Detection of electron spin resonance down to 10 K using localized spoof surface plasmon Preprint, compiled January 28, 2021 Subhadip Roy , Anuvab Nandi , Pronoy Das , and Chiranjib Mitra* Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, India. Abstract In this study, novel use of the electromagnetic field profile of a localized spoof surface plasmonic mode to detect electron spin resonance is being reported. The mode is supported on a resonator with a complementary metallic spiral structure, etched on the ground plane of a microstrip line having a characteristic impedance of 50 Ω. The change in characteristics of the mode of interest with lowering of temperature has been observed and analyzed. 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 microwave Rashba field-driven electron spin resonance has been discussed. Keywords Localized Spoof Surface Plasmon · Complementary Metallic Spiral Structure · Electron Spin Resonance 1 Introduction 2 The Localized Spoof Surface Plasmonic esonator Surface plasmons are electromagnetic waves which exist on R metal and dielectric interface at optical frequencies [1],[2],[3]. 2.1 Geometry They can either propagate at the interface as surface plasmon polaritons or can be resonant in the form of localized surface The Localized Spoof Surface Plasmonic Resonator (LSSPR) plasmons (LSPs) [4],[5]. However, at low-frequency range comprises a CMSS etched on the ground plane of a microstrip such as at microwave and terahertz frequencies, metals behave transmission line along with conducting trace on the other side as nearly perfect electric conductors which prevent the excita- which excites the LSSP modes. Four spiral air slots of width w tion of these surface modes [6]. Patterned metallic surfaces can = 0.24 mm and having a separation s = 0.2 mm with respect to support surface waves at low frequencies, which have features adjacent slot wraps 1.5 times to form the CMSS structure with similar to original surface plasmons, and are known as spoof outer radius R = 2.88 mm. The signal trace on the opposite face surface plasmons [7],[8],[9]. Similar to the original LSPs, the has a width b = 1.2 mm, which corresponds to 50 Ω character- localized spoof surface plasmons (LSSPs) show strong field istic impedance. Figures 1 (a) & (b) illustrate the LSSPR and confinement [10],[11]. This property of LSSPs has been uti- the CMSS, respectively. lized in this work for the detection of electron spin resonance a) b) (ESR) and related measurements. Previously, LSSP modes Port 1 s have 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 an b w external Zeeman magnetic field in paramagnetic systems [14]. R The sample under study is placed in the region of a uniform mi- crowave magnetic field, orthogonalto the Zeeman field to cause Port 2 ESR transitions [15]. So far, cavity resonators [16], lumped res- 200 200 ¡ m onators [17] and planar resonators [18] have been used for mi- arXiv:2101.11528v1 [physics.app-ph] 27 Jan 2021 crowave magnetic field generation at the position of the sample. Figure 1: (a) The LSSPR along with excitation ports. (b) The LSSP modes can be generated on a complementarymetallic spi- CMSS located on the ground plane with dimensions marked. ral structure (CMSS) [19],[20]. An LSSP mode supported on a resonator, consisting of a CMSS excited by a microstrip line [13] has been used in this work for detection of ESR. The LSSP 2.2 Simulation & Fabrication resonator has been simulated, and the fabricated resonator is used to record ESR spectra of 2,2-diphenyl-1-picrylhydrazyl Simulation of the LSSPR having dimensions indicated in sub- (DPPH) down to 10 K. In section 2, detailed description of section 2.1 is carried out in CST Microwave Studio (CST the LSSP resonator has been provided. Elaborate description MWS) software. The microwave laminate used in the process of low-temperature setup for recording ESR spectra is done in is AD1000 [21] (Rogers Corporation, USA). The laminate has section 3, followed by section 4 containing the results and re- a dielectric constant of 10.7 for a thickness of 1.5 mm and a dis- lated discussion. The study is concluded in section 5, with a dis- sipation factor of 0.0023 defined at 10 GHz. A 17.5 µm thick cussion on the potential application of the designed resonator in copper layer is present on both sides of the dielectric. In the simulation setup, the electrical conductivity of copper is taken the detection of ESR transitions caused by a microwave Rashba 7 field in low dimensional systems. as 5.96× 10 S/m, which is the pre-defined value available in CST MWS. Frequency-domain solver with open (add space) *correspondence: [email protected] Preprint –Detection of electron spin resonance down to 10 K using localized spoof surface plasmon 2 boundary condition on the ground plane side and open bound- 3 Application of the LSSPR in detection of ary condition on all other sides of the structure has been used electron spin resonance down to 10 K while running the simulation. The fabrication of the structure is carried out using a rapid pro- The LSSP mode M2 resonating at 3.46 GHz (measured) as totyping process employing optical lithography [22] followed shown in figure 3 is chosen for the application in the detec- by wet etching [23]. SMA connectors are soldered at either end tion of electron spin resonance. A uniform magnetic field is of the conducting trace for the propagation of microwave signal. obtained in the central part of the resonator as shown in figure The fabricated LSSPR with the CMSS on the ground plane and 4. the signal trace are shown in figures 2 (a) & (b) respectively. a) b) Figure 4: Cross-sectional view of the simulated microwave yz Figure 2: (a) The CMSS structure after fabrication. (b) The magnetic field distribution in the plane. signal trace with SMA connectors soldered on it. The Zeeman field B0 is applied along the x-direction as shown in figure 5. Hence the magnitude of the component of the mi- 2.3 Characterization crowave magnetic field perpendicular to B0 is given by |B⊥| = The LSSPR is characterized by measuring its transmission |B |2 + |B |2. Figures 5 and 6 show the distribution of |B | spectrum and comparing it with the simulated result. The q 1z 1y ⊥ measurement is carried out using a Vector Network Analyzer and the electric field just above the CMSS structure, respec- (VNA) (ZVA 24, Rohde & Schwarz). The VNA is calibrated tively. using through, open, short and match (TOSM) standards before performing the measurements. Figure 3 compares the measured response (black) with the simulated one (red). The deviation between the two responses may be attributed to the tolerance of the fabrication process. In the 2-4 GHz frequency range, the transmission spectrum shows two dips marked as M1 & M2 which are the two fundamental LSSP resonance modes. M1 is the magnetic LSSP mode and M2 is the electrical LSSP mode [13],[19]. B0 Figure 5: Distribution of |B⊥| just above the CMSS structure. 0 The direction of B0 along x-axis is indicated. -5 M M 1 1 -10 (dB) -15 21 Measured S Simulated -20 M 2 -25 M 2 2.0 2.5 3.0 3.5 4.0 Frequency (GHz) Figure 3: Comparison of the simulated (red) & measured Figure 6: Distribution of the electric field just above the CMSS (black) transmission spectra of the LSSPR in 2-4 GHz range. structure. Temperature variation of the M2 mode’s properties is investi- gated by mounting the LSSPR inside a closed-cycle cryogen- free cryostat (OptistatDry BLV, Oxford Instruments) on a cus- tom designed copper holder attached to the cold head. The Preprint –Detection of electron spin resonance down to 10 K using localized spoof surface plasmon 3 stability of temperature during measurements is maintained by The cryostat loaded with the sample is placed between the pole using a temperature controller (MercuryiTC, Oxford Instru- pieces of an electromagnet (3473-70, GMW). The electromag- ments). The LSSPR is attached to a dielectric spacer for elec- net provides the external Zeeman field. The VNA connected trical insulation which in turn is stuck to the holder. Apiezon to the LSSPR acts as the source and detector of microwaves. N grease and a cyanoacrylate adhesive are used to provide ther- It is set to have a measurement bandwidth of 1 MHz with a mal contact and mechanical stability respectively. The arrange- frequency step size of 500 kHz. An averaging factor of 25 ment is depicted in Figure 7. Hand formable microwave cables with 15 dBm port power is used for recording the ESR spec- (086-2SM+, Mini-Circuits) connect the LSSPR to the VNA via tra. The programmable power supply (SGA60X83D, Sorensen) hermetically sealed adapters (PE9184, Pasternack) fitted to the connected to the electromagnet, and the VNA are interfaced us- cryostat body. TOSM calibration is performed at room temper- ing a Python script. Temperature is manually set on the tem- ature before the commencement of measurement at low temper- perature controller before recording an ESR spectrum. The atures. schematic of the low temperature ESR setup is shown in figure 9. Cryostat Temperature Controller Cold Head Power Supply S N B0 Copper holder Personal Computer++ V.N.A. Resonator Dielectric Figure 9: Schematic of the low temperature ESR setup Spacer Flexible SMA cable 4 Results &Discussion The temperature evolution of M2 mode for the empty LSSPR is plotted in figure 10.