Nature of Magnetic Excitations in the High-Field Phase of α-RuCl_{3}.

We present comprehensive electron spin resonance (ESR) studies of in-plane oriented single crystals of α-RuCl_{3}, a quasi-two-dimensional material with honeycomb structure, focusing on its high-field spin dynamics. The measurements were performed in magnetic fields up to 16 T, applied along the [110] and [100] directions. Several ESR modes were detected. Combining our findings with recent inelastic neutron- and Raman-scattering data, we identified most of the observed excitations. Most importantly, we show that the low-temperature ESR response beyond the boundary of the magnetically ordered region is dominated by single- and two-particle processes with magnons as elementary excitations. The peculiarities of the excitation spectrum in the vicinity of the critical field are discussed.

Frustrated magnets in high magnetic fields-selected examples.

An indispensable parameter to study strongly correlated electron systems is the magnetic field. Application of high magnetic fields allows the investigation, modification and control of different states of matter. Specifically for magnetic materials experimental tools applied in such fields are essential for understanding their fundamental properties. Here, we focus on selected high-field studies of frustrated magnetic materials that have been shown to host a broad range of fascinating new and exotic phases. We will give brief insights into the influence of geometrical frustration on the critical behavior of triangular-lattice antiferromagnets, the accurate determination of exchange constants in the high-field saturated state by use of electron spin resonance measurements, and the coupling of magnetic degrees of freedom to the lattice evidenced by ultrasound experiments. The latter technique as well allowed new, partially metastable phases in strong magnetic fields to be revealed.

Origin of the Zero-Field Splitting in Mononuclear Octahedral Mn(IV) Complexes: A Combined Experimental and Theoretical Investigation.

The aim of this work was to determine and understand the origin of the electronic properties of Mn(IV) complexes, especially the zero-field splitting (ZFS), through a combined experimental and theoretical investigation on five well-characterized mononuclear octahedral Mn(IV) compounds, with various coordination spheres (N6, N3O3, N2O4 in both trans (trans-N2O4) and cis configurations (cis-N2O4) and O4S2). High-frequency and -field EPR (HFEPR) spectroscopy has been applied to determine the ZFS parameters of two of these compounds, MnL(trans-N2O4) and MnL(O4S2). While at X-band EPR, the axial-component of the ZFS tensor, D, was estimated to be +0.47 cm(-1) for MnL(O4S2), and a D-value of +2.289(5) cm(-1) was determined by HFEPR, which is the largest D-magnitude ever measured for a Mn(IV) complex. A moderate D value of -0.997(6) cm(-1) has been found for MnL(trans-N2O4). Quantum chemical calculations based on two theoretical frameworks (the Density Functional Theory based on a coupled perturbed approach (CP-DFT) and the hybrid Ligand-Field DFT (LF-DFT)) have been performed to define appropriate methodologies to calculate the ZFS tensor for Mn(IV) centers, to predict the orientation of the magnetic axes with respect to the molecular ones, and to define and quantify the physical origin of the different contributions to the ZFS. Except in the case of MnL(trans-N2O4), the experimental and calculated D values are in good agreement, and the sign of D is well predicted, LF-DFT being more satisfactory than CP-DFT. The calculations performed on MnL(cis-N2O4) are consistent with the orientation of the principal anisotropic axis determined by single-crystal EPR, validating the calculated ZFS tensor orientation. The different contributions to D were analyzed demonstrating that the d-d transitions mainly govern D in Mn(IV) ion. However, a deep analysis evidences that many factors enter into the game, explaining why no obvious magnetostructural correlations can be drawn in this series of Mn(IV) complexes.

Establishing the fundamental magnetic interactions in the chiral Skyrmionic Mott insulator Cu(2)OSeO(3) by terahertz electron spin resonance.

The recent discovery of Skyrmions in Cu(2)OSeO(3) has established a new platform to create and manipulate Skyrmionic spin textures. We use high-field electron spin resonance with a terahertz free-electron laser and pulsed magnetic fields up to 64 T to probe and quantify its microscopic spin-spin interactions. In addition to the previously observed long-wavelength Goldstone mode, this technique probes also the high-energy part of the excitation spectrum which is inaccessible by standard low-frequency electron spin resonance. Fitting the behavior of the observed modes in magnetic field to a theoretical framework establishes experimentally that the fundamental magnetic building blocks of this Skyrmionic magnet are rigid, highly entangled and weakly coupled tetrahedra.

Direct determination of exchange parameters in Cs2CuBr4 and Cs2CuCl4: high-field electron-spin-resonance studies.

Spin-1/2 Heisenberg antiferromagnets Cs2CuCl4 and Cs2CuBr4 with distorted triangular-lattice structures are studied by means of electron spin resonance spectroscopy in magnetic fields up to the saturation field and above. In the magnetically saturated phase, quantum fluctuations are fully suppressed, and the spin dynamics is defined by ordinary magnons. This allows us to accurately describe the magnetic excitation spectra in both materials and, using the harmonic spin-wave theory, to determine their exchange parameters. The viability of the proposed method was proven by applying it to Cs2CuCl4, yielding J/kB=4.7(2) K, J'/kB=1.42(7) K, [J'/J≃0.30] and revealing good agreement with inelastic neutron-scattering results. For the isostructural Cs2CuBr4, we obtain J/kB=14.9(7) K, J'/kB=6.1(3) K, [J'/J≃0.41], providing exact and conclusive information on the exchange couplings in this frustrated spin system.

Low-spin hexacoordinate Mn(III): synthesis and spectroscopic investigation of homoleptic tris(pyrazolyl)borate and tris(carbene)borate complexes.

Three complexes of Mn(III) with "scorpionate" type ligands have been investigated by a variety of physical techniques. The complexes are [Tp(2)Mn]SbF(6) (1), [Tp(2)*Mn]SbF(6) (2), and [{PhB(MeIm)(3)}(2)Mn](CF(3)SO(3)) (3a), where Tp(-) = hydrotris(pyrazolyl)borate anion, Tp*(-) = hydrotris(3,5-dimethylpyrazolyl)borate anion, and PhB(MeIm)(3)(-) = phenyltris(3-methylimidazol-2-yl)borate anion. The crystal structure of 3a is reported; the structures of 1 and 2 have been previously reported, but were reconfirmed in this work. The synthesis and characterization of [{PhB(MeIm)(3)}(2)Mn]Cl (3b) are also described. These complexes are of interest in that, in contrast to many hexacoordinate (pseudo-octahedral) complexes of Mn(III), they exhibit a low-spin (triplet) ground state, rather than the high-spin (quintet) ground state. Solid-state electronic absorption spectroscopy, SQUID magnetometry, and high-frequency and -field electron paramagnetic resonance (HFEPR) spectroscopy were applied. HFEPR, in particular, was useful in characterizing the S = 1 spin Hamiltonian parameters for complex 1, D = +19.97(1), E = 0.42(2) cm(-1), and for 2, D = +15.89(2), E = 0.04(1) cm(-1). In addition, frequency domain Fourier-transform THz-EPR spectroscopy, using coherent synchrotron radiation, was applied to 1 only and gave results in good agreement with HFEPR. Variable-temperature dc magnetic susceptibility measurements of 1 and 2 were also in good agreement with the HFEPR results. This magnitude of zero-field splitting (zfs) is over 4 times larger than that in comparable hexacoordinate Mn(III) systems with S = 2 ground states. Complexes 3a and 3b (i.e., regardless of counteranion) have a yet much larger magnitude zfs, which may be the result of unquenched orbital angular momentum so that the spin Hamiltonian model is not appropriate. The triplet ground state is rationalized in each complex by ligand-field theory (LFT) and by quantum chemistry theory, both density functional theory and unrestricted Hartree-Fock methods. This analysis also shows that spin-crossover behavior is not thermally accessible for these complexes as solids. The donor properties of the three different scorpionate ligands were further characterized using the LFT model that suggests that the tris(carbene)borate is a strong σ-donor with little or no π-bonding.

High spin Co(I): high-frequency and -field EPR spectroscopy of CoX(PPh3)3 (X = Cl, Br).

The previously reported pseudotetrahedral Co(I) complexes, CoX(PR(3))(3), where R = Me, Ph, and chelating analogues, and X = Cl, Br, I exhibit a spin triplet ground state, which is uncommon for Co(I), although expected for this geometry. Described here are studies using electronic absorption and high-frequency and -field electron paramagnetic resonance (HFEPR) spectroscopy on two members of this class of complexes: CoX(PR(3))(3), where R = Ph and X = Cl and Br. In both cases, well-defined spectra corresponding to axial spin triplets were observed, with signals assignable to three distinct triplet species, and with perfectly axial zero-field splitting (zfs) given by the parameter D = +4.46, +5.52, +8.04 cm(-1), respectively, for CoCl(PPh(3))(3). The crystal structure reported for CoCl(PPh(3))(3) shows crystallographic 3-fold symmetry, but with three structurally distinct molecules per unit cell. Both of these facts thus correlate with the HFEPR data. The investigated complexes, along with a number of structurally characterized Co(I) trisphosphine analogues, were analyzed by quantum chemistry calculations (both density functional theory (DFT) and unrestricted Hartree-Fock (UHF) methods). These methods, along with ligand-field theory (LFT) analysis of CoCl(PPh(3))(3), give reasonable agreement with the salient features of the electronic structure of these complexes. A spin triplet ground state is strongly favored over a singlet state and a positive, axial D value is predicted, in agreement with experiment. Quantitative agreement between theory and experiment is less than ideal with LFT overestimating the zfs, while DFT underestimates these effects. Despite these shortcomings, this study demonstrates the ability of advanced paramagnetic resonance techniques, in combination with other experimental techniques, and with theory, to shed light on the electronic structure of an unusual transition metal ion, paramagnetic Co(I).

Dimensional reduction and incommensurate dynamic correlations in the [Formula: see text] triangular-lattice antiferromagnet Ca3ReO5Cl2.

The observation of spinon excitations in the [Formula: see text] triangular antiferromagnet Ca3ReO5Cl2 reveals a quasi-one-dimensional (1D) nature of magnetic correlations, in spite of the nominally 2D magnetic structure. This phenomenon is known as frustration-induced dimensional reduction. Here, we present high-field electron spin resonance spectroscopy and magnetization studies of Ca3ReO5Cl2, allowing us not only to refine spin-Hamiltonian parameters, but also to investigate peculiarities of its low-energy spin dynamics. We argue that the presence of the uniform Dzyaloshinskii-Moriya interaction (DMI) shifts the spinon continuum in momentum space and, as a result, opens a zero-field gap at the Γ point. We observed this gap directly. The shift is found to be consistent with the structural modulation in the ordered state, suggesting this material as a perfect model triangular-lattice system, where a pure DMI-spiral ground state can be realized.

Ultrasound measurement technique for the single-turn-coil magnets.

Ultrasound is a powerful means to study numerous phenomena of condensed-matter physics as acoustic waves couple strongly to structural, magnetic, orbital, and charge degrees of freedom. In this paper, we present such a technique combined with single-turn coils (STCs) that generate magnetic fields beyond 100 T with the typical pulse duration of 6 µs. As a benchmark of this technique, the ultrasound results for MnCr2S4, Cu6[Si6O18]·6H2O, and liquid oxygen are shown. The resolution for the relative sound-velocity change in the STC is estimated as Δv/v ∼ 10-3, which is sufficient to study various field-induced phase transitions and critical phenomena.

Cobalt(II) "scorpionate" complexes as models for cobalt-substituted zinc enzymes: electronic structure investigation by high-frequency and -field electron paramagnetic resonance spectroscopy.

A series of complexes of formula Tp(R,R')CoL, where Tp(R,R'-) = hydrotris(3-R,5-R'-pyrazol-1-yl)borate ("scorpionate") anion (R = tert-butyl, R' = H, Me, 2'-thienyl (Tn), L = Cl(-), NCS(-), NCO(-), N(3)(-)), has been characterized by electronic absorption spectroscopy in the visible and near-infrared (near-IR) region and by high-frequency and -field electron paramagnetic resonance (HFEPR). Reported here are also crystal structures of seven members of the series that have not been reported previously: R' = H, L = NCO(-), N(3)(-); R' = Me, L = Cl(-), NCS(-), NCO(-), N(3)(-); R' = Tn, L = Cl(-), NCS(-). These include a structure for Tp(t-Bu,Me)CoCl different from that previously reported. All of the investigated complexes contain a four-coordinate cobalt(II) ion (3d(7)) with approximate C(3v) point group symmetry about the metal ion and exhibit an S = (3)/(2) high-spin ground state. The use of HFEPR allows extraction of the full set of intrinsic S = (3)/(2) spin Hamiltonian parameters (D, E, and g values). The axial zero-field splitting parameter, D, for all investigated Tp(R,R')CoL complexes is always positive, a fact not easily determined by other methods. However, the magnitude of this parameter varies widely: 2.4 cm(-1)

Pressure-tuning the quantum spin Hamiltonian of the triangular lattice antiferromagnet Cs2CuCl4.

Quantum triangular-lattice antiferromagnets are important prototype systems to investigate numerous phenomena of the geometrical frustration in condensed matter. Apart from highly unusual magnetic properties, they possess a rich phase diagram (ranging from an unfrustrated square lattice to a quantum spin liquid), yet to be confirmed experimentally. One major obstacle in this area of research is the lack of materials with appropriate (ideally tuned) magnetic parameters. Using Cs2CuCl4 as a model system, we demonstrate an alternative approach, where, instead of the chemical composition, the spin Hamiltonian is altered by hydrostatic pressure. The approach combines high-pressure electron spin resonance and r.f. susceptibility measurements, allowing us not only to quasi-continuously tune the exchange parameters, but also to accurately monitor them. Our experiments indicate a substantial increase of the exchange coupling ratio from 0.3 to 0.42 at a pressure of 1.8 GPa, revealing a number of emergent field-induced phases.

Magnetic structure and spin waves in the frustrated ferro-antiferromagnet Pb2VO(PO4)2.

Single crystal neutron diffraction, inelastic neutron scattering, and electron spin resonance experiments are used to study the magnetic structure and spin waves in Pb2VO(PO4)2, a prototypical layered S = 1/2 ferromagnet with frustrating next-nearest neighbor antiferromagnetic interactions. The observed excitation spectrum is found to be inconsistent with a simple square lattice model previously proposed for this material. At least four distinct exchange coupling constants are required to reproduce the measured spin wave dispersion. The degree of magnetic frustration is correspondingly revised and found to be substantially smaller than in all previous estimates.

Tunable-frequency high-field electron paramagnetic resonance.

A tunable-frequency methodology based on backward wave oscillator sources in high-frequency and -field EPR (HFEPR) is described. This methodology is illustrated by an application to three non-Kramers transition metal ion complexes and one Kramers ion complex. The complexes are of: Ni(II) (S=1) as found in dichlorobistriphenylphosphanenickel(II), Mn(III) (S=2) as found in mesotetrasulfonatoporphyrinatomanganese(III) chloride, Fe(II) (S=2) as found in ferrous sulfate tetrahydrate, and Co(II) (S=3/2) as found in azido(tris(3-tert-butylpyrazol-1-yl)hydroborate)cobalt(II). The above Ni(II) and Mn(III) complexes have been studied before by HFEPR using the multifrequency methodology based on Gunn oscillator sources, but not by the present method, while the Fe(II) and Co(II) complexes presented here have not been studied by any form of HFEPR. Highly accurate spin Hamiltonian parameters can be obtained by the experimental methodology described here, in combination with automated fitting procedures. This method is particularly successful in determining g-matrix parameters, which are very difficult to extract for high-spin systems from single frequency (or a very limited set of multi-frequency) HFEPR spectra, but is also able to deliver equally accurate values of the zero-field splitting tensor. The experimental methods involve either conventional magnetic field modulation or an optical modulation of the sub-THz wave beam. The relative merits of these and other experimental methods are discussed.

ESR of coupled spin-1/2 chains in copper pyrazine dinitrate: unveiling geometrical frustration.

The spin dynamics of copper pyrazine dinitrate (Cu(C4H4N2)(NO3)2), a model spin-1/2 Heisenberg antiferromagnetic (AF) chain system, was investigated by means of electron spin resonance (ESR). Using the high-field ESR we evidenced the inequivalence of Cu sites belonging to adjacent spin chains in the ac planes of this compound. It was revealed that the dominating interchain interaction is of zig-zag-type. This interaction gives rise to geometrical frustration strongly affecting the character of AF ordering. Combining our experimental findings with the results of a quasiclassical approach we predict that at low temperatures the system orders in an incommensurate spiral state.

Terahertz-range free-electron laser electron spin resonance spectroscopy: techniques and applications in high magnetic fields.

The successful use of picosecond-pulse free-electron-laser (FEL) radiation for the continuous-wave terahertz-range electron spin resonance (ESR) spectroscopy has been demonstrated. The combination of two linac-based FELs (covering the wavelength range of 4-250 microm) with pulsed magnetic fields up to 70 T allows for multifrequency ESR spectroscopy in a frequency range of 1.2-75 THz with a spectral resolution better than 1%. The performance of the spectrometer is illustrated with ESR spectra obtained in the 2,2-diphenyl-1-picrylhydrazyl and the low-dimensional organic material (C6H9N2)CuCl3.

Magnetic excitations in the spin-1 anisotropic Heisenberg antiferromagnetic chain system NiCl(2)-4SC(NH(2))(2).

NiCl(2)-4SC(NH(2))(2) (DTN) is a quantum S=1 chain system with strong easy-pane anisotropy and a new candidate for the Bose-Einstein condensation of the spin degrees of freedom. ESR studies of magnetic excitations in DTN in fields up to 25 T are presented. Based on analysis of the single-magnon excitation mode in the high-field spin-polarized phase and previous experimental results [Phys. Rev. Lett. 96, 077204 (2006)10.1103/PhysRevLett.96.077204], a revised set of spin-Hamiltonian parameters is obtained. Our results yield D=8.9 K, J(c) = 2.2 K, and J(a,b) = 0.18 K for the anisotropy, intrachain, and interchain exchange interactions, respectively. These values are used to calculate the antiferromagnetic phase boundary, magnetization, and the frequency-field dependence of two-magnon bound-state excitations predicted by theory and observed in DTN for the first time. Excellent quantitative agreement with experimental data is obtained.

Electronic structure of four-coordinate C3v nickel(II) scorpionate complexes: investigation by high-frequency and -field electron paramagnetic resonance and electronic absorption spectroscopies.

A series of complexes of formula TpNiX, where Tp*- = hydrotris(3,5-dimethylpyrazole)borate and X = Cl, Br, I, has been characterized by electronic absorption spectroscopy in the visible and near-infrared (NIR) region and by high-frequency and -field electron paramagnetic resonance (HFEPR) spectroscopy. The crystal structure of TpNiCl has been previously reported; that for TpNiBr is given here: space group = Pmc2(1), a = 13.209(2) A, b = 8.082(2) A, c = 17.639(4) A, alpha = beta = gamma = 90 degrees , Z = 4. TpNiX contains a four-coordinate nickel(II) ion (3d8) with approximate C3v point group symmetry about the metal and a resulting S = 1 high-spin ground state. As a consequence of sizable zero-field splitting (zfs), TpNiX complexes are "EPR silent" with use of conventional EPR; however, HFEPR allows observation of multiple transitions. Analysis of the resonance field versus the frequency dependence of these transitions allows extraction of the full set of spin Hamiltonian parameters. The axial zfs parameter for TpNiX displays pronounced halogen contributions down the series: D = +3.93(2), -11.43(3), -22.81(1) cm(-1), for X = Cl, Br, I, respectively. The magnitude and change in sign of D observed for TpNiX reflects the increasing bromine and iodine spin-orbit contributions facilitated by strong covalent interactions with nickel(II). These spin Hamiltonian parameters are combined with estimates of 3d energy levels based on the visible-NIR spectra to yield ligand-field parameters for these complexes following the angular overlap model (AOM). This description of electronic structure and bonding in a pseudotetrahedral nickel(II) complex can enhance the understanding of similar sites in metalloproteins, both native nickel enzymes and nickel-substituted zinc enzymes.

Electron spin resonance in sine-gordon spin chains in the perturbative spinon regime.

We report the low-temperature multifrequency ESR studies of copper pyrimidine dinitrate, a spin-1/2 antiferromagnetic chain with alternating g tensor and the Dzyaloshinskii-Moriya interaction, allowing us to test a new theoretical concept proposed recently by Oshikawa and Affleck [Phys. Rev. Lett. 82, 5136 (1999)]. Their theory, based on bosonization and self-energy formalism, can be applied for precise calculation of ESR parameters of S=1/2 antiferromagnetic chains in the perturbative spinon regime. Excellent quantitative agreement between the theoretical predictions and experiment is obtained.

High-frequency/high-field EPR spectroscopy of the high-spin ferrous ion in hexaaqua complexes.

Electron paramagnetic resonance (EPR) at conventional magnetic fields and microwave frequencies, respectively, B0 < or = 1.5 T, nu < or = 35 GHz, has been widely applied to odd electron-number (S = 1/2) transition metal complexes. This technique is less successfully applied to high-spin systems that have even electron configurations, e.g. Fe2+ (S = 2). The recently developed technique of high-frequency and high-field EPR (HFEPR), employing swept fields up to 25 T combined with multiple, sub-THz frequencies readily allows observation of EPR transitions in such high-spin systems. A parallel spectroscopic technique is frequency-domain magnetic resonance spectroscopy (FDMRS), in which the frequency is swept while at zero, or at discrete applied magnetic fields. We describe here the application of HFEPR and FDMRS to two simple high-spin (HS) ferrous (Fe2+) salts: ferrous perchlorate hydrate, [Fe(H2O)6](ClO4)2 and (NH4)2[Fe(H2O)6](SO4)2, historically known as ferrous ammonium sulfate. Both compounds contain hexaaquairon(II). The resulting spectra were analyzed using a spin Hamiltonian for S = 2 to yield highly accurate spin-Hamiltonian parameters. The complexes were also studied by powder DC magnetic susceptibility and zero-field Mössbauer effect spectroscopy for corroboration of magnetic resonance results. In the case of [Fe(H2O)6](ClO4)2, all the magnetic techniques were in excellent agreement and gave as consensus values: D = 11.2(2) cm(-1), E = 0.70(1) cm(-1). For (NH4)2[Fe(H2O)6](SO4)2, FDMRS and HFEPR gave D = 14.94(2) cm(-1), E = 3.778(2) cm(-1). We conclude that the spin-Hamiltonian parameters for the perchlorate best represent those for the isolated hexaaquairon(II) complex. To have established electronic parameters for the fundamentally important [Fe(H2O)6]2+ ion will be of use for future studies on biologically relevant systems containing high-spin Fe2+.