Measurement of electron paramagnetic resonance using terahertz time-domain spectroscopy

Kohei Kozuki; Takeshi Nagashima; Masanori Hangyo

doi:10.1364/OE.19.024950

1. Introduction

Electron spin resonance (ESR) is a useful tool for material analysis in various fields including physics, chemistry, and biology. When the applied magnetic field B and the angular frequency ω of radiation transmitted through a paramagnetic sample with negligible interaction between electron spins satisfy $ℏ ω = g μ_{B} B$ (where $ℏ$ is the reduced Planck constant; μ_B, the Bohr magneton; and g, the g-factor), resonant absorption of the radiation occurs [1]. The resonance condition is modified by total spin angular momentum, anisotropy, interaction between electron spins, magnetic field-induced transitions, and so on. Thus, knowledge of B and ω at resonances provides abundant information on the electronic state and microscopic structure around atoms associated with the electron spins.

ESR using X-band microwaves (~10 GHz) is a well-established technique. Recently, ESR measurements at terahertz frequencies (THz-ESR) have attracted much attention [2–9]. By THz-ESR, the resolution of electron paramagnetic resonance measurements should be improved, thus enabling signals from slightly different g-factors to be separated [2,3]. THz-ESR allows for high and/or integer spin systems with large zero-field splitting to be investigated [4–6].

In conventional ESR measurements, an applied magnetic field is continuously varied while the frequency of a monochromatic radiation source is fixed. In such a scheme, to detect resonances with zero-field splitting, the radiation source with the frequency close to the zero-field splitting has to be used. However, it is difficult to select an appropriate frequency of the radiation source when the magnitude of the zero-field splitting of materials is unknown. In contrast, using a spectroscopic technique, the resonances with unknown zero-field splitting can be observed if the radiation source has a sufficient broadband spectrum. Thus, frequency-domain ESR is needed for investigating those resonances [7–9]. In addition, field-frequency maps [4,5,7,8], which provide abundant information of spin structures, are more easily obtained by frequency-domain ESR compared with conventional ESR where the radiation source must be replaced to change the frequency [4,5].

In this article, we report the development of a frequency-domain ESR measurement system using terahertz time-domain spectroscopy (THz-TDS) for analyzing paramagnetic materials. A crossed polarizer technique is utilized to increase the sensitivity in detecting weak ESR signals. We show the validity of the developed system by measuring an ESR standard material. The proposed ESR measurements using subpicosecond terahertz pulses represent progress toward realizing time-resolved ESR with extremely high time-resolution.

2. Principle of measurements and setup

ESR signals originate from the absorption of a circularly polarized wave via magnetic dipole transitions between magnetic sublevels. The ESR absorption of paramagnetic materials, however, is too small to detect with conventional transmission measurements using THz-TDS. As shown in Fig. 1(a) , a circularly polarized component at ESR frequencies is absorbed. This results in the induction of polarization perpendicular to the incident linearly polarized wave. In this work, to detect ESR signals from paramagnets, crossed polarization at resonance frequencies induced by the absorption of the circularly polarized wave is detected by means of a pair of crossed wire grid polarizers [10,11]. Since this scheme is a null method, the sensitivity of the detection can be increased, thus enabling crossed polarization with small amplitude to be measured.

Fig. 1 (a) Schematic diagram of absorption and emission of circularly polarized electromagnetic waves caused by magnetic dipole transitions between magnetic sublevels. (b) Schematic diagram of experimental setup.

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A schematic diagram of the experimental setup is shown in Fig. 1(b). A superconducting magnet that generates 10 T at maximum is installed in a conventional THz-TDS system. Photoconductive antennas excited by optical pulses (center wavelength, 780 nm; duration, 98 fs; repetition rate, 50 MHz; average power, 12 mW) were used as the emitter and detector of THz pulses. Free-standing wire grids (Specac) with a wire diameter of 5 μm, a spacing of 12.5 μm, and a nominal cutoff frequency of ~6 THz were used as a polarizer (WG1) and an analyzer (WG2). The wires of WG1 were set perpendicular to those of WG2. For better sensitivity in detecting the crossed polarization, stacks of two wire grids were used in WG1 and WG2. The THz pulse waveform E_s(t) with polarization orthogonal to that of pulses incident on the samples were measured in the experiments.

Here, we define the ESR signal as |E_s(ω)/E₀(ω)|, where E_s(ω) and E₀(ω) are the complex amplitude spectra deduced from the waveforms of the crossed polarization (E_s(t)) and incident THz waves (E₀(t)) by complex Fourier transformation. The linearly polarized incident wave can be viewed as a superposition of right- and left-handed circularly polarized waves with complex amplitude E₀(ω)/2. E_s(ω) in magnetic field B is described by

E_{s} = i E_{0} (t_{-} - t_{+}) / 2,

where

t_{+}

and

t_{-}

are the complex amplitude transmittance spectra of the left- and right-handed circularly polarized waves, respectively. When interference from multiply reflected THz waves in a sample is ignored,

t_{+}

and

t_{-}

are given by

t_{\pm} = \frac{4 Z_{\pm}}{{(Z_{\pm} + 1)}^{2}} e^{- i k_{0} n_{\pm} d},

where k₀ is the wavenumber of THz wave in free space, d is the thickness of the sample, and Z _± = (μ _± /ε)^1/2 and n _± = (μ _± ε)^1/2 are the complex impedance and complex refractive index for the circularly polarized waves, respectively. The dielectric constant ε is assumed to be a real constant independent of ω and B, which is reasonable in insulating paramagnets used in this study.

μ_{\pm} = {μ^{'}}_{\pm} - i {μ^{″}}_{\pm}

are the complex permeability for the circularly polarized waves. For paramagnets,

{μ^{'}}_{\pm} ~ 1

and

{μ^{″}}_{\pm} < < 1

hold due to their weak magnetic response. Considering above approximations, Eq. (1) reduces to

E_{s} / E_{0} \propto ω ({χ^{″}}_{+} - {χ^{″}}_{-}) d

, where

{χ^{″}}_{\pm}

are the imaginary parts of the complex magnetic susceptibility

χ_{\pm} = {χ^{'}}_{\pm} - i {χ^{″}}_{\pm}

for the circularly polarized waves having the relation of

{μ^{'}}_{\pm} - i {μ^{″}}_{\pm} = 1 + 4 π {χ^{'}}_{\pm} - i 4 π {χ^{″}}_{\pm}

. Under the condition that the magnetic field of the THz pulses is sufficiently weak, the expressions for

{χ^{'}}_{\pm}

and

{χ^{″}}_{\pm}

derived from the Bloch equations [12] are

χ_{\pm}^{'} = \frac{1}{2} χ_{0} ω_{0} \frac{(ω_{0} \mp ω)}{d ω^{2} + {(ω_{0} \mp ω)}^{2}} a n d χ_{\pm}^{"} = \frac{1}{2} χ_{0} ω_{0} \frac{d ω}{d ω^{2} + {(ω_{0} \mp ω)}^{2}},

respectively, where χ₀ is the static magnetic susceptibility,

ω_{0} = g μ_{B} B / ℏ

is the resonance angular frequency, and dω is the inverse of the transverse relaxation time T₂. Using the absorption coefficients

α_{\pm} \propto ω ε {χ^{″}}_{\pm}

for the circularly polarized waves, we obtain

E_{s} / E_{0} \propto (α_{+} - α_{-}) d

, which means that |E_s(ω)/E₀(ω)| corresponds to lineshape of the ESR absorption at frequencies near the resonances. Thus, |E_s(ω)/E₀(ω)| is defined as the ESR signal in this study.

3. Experiments

The validity of the proposed scheme is investigated by measuring Copper(II) sulfate pentahydrate (CuSO₄·5H₂O), which is an ESR standard material as samples. Powder of the material was pressed to obtain disks (diameter, 13 mm; thickness, ~2 mm; mass, 566 mg). Waveforms of E_s were recorded up to ~800 ps. Thus, the frequency resolution of deduced ESR signals was ~1.25 GHz. The waveforms shown in this article are averages of 50 scans. All measurements were carried out at room temperature.

First, the crossed polarization waveforms in magnetic fields with positive and negative polarities were measured. Oscillations with a period of ~3 ps induced by ESR were observed in the waveforms in ± 10 T fields (inset, Fig. 2(a) ). When the polarity of the applied magnetic field is reversed, the helicity of the dominantly absorbed circular polarization is switched, which results in the polarity reversal of E_s(t). On the waveforms, there are small artifacts that originate from leakage of the incident polarization caused by the low extinction ratios of the wire grids. The phase of those components remains the same when the direction of the magnetic field is reversed. According to Refs. 10 and 11 signals induced by only ESR can be extracted by subtracting E_s(t) in negative magnetic field -B from that in positive magnetic field + B. In Fig. 2(a), the extracted waveform ([E_s(t, B = + 10 T)-E_s(t, B = −10 T)]/2) is shown by the solid curve.

Fig. 2 (a) Waveform of crossed polarization induced by ESR. Solid curve shows the waveform extracted by subtracting the waveform of the crossed polarization induced in CuSO₄·5H₂O in a −10 T field from that in a + 10 T field. Waveforms in ± 10 T fields are shown by solid and open circles, respectively, in the inset. Waveform of the incident THz pulses is shown by the gray curve for comparison. (b) ESR spectrum of CuSO₄·5H₂O. Inset shows a typical spectrum of the imaginary part of the effective magnetic susceptibility.

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4. Results and discussions

The spectrum of the ESR signal deduced from the extracted waveform in a 10 T field is displayed in Fig. 2(b). The absolute value of ESR signal |E_s(ω)/E₀(ω)| is ~3.7 × 10⁻³ at 0.29 THz where a prominent peak is observed. CuSO₄·5H₂O has uniaxial anisotropy of the g-factor, owing to the tetragonal crystal field around Cu²⁺ ions with S = 1/2. The g-factors with magnetic fields parallel and perpendicular to the tetragonal axis have been reported to be g_// = 2.38 and g_⊥ = 2.05, respectively [13]. The effective magnetic susceptibility χ_eff of a powder sample with uniaxial anisotropy is given by

χ_{e f f} (ω) = \int_{0}^{\frac{π}{2}} χ_{d i s t} (ω, θ) \sin θ d θ,

where θ is the angle between the tetragonal axis and the magnetic field and χ_dist is the distribution function of the complex magnetic susceptibility obtained from χ _± by replacing ω₀ in Eq. (2) with [14]

ω (θ) = \frac{μ_{B}}{ℏ} B \sqrt{g_{/ /}^{2} \cos^{2} θ + g_{⊥}^{2} \sin^{2} θ} .

A typical lineshape of the imaginary part of χ_eff that corresponds to the ESR signal is schematically shown in the inset of Fig. 2(b). A peak and a discontinuity, respectively, are expected at angular frequencies around

ω_{⊥, / /} = g_{⊥, / /} μ_{B} B / ℏ

. The ESR signal in a 10 T field (Fig. 2(b)) appears to be consistent with the expected results. However, the lineshape of the ESR signals depends on the applied magnetic field and on the sample thickness as shown by the solid curves in Fig. 3(a) and 3(b), respectively. This is attributed to interference effects of multiply reflected THz waves in the samples used in this study, which were parallel plates. Here, we calculate the ESR signals |E_s(ω)/E₀(ω)| as follows. Taking into account the interference effects of the THz waves, the complex amplitude transmittance of the parallel plate with thickness d is expressed by [15]

\tilde{t} (ω) = \frac{t_{01} t_{10} e^{- i n ω d / c}}{1 - r_{10}^{2} e^{- i 2 n ω d / c}},

where n = [ε (1 + χ_eff)]^1/2 is the complex refractive index of the sample and t₀₁ = 2 Z/(Z₀ + Z), t₁₀ = 2 Z₀/(Z₀ + Z), and r₁₀ = (Z₀-Z)/(Z₀ + Z), where Z₀ and Z = Z₀ [(1 + χ_eff)/ε] ^1/2 are the impedances of vacuum and sample, respectively. ε = 4.84-0.01i determined by transmission THz-TDS measurements without magnetic field is used in the calculations. Using χ_eff for the left- and right-handed circularly polarized waves, t₊ and t_- in Eq. (1) are calculated by using Eq. (6), and then |E_s(ω)/E₀(ω)| is obtained. In the calculations, the parameters dω ≈ 11 GHz, g_// = 2.40, and g_⊥ = 2.09 are used, which are consistent with the previously reported values [13]. The measured ESR signals are reproduced well by the calculations shown by the dashed curves in Fig. 3. The interference effects mentioned above can be reduced using wedged-shaped samples.

Fig. 3 ESR spectra of CuSO₄·5H₂O (a) with sample thickness of 1.9 mm in various magnetic fields and (b) with various sample thicknesses in a 10 T field. Results of experiments and calculations are shown by solid and dashed curves, respectively.

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The frequency resolution presented in this study is ~1.25 GHz, which is determined by the length of the delay stage used in THz-TDS. 2,2-diphenyl-1-picrylhydrazyl (DPPH), one of the ESR standard samples, is expected to have ESR absorption line with a linewidth of ~14 MHz at 10 T [16]. To resolve such narrow resonances, a delay stage with a length longer than several tens of meters is needed, which is unrealistic. One of the options to resolve the problem may be to use an asynchronous optical sampling technique with two sets of femtosecond pulse lasers operated at a repetition rate lower than ~10 MHz. Besides this, maximum entropy method may be used to obtain spectra with improved frequency resolution from measured waveforms with an ordinary delay stage.

Finally, we would like to point out a possibility of time-resolved ESR measurements with extremely high time resolution based on the system with a THz pulse source developed in this study. Time-resolved ESR is used to study the mechanisms of reaction processes since it can detect generated free radicals that induce paramagnetic ESR. However, the time resolution of conventional ESR systems is ~1 ns at best [17]. Thus, free radicals and excitation states with shorter lifetime in photoinduced reactions, such as photosynthesis reactions and photoinduced damage of DNA, have rarely been investigated by time-resolved ESR. Since the duration of the THz pulses is on the order of sub-picoseconds, an ESR system with optical pump-THz pulse probe spectroscopy is expected to have substantially improved time resolution.

5. Summary

In summary, for analyzing paramagnetic materials, we developed a frequency-domain ESR technique using THz-TDS. The ESR signal of the powder samples of CuSO₄·5H₂O was measured. The lineshape of the obtained ESR signals agrees well with the theoretical predictions for a powder sample with uniaxial anisotropy. The proposed ESR measurement scheme using subpicosecond terahertz pulses paves the way for future realization of time-resolved ESR with extremely high time-resolution.

Acknowledgments

We thank Prof. S. Okubo in Kobe University for his helpful comments and discussions. This work was partially supported by KAKENHI 21656019.

References and links

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Measurement of electron paramagnetic resonance using terahertz time-domain spectroscopy

Abstract

1. Introduction

2. Principle of measurements and setup

3. Experiments

4. Results and discussions

5. Summary

Acknowledgments

References and links

Cited By

Figures (3)

Equations (6)

Optics Express