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In this review, the importance of the Dzyaloshinskii–Moriya Interaction (DMI) to the magnetic properties of quantum spin systems is discussed mainly focusing on the determination of or understanding the role of DMI extracted from high-frequency high-field electron spin resonance (ESR) measurements. This review includes the ESR theories of the S = 1/2 one-dimensional (1D) antiferromagnet with the staggered field (Oshikawa–Affleck theory) and with the uniform DMI, and several related experimental results are shown. Then, the proposed mechanisms of the singlet–triplet transition in quantum spin systems together with the ESR selection rules are introduced in connection with various experimental results. Finally, the role of DMI in the ground state of kagome lattice antiferromagnets and the honeycomb lattice antiferromagnet is discussed with some experimental results.

We have developed a pressure calibration method in the high-pressure THz ESR system using induction coils set outside the pressure cell. The pressure is calibrated using alternating current (AC) magnetization measurements of the superconducting transition temperature of tin set inside the pressure cell with an ESR sample. The system fits the developed pressure cell with a wide frequency range of 0.05–0.8 THz. The pressure range was extended to 2.8 GPa. The ESR system was applied to the well-known cobalt Tutton’s salt $$({\text {NH}}_{4})_{2} {\rm {Co}}({\text {SO}}_{4})_{2}\cdot {\rm {6H}}_{2} {\text {O}}$$ , and its g principal values at 0 GPa were determined as $$g_{1}=6.61$$ , $$g_{2}=3.05$$ , and $$g_{3}=2.94$$ for the first time. Furthermore, we succeeded in observing the large change in these g values with pressure.

In solid-state physics, pressure is an essential parameter, which can continuously change the interaction between electrons. The combination of terahertz electron spin resonance (THz ESR) with pressure is a powerful approach to clarify the spin state under pressure from the microscopic point of view, especially for quantum magnets. The most important feature of our high-pressure THz ESR system is that our pressure cell ensures the high pressure and wide frequency range using ceramics in internal parts, which are well balanced in terms of toughness and transmittance of electromagnetic waves. This approach allowed to very accurately describe the spin state under pressure. In this review, high-pressure ESR systems are reviewed with a focus on those in the high-frequency region. In addition, we show differences between other systems and our system. Moreover, we show the usefulness of our system by showing application examples of several magnetic materials of interest.

THz electron spin resonance (ESR) measurements of the spinel compound GeCo2O4, which consists of the Co2+ pyrochlore structure, were performed. The temperature dependence measurements revealed new antiferromagnetic phases, AF1 and AF2, below TN. Moreover, a wide magnetic field range of ESR study using a single crystal at 1.8 K also revealed various field-induced phases due to the competition between the spin–lattice coupling and the spin frustration. Critical field resonances were observed at 5.0 T, 8.6 T, and 11.0 T for B//[111] and 5.1 T, 7.7 T, 11.2 T, and 13.0 T for B//[110] at 1.8 K. Although it became difficult to observe ESR above 86 K, the g-values of Co2+ ions were estimated to be g[111] = 3.34 and g[110] = 3.27 for [111] and [110], respectively, from the observed ESR mode above the saturation field at 1.8 K. Detailed frequency-field diagrams of the ESR modes at 1.8 K suggested the existence of spin–lattice coupling energy of 250 GHz (= 1.03 meV = 12 K) at the critical field resonances. The spin gap mode in the frequency-field diagram at 1.8 K showed excitation energies of E[111] = 1004 GHz (= 4.15 meV = 48 K) and E[110] = 1044 GHz (= 4.32 meV = 50 K) for [111] and [110], respectively. These results will be discussed in connection with the di-tetramer model suggested previously.

KCuCl$_3$ is known to show a quantum phase transition from the disordered to antiferromagnetically ordered phases by applying pressure. There is a longitudinal excitation mode (Higgs amplitude mode) in the vicinity of the quantum critical point in the ordered phase. To detect the Higgs amplitude mode, high-pressure ESR measurements are performed in KCuCl$_3$. The experimental data are analyzed by the extended spin-wave theory on the basis of the vector spin chirality. We report the first ESR detection of the Higgs amplitude mode and the important role of the electric dipole described by the vector spin chirality., 24 pages, 12 figures

The flashback of the investigation of CuGeO3 doped with magnetic impurities carried out by high-frequency EPR brings to light physics still actual for one-dimensional S = 1/2 quantum spin chains and covering a vast area from disorder-driven quantum critical phenomena to a new type of magnetic oscillations. It is shown that a key opening the door for a better understanding of this field of research is the Oshikawa and Affleck (OA) theory and, especially, following from it the universal link between the line width and g factor. The most puzzling problem appears around the staggered field, which contributes to different physical properties and serves as a driving force in the onset of anomalous growth of the line width and g factor at low temperatures. Accent is made on unsolved problems still providing a challenge for the theoretical explanation, including the genesis of the staggered field in doped systems, the contribution of the staggered magnetization to the integrated intensity, and spin susceptibility of a Griffiths phase and its magnetic properties on the nanoscale. A new type of magnetic oscillations, having explanation neither in OA theory nor within the framework of the semi-classical magnetization motion, is described in detail. This experimental finding poses the most difficult case and a touchstone for theory, as long as the corresponding modes of magnetic oscillations may be likely treated as violating Landau–Lifshits equation of motion.

In this review, mechanically detected electron spin resonance (MDESR) in the terahertz (THz) region is described to demonstrate its usability as a novel methodology for obtaining microscopic insights into local electronic structures. Using micromechanical devices, the sensitivity to a small-volume sample is greatly enhanced even for a cavityless setup. Moreover, there are plenty of options in the setup of MDESR, including detection modes, mechanical devices, and detection techniques. ESR spectroscopy of single-crystalline, powder, and frozen solution samples in the THz region are demonstrated.

Cerium hexaboride attracts attention of solid-state community for almost 50 years. Nowadays, this material is considered as a unique example of a system with orbital ordering resulting in formation of low-temperature magnetic phase with quadrupolar order, the so-called antiferroquadrupole phase. In crystal electric field 4f 1 state of Ce3+ splits into Γ7 doublet and Γ8 quartet, the latter is believed to be the ground state, as long as just Γ8 allows quadrupolar effects. An additional tool for studying rich physics of CeB6 appeared since the discovery in this material the ESR, which is specific to antiferroquadrupole (AFQ) phase and is missing in the paramagnetic phase. In the present review, we have brought together electron spin resonance and inelastic neutron scattering data, which allowed obtaining most detailed structure of the magnetic resonance modes in the AFQ phase in a wide-frequency range up to 0.6 THz. It is shown that apart paramagnetic resonance main mode with homogeneous precession of the magnetization, there are antiferromagnetic resonance modes as well, some of them existing in the AFQ phase. Analysis of the g factors demonstrates that available theories based on Γ8 ground state are facing difficulties with accounting experimental data, thus providing a challenge for developing of a theory correctly describing dynamic magnetic properties of this interesting material.

As THz electron spin resonance (ESR) measurement has several advantages of high spectral resolution, ESR measurement beyond the zero-field splitting or the magnetic phase transition, it is a powerful means to study novel magnetic systems. Focusing on these advantages, we have been developing this THz ESR, and we are now extending to the multi-extreme THz ESR. Here the multi-extreme corresponds to the high magnetic field, the high pressure, the low temperature and the micro-mechanically detected highly sensitive THz ESR. Recent new developments and applications, especially focusing on the high pressure THz ESR, will be shown.

Frequency-domain terahertz (THz) spectroscopy using a continuously tunable photomixer is a powerful analytical technique, offering unique advantages such as high frequency resolution. Here, we report an improved method to increase the spectral resolution using a pair of fiber stretchers. In this method, the amplitude of transmitted THz waves was determined at each frequency by modulating the optical path difference. As a result, the spectral resolution of about 1 MHz was achieved in this study. We applied this technique to frequency-domain electron paramagnetic resonance (EPR) spectroscopy, and successfully observed EPR spectra with a 20-MHz line width.

We systematically studied the zero-field splitting (ZFS) parameters of Fe(III) protoporphyrin IX chloride, or hemin, using the terahertz electron paramagnetic resonance (EPR) spectroscopy technique at ambient and high pressures. Although hemin is known as a model substance of hemoproteins, the pressure effect on the electronic structure has not yet been explored owing to the large ZFS. In this study, high-field and high-frequency EPR measurements were carried out in the frequency range up to 700 GHz and at hydrostatic pressures up to 2 GPa. At ambient pressure, multiple EPR branches were clearly observed, and the axial and rhombic components of ZFS were determined as $$D = 6.90\pm 0.01\hbox { cm}^{-1}$$ and $$E = 0.055 \pm 0.005\hbox { cm}^{-1}$$ , respectively. Upon pressure application, we observed a systematic shift of the resonance field, indicating a monotonous increase of the axial component from D = 6.9 to 7.9 $$\hbox {cm}^{-1}$$ at 2 GPa. The origin of this unusually large shift was discussed from a microscopic viewpoint of the electronic structure of iron under pressure.

Salts of cationic sandwich complexes often exhibit an ionic plastic phase; however, only a few exhibit a plastic phase at room temperature. To explore the use of the CF3BF3 anion to lower the transition temperature to the plastic phase, we prepared salts of CF3BF3 with various ferrocene derivatives, [D][CF3BF3] (D=FeCp*(2), Fe(C5Me4H)(2), Fe(C5H4Me)(2), FeCp(C5H4Me), FeCp2; Cp*=C5Me5, Cp=C5H5). Although [FeCp*(2)][CF3BF3] exhibited a plastic phase above 417 K, the other salts formed room-temperature ionic plastic crystals with a phase transition to the plastic phase in the range 266-291 K. The crystal structure and thermal properties of [FeCp2][OTf] were elucidated for comparison. In addition, decamethylferrocenium salts with other anions were synthesized and structurally characterized: [FeCp*(2)][X] (X=N(SO2F)(2) and B(CN)(4)) exhibited a phase transition to the plastic phase above 400 K, whereas carborane-containing salts [FeCp*(2)](2)[B12F12] and [FeCp*(2)][Co(C2B9H11)(2)] did not exhibit a plastic phase.

We report the results of the pressure-dependent measurements of the static magnetization and of the ferromagnetic resonance (FMR) of ${\mathrm{Cr}}_{2}{\mathrm{Ge}}_{2}{\mathrm{Te}}_{6}$ to address the properties of the ferromagnetic phase of this quasi-two-dimensional van der Waals magnet. The static magnetic data at hydrostatic pressures up to 3.4 GPa reveal a gradual suppression of ferromagnetism in terms of a reduction of the critical transition temperature, a broadening of the transition width, and an increase of the field necessary to fully saturate the magnetization ${M}_{\mathrm{s}}$. The value of ${M}_{\mathrm{s}}\ensuremath{\simeq}3{\ensuremath{\mu}}_{\mathrm{B}}/\mathrm{Cr}$ remains constant within the error bars up to a pressure of 2.8 GPa. The anisotropy of the FMR signal continuously diminishes in the studied hydrostatic pressure range up to 2.39 GPa, suggesting a reduction of the easy-axis-type magnetocrystalline anisotropy energy (MAE). A quantitative analysis of the FMR data gives evidence that up to this pressure the MAE constant ${K}_{\mathrm{U}}$, although getting significantly smaller, still remains finite and positive, i.e., of the easy-axis type. Therefore, a recently discussed possibility of switching the sign of the magnetocrystalline anisotropy in ${\mathrm{Cr}}_{2}{\mathrm{Ge}}_{2}{\mathrm{Te}}_{6}$ could only be expected at still higher pressures, if possible at all, due to the observed weakening of the ferromagnetism under pressure. This circumstance may be of relevance for the design of strain-engineered functional heterostructures containing layers of ${\mathrm{Cr}}_{2}{\mathrm{Ge}}_{2}{\mathrm{Te}}_{6}$.

THz electron spin resonance (ESR) measurement has been a powerful means to study novel magnetic systems because of the advantages of high spectral resolution, ESR measurement beyond the zero-field splitting or the magnetic phase transition. Therefore, we have been developing this THz ESR system since 1988, and we are now extending to the multi-extreme THz ESR. Here the multi-extreme corresponds to the high magnetic field, the high pressure, the low temperature and the micro-mechanically detected ESR. Recent new developments, especially focusing on the high pressure THz ESR, will be shown.

A neutral heteroleptic Fe(III) complex 1 derived from a π-extension of the parent complex 2 was prepared and characterized. Complex 1 exhibited an abrupt spin crossover (SCO) transition exactly at room temperature (T-SCO = 298 K). A crystal structure analysis of 1 revealed that the Fe(III) complex molecules formed a three-dimensional π-stacking interaction network. To thermodynamically clarify the mechanism of the SCO transition, the thermodynamic parameters of the SCO transitions for 1 and 2 were deduced from the temperature dependence of the magnetic susceptibility in the solid and solution states using the regular solution model. A comparison of the SCO enthalpy difference between the solid and molecule for 1 and 2 revealed that the lattice enthalpy difference would largely contribute to the SCO transition enthalpy difference. A computational evaluation of intermolecular interactions and lattice energies before and after the SCO transitions in 1 and 2 disclosed the significant contribution of the next-nearest neighbor dispersion interactions to the lattice enthalpy differences. This finding indicates that not only conventional nearest neighbor intermolecular interactions but also next-nearest neighbor dispersion interactions should be taken into account to understand the fundamental mechanism of a phase transition in molecular solids.

We report the discovery of a first-order phase transition at around 125 K in NbCrP, which is a nonsymmorphic crystal with Pnma space group. From the resistivity, magnetic susceptibility, and nuclear magnetic resonance measurements using the crystals made by the Sn-flux method, the high-temperature (HT) phase is characterized to be metallic with a non-negligible magnetic anisotropy. The low-temperature (LT) phase is also found to be a nonmagnetic metallic state with a crystal of lower symmetry. In the LT phase, the spin susceptibility is reduced by ~30 % from that in the HT phase, suggesting that the phase transition is triggered by the electronic instability. The possible origin of the phase transition in NbCrP is discussed based on the electronic structure by comparing with those in other nonsymmorphic compounds RuP and RuAs., Comment: 9 pages, 9 Postscript figures

We synthesized paramagnetic organometallic ionic liquids [Fe(C5Me4Bu)(SC6H4R)(CO){P(OEt)3}][Tf2N] (R = CF3 (1), H (2), OMe (3)), comprising a cationic half-metallocenium iron-thiolate complex and a bis(trifluoromethanesulfonyl)amide (Tf2N) anion. These liquids exhibited thermochromism based on the monomer–dimer equilibrium of the cation.

Utilizing the package MSH/VBA, based on the microscopic spin Hamiltonian (MSH) approach, spectroscopic and magnetic properties of Fe 2+ (3d 6 ; S = 2) ions at (nearly) orthorhombic sites in Fe(NH 4 ) 2 (SO 4 ) 2 ·6H 2 O (FASH) are modeled. The zero-field splitting (ZFS) parameters and the Zeeman electronic (Ze) factors are predicted for wide ranges of values of the microscopic parameters, i.e. the spin-orbit (λ), spin-spin (ρ) coupling constants, and the crystal-field (ligand-field) energy levels (Δ i ) within the 5 D multiplet. This enables to consider the dependence of the ZFS parameters b k q (in the Stevens notation), or the conventional ones (e.g., D and E ), and the Zeeman factors g i on λ, ρ, and Δ i . By matching the theoretical SH parameters and the experimental ones measured by electron magnetic resonance (EMR), the values of λ, ρ, and Δ i best describing Fe 2+ ions in FASH are determined. The novel aspect is prediction of the fourth-rank ZFS parameters and the ρ(spin-spin)-related contributions, not considered in previous studies. The higher-order contributions to the second- and fourth-rank ZFSPs are found significant. The MSH predictions provide guidance for high-magnetic field and high-frequency EMR (HMF-EMR) measurements and enable assessment of suitability of FASH for application as high-pressure probes for HMF-EMR studies. The method employed here and the present results may be also useful for other structurally related Fe 2+ ( S = 2) systems.

A Series of [Fe-II(L)(2)](BF4)(2) compounds were structurally and physically characterized (L = 2,6-bis(2-methylthiazol-4-yl)pyridine). A crystal structure phase transformation from dihydtate compound 1 to anhydrous compound 3 through partially hydrated compounds 2 and 2' upon dehydration was found. Compounds 1 and 3 exhibited a gradual spin crossover (SCO) conversion, whereas compounds 2 and 2' demonstrated two-step and one-step abrupt SCO transitions, respectively. An X-ray single-crystal structural analysis revealed that one-dimensional and two-dimensional Fe cation networks linked by π stacking and sulfur-sulfur interactions. Were formed in 1 and 3, respectively. A thermodynamic analysis of the magnetic susceptibility for 1, 2', and 3 suggests that the enthalpy differences may govern SCO transition behaviors in the polymorphic compounds 2' and 3. A structural comparison between 1 and 3 indicates that the SCO behavior variations and crystal structure transformation in the present [Fe-II(L)(2)](BF4)(2) compounds can be interpreted by the relationship between the lattice enthalpies mainly arising froth Coulomb interactions between the Fe cations and BF4 anions as in typical ionic crystals.

Frequency-domain electron spin resonance (FDESR) spectroscopy in the terahertz (THz) region using continuously tunable photomixers was demonstrated. Spectral resolution was greatly improved with the use of a pair of fiber stretchers. In this setup, the amplitude of the THz electric field was determined at each frequency by externally sweeping the optical path difference, resulting in a spectral resolution of about 1 MHz. With this technique, we observed narrow ESR spectra with a 20-MHz linewidth, enabling high-resolution FDESR spectroscopy in a broad frequency range.

We report the thermally detected electron spin resonance (ESR) spectroscopy in the frequency range of millimeter and submillimeter waves. Under high vacuum conditions, a cantilever-shaped device detects ESR absorption of a mounted sample as a temperature difference in its beam direction. Despite the simple experimental setup, the spin sensitivity of the order of 10(12) spins/G was achieved at 10 K. The developed sample stage is small enough to be used in a 10 T split-pair superconducting magnet with a bore of 25 mm, enabling precise field-angle-dependent ESR measurements at multi-frequencies above 500 GHz. We demonstrate its usefulness by studying the field-angle dependence of the excitation energy of the dimer triplet state in the Shastry–Sutherland magnet SrCu2(BO3)2.

Recent wide-band (65–850 GHz) electron magnetic resonance (EMR) study determined the zero field splitting (ZFS) parameters (ZFSPs) for Fe2+ in natural and synthetic forsterite (Mg2SiO4) based on the fictitious spin S′ = 1 approach. So-obtained ZFSPs (D′, E′) are incompatible with those available in literature for 3d6 (Fe2+) and 3d4 (Fe4+, Mn3+, Cr2+) ions with the electronic spin S = 2, which predominantly pertain to the effective spin S ˜ = 2. Background for the effective spin S ˜ versus the fictitious ‘spin’ S′ (J′) approaches is provided with focus on application to Fe2+ ions. To enable comparison of the S′ = 1 ZFSPs with the S ˜ = 2 ones methodology for conversions has been worked out and appropriate conversion relations derived for various combinations of the possible energy level schemes for the spin S ˜ = 2 and S′ = 1. The second-rank S′ = 1 ZFSPs (D′, E′) measured by high-frequency EMR for Fe2+ in Mg2SiO4 are converted to the S ˜ = 2 ZFSPs (D, E) and compared with literature data. Suitability of Fe2+:Mg2SiO4 systems for application as high-pressure probes for high-magnetic field and high-frequency EMR (HMF-EMR) is then considered. The results of this study may be applied to other cases of 3d6 and 3d4 (S = 2) ions in various hosts.

Novel pseudopolymorphic Hdabco compounds with an Fe(III) complex anion, (Hdabco)[Fe(aznp)2]·CH2Cl2 1 and (Hdabco)[Fe(aznp)2]·0.5H2O 2 [dabco = 1,4-diazabicyclo[2.2.2]octane, H2aznp = (2′-hydroxyphenylazo)-2-hydroxynaphthalene], were prepared and characterized. The magnetic susceptibility for 1 and 2 revealed that both complexes were in a high-spin (HS) state in the whole temperature range and exhibited weak ferromagnetic interactions below 40 K. The crystal structural analyses suggested that strong N–H⋯O hydrogen bonding interactions between the Hdabco cation and [Fe(aznp)2] anion may induce the distortion of a coordination structure resulting in the HS complexes, whereas π-stacking interactions between the π-ligands in the [Fe(aznp)2] anion and additional C–H⋯N hydrogen bonding interactions between the Hdabco cation and [Fe(aznp)2] anion constructed a intermolecular interaction framework structure with one-dimensional channels. The thermogravimetry analysis for compound 1 indicated the adsorption of a water molecule took place after the desorption of a dichloromethane molecule. This transformation of 1 into 2 proved to proceed in a single-crystal-to-single-crystal way by powder X-ray diffractions and single crystal X-ray structural analysis.

In this work, the effect of substituents on the valence states of biferrocenium salts was investigated in order to explore the valence control of ionic molecular materials. Reactions of 1′,1‴-disubstituted biferrocene derivatives (R2-bifc) and fluoro tetracyanoquinodimethanes (Fn-TCNQ; n = 1, 2, 4) produced single crystals of six salts (1–6), most of which were either monovalent ([D]+[Am]−; m = 1–3) or divalent ([D]+[Am]−) salts. (Et2-bifc)(F1-TCNQ)2 (1) was a mixed-stack monovalent salt, whereas the corresponding F2-TCNQ salt was a divalent salt. (MeO2-bifc)(F1-TCNQ)2 (2) was a monovalent salt because of the small Madelung energy of its segregated-stack structure, despite the low redox potential of the donor. (MeS2-bifc)(2,6-F2-TCNQ)2 (3) was a mixed-stack salt with an apparent intermediate valence state ([D]1.5+[A2]1.5–), containing [D]2+ and [D]+ in a 1:1 ratio. Its valence state, which is intermediate between those of corresponding salts with F1-TCNQ and 2,5-F2-TCNQ, is probably related to the unsymmetrical crystalline environment. (Bu2-bifc)(F1-TCNQ)3 (4) was a divalent salt with a segregated-stack structure, whereas the corresponding TCNQ salt was monovalent. (R2-bifc)(F4-TCNQ) [R = Bu (5), I (6)] were monovalent salts. Their magnetic susceptibilities were found to be consistent with their valence states. These results demonstrated that the valence control of biferrocenium salts could be achieved via the fluorine substitution of acceptors and crystal engineering.

The spin Hamiltonian (SH) parameters experimentally determined by EMR (EPR) may be corroborated or otherwise using various theoretical modeling approaches. To this end semiempirical modeling is carried out for high-spin (S=2) manganese (III) 3d4 ions in complex of tetraphenylporphyrinato manganese (III) chloride (MnTPPCl). This modeling utilizes the microscopic spin Hamiltonians (MSH) approach developed for the 3d4 and 3d6 ions with spin S=2 at orthorhombic and tetragonal symmetry sites in crystals, which exhibit an orbital singlet ground state. Calculations of the zero-field splitting (ZFS) parameters and the Zeeman electronic (Ze) factors (g||=gz, g⊥=gx=gy) are carried out for wide ranges of values of the microscopic parameters using the MSH/VBA package. This enables to examine the dependence of the theoretically determined ZFS parameters bkq (in the Stevens notation) and the Zeeman factors gi on the spin-orbit (λ), spin-spin (ρ) coupling constant, and the ligand-field energy levels (Δi) within the 5D multiplet. The results are presented in suitable tables and graphs. The values of λ, ρ, and Δi best describing Mn(III) ions in MnTPPCl are determined by matching the theoretical second-rank ZFSP b20(D) parameter and the experimental one. The fourth-rank ZFS parameters (b40, b44) and the ρ (spin-spin)-related contributions, which have been omitted in previous studies, are considered for the first time here and are found important. Semiempirical modeling results are compared with those obtained recently by the density functional theory (DFT) and/or ab initio methods.

We present a historical review of high-pressure ESR systems with emphasis on our recent development of a high-pressure, high-field, multi-frequency ESR system. Until 2000, the X-band system was almost established using a resonator filled with dielectric materials or a combination of the anvil cell and dielectric resonators. Recent developments have shifted from that in the low-frequency region, such as X-band, to that in multi-frequency region. High-pressure, high-field, multi-frequency ESR systems are classified into two types. First are the systems that use a vector network analyzer or a quasi-optical bridge, which have high sensitivity but a limited frequency region; the second are like our system, which has a very broad frequency region covering the THz region, but lower sensitivity. We will demonstrate the usefulness of our high-pressure ESR system, in addition to its experimental limitations. We also discuss the recent progress of our system and future plans.