH sample is affected by the application of dc bias magnetic field, resistance and reactance of the strip coil also changes. R and X were recorded without and with the sample inside the strip coil and data for each frequency and magnetic field were subtracted to obtain only the sample contribution. As the impedance analyzer measures the radio-frequency current–voltage characteristics of the strip coil, there is no need extra analysis to extract the impedance from scattering “S” parameters as in a network analyzer.

(1) |

(2) |

The first term in the above equation describes the absorption while the second term represents the dispersion. α denotes the dispersion-to-absorption ratio. The asymmetricity is prominent in conducting samples since the electric and magnetic rf components in conducting samples become out of phase with each other leading to an admixture of the dispersion into the absorption spectra. α = 0 when the skin effect is negligible as in insulating samples while α = 1 for highly conducting samples where the skin depth is very small compared to the sample size. In this case the absorption and dispersion are of equal strength. So, a dP/dH measurement alone cannot isolate the absorption and dispersion effect whereas, the R and X responses from the magnetoimpedance measurements can provide this information and enable accurate analysis of the physical parameters.

In Fig. 2(a), the field dependence of R for various frequencies from 1.5 GHz to 2.2 GHz are shown. The peak in R shifts towards a higher magnetic field with increasing frequency of current. We performed the line shape analysis for all the frequencies and extracted the frequency dependent line widths (ΔH) as well as the resonance fields (H_{r}) using eqn (1). It is known that the resonance frequency (f_{r}) for EPR is proportional to the dc magnetic field and follows the relation where γ is the gyromagnetic ratio (γ = gμ_{B}/ℏ, where g is the Landé g factor, μ_{B} is the Bohr magneton and ℏ is the reduced Planck's constant). Therefore, with increasing H_{dc} the resonance frequency increases linearly. This linear behavior was observed in the plot of f_{r} vs. H_{dc} presented in Fig. 2(b) and we obtain γ/2π = 2.799 ± 0.0276 MHz Oe^{−1}. This γ/2π value corresponds to a Landé g value of 1.999 ± 0.0197 which is well within the reported value of 2.0036. The small error in the g value is possibly due to inhomogeneity in dc magnetic field or determination of the magnetic field. The line width in this frequency range was about 2 Oe which is consistent with the dilute nature of paramagnetic species (free radicals) in DPPH.^{36}

To verify the results obtained through the MI method, we measured the EPR spectra with a broad band ferromagnetic resonance spectrometer (Cryo-FMR by NanoOsc™ from Quantum Design Inc. USA). This spectrometer makes use of the lock-in technique and records the derivative of power absorbed (dP/dH) by the DPPH sample placed on top of a wave guide while H_{dc} is swept for fixed rf excitations of 2 GHz, 4 GHz, 10 GHz and 12 GHz as shown in Fig. 3(a). We can see that the resonance field (H_{r}) which corresponds to the zero crossing point and amplitude of dP/dH increase with increasing frequency. The inset in Fig. 3(b) shows H_{r} increasing linearly with frequency and γ/2π = 2.801 GHz kOe^{−1}, which is close to the value observed in the MI measurement. The dP/dH line shape was fitted to eqn (3):

(3) |

Fig. 3 (a) The EPR spectroscopic signal (dP/dH) for the DPPH sample measured using the Cryo-FMR spectrometer for excitation frequencies of 2 GHz (squares), 4 GHz (circles), 10 GHz (upward triangle) and 16 GHz (downward triangle). (b) dP/dH curve at 2 GHz along with the line shape fit using eqn (3), the single integrated signal: ∫(dP/dH)dH_{dc} and the double integrated signal: ∫∫(dP/dH)dH_{dc} of the curve fitted dP/dH curve. Inset: plot of f vs. H_{dc} with open circles used to depict the resonance fields (H_{r}) obtained using the dP/dH data. |

In Fig. 4(a) R is presented for various angles which H_{dc} makes with h_{rf}. When H_{dc} is perpendicular to h_{rf} the signal is the most intense while it disappears when H_{dc} is parallel to h_{rf}. The R response for different masses of DPPH is also presented in Fig. 4(b). The signal strength is proportional to the mass of the DPPH with 23 mg of DPPH exhibiting the largest response. Since R is proportional to χ′′, a single integration of the R response can be used to estimate the number of spins in the sample. The single integration of R is presented in the inset of Fig. 4(b) which provides the EPR intensity of absorption by the DPPH samples and increases with increase in number of spins. For 13 mg, 19 mg and 23 mg of DPPH, we obtain 1.9853 × 10^{19}, 2.9017 × 10^{19} and 3.5125 × 10^{19} spins, respectively.

Although the presented strip coil method does not need microfabrication, use of this method is constrained by the natural frequency of the strip coil and maximum frequency of the signal sourced (f = 3 GHz) by the impedance analyzer. In this study, natural resonance of the strip coil was around 2.6 GHz. However, one can prepare a cylindrical coil or a cuboidal coil depending on the shape and physical state (thin film/bulk sample/powder) of the sample and it can be extended to study liquid samples as well. We had successfully tested for ferrofluids (not shown here). These limitations should be taken into consideration.

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