Detection of electron spin resonance down to 10 K using localized spoof surface plasmon
aa r X i v : . [ phy s i c s . a pp - ph ] J a n *correspondence: [email protected] D etection of electron spin resonance down to
10 K using localizedspoof surface plasmon P reprint , compiled J anuary
28, 2021
Subhadip Roy , Anuvab Nandi , Pronoy Das , and Chiranjib Mitra * Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, India. A bstract In this study, novel use of the electromagnetic field profile of a localized spoof surface plasmonic mode todetect electron spin resonance is being reported. The mode is supported on a resonator with a complementarymetallic spiral structure, etched on the ground plane of a microstrip line having a characteristic impedance of50 Ω . The change in characteristics of the mode of interest with lowering of temperature has been observed andanalyzed. Electron spin resonance spectra of a standard paramagnetic sample, 2,2-diphenyl-1-picrylhydrazyl,are recorded using this resonator down to 10 K. Potential application of the mode in the detection of microwaveRashba field-driven electron spin resonance has been discussed. K eywords Localized Spoof Surface Plasmon · Complementary Metallic Spiral Structure · Electron Spin Resonance ntroduction
Surface plasmons are electromagnetic waves which exist onmetal and dielectric interface at optical frequencies [1],[2],[3].They can either propagate at the interface as surface plasmonpolaritons or can be resonant in the form of localized surfaceplasmons (LSPs) [4],[5]. However, at low-frequency rangesuch as at microwave and terahertz frequencies, metals behaveas nearly perfect electric conductors which prevent the excita-tion of these surface modes [6]. Patterned metallic surfaces cansupport surface waves at low frequencies, which have featuressimilar to original surface plasmons, and are known as spoofsurface plasmons [7],[8],[9]. Similar to the original LSPs, thelocalized spoof surface plasmons (LSSPs) show strong fieldconfinement [10],[11]. This property of LSSPs has been uti-lized in this work for the detection of electron spin resonance(ESR) and related measurements. Previously, LSSP modeshave been used for sensing purposes only [12],[13].ESR occurs when a resonant microwave radiation cause tran-sition of electrons between spin levels in the presence of anexternal Zeeman magnetic field in paramagnetic systems [14].The sample under study is placed in the region of a uniform mi-crowave magnetic field, orthogonal to the Zeeman field to causeESR transitions [15]. So far, cavity resonators [16], lumped res-onators [17] and planar resonators [18] have been used for mi-crowave magnetic field generation at the position of the sample.LSSP modes can be generated on a complementary metallic spi-ral structure (CMSS) [19],[20]. An LSSP mode supported ona resonator, consisting of a CMSS excited by a microstrip line[13] has been used in this work for detection of ESR. The LSSPresonator has been simulated, and the fabricated resonator isused to record ESR spectra of 2,2-diphenyl-1-picrylhydrazyl(DPPH) down to 10 K. In section 2, detailed description ofthe LSSP resonator has been provided. Elaborate descriptionof low-temperature setup for recording ESR spectra is done insection 3, followed by section 4 containing the results and re-lated discussion. The study is concluded in section 5, with a dis-cussion on the potential application of the designed resonator inthe detection of ESR transitions caused by a microwave Rashbafield in low dimensional systems. he L ocalized S poof S urface P lasmonic R esonator The Localized Spoof Surface Plasmonic Resonator (LSSPR)comprises a CMSS etched on the ground plane of a microstriptransmission line along with conducting trace on the other sidewhich excites the LSSP modes. Four spiral air slots of width w = s = R = b = Ω character-istic impedance. Figures 1 (a) & (b) illustrate the LSSPR andthe CMSS, respectively. Port 1Port 2 ba)
R w --- s b) (cid:1) m Figure 1: (a) The LSSPR along with excitation ports. (b) TheCMSS located on the ground plane with dimensions marked. & Fabrication
Simulation of the LSSPR having dimensions indicated in sub-section 2.1 is carried out in CST Microwave Studio (CSTMWS) software. The microwave laminate used in the processis AD1000 [21] (Rogers Corporation, USA). The laminate hasa dielectric constant of 10.7 for a thickness of 1.5 mm and a dis-sipation factor of 0.0023 defined at 10 GHz. A 17.5 µ m thickcopper layer is present on both sides of the dielectric. In thesimulation setup, the electrical conductivity of copper is takenas 5.96 × S / m, which is the pre-defined value available inCST MWS. Frequency-domain solver with open (add space) reprint – D etection of electron spin resonance down to
10 K using localized spoof surface plasmon a) b)
Figure 2: (a) The CMSS structure after fabrication. (b) Thesignal trace with SMA connectors soldered on it.
The LSSPR is characterized by measuring its transmissionspectrum and comparing it with the simulated result. Themeasurement is carried out using a Vector Network Analyzer(VNA) (ZVA 24, Rohde & Schwarz). The VNA is calibratedusing through, open, short and match (TOSM) standardsbefore performing the measurements. Figure 3 compares themeasured response (black) with the simulated one (red). Thedeviation between the two responses may be attributed to thetolerance of the fabrication process. In the 2-4 GHz frequencyrange, the transmission spectrum shows two dips marked as M & M which are the two fundamental LSSP resonance modes. M is the magnetic LSSP mode and M is the electrical LSSPmode [13],[19]. M2 M2M1
Measured Simulated S ( d B ) Frequency (GHz) M1 Figure 3: Comparison of the simulated (red) & measured(black) transmission spectra of the LSSPR in 2-4 GHz range. pplication of the
LSSPR in detection ofelectron spin resonance down to
10 K
The LSSP mode M resonating at GHz (measured) asshown in figure 3 is chosen for the application in the detec-tion of electron spin resonance. A uniform magnetic field isobtained in the central part of the resonator as shown in figure4.Figure 4: Cross-sectional view of the simulated microwavemagnetic field distribution in the yz plane.The Zeeman field B is applied along the x -direction as shownin figure 5. Hence the magnitude of the component of the mi-crowave magnetic field perpendicular to B is given by | B ⊥ | = q | B | + | B | . Figures 5 and 6 show the distribution of | B ⊥ | and the electric field just above the CMSS structure, respec-tively. B0 Figure 5: Distribution of | B ⊥ | just above the CMSS structure.The direction of B along x -axis is indicated.Figure 6: Distribution of the electric field just above the CMSSstructure.Temperature variation of the M mode’s properties is investi-gated by mounting the LSSPR inside a closed-cycle cryogen-free cryostat ( Optistat
Dry BLV, Oxford Instruments) on a cus-tom designed copper holder attached to the cold head. The reprint – D etection of electron spin resonance down to
10 K using localized spoof surface plasmon
Mercury iTC, Oxford Instru-ments). The LSSPR is attached to a dielectric spacer for elec-trical insulation which in turn is stuck to the holder. ApiezonN grease and a cyanoacrylate adhesive are used to provide ther-mal contact and mechanical stability respectively. The arrange-ment is depicted in Figure 7. Hand formable microwave cables(086-2SM + , Mini-Circuits) connect the LSSPR to the VNA viahermetically sealed adapters (PE9184, Pasternack) fitted to thecryostat body. TOSM calibration is performed at room temper-ature before the commencement of measurement at low temper-atures. Cold HeadCopper holder
Dielectric Spacer
FlexibleSMA cable
Resonator
Figure 7: The mounted empty LSSPR inside the cryostat.Continuous wave electron spin resonance spectroscopy is per-formed on 4mg of DPPH sample at di ff erent temperature valuesin the 10 K to 295 K temperature range. The powder sample iswrapped in teflon tape and is a ffi xed on the CMSS structurewith the help of Apiezon N grease. It is placed on the centralpart of the resonator as the microwave magnetic field is uniformthere. Figure 8 shows the sample location on the LSSPR.Figure 8: Location of the sample on the LSSPR The cryostat loaded with the sample is placed between the polepieces of an electromagnet (3473-70, GMW). The electromag-net provides the external Zeeman field. The VNA connectedto the LSSPR acts as the source and detector of microwaves.It is set to have a measurement bandwidth of 1 MHz with afrequency step size of 500 kHz. An averaging factor of 25with 15 dBm port power is used for recording the ESR spec-tra. The programmable power supply (SGA60X83D, Sorensen)connected to the electromagnet, and the VNA are interfaced us-ing a Python script. Temperature is manually set on the tem-perature controller before recording an ESR spectrum. Theschematic of the low temperature ESR setup is shown in figure9. V.N.A. ++ PowerSupplyPersonalComputer TemperatureController
Cryostat NS B0 Figure 9: Schematic of the low temperature ESR setup esults & D iscussion
The temperature evolution of M mode for the empty LSSPRis plotted in figure 10. The shift of the resonant frequency ( f res )and the variation in the loaded quality factor (Q-factor) of the M mode for the empty LSSPR with temperature are shownin figure 11. The Q-factor is calculated using the relation, Q-factor = f res ∆ f dB , where ∆ f dB is the bandwidth at + ffi cient S value whichoccurs at f res [24],[25],[26].
10 K S ( d B ) Frequency (GHz)
10 K 25 K 50 K 75 K 100 K 125 K 150 K 175 K 200 K 225 K 250 K 275 K 295 K
295 K
Figure 10: Temperature evolution of M mode for the emptyLSSPR. reprint – D etection of electron spin resonance down to
10 K using localized spoof surface plasmon f res Q-factor
Temperature (K) f r es ( G H z ) Q -f ac t o r ( a r b . un i t s ) Figure 11: Change in the resonant frequency, f res (black) andQ-factor (red) with temperature for the empty LSSPR.A shift of 67 MHz is observed in f res at 10 K in comparison toits value at 295 K. Thermal contraction and change in dielec-tric properties of the microwave laminate [21] can qualitativelyexplain this shift [27], [28], [29]. The value of the Q-factorreaches a maximum of 386 at 75 K after which it decreasesslightly down to 10 K. The enhancement in Q-factor at lowtemperature can be attributed to the reduction in resistive powerloss [29].Figure 12 shows the temperature evolution of the M mode af-ter placement of the DPPH sample. In comparison to figure10, after placement of the sample, f res shifts to lower values forthe entire measurement temperature range (10 K-295 K). Thedielectric property of the teflon wrapped sample perturbs theelectric field (figure 6) on the CMSS [19] leading to the shift in f res values at di ff erent temperatures. S ( d B ) Frequency (GHz)
10 K 25 K 50 K 75 K 100 K 150 K 200 K 250 K 295 K295 K10 K
Figure 12: Temperature evolution of M mode for the LSSPRloaded with sample. The change in the transmission dip of the M mode as a func-tion of externally swept B is recorded for obtaining the ESRspectrum at di ff erent temperature values. The recorded ESRspectra at 10 K and room temperature along with a fit to aLorentzian is shown in figure 13. (a) (b) Figure 13: ESR signal fitted by a Lorentzian curve (red)recorded at (a) 10 K (b) 295 K (room temperature)The g-factor and ESR line width [30] are measured & plottedfor di ff erent temperature values as shown in figure 14 (a) &(b) respectively. The measured values of the g-factor and linewidth of the DPPH sample show satisfactory agreement withthe values reported in the literature [31].Figure 14: Measured (a) g-factor & (b) ESR line width at dif-ferent temperature values.The signal to noise ratio (SNR) [32],[33] is around 46 at 10 K &34 at 295 K. Spin sensitivity [34],[35] is about 10 spins / gaussfor the sample used with a measured ESR line width of 3.36 Gat 10 K. The LSSPR based ESR spectrometer has SNR valuewhich is one order lower than the spectrometers developedby us [22],[23] that utilize planar transmission line based res-onators in reflection geometry and consequently has spin sensi-tivity value which is one order higher. onclusion The LSSPR has been successfully fabricated using a rapid pro-totyping technique, resulting in a good agreement between themeasured and simulated responses. Temperature evolution ofthe used LSSP mode has been shown and explained. Estimatedvalues of the g-factor and line width show good agreement withpreviously reported values. This is the first study to the best ofour knowledge, where the magnetic field of an LSSP mode hasbeen used to detect ESR spectra of a paramagnetic sample.The simultaneous confinement of microwave electric and mag-netic fields in the M mode can make detection of ESR sig- reprint – D etection of electron spin resonance down to
10 K using localized spoof surface plasmon ff ects ofZeeman field and Rashba field in the same ESR spectrum. Themicrowave electric field induces a microwave Rashba field inlow symmetry systems (1D & 2D samples) which can give riseto ESR transition apart from the conventional ESR transitionscaused by microwave magnetic field [36],[37]. A cknowledgements The authors gratefully acknowledge the Ministry of Education(MoE), Government of India & Science and Engineering Re-search Board (SERB) (grant no.- EMR / / R eferences [1] Visser, T. D. "Surface plasmons at work?." Nature Physics, (8), 509-510(2006).[2] Raether, H. “Surface Plasmons on Smooth and Rough Sur-faces and on Gratings.” (Springer, Berlin, 1988).[3] Barnes, W., Dereux, A. & Ebbesen, T. "Surface plasmonsubwavelength optics." Nature, , 824–830 (2003).[4] Yu, H., Peng, Y., Yang, Y., & Li, Z. Y. "Plasmon-enhancedlight–matter interactions and applications." npj Computa-tional Materials, (1), 1-14(2019).[5] Maier, S.A. 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