The optical spectra of antiferromagnetic copper metaborate CuB_2O_4 are characterized by an exceptionally rich structure of narrow absorption lines due to electronic transitions within the magnetic Cu^2+ ions, but their unambiguous identification and behavior in magnetic field remain far from being fully understood. We studied the polarized magneto-absorption spectra of this tetragonal antiferromagnet with a high spectral resolution in the range of 1.4055-1.4065 eV in magnetic fields up to 9.5 T and temperatures from 1.6 up to T_N = 20 K. We observed a set of eight absorption lines at T=1.6 K in magnetic fields exceeding 1.4 T which we identified as arising from Frenkel excitons related to the ground and the first excited state of Cu^2+ ions. The number of these excitons is defined by the presence of the four Cu^2+ ions with the doubly-degenerate spin state S = 1/2 at the 4b positions in the crystallographic unit cell. The energies of these excitons are determined the exchange interaction of 0.5 meV of Cu^2+ ions in the excited state with surrounding ions and by the Davydov splitting of 0.12 meV. In large magnetic field the observed Zeeman splitting is controlled by the anisotropic g-factors of both the ground and excited states. We developed a theoretical model of Frenkel excitons in magnetic field that accounts for specific features of the spin structure and exchange interactions in CuB_2O_4. The model was used for fitting the experimental data and evaluation of Frenkel exciton parameters, such as the Davydov splitting, the molecular exchange energy, and the g-factors of the ground and excited states of the Cu^2+ ions.

The quantum-spin S = 1=2 chain system Cs$_2$CuCl$_4$ is of high interest due to competing anti-ferromagnetic intra-chain J and inter-chain exchange J' interactions and represents a paramount example for Bose-Einstein condensation of magnons [R. Coldea et al., Phys. Rev. Lett. 88, 137202 (2002)]. Substitution of chlorine by bromine allows tuning the competing exchange interactions and corresponding magnetic frustration. Here we report on electron spin resonance (ESR) in single crystals of Cs$_2$CuCl$_{4-x}$Br$_x$ with the aim to analyze the evolution of anisotropic exchange contributions. The main source of the ESR linewidth is attributed to the uniform Dzyaloshinskii-Moriya interaction. The vector components of the Dzyaloshinskii-Moriya interaction are determined from the angular dependence of the ESR spectra using a high-temperature approximation. The obtained results support the site selectivity of the Br substitution suggested from the evolution of lattice parameters and magnetic susceptibility dependent on the Br concentration.

Within the framework of the quantum mechanical approach, the available experimental data are analyzed to identify the electronic structure of the multiferroic FeCr 2 O 4 . The relative values of the key contributions to the parameters of even and odd crystal fields acting on the 3 d electrons of the Fe 2+ ion are determined. Data on local lattice distortions are systematized. The parameter of the electron-deformation interaction of the ground term Fe 2+ ( 5 E ) is determined considering lattice distortions, and the parameters of binding of the spins of Fe 2+ and Cr 3+ to the electric field are estimated. The calculation results are compared with the available experimental data on the magnetic and structural characteristics of FeCr 2 O 4 , the critical temperature of the transition to an orbitally ordered state, optical conductivity data, the Mössbauer effect study, and measurements of spontaneous electric polarization.

Among the large class of A-site ordered perovskites of stoichiometry AC(3) B4O12, the rare-earth (R) ruthenates RCu3Ru4O12 (R = La, Pr, Nd) are interesting compounds due both to Ru-4d-derived electronic correlations and to unconventional crystal-electric-field effects of the R ions. Here we report on detailed investigations of these compounds utilizing x-ray diffraction, neutron scattering, magnetic susceptibility, and electrical resistivity measurements as well as heat capacity and nuclear resonance experiments. A broad range of external parameters is scanned and depending on the specific technique, temperatures range from 100 mK to 730 K in external magnetic fields up to 14 T. In this work LaCu3Ru4O12 serves as reference compound with a nonmagnetic A site, characterized in detail recently [S. Riegg et al., Phys. Rev. B 93, 115149 (2016)]. All compounds investigated reveal heavy-fermion behavior with a T-2 dependence of the low-temperature electrical resistivity and significantly enhanced Sommerfeld coefficients. Toward low temperatures, the compounds with R = Pr and Nd are dominated by the magnetic moments of the R ions, which occupy crystallographic positions with point-group symmetry T-h. The crystal-electric-field effects are clearly visible especially in heat capacity and inelastic neutron scattering data from which the crystal-electric-field parameters are derived. The ground state of the Pr3+ ion is identified as a triplet (Gamma((1))(4)), whereas for Nd3+ it is a quartet (Gamma(67)). Evidence for lowering of the T-h symmetry is observed at the Pr site at temperatures below 10 K, suggesting the formation of orbital order. Moreover, the spin-lattice relaxation derived from Cu-63 nuclear quadrupole resonance indicates characteristic temperatures close to 7 K and 350 mK, probably related to orbital and magnetic order, respectively.

A microscopic theory of the interaction of Cr spins with electric and magnetic fields in DyCrO4 is described. The derived effective energy operator allows calculating the electric polarization vector using information about the magnetic structure. The calculated linear electric polarization in electric and magnetic fields at H < 3 T is consistent with the available experimental data. The electric field is induced by an odd crystalline field on chromium ions and the charge transfer process from the nearest oxygen ions. The enhancement of the magnetic field is associated with magnetic susceptibility, mainly due to dysprosium ions.

We report on the low-frequency optical excitations in the multiferroic ground state of polycrystalline FeCr2S4 in the frequency range 0.3-3 THz and their changes upon applying external magnetic fields up to 7 T. In the ground state below the orbital-ordering temperature T-OO = 9 K we observe the appearance of several new modes. By applying the external magnetic field parallel and perpendicular to the propagation direction of the THz radiation, we can identify the strongest absorptions to be of predominantly electric-dipole origin. We discuss these modes as the low-energy electronic excitations of the Fe2+ ions (3d(6), S = 2) in an tetrahedral S2- environment. The eigenfrequencies and relative intensities of these absorption lines are satisfactorily reproduced by our calculation assuming an effective exchange field of 12.8 cm(-1) at the Fe2+-ions sites. The direction of the exchange field is found to be slightly tilted out of the ab plane. With our approach we can also describe previously reported results from Mossbauer studies and the order of magnitude of the electric polarization induced by orbital and noncollinear spin ordering.

The analytical expressions for the energy coupling of exchange coupled spins with electric field, induced by odd crystal field has been derived in the third order perturbation theory, combining the action of electric field, spin-orbit and exchange interactions. The magnetoelectric coupling due to the partial replacement of the Cu2+ positions by Li+ in LiCuVO4 has been discussed.

The microscopic mechanism of the interaction of exchange-coupled Fe and V spins in a FeV2O4 ferrimagnet with the electric field has been described. The derived effective energy operator makes it possible to calculate the electric polarization vector using the information about the magnetic structure. The calculated electric polarization is consistent with the available experimental data.

We report magnetic, thermodynamic, thermal expansion, and on detailed optical experiments on the layered compound α-RuCl_3 focusing on the THz and sub-gap optical response across the structural phase transition from the monoclinic high-temperature to the rhombohedral low-temperature structure, where the stacking sequence of the molecular layers is changed. This type of phase transition is characteristic for a variety of tri-halides crystallizing in a layered honeycomb-type structure and so far is unique, as the low-temperature phase exhibits the higher symmetry. One motivation is to unravel the microscopic nature of spin-orbital excitations via a study of temperature and symmetry-induced changes. We document a number of highly unusual findings: A characteristic two-step hysteresis of the structural phase transition, accompanied by a dramatic change of the reflectivity. An electronic excitation, which appears in a narrow temperature range just across the structural phase transition, and a complex dielectric loss spectrum in the THz regime, which could indicate remnants of Kitaev physics. Despite significant symmetry changes across the monoclinic to rhombohedral phase transition, phonon eigenfrequencies and the majority of spin-orbital excitations are not strongly influenced. Obviously, the symmetry of the single molecular layers determine the eigenfrequencies of most of these excitations. Finally, from this combined terahertz, far- and mid-infrared study we try to shed some light on the so far unsolved low energy (< 1eV) electronic structure of the ruthenium 4d^5 electrons in α-RuCl_3.

The PbMnBO4 orthoborate single crystals were first grown and their magnetic properties and ferromagnetic resonance were studied. It was found that the ferromagnetic state below the Curie temperature TC=31K is characterized by the strong magnetic anisotropy. The significant effective anisotropy fields of PbMnBO4 determine the energy gap in the FMR spectrum, which is extraordinary large for ferromagnets (112GHz at T=4.2K). It was shown that the static Jahn–Teller effect characteristic of the Mn3+ ion leads to both the ferromagnetic ordering and the strong magnetic anisotropy in the crystal. In the strong external magnetic field the induced ferromagnetic ordering is retained in the crystal above the Curie temperature up to the temperatures multiply higher than TC. A weak anomaly of the dielectric permittivity was observed in PbMnBO4 at the Curie temperature at which the long-range ferromagnetic order is established.

The Mn spin correlations were studied near the O'-O phase transition at T-JT = 750 K up to 950 K with O-17 and La-139 NMR in a stoichiometric LaMnO3 crystalline sample. The measured local hyperfine fields originate from the electron density transferred from the e(g) and t(2g) orbitals to the 2s(O) and 6s(La) orbits, respectively. By probing the oxygen nuclei, we show that the correlations of the Mn spins are ferromagnetic in the ab plane and robust up to T-JT, whereas along the c axis they are antiferromagnetic and start to melt below T-JT, at about 550 K. Above T-JT, the ferromagnetic Mn-Mn exchange interaction is found isotropic. The room-temperature orbital mixing angle, phi(NMR) = 109 +/- 1.5 degrees, of the e(g) ground state is close to the reported value which was deduced from structural data on Jahn-Teller distorted MnO6 octahedra. For T > T-JT, LaMnO3 can be described in terms of nonpolarized e(g) orbitals since both e(g) orbitals are equally occupied. DOI: 10.1103/PhysRevB.87.125142

Quasi-one-dimensional (1D) spin systems are highly unconventional materials, which exhibit a wide variety of phenomena, including spin-Peierls transition and charge ordering. In this paper, we show that electron spin resonance (ESR) is a very powerful tool to study spin relaxation mechanisms in these systems. We review the microscopic theory of superexchange and include a discussion of some recent experimental and theoretical developments concerning ESR in 1D solids. Furthermore, we evaluate the anisotropy and the temperature dependence of the ESR linewidth in three 1D systems (LiCuVO4, CuGeO3, α′-NaV2O5). Thus, we can determine the type and the magnitude of the anisotropic exchange interactions between spins and investigate the effects of fluctuations of charge and lattice degrees of freedom in the vicinity of phase transitions in these systems.

So far calculations of the spin susceptibility in the superconducting state of cuprates have been performed in the framework of weak-coupling approximations. However, it is known that cuprates belong to Mott–Hubbard doped materials where electron correlations are important. In this paper an analytical expression for the spin susceptibility in the superconducting state of cuprates is derived within the singlet-correlated band model, which takes into account strong correlations. The expression of the spin susceptibility is evaluated using values for the hopping parameters adapted to measurements of the Fermi surface of the materials YBa2Cu3O7 and Bi2Sr2CaCu2O8. We show that the available experimental data which are directly related to the spin susceptibility can be explained consistently within one set of model parameters for each material. These experiments include the magnetic resonance peak observed by inelastic neutron scattering and the temperature dependence of nuclear magnetic resonance properties like the spin shift and the spin–spin and spin–lattice relaxation rates in the superconducting state.

An analytic expression for the spin susceptibility in the superconducting state is derived taking into account strong correlation effects and the temperature dependence of the transverse nuclear spin–spin relaxation rates is calculated for both s- and d-wave pairing symmetries.

The divergences, on cooling, of NMR-NQR relaxation rates and muon spin rotation in underdoped cuprates, until now interpreted in terms of glassy spin freezing of magnetic moments resulting from charge inhomogeneities, are critically reconsidered. The relaxation data are analyzed in the light of the lack of dependence from an external magnetic field, of the strength of the effective field driving the divergences and of the stretched exponential character of the recovery processes. By resorting also to the theoretical conclusions of the extended t-J model including the intersite Coulomb interactions, it is argued that the divergences of the relaxation rates, rather than arising from magnetic moments could be related to sliding motions of vortex-antivortex orbital currents coexisting with d-wave superconducting state.

The spin-freezing process in underdoped cuprate superconductors, observed most by NMR-NQR relaxation and muon spin rotation and sometimes interpreted as coexistence of antiferromagnetic and superconducting states, is generally thought to result from randomly distributed magnetic moments related to charge inhomogeneities (possibly stripes) which exhibit slowing down of their fluctuations on cooling below T(c). Instead, we describe the experimental findings as due to fluctuating magnetic fields caused by sliding motions of orbital currents coexisting with d-wave, superconducting state. A direct explanation of the experimental results, in underdoped Y(2-x)Ca(x)Ba(2)Cu(3)O(6.1) and La(2-x)Sr(x)CuO(4), is thus given in terms of freezing of orbital current fluctuations, and mean squared amplitudes of the related internal magnetic fields are estimated.

We have calculated the dynamical charge and spin susceptibilities using the new analytical expression obtained beyond a conventional random phase approximation scheme. Both susceptibilities are strongly peaked along a contour around wave vector Q = (π, π). We have analyzed the dispersions of the collective excitations near Q = (π, π) corresponding to a spin density wave and charge density wave modes, respectively. In addition we have calculated the momentum dependence of the imaginary part of the charge and spin susceptibilities along the instability contour and show that both susceptibilities display a maximum around the points (π, ± q 0 ), (± q 0 , π) in Brillouine zone with decreasing temperature that indicates that the stripe-like instability may become preferable.