Stimuli‐Responsive Low‐Frequency Terahertz Absorption ON‐OFF Switchability in Spin‐Crossover Material

Abstract

Thermal and optical‐induced ON‐OFF switchable materials show vast potential in various fields like sensors, spintronics, and electronic devices, but remain underexplored in the essential terahertz (THz) region. In this context, a unique 1D spin‐crossover (SCO) network, {[Fe^II(4‐cyanopyridine)₂][Hg^II(µ‐SCN)₂(SCN)(4‐cyanopyridine)]₂}_n (1), has been designed. Temperature‐dependent crystallographic, magnetic, and THz absorption spectroscopic studies indicate an abrupt SCO phenomenon from a high‐spin (HS) state to a complete or partial low‐spin (LS) state, depending on the cooling rate. At low temperatures, the LS state can be converted into the metastable HS state via the light‐induced excited spin‐state trapping (LIESST) effect using visible or near‐infrared lights. Both temperature and light reversibly modulate the THz absorbance (e.g., 0.82 and 1.37 THz) associated with phonons around Fe(II) centers, confirmed by first‐principles calculations and photocrystallographic analysis. This work advances comprehension of the intersection between structures, THz properties, and external‐stimuli switching effects and is pivotal for future THz device applications.

A switchable Fe(II)–Hg(II) coordination polymer exhibits reversible ON‐OFF terahertz (THz) absorption through temperature‐ and light‐induced spin‐crossover. The material shows strong, tunable THz responses linked to phonon modes around Fe(II) centers, supported by spectroscopic measurements and calculations. This work highlights the potential of spin‐crossover materials in future THz‐responsive devices.

1. Introduction

Terahertz (THz) radiation, encompassing the frequency range from 100 GHz to 30 THz in the electromagnetic spectrum, occupies the frequency gap between the infrared and microwaves.^{[ 1} , ² , ^{3 ]} Recent technological advances in laser technology, nanotechnology, and photonics, such as the development of high‐power THz generators through nonlinear effects, THz imaging, and THz time‐domain spectroscopy (THz‐TDS), have significantly accelerated research in many independent fields.^{[ 4} , ⁵ , ^{6 ]} Moreover, THz‐TDS, employing non‐destructive and non‐invasive THz radiations, is often far superior to conventional tools in material science, providing valuable insights on the fingerprint of molecular structures, building block arrangement, inter/intramolecular interactions, as well as their stimuli‐responsive dynamic changes.^{[ 7} , ^{8 ]} For example, irradiating THz light to epsilon iron oxide instantly switches its magnetic pole direction with a suppressed heat‐up effect, indicating potential applications in recording memory.^{[ 9 ]} Consequently, there is a strong demand for novel materials with switchable low‐frequency THz absorbing capability. Such materials can accelerate THz technologies in unprecedented recording and sensing capabilities (high‐density magnetic recordings, quality control of food and agricultural products, sensing in the event of natural and human‐related disasters) and communications (wireless communication, high‐speed data processing, and satellite communication).^{[ 10} , ¹¹ , ¹² , ¹³ , ^{14 ]}

Meanwhile, the pursuit of smart molecular materials with easy preparation strategies, whose physical properties can be dynamically modulated by external stimuli (e.g., light, heat, chemicals, magnetic/electric field, and mechanical force), is pivotal due to their promising applications in devices and information storage.^{[ 15} , ¹⁶ , ^{17 ]} Stimuli‐responsive magnetic materials, as a key branch, have captivated increasing attention owing to their facile synthesis, structural modifiability, and spin manipulation capabilities.^{[ 18} , ¹⁹ , ^{20 ]} As such, a judicious choice of metal ions and ligands allows for the modulation of the final physical properties of the complexes, and even in some cases, the synergistic combination of different physical properties. Among them, Fe(II) spin‐crossover (SCO) materials stand out as one of the most exciting magnetically switchable materials, between the diamagnetic nature of their low‐spin (LS) state (S = 0) and paramagnetic high‐spin (HS) state (S = 2) associated with substantial structural changes.^{[ 21} , ²² , ^{23 ]} The switchability in color, structure, magnetic and optical behaviors, as well as electronic and mechanical features of Fe(II) SCO materials, can be induced by numerous external stimuli.^{[ 24} , ²⁵ , ²⁶ , ^{27 ]} These switching characteristics make them of interest in a variety of applications, including sensors, spintronics, information storage, and electronic devices.^{[ 28} , ²⁹ , ^{30 ]} Specifically, the photoswitching on Fe(II) centers from LS states to metastable HS states is known as the light‐induced excited spin‐state trapping (LIESST) effect, which is particularly appealing because the light is a cost‐effective and convenient trigger.^{[ 31} , ^{32 ]} Conversely, the excited HS states can be reversibly converted into LS states through irradiation at a specific wavelength called reverse‐LIESST (r‐LIESST).^{[ 33} , ^{34 ]} The exploration for materials exhibiting highly efficient LIESST and r‐LIESST effects with visible or near‐infrared (NIR) lights holds significant promise for modulating the physical properties of the complexes, making use of solar irradiation or other environmental light sources.^{[ 35 ]}

To date, the THz‐TDS studies for Fe(II) complexes are sparse, with limited information available for [Fe(1,10‐phen)₂(NCS)₂] (1,10‐phen = 1,10‐phenanthroline) and a series of [Fe(NH₂‐triazole)₃]²⁺ compounds.^{[ 36} , ³⁷ , ^{38 ]} Additionally, the exploration of thermal and photo‐controllable THz absorbance along with their impact on associated phonon modes remains in its infancy, representing a promising subject for future research. Recently, the building block [Hg(SCN)₄]²⁻, featuring heavy Hg ions and flexible thiocyanate ligands, has emerged as a promising candidate for creating a wide variety of remarkable coordination networks with promising THz absorbing capability.^{[ 39} , ⁴⁰ , ⁴¹ , ^{42 ]} By integrating with Fe(II) centers, there is a possibility of strategically designing a novel network exhibiting not only thermal SCO behavior and LIESST or r‐LIESST effects but also low‐frequency THz absorbing capability. Recently, there was a report on the observation of photo and thermal tuning of THz absorption based on Fe(II)–Hg(II) network.^{[ 40 ]} The compound is crystallized in a complex 3D network with a large unit cell and exhibits incomplete SCO with two types of Fe(II) centers (Fe1^HS and Fe2^LS) upon cooling. Nevertheless, compared to relatively flexible low‐dimensional structures with complete SCO, this compound lacks of pronounced structural tunability and associated THz absorption tunability and has complicated THz absorption spectra with many broad THz peaks, potentially masking newly generated and weak THz peaks associated with SCO and LIESST effect, and hinders further analysis and assignments on phonon origins through computational methods.

In this context, we strategically designed and synthesized a novel 1D Fe(II) complex, {[Fe(4‐CNpy)₂[Hg(SCN)₃(4‐CNpy)]₂}_n (1), showing complete and abrupt SCO property, incorporating [Hg(SCN)₄]²⁻ anions and 4‐cyanopyridine (4‐CNpy), and have investigated its pronounced thermal‐ and photo‐switchable magnetic and THz absorbing properties, supported by (photo)crystallographic analysis and theoretical calculations.

2. Results and Discussion

2.1. Synthesis and Crystallographic Analysis

The yellow compound 1 was obtained as a result of slow evaporation of a methanol/water mixed solution containing Fe(BF₄)₂·6H₂O, K₂[Hg(SCN)₄]·H₂O, and an excess amount of 4‐CNpy. The details of the synthesis can be referred to in the method section. The composition was corroborated by the existence of ν(C≡N)_SCN, ν(C≡N)_4‐CNpy, and 4‐CNpy fingerprint featured peaks in the infrared (IR) absorption and Raman scattering spectra (Figures S1 and S2, Supporting Information). The absence of solvent in crystalline materials is essential for good thermal stability, which is confirmed by thermogravimetric analysis, with 1 showing a total mass loss < 0.2% up to ≈123 °C (Figure S11, Supporting Information). The crystal structures of 1 were systematically determined from 300 to 40 K using synchrotron X‐rays (λ = 0.4131 Å) at the Super Photon ring‐8 GeV (SPring‐8) radiation facility. Single crystal diffraction analysis reveals that sample 1 is crystallized in a 1D network with monoclinic space group P2₁/c at various temperatures (Figure 1 ; Tables S1–S3, Supporting Information). The structural unit comprises [Fe^II(4‐CNpy)₂(µ‐NCS)₄] and [Hg^II(µ‐SCN)₂(SCN)(4‐CNpy)] units (Figure 1a; Figures S12 and S13, Supporting Information), where Fe(II) centers are coordinated by six N atoms from four µ‐SCN⁻ ligands with an average <Fe–N> distance of 2.1498(14) Å and two N‐donor 4‐CNpy ligands in axial positions with a longer average distance of 2.2222(15) Å at 300 K (Table S4, Supporting Information). Meanwhile, the Hg(II) ions are bridged by two µ‐SCN⁻, one terminal SCN⁻ through S atoms with <Hg–S> distance of 2.5083(5) Å, and one 4‐CNpy through N atoms with a shorter <Hg–N> distance of 2.4549(15) Å at 300 K (Table S4, Supporting Information). The substitution of SCN⁻ with 4‐CNpy ligand around Hg(II) centers was due to the excess amount of 4‐CNpy in the synthesis. The Fe(II) centers exhibit elongated octahedral geometries, while Hg(II) centers show distorted tetrahedral geometries. These structural characteristics are in accordance with previously reported Fe(II)–Hg(II) networks in the literature.^{[ 39} , ⁴⁰ , ⁴¹ , ^{42 ]}

Figure 1.

a) Structural unit of 1 along the b‐axis with selected atom labels measured at 40 K. Legend: C grey; Fe, red; Hg, pink; N, blue; S, yellow. Thermal ellipsoids of 50% probability are shown. b) Superimposed structural units of 1 along the b‐axis measured at diverse temperatures. The arrows indicate the structural changes upon cooling. c) Temperature dependencies of average <Fe1–N_x> bond lengths and unit cell parameters in different vertical axis ranges along with B‐spline dotted lines as a guide to the eye. d) Crystal packing of 1 along the a‐axis measured at 80 K (left) and 90 K (right). Legend: high‐spin Fe (Fe^HS), red balls; low‐spin Fe (Fe^LS), blue balls; Hg, pink balls; µ‐SCN⁻, grey sticks; terminal SCN⁻, green sticks; 4‐CNpy ligand, black sticks. Hydrogen atoms in all structural figures were omitted for clarity.

It is noticeable that structural units and Fe–N distances evolve with temperature (Figure 1b–d; Tables S1,S2,S4 and S5, Supporting Information); superimposed structural units of 1 suggest the gradual movement of SCN⁻ ligands and a reduction in the distance between Fe(II) or Hg(II) centers and coordinated 4‐CNpy ligands with decreasing temperature (Figure 1b). Specifically, while Fe–N bond length decreases gradually when cooling from room temperature to 125 K, more abrupt changes in Fe–N bond length for all six Fe1–N_x bonds occur at the 80– 90 K temperature range evolving from <Fe1–N> = 2.1739(14) Å (300 K) and 2.1216(15) Å (90 K) to 1.9931(14) Å (80 K) and 2.009(3) Å (40 K) (Figure 1c; Tables S4 and S5, Supporting Information). Analogously, the unit cell parameters a, b, c, and volume V gradually decrease by 0.75, 1.08, 1.28, and 3.42% upon cooling from 300 to 90 K, respectively (Figure 1c; Tables S1 and S2, Supporting Information), while a far more significant decrease occurs between 90 and 80 K, especially for the a, b, and V parameters, shrinking by 1.16, 0.53, and 1.58%, while the c parameter remains nearly constant (0.02% shrinking). Moreover, the octahedral distortion analysis for Fe(II) centers using the OctaDist program reveals the angle (Σ) and torsional (Θ) distortions of Fe(II) centers experience a substantial reduction between 90 and 80 K upon cooling, a phenomenon similar to previous unit cell parameters evolutions (Figure S15, Table S10, Supporting Information).^{[ 43 ]} In contrast, Fe(II) centers show a negligible increase in distance (ζ) and tilting (Δ) distortion parameters in the range of 80–90 K. Such structural parameters and octahedral distortion alternations with temperature suggest a complete and abrupt SCO in the Fe(II) centers between 80 and 90 K. The crystal packing of 1 in Figure 1d reveals the existence of 1D chains along the a‐axis stabilized by van der Waals interactions, as well as the LS and HS Fe(II) centers in the crystal structures. Additionally, the phase purity of 1 is confirmed by powder X‐ray diffractogram (PXRD) measurements compared to the expected pattern calculated from the crystal structure at 300 K (Figure S16, Supporting Information).

2.2. Thermal and Optical Switchable Magnetic Properties

The product of molar magnetic susceptibility per Fe(II) center and temperature (χ _M T) for compound 1 reaches 3.5 cm³ K m ⁻¹ at 300 K (Figure 2a), corresponding to Fe(II) centers in the HS state (S = 2, g = 2.2, t_2g ⁴e_g ²). However, upon cooling, the χ _M T values exhibit a substantial decrease below 90 K, reaching a χ _M T value of 0.1 cm³ K m ⁻¹ at 10 K, indicating the presence of LS Fe(II) centers (S = 0, t_2g ⁶e_g ⁰). As such, the complete and abrupt SCO phenomenon can be observed for the Fe(II) centers supported by previous structural analysis. It should be noted that the cooling (T _↓) and heating (T _↑) transition temperature T _1/2 determined by the largest first derivative of χ _M T values is strongly correlated to the sweeping rate (Figure 2a; Figure S17, Supporting Information). Thermal hysteresis loops are observed in the cooling and heating processes, which become wider at higher sweeping rates, ranging from 6.6 (0.5 K min⁻¹), 7.3 (1 K min⁻¹), 10 (2 K min⁻¹) to 14 K (5 K min⁻¹). The linear fit for transition temperature T _1/2 as a function of sweeping rate during the cooling and heating processes reveals the extrapolation at an infinitely slow scan rate with cooling T _1/2 = 86 K and heating T _1/2 = 93 K (Figure S17c, Supporting Information). Notably, at a higher temperature sweeping rate, the system is capable of trapping the Fe(II) centers partially or fully in the HS states below the transition temperature, which is known as the temperature‐induced excited spin‐state trapping (TIESST) effect (Figure 2b; Figures S17 and S18, Supporting Information).^{[ 44} , ⁴⁵ , ^{46 ]} To be more specific, the ratios of HS Fe(II) centers (γ _HS ) calculated from the χ _M T values at around 10 K are tunable from ca. 0 (1–5 K min⁻¹), 2 (6.25 K min⁻¹), 10 (7.5 K min⁻¹), 27 (8.75 K min⁻¹), 39 (10 K min⁻¹), and 100% (quenching > 10 K min⁻¹); subsequently, the trapped HS states can be relaxed to the LS state by heating. Analogous to sweeping rate‐dependent transition temperatures T _1/2, the relaxation temperature T_TIESST , determined by the largest first derivative of χ _M T values upon heating after a trapping experiment, shifts to a higher temperature at a larger heating rate (Figure S18, Supporting Information). For example, the relaxation temperature T_TIESST alters from 63 (0.5 K min⁻¹), 66 (1 K min⁻¹), 69 (2 K min⁻¹), 74 (5 K min⁻¹) to 78 K (10 K min⁻¹) after trapping with fast cooling at 10 K min⁻¹ (Figure S18a, Supporting Information).

Figure 2.

a) Temperature dependences of χ _M T curves of 1 in the H _dc = 1000 Oe with different sweeping rates from 0.5 to 5 K min⁻¹. Inset: the χ _M T values in the zoomed temperature region. b) Temperature dependences of χ _M T plots of 1 in the H _dc = 1000 Oe after quenching (>10 K min⁻¹), fast cooling (10 K min⁻¹), and slow cooling (1 K min⁻¹), followed by heating in different sweeping rates from 0.5 to 5 K min⁻¹. c) Temperature dependencies of χ _M T curves of 1 in the H _dc = 1000 Oe after photoirradiation with indicated lasers at 10 K (LIESST effect) or photoirradiation for the metastable HS state excited by 532 nm laser (r‐LIESST effect), followed by heating. d) The LIESST and r‐LIESST efficiencies after photoirradiation with different lasers at 10 K.

Photomagnetic studies were conducted at 10 K to systematically investigate the influence of light on the Fe(II) spin state using various diode‐pumped solid‐state lasers (DPSS) (see details in the method section, Figure 2c,d; Figures S19–S22, Supporting Information). In particular, upon photoexcitation of the LS state at 10 K with 532, 658, and 1064 nm lasers, the χ _M T values increase significantly over time and reach saturation values of 2.8, 2.5, and 2.8 cm³ K m ⁻¹ after 20, 55, and 871 min, respectively, indicating LS Fe(II) centers can be converted to metastable HS Fe(II) centers (LIESST effect). These values are lower than the χ _M T value at room temperature due to the zero‐field splitting effect. After the LIESST effects, the lasers were switched off and sample 1 was heated. The χ _M T values increase with maximum values of 3.3, 3.1, and 3.2 cm³ K m ⁻¹ at ca. 60 K, respectively, followed by significantly decreased values due to the thermal relaxations into LS states and overlapping with the heating χ _M T vs T plot above 80 K (Figure 2c). The LIESST relaxation temperature T_LIESST , determined by the maximum first derivative of χ _M T values, is strongly dependent on the heating sweeping rate ranging from 72 (1 K min⁻¹), 75 (2 K min⁻¹), 80 (5 K min⁻¹) to 84 K (10 K min⁻¹) in the case of 658 nm photoirradiation, similar to T_TIESST (Figure S19, Supporting Information). Notably, lower‐efficiency LIESST effects are observed for 730 and 785 nm laser light excitations with smaller χ _M T values of 1.4 and 0.5 cm³ K m ⁻¹, respectively, at 10 K, as shown in Figure 2c. Reversibly, similar χ _M T values of 1.6 and 0.5 cm³ K m ⁻¹ can be reached after photoirradiation with both 730 and 785 nm laser lights (r‐LIESST effect) for the metastable HS state generated by 532 nm laser. To systematically explore the light‐dependent LIESST and r‐LIESST behaviors, ten laser lights ranging from visible (407 nm) to NIR regions (1064 nm) were applied to either photoirradiate the samples at 10 K (LIESST) or relax the fully excited metastable HS Fe(II) states (r‐LIESST) (Figure 2d; Figures S19–S22, Supporting Information). It is noteworthy that the most obvious LIESST effects occur in both visible (around 532 and 658 nm) and NIR (around 1064 nm) wavelengths, while both 785 and 840 nm lasers, positioned between the two aforementioned regions, induce the most pronounced r‐LIESST effect with ca. 87% efficiencies derived from corresponding χ _M T values at around 10 K.

To probe the underlying molecular origins contributing to LIESST and r‐LIESST effects, especially in the rarely investigated NIR region, the room‐temperature solid‐state UV‐vis‐NIR absorption spectrum of 1 was measured, revealing intense absorbance between 300–600 nm (visible region) and relatively weak absorbance in the 700–1200 nm range (NIR region) with a maximum at 855 nm (Figure S3, Supporting Information). The considerably weaker absorbance in the NIR region accounts for the substantially extended photoirradiation time from 20 (532 nm) to 240 (980 nm) and 871 min (1064 nm). First‐principles periodic density functional theory (DFT) calculations in VASP using representative crystal structures (300 K (HS model), 80 K (LS model), and 40 K after photoirradiation (40 K hv) with 658 nm light (metastable HS model)) without optimization, suggest that the calculated optical absorption spectra of 1 closely resemble the experimental spectra within the calculation approximations, despite with blueshift in peak positions (see Figure S3, Supporting Information).^{[ 47} , ⁴⁸ , ^{49 ]} Specifically, the maximum absorbance in the NIR region shows a blueshift from ca. 664 (300 K) to 698 nm (80 K), while the optical spectra of the HS model (300 K) and metastable HS model (40 K hv) are similar. Thus, theoretical calculations predict the maximum NIR absorbance at a higher wavelength for the LS structure. Additionally, the band structures and total and partial density of states (DOS) were calculated in first‐principles calculations (Figure 3a,b; Figures S4 and S5, Supporting Information). The band gap between the occupied valence bands and unoccupied conduction bands becomes narrower from 1.54 eV (805 nm) in the HS model (300 K) and 1.56 eV (795 nm) in the metastable HS model (40 K hv) to 1.47 eV (843 nm) in the LS model (80 K). Based on the partial DOS containing the atomic contributions to the band structures and the electronic densities for orbitals close to Fermi energy (Figure 3; Figures S4–S10, Supporting Information), the lowest electronic transitions in both spin‐up and spin‐down cases for the HS system (300 K, Δε = 1.54–1.85 eV, 670–805 nm) and metastable system (40 K hv, Δε = 1.56–1.80 eV, 689–795 nm) in the NIR region are almost identical and dominantly originate from the d–d transitions from Fe(II) orbitals. Nonetheless, in the LS system (80 K), the dominant lowest electronic transitions in the NIR region ranging from 1.47 (843 nm) to 2.10 eV (590 nm) reveal the metal‐to‐ligand charge transfer (MLCT) from Fe(II) 3d orbitals to 4‐CNpy π orbitals as well as ligand‐to‐ligand charge transfer (LLCT) from SCN⁻ p orbitals to 4‐CNpy π orbitals. The higher‐energy transitions close to the visible region for the HS system (300 K, Δε = 1.78–2.21 eV, 561–697 nm) and metastable HS system (40 K hv, Δε = 1.69– 2.12 eV, 584–734 nm) mainly originate from MLCT (from Fe(II) 3d orbitals to 4‐CNpy π orbitals) and LLCT (from SCN⁻ p orbitals to 4‐CNpy π orbitals), while in the LS system (80 K), the dominant transitions in the visible region range from 2.08 (596 nm) to 2.65 eV (468 nm), attributed to d–d transitions in Fe(II) orbitals. Therefore, the LIESST effects in the NIR region (e.g., 980 and 1064 nm hv) can be primarily ascribed to charge transfer (MLCT and LLCT) processes, whereas d–d transitions of Fe(II) metals start to dominate for the LIESST effect in the visible region (e.g., 532 and 658 nm hv). Meanwhile, the origins of r‐LIESST effects in the NIR region (e.g., 785 and 840 nm hv) are more likely due to a non‐trivial combination of both d–d transitions and charge transfer (MLCT and LLCT) processes.

Figure 3.

The band structures (left) and total and partial density of states (DOS, right) in the zoomed regions calculated in first‐principles calculations using crystal structures of 1 at 300 K a) and 80 K (b). The green dashed lines and arrows indicate the Fermi energy and band gap, respectively. The electronic densities in yellow and blue colors for orbitals 274 (0.00 eV) and 275 (1.47 eV) in first‐principles calculations using crystal structures of 1 at 300 K c) and 80 K d). Colors: Fe^HS, red balls; Fe^LS, blue balls; Hg, pink balls; S, yellow balls; C, dark grey balls; N, light grey balls; H, light orange balls. The arrows indicate the electronic transitions from orbital 274 to orbital 275.

2.3. Terahertz Absorbing Properties and First‐Principles Calculations

Room‐temperature THz absorption spectra for powders of 1 were measured using THz‐TDS to investigate the low‐frequency phonons within the range of 0.5–1.5 THz. Consistency and reproducibility were confirmed by measuring the THz absorption spectra of pellets of 1 for multiple masses and thicknesses (Figure S23, Supporting Information). Increasing the amount of sample placed between the holders resulted in a simultaneous increase in absorbance without altering the peak position (fitted with Lorentzian functions). The THz absorption spectrum in the low‐frequency range at 300 K predominantly reveals three peaks: a broad peak β (0.70 THz), a sharp peak γ (0.85 THz), and another broad peak δ (1.05 THz) (Figure 4a). Upon cooling at 2 K min⁻¹ sweeping rate, temperature‐dependent THz absorption spectra and the corresponding colormap reveal a conspicuous blueshift to higher frequencies (gradual shrinkage in crystal structural unit cell parameters and volumes), increased intensity (decrease in anharmonic thermal vibrations), as well as the appearance of new phonons (SCO phenomenon), featuring five dominant peaks α (0.58 THz), β (0.93 THz), γ (0.99 THz), δ (1.25 THz), and ε (1.37 THz) at 10 K (Figure 4a–d). These changes are reversible and recoverable to the previous spectrum at 300 K during the heating process (Figure 4b; Figure S24, Supporting Information). In particular, analysis of the THz absorbances at 0.58, 0.93, and 1.37 THz along with peak position evolutions with temperature indicates that the most substantial changes occur between 80 and 70 K in the cooling process and between 80 and 90 K during the heating process, reasonably consistent with the transition temperature T _1/2 ≈ 84 K (cooling, 2 K min⁻¹) and 94 K (heating, 2 K min⁻¹) with 10 K hysteresis width determined from magnetic studies. Peak γ below 80 K exhibits slight fluctuations in its intensity, likely attributable to strong signals, which may induce saturations and contribute to intensity uncertainties. Of note is the approximately linear increase in three peak frequencies up to 118 (peak β, 0.6 GHz K⁻¹), 76 (peak γ, 0.3 GHz K⁻¹), and 160 GHz (peak δ, 0.7 GHz K⁻¹) from 300 to 80 K (Figure 4d, left). Moreover, the reversibility and reproducibility can be confirmed in Figure 4d (right) after repeating three cooling‐heating cycles. These suggest the new emergence of peaks α and ε and the substantial blueshift (peaks β, γ, and δ) around the transition temperature are associated with the SCO‐induced structural changes. These features, together with exceptional reproducibility, suggest potential thermometric applications in the THz region, originating from the shrinkage in unit cell parameters and volume.

Figure 4.

Temperature dependencies of THz absorption spectra of 1 during cooling a) and heating b). Inset: the absorbances at ≈0.58 (peak α), 0.99 (peak γ), and 1.37 THz (peak ε) with temperature. c) Colormap depicting THz absorbance as a function of frequency and temperature. The blue and red dashed lines indicate the cooling and heating transition temperatures determined in the magnetic experiment. d) The linear fit (colored lines) for peak positions (colored dots) determined from fitted THz absorption spectra during the cooling process by using Lorentz functions as a function of temperature (left). The 99.9% confidence bands are indicated in colored bands. Repeatability of peak positions for peaks β, γ, and δ within three cooling‐heating cycles (right). e) Vertical bars showing the position and relative intensities of the representative IR active phonon modes a for 1 at 80 K and b at 300 K in the indicated region. The frequencies and IR‐active intensity of each phonon mode are listed in the Supporting Information. f) Calculated total phonon density of states (DOS) in light blue colored peaks of 1 for crystal structures at 80 K and its partial phonon DOS of Hg, pink colored peaks; Fe, red line; C, dark grey line; N, blue line; S, orange line; H, light grey line. g) Atomic motion projections of the phonon modes for the representative phonon mode a‐7 at 0.948 THz. Color: Fe, blue balls; Hg, pink balls; µ‐SCN⁻, grey sticks; terminal SCN⁻, green sticks; 4‐CNpy ligand connected to Fe centers, blue sticks; 4‐CNpy ligand connected to Hg centers, black sticks. The orange arrows indicate the vibration vectors. Hydrogen atoms are omitted for clarity.

To comprehensively elucidate the origins of these THz absorbance peaks, periodic ab initio calculations through VASP were performed using crystal structures of 1 at 80 and 300 K to obtain corresponding phonon modes a for the LS system (80 K) and b for the HS system (300 K), respectively (Figure 4e–g; Figures S28–S30, Table S11, Supporting Information).^{[ 47} , ⁴⁸ , ^{50 ]} The calculation details are provided in the method section and Supporting Information. The computed phonon modes in the range of 0–1.5 THz range consist of primary IR‐active phonon modes a for crystal structure at 80 K: 0.423 (a‐1), 0.940 (a‐6), 0.948 (a‐7), 0.980 (a‐8), 1.251 (a‐14), and 1.339 (a‐16), and phonon modes b for crystal structure at 300 K: 0.376 (b‐1), 0.743 (b‐6), 0.914 (b‐9), 1.132 (b‐15), 1.254 (b‐18), and 1.358 (b‐20) (Figure 4e; Table S11, Supporting Information). The calculation results exhibit a phonon distribution comparable to the experimental THz peaks with phonon modes a‐1 and b‐1 assigned to experimental peak α, modes a‐6 and b‐6 assigned to peak β, modes a‐7, a‐8, and b‐9 assigned to peak γ, modes a‐14, b‐15, and b‐18 assigned to peak δ, as well as a‐16 assigned to peak ε. The higher frequencies observed for phonon mode a (80 K) compared to phonon mode b (300 K) corroborate with the blueshift in peak positions upon cooling. Moreover, the larger difference in frequency (171 GHz) between phonon modes b‐6 and b‐9, in contrast to the 8 GHz difference for a‐6 and a‐7, reliably reproduces the experimental larger peak position differences between peaks β and γ at 300 K (151 GHz) relative to 80 K (65 GHz). The experimental weak intensity of peak α can be accounted for by the weak infrared intensities in phonons a‐1 and b‐1. Due to the much lower frequency and infrared intensity of mode b‐1 compared to a‐1, it predicts that peak α might exist below 0.5 THz with weak intensity out of the measurement range and detection limit, thus explaining the absence of peak α in the THz absorption spectra at room temperature. Meanwhile, the higher intensity of a‐6 and a‐7, with respect to b‐6 and b‐9, concurs with the experimentally observed increase in intensity after cooling. The reliable reproduction of the experimental peak positions and intensities for both HS and LS systems confirms the validity of the phonon calculations. Further analysis of the total and partial phonon density of states (phonon DOS) in the low‐frequency region indicates similar distributions of partial DOS of atoms for both HS and LS systems with the largest contribution to the total phonon DOS in the sub‐terahertz region (<1 THz) originating from Hg atoms, followed by C, N, S, and Fe atoms (Figure 4f; Figure S28, Supporting Information). However, the contributions from C, N, and S start to surpass those from Hg atoms in the range of 1.0–1.5 THz. Based on the visualization of the atomic movements (Figure 4g; Figure S29, Movies S1 and S2, Supporting Information), the major phonon vibrations in the low‐frequency region of 1 for both HS and LS states are generally quite similar and can be interpreted as the swaying or translational modes of SCN⁻ and 4‐CNpy ligands together with the Fe(II) and Hg(II) metal ions. The involvement of translational vibrations of Fe(II) centers with coordinated SCN⁻ can explain the SCO‐induced substantial tunability of THz absorbing properties.

Following the photomagnetic investigations on the LIESST and r‐LIESST effects for compound 1, the THz absorbing properties after photoirradiation at 10 K were investigated with four representative lasers based on photomagnetic studies (532, 658, 785, and 1064 nm) (Figure  5 ; Figure S25 and S26, Supporting Information). As depicted in Figure 5a,b, after photoirradiation with 658 nm for 45 min, peaks α and ε, as characteristic THz absorbance for the LS state, disappear and peaks β and γ significantly shift to lower frequency due to the conversion from LS Fe(II) centers to the metastable HS state (LIESST effect). Upon heating the metastable HS 1 from 10 to 100 K in 2 K min⁻¹, peaks α and ε gradually increase in intensity due to relaxation into the LS state, reaching maximum intensity at ca. 70 K, followed by a drastic decrease after 80 K (Figure S25, Supporting Information). Conversely, the plot of absorbance vs T for peak β at 0.82 THz shows absorbance increases with 658 nm photoirradiation time, decreases significantly upon heating, and finally overlaps with the cooling plot after ca. 60 K (Figure 5a). Similar to 658 nm photoirradiation, the THz absorption spectra reveal similar changes after irradiating with 532 and 1064 nm lights (Figure S25, Supporting Information). It should be noted that the THz absorption spectra after visible (532 and 658 nm) and NIR (1064 nm) laser excitations are similar, which suggests similar structural arrangements after photoexcitations. However, the photoirradiation time required for reaching a stable metastable HS state is much longer for 1064 (90 min) than 532 (30 min) and 658 nm (45 min), which is in good agreement with the photomagnetic studies due to the relatively low absorbance in the NIR region compared to visible light. The extraordinary switchability and reversibility for THz absorbance at 0.82 THz (peak β) and 1.37 THz (peak ε) during photoirradiation with either 532, 658, or 1064 nm lasers at 10 K, followed by thermal relaxation, is depicted in Figure 5c. The additional photoirradiation using a 785 nm laser for the metastable HS state generated by 658 nm light is capable of increasing the intensity of characteristic LS THz absorbing peaks α and ε, suggesting the observation of the r‐LIESST effect in the THz region (Figure S26, Supporting Information). The alternative excitations of sample 1 at 10 K by 658 nm (LIESST effect) and 785 nm (r‐LIESST effect) lights allow reversible modulation of peak intensity and positions with good reproducibility in three cycles (Figure 5d; Figure S26, Supporting Information). This presents the first detection of the r‐LIESST effect in the THz region and proves the feasibility of reversibly switching THz absorbing properties by selectively applying different wavelengths in the visible and NIR range.

Figure 5.

a) The THz absorption spectra of 1 after photoirradiation with 658 nm for 0, 15, and 45 min at 10 K, followed by heating to 100 K. Inset: the THz absorbance with the temperature at 0.82 THz (peak β) during cooling (T _↓), photoirradiation (hν) with 658 nm laser light, followed by heating up to 100 K (T _↑). b) Colormap for THz absorbance after photoirradiation (hν) using 658 nm laser light with time at 10 K and heating up to 100 K (T _↑). The white gap represents the separation between photoirradiation and the heating process. c) The THz absorbance at 0.82 THz (peak β) and 1.37 THz (peak ε) during photoirradiation (hν) with 658 (red), 532 (green), and 1064 nm (grey) laser lights at 10 K, followed by heating up to 60 K (T _↑) for relaxation. d) The THz absorbance in 0.82 THz (peak β) and 1.37 THz (peak ε) during photoirradiation (hν) with 658 (red) and 785 nm (wine) within three LIESST and reverse‐LIESST cycles. e) The THz absorption spectra of 1 at 100 K (orange line) cooled down in 2 K min⁻¹, at 10 K after photoirradiation with 532 (green line), 658 (red line), and 1064 nm (grey line), at 10 K after quenching (blue line) with flash 20 K min⁻¹ cooling sweeping rate, and at 10 K (violet line) cooled down in 2 K min⁻¹. f) Average <Fe1–N_x> bond distances (red dots) and unit cell volumes (blue dots) obtained in the indicated crystal structures. g) Superimposed structural units along the b‐axis measured for crystal 1 at 40 K after photoirradiation with 532 (green sticks, 1@40K(532 nm)), 658 (red sticks, 1@40K(658 nm)), and 1064 nm (grey sticks, 1@40K(1064 nm)), at 40 K after quenching (blue sticks, 1@40K(quench)) with flash 50 K min⁻¹ cooling sweeping rate.

Additionally, the TIESST effect in the THz region was also investigated by quenching the sample at a flash cooling sweeping rate (Figure 5e; Figure S27, Supporting Information). The resulting quenched THz absorption spectrum exhibits the negligible intensity of peak ε and can recover back to the THz absorption spectrum for the LS state system at 70 K by thermal relaxation, which concurs with the HS state in the magnetic studies (Figure S27, Supporting Information). Remarkably, notwithstanding similar spectra shape, a notable shift to a higher frequency was observed for the quenched spectrum, compared to those induced by photoexcitation with 532, 658, and 1064 nm lights, suggesting similar structural arrangements with distinct unit cell parameters between quenched and photoexcited states. This study represents the first detection of such structural differences using the THz‐TDS technique, leveraging its exceptional sensitivity to structural modifications.

2.4. Photocrystallographic Analysis

Photocrystallographic studies were conducted at 40 K following irradiations with DPSS lasers at the BL02B1 beamline of the SPring‐8 synchrotron to explore the structural changes in the LIESST and r‐LIESST effects (Figure 5f,g; Figure S13, Tables S3,S6 and S9, Supporting Information). The generation of photoexcited metastable HS Fe(II) centers in the LIESST effect is confirmed by the determination of crystal structures at 40 K after excitations with 532 (1@40K(532 nm)), 658 (1@40K(658 nm)), and 1064 nm (1@40K(1064 nm)) lasers. They reveal characteristic HS <Fe1–N> distances of 2.154(3), 2.148(2), and 2.155(2) Å as well as HS unit cell volumes of 1964.05(6), 1958.83(5), and 1962.91(5) ų, respectively (Figure S13, Tables S3 and S6, Supporting Information). Meanwhile, the achieved LS Fe(II) centers in the r‐LIESST effect are further testified by the determined crystal structures at 40 K by excitations with 785 nm for the metastable HS states achieved by 30 min irradiations using lasers at 532 (1@40K(785nm_1)) or 658 nm (1@40K(785nm_2)) at 40 K (Figure S13, Tables S3 and S6, Supporting Information). As such, both of them have similar LS <Fe1–N> distances of 2.047(3) and 2.067(2) Å as well as unit cell volumes of 1927.34(7) and 1926.43(6) ų, respectively (Tables S3 and S6, Supporting Information). Nevertheless, it should be noted that they are slightly higher than the <Fe1–N> distance (2.009(3) Å) and volume (1913.21(8) ų) in the LS crystal structure at 40 K (1@40K), which correspond well with the 87% r‐LIESST efficiencies stated in aforementioned photomagnetic studies.

To get insights into potential crystal structural similarity and disparity of compound 1 between the metastable HS state (LIESST effect) and the quenched state (TIESST effect), the crystal structures were also determined at 40 K after a flash cooling (1@40K(quench)) from 100 to 40 K directly in a 50 K min⁻¹ sweeping rate (Figure 5f,g; Figure S13, Tables S3,S6 and S9, Supporting Information). Despite all structures showing similar crystal packing and structural packing (Figure 5g), the distinct unit cell parameters and bond distances (especially the Fe1–N_x bond) reveal differences in crystal structures (Figure 5f; Tables S3 and S6, Supporting Information). For instance, the structures after photoirradiation with 532, 658, and 1064 nm lasers show characteristic HS average <Fe1–N> distances of 2.154(3), 2.148(2), and 2.155(2) Å at 40 K, respectively, comparable with 2.1467(13) Å in the crystal structure at 100 K (1@100K), confirming the HS nature of Fe(II) centers. However, the <Fe1–N> distances in the quenched state (1@40K(quench)) reveal a shorter <Fe1–N> distances of 2.075(2) Å at 40 K, which situated between the distances of HS (2.1467(13) Å in 1@100K) and LS (2.009(3) Å in 1@40K) crystal structures. Moreover, the volume (1937.94(4) ų in 1@40K(quench)) after quenching exhibits similar trends with <Fe1–N_x> bond length, located between HS crystal structures at 100 K (1965.55(4) ų in 1@100K) or after photoirradiation (e.g., 1964.05(6) ų in 1@40K(532 nm)) and LS crystal structure (1913.21(8) ų in 1@40K), correlate well with the intermediate THz peak position between HS and LS THz spectra (Figure 5e; Tables S3 and S6, Supporting Information).

The crystal structures before and after photoirradiation, together with THz‐TDS, play a pivotal role in comprehending the various switching properties (LIESST, r‐LIESST, and TIESST effects) in the SCO materials. Overall, this investigation underscores the immense potential of the THz‐TDS as an effective tool for detecting subtle changes in molecular fingerprints and arrangements, offering valuable insights into structural, magnetic, and photomagnetic properties. This technique demonstrates substantial potential for application to other switchable materials, offering opportunities for further investigations.

3. Conclusion

In this work, a complete SCO material {[Fe(4‐CNpy)₂][Hg(SCN)₃(4‐CNpy)]}_n crystallized in 1D chains was strategically designed to achieve the first example of thermal‐ and photo‐responsive ON‐OFF switchable THz absorbance reversibly through the spin manipulations of Fe(II) center. The spin‐switching properties triggered by temperature variations (slow and flash cooling TIESST effects) and light exposure (LIESST and r‐LIESST effects ranging from visible to NIR lights) are in exceptional agreement with (photo)crystallographic and THz absorbing studies. Particularly, similar to photoirradiations with visible light (532 and 658 nm), metastable HS states using NIR 1064 nm are also highly efficient, corresponding to the MLCT and LLCT from Fe(II) 3d orbitals and SCN⁻ p orbitals to 4‐CNpy π orbitals, respectively. Further investigations into the detailed dynamic mechanisms using time‐resolved ultrafast techniques, as well as comparing different time scales of multiple spin states using various visible and NIR lights, or with even higher wavelengths, can be another intriguing topic for future research. THz‐TDS, as a powerful and precise tool for detecting intricate structural evolutions, elucidates the structural resemblance between metastable HS structures after visible or NIR light excitations and dissimilarities between quenched and photoexcited HS states, in agreement with the photocrystallographic studies. Periodic ab initio calculations reliably reproduce the experimental THz absorption spectra and allow us to interpret the phonon modes in the low‐frequency THz region strongly involved with Fe(II) centers, highlighting the likely presence of spin‐phonon coupling effects. This work deepens our understanding of the intersection between crystal structures, spectroscopic properties, especially in the THz region, and external stimuli such as temperature and light in SCO systems. Moving the SCO transition temperature to a desired range and maximizing the difference between ON and OFF states should be able to be tailored by modifying the structure and composition of these materials, as identified by the strong structure‐property relationships discussed here, which provides a route to improve the applicability of these materials.

4. Experimental Section

Materials and Physical Measurements

All chemicals used in syntheses were bought from commercial sources (Wako Pure Chemical Industries, Ltd., Sigma‐Aldrich, and TCI Chemicals) without further purification. K₂[Hg(SCN)₄]·H₂O salt was prepared according to the literature procedure.^{[ 51 ]} Elemental analysis (C, H, N) was conducted with an Elementar Analysensysteme GmbH: Vario MICRO cube. The infrared (IR) absorption spectra were collected with a JASCO FT/IR‐4100 spectrometer for samples dispersed in the KBr pellet. Solid‐state UV‐vis‐NIR diffuse‐reflectance spectra were recorded for samples smashed on the surface of a cellulose disc with a JASCO V‐670 UV‐vis spectrophotometer equipped with an ISN‐723 integrating sphere accessory. The THz wave absorption measurements were conducted by using Advantest TAS7400TS THz Time‐domain Spectroscopy working in the transmittance mode for different amounts of powdered samples compressed into pellets with varied thicknesses. The temperature‐dependent THz absorption spectra were determined for the powdered sample immersed in paraffin sandwiched between two transparent polyethylene plates and placed inside the liquid‐helium‐cooled MicrostatHe (Oxford Instruments) connected to the digital temperature controller MercuryiTC (The sweeping rate was set to 2 K min⁻¹). Photoirradiation studies of THz absorption spectra were performed at 10 K by using DPSS laser sources of 532 (P ≈11 mW cm⁻²), 658 (P ≈10 mW cm⁻²), 785 nm (P ≈4 mW cm⁻²), and 1064 nm (P ≈10 mW cm⁻²). For improving photoirradiation efficiency, the pellets with a smaller thickness by reducing the amount of sample 1 and adding more paraffin were applied in the photoirradiation studies for the THz absorption spectra. Thermogravimetric analysis was performed on a Rigaku Thermo Plus TG8120 in the 25–400 °C range in dry air with a 2 °C min⁻¹ heating rate and Al₂O₃ was used as reference material. Magnetic studies were performed with a Quantum Design MPMS XL magnetometer on powder samples inside a polyethylene bag at a sweeping rate from 0.5 to 10 K min⁻¹ in the sweep mode. The quenching measurements were performed by fast cooling the sample from room temperature to 5 K (sweeping rate > 10 K min⁻¹), followed by heating the quenched sample 1 at a sweeping rate from 0.5 to 10 K min⁻¹. Photomagnetic studies were conducted at 10 K on about 1 mg of samples in the form of a 3 mm diameter spot blocked by two pieces of transparent tape and mounted in the probe connected by optical fiber to DPSS laser source of 407 (P ≈149 mW cm⁻²), 473 (P ≈122 mW cm⁻²), 532 (P ≈147 mW cm⁻²), 658 (P ≈130 mW cm⁻²), 705 (P ≈158 mW cm⁻²), 730 (P ≈144 mW cm⁻²), 785 (P ≈133 mW cm⁻²), 840 (P ≈167 mW cm⁻²), 980 (P ≈153 mW cm⁻²), and 1064 nm (P ≈110 mW cm⁻²) laser lights. All magnetic measurements were corrected for the diamagnetic contribution of the sample holders and the constituent atoms (Pascal's tables).^{[ 52 ]}

The Preparation of [Fe(4‐cyanopyridine)₂][Hg(SCN)₃(4‐cyanopyridine)]₂ (1)

The 0.8 mm of 4‐cyanopyridine (4‐CNpy) dissolved in 6 mL of methanol (MeOH) was mixed with 0.2 mm of Fe(BF₄)₂·6H₂O in 6 mL of methanol to produce a yellow solution. Meanwhile, 0.2 mm of K₂[Hg(SCN)₄]·H₂O was dissolved in 4 mL deionized water to obtain transparent solutions containing the [Hg(SCN)₄]²⁻ ions. This solution was added to the iron(II) complex solution, resulting in a yellow solution. The solution was left for slow evaporation. The yellow crystals were obtained after two weeks, filtered, and dried under air to obtain the air‐stable products and used for further investigations.

Yield: 42.4 mg (34% based on Hg). Anal. Calcd for FeHg₂C₃₀H₁₆N₁₄S₆ (1, molar mass = 1221.96 g m ⁻¹): C, 29.49%; H, 1.32%; N, 16.05%. Found: C, 29.26%; H, 1.03%; N, 16.05%. FT‐IR (KBr, cm⁻¹): 2239w [ν(C≡N)_4‐CNpy], 2132 vs [ν(C≡N)_SCN]. Raman (crystal, cm⁻¹): 2237 vs [ν(C≡N)_4‐CNpy], 2141w, 2132w [ν(C≡N)_SCN].

Single Crystal and Powder X‐ray Diffraction

Data were collected for crystals from 300 to 40 K at a sweeping rate of 2 K min⁻¹. The crystals were submerged in a paratone‐N oil and mounted with a 100 µm Dual Thickness Micro Mount loop on a 4‐axis (ψ, υ, φ, 2θ) diffractometer from beamline BL02B1 in Super Photon ring‐8 GeV (SPring‐8). The beamline used 30 keV synchrotron X‐rays (λ = 0.4131 Å) from the bending magnet source incident onto a double‐crystal monochromator. Crystallographic measurements at 40 K were initially conducted in the dark (1@40K), followed by photocrystallographic studies after 30 min irradiations using DPSS laser sources at 532 (1@40K(532 nm), P ≈158 mW cm⁻²), 658 (1@40K(658 nm), P ≈82 mW cm⁻²), and 1064 nm (1@40K(1064 nm), P ≈127 mW cm⁻²). After each photoirradiation, the sample was relaxed at 80 K, then cooled back down to 40 K in the dark, with recovery to the initial state confirmed by crystal structure determination at both temperatures. Moreover, after 30 min irradiations using lasers at 532 or 658 nm at 40 K, additional photoirradiations using 785 nm lasers (P ≈78 mW cm⁻²) were also conducted for transforming the metastable HS states to LS states, which can be referred to as 1@40K(785nm_1) and 1@40K(785nm_2), respectively. In addition, the quenched crystal structure at 40 K of 1 (1@40K(quench)) was determined through flash and direct cooling from 100 to 40 K at the sweeping rate of 50 K min⁻¹. All unit cell determination and data reduction were performed using the CrysAlisPro program.^{[ 53 ]} Structures were solved by direct methods using the SHELXT 2018/2 and refined using an F ² full‐matrix least‐squares method of SHELXL 2019/3 included in the OLEX‐2 1.5 software package.^{[ 54} , ^{55 ]} All atoms, except hydrogens, were refined anisotropically. Hydrogen atoms were positioned with idealized geometry and refined using a riding pattern. Crystal data, data collection, refinement parameters, and selected distances and angles for 1 were listed in the Supporting Information. CCDC records 2418849 (for 1@300K), 2418850 (for 1@275K), 2418851 (for 1@250K), 2418852 (for 1@225K), 2418853 (for 1@200K), 2418854 (for 1@175K), 2418855 (for 1@150K), 2418856 (for 1@125K), 2418857 (for 1@100K), 2418858 (for 1@90K), 2418859 (for 1@80K), 2418860 (for 1@40K), 2418861 (for 1@40K(quench)), 2418862 (for 1@40K(532 nm)), 2418863 (for 1@40K(658 nm)), 2418864 (for 1@40K(1064 nm)), 2418865 (for 1@40K(785nm_1)), and 2418866 (for 1@40K(785nm_2)) contained the supplementary crystallographic data. These data could be obtained free of charge from the Cambridge Crystallographic Data Center via www.ccdc.cam.ac.uk/data_request/cif. The structural models presented as figures were generated using the CCDC Mercury 2023.2.0 visualization software.^{[ 56 ]} Powder X‐ray diffraction patterns of all samples were recorded with a RIGAKU Miniflex600 diffractometer equipped with monochromated Cu‐Kα radiation (λ = 1.541 Å).

Theoretical Calculations

Periodic electronic structure and phonon calculations were performed for 1 utilizing crystal structures obtained at 80 K (low‐spin, LS model) and 300 K (high‐spin, HS model) by using the Vienna ab initio simulation package (VASP).^{[ 47} , ^{48 ]} The electronic structure calculations were conducted in a self‐consistent field (SCF) energy convergence of 10⁻⁶ eV with Gaussian smearing (smearing value of 0.05 eV) for the spin‐polarized structures at 300 K (HS model) and 40 K after photoirradiation with 658 nm light (metastable HS model) and non‐spin‐polarized 80 K structure (LS model) with the assistance of VASPKIT package.^{[ 49 ]} For phonon mode calculations, the input structures in the 1 × 1 × 1 unit cell were fully optimized with a convergence energy of 10⁻⁶ eV and the maximal residual forces on each atom less than 0.01 eV Å⁻¹ at first. The optimized 1 × 1 × 1 structures of 1 were used for phonon calculations by the direct method implemented in the Phonon code with displacements of 2 pm.^{[ 50 ]} The correlation energy was calculated using the generalized gradient approximation developed by Perdew, Burke, and Ernzerhof (GGA‐PBE).^{[ 57 ]} A plane‐wave basis set was used with the cut‐off energy of 400 eV throughout the phonon calculations. The k‐mesh of 2 × 2 × 1 for 1 was used for the Brillouin zone samplings, respectively.

Conflict of Interest

The authors declare no conflict of interest.

Supporting information

Supporting Information

Supplemental Movie 1

Supplemental Movie 2

Li G., Stefanczyk O., Kumar K., et al. “Stimuli‐Responsive Low‐Frequency Terahertz Absorption ON‐OFF Switchability in Spin‐Crossover Material.” Adv. Mater. 37, no. 38 (2025): 37, 2507457. 10.1002/adma.202507457

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.