Magnetic control of correlated spin systems is central to the development of next-generation spin-based technologies. Rare-earth orthoferrites provide an interesting platform in which exchange coupling between rare-earth 4f and transition-metal 3d moments generates competing magnetic interactions and multiple metastable states. Here, we show that the orientation of the applied magnetic field drives different magnetic phase transition sequences in NdFeO3 across a broad temperature range. Using Raman and polarized terahertz spectroscopies, supported by magnetization and specific-heat measurements, we track the temperature- and field-dependent evolution of the different magnetic phases and the successive spin rearrangements, driven by 4f - 3d magnetic anisotropic interactions. For fields applied along the crystallographic c-axis, a spin-reorientation transition is followed by spin-flop and spin-flip processes, producing an unexpectedly complex magnetic phase sequence at low temperatures. Below 8 K, precursor effects associated with ordering of the Nd-sublattice strongly modify the transition pathway. Our results demonstrate how anisotropic 4f-3d coupling enables magnetic-field control of coupled spin excitations and provide a route to accessing novel spin configurations in rare-earth orthoferrites.

BaHoFeO4 is a recently discovered low-temperature multiferroic exhibiting a unique magnetic-field-induced ferroelectric behavior whose origin remains unexplained so far. The complex magnetic interactions between the spins of 3d Fe electrons and of 4f Ho electrons give rise to a rich temperature-magnetic-field phase diagram. We investigated the properties of BaHoFeO4 using THz time-domain spectroscopy, X-ray diffraction, neutron powder diffraction, Mössbauer spectroscopy and magnetization measurements. Whereas the orthorhombic crystal structure remains stable down to 3 K, three different antiferromagnetic structures were observed on cooling, as well as two metamagnetic phase transitions induced by magnetic field of up to 7 T.

We investigate the terahertz conductivity of conventional superconductors in Voigt and Faraday magneto-optical configurations. First, we review theoretical approaches describing the fundamental processes of suppression of superconductivity in magnetic field and how the in-gap states are filled. In the Voigt geometry, thin superconducting films are fully penetrated by the magnetic field which interacts with the spin, thus modifying the magnitudes of the optical gap and of the density of the condensate. In this configuration, we provide an alternative description of the recent experiments showing the gapless conductivity of a Nb film measured by Lee et al. [Nat. Commun. 14,2737 (2023)], which better fits their data for magnetic fields above 1 T. In the Faraday geometry, we measured and analyzed the terahertz conductivity of three NbN films with varying thicknesses using the Maxwell-Garnett model, treating vortices as normal-state inclusions within a superconducting matrix. In both geometries, the optical conductivity can be comprehensively described by the model of Herman and Hlubina [Phys. Rev. B 96, 014509 (2017)] involving pair-conserving, and magnetic-field-dependent pair-breaking disorder scattering processes.

We investigate the terahertz conductivity of conventional superconductors in Voigt and Faraday magneto-optical configurations. In the Voigt geometry, an ultrathin superconducting film is fully penetrated by the magnetic field which interacts with the spin, thus modifying the magnitudes of the optical gap and of the density of the condensate. We provide an alternative interpretation of the recent experiments showing the gapless conductivity of a Nb film measured by Lee et al. [1] which describes better their data for magnetic field above 1 T. In the Faraday geometry, we analyze the terahertz conductivity of three NbN films with varying thicknesses using the Maxwell-Garnett model, treating vortices as normal-state inclusions within a superconducting matrix. Moreover, we effectively account for ubiquitous pair-conserving and magnetic-field-dependent pair-breaking disorder scattering processes using the model of Herman and Hlubina [2].

We present an improved model for studying the interactions between dipole moments of water molecules confined in beryl crystals, inspired by recent NMR experiments. Our model is based on a local crystal potential with dihexagonal symmetry for the rotations of water dipole moments, leading to deflection from the $ab$ hexagonal crystallographic plane. This potential shape has significant implications for dipole ordering, which is linked to the non-zero projection of the dipole moment on the hexagonal $c$ axis. To reveal the tendency toward equilibrium-ordered states, we used a variational mean-field approximation, Monte Carlo simulations, and quantum tunneling. Our analysis reveals three types of equilibrium-ordered states: a purely planar dipole order with an antiparallel arrangement in the adjacent planes, a configuration with deflected dipole moments ordered in antiparallel directions, and a helical structure of the dipoles twisting along the $c$ axis.

Behavior of individual molecules of normal and heavy water in beryl single crystals was studied by 1H and 2H nuclear magnetic resonance spectroscopy. From temperature dependences of the spectra, we deduce that type-I water molecules embedded in the beryl voids are oriented quite differently from the view established in the literature: Different from the earlier assumptions, their H-H lines deviate by about 18° from the hexagonal axis. We suggest that this is due to the molecules attaching to the oxygen atoms forming the beryl structural voids by a hydrogen bond. Our analysis shows that the molecules perform two types of movement: (i) rapid librations around the axis of the hydrogen bond and (ii) less frequent orientational jumps among the 12 possible binding sites in the beryl voids. The frequencies of the librational motions are evaluated from a simple thermodynamic model, providing good quantitative agreement with the frequencies of librations from optical experiments reported earlier.

Electron-hole plasma expansion with velocities exceeding c/50 and lasting over 10 ps at 300 K was evidenced by time-resolved terahertz spectroscopy. This regime, in which the carriers are driven over >30  μm is governed by stimulated emission due to low-energy electron-hole pair recombination and reabsorption of the emitted photons outside the plasma volume. At low temperatures a speed of c/10 was observed in the regime where the excitation pulse spectrally overlaps with emitted photons, leading to strong coherent light-matter interaction and optical soliton propagation effects.

Ultrafast and long-distance expansion of electron-hole plasma in bulk GaAs crystal at temperatures ranging from 20 K to 300 K is observed by means of the optical pump – THz probe experimental technique. The expansion speed $\sim c/50$ at 300 K notably exceeds values reported earlier in the literature but it also exceeds the values permitted by the GaAs band structure for a bare electron. This observation is interpreted in terms of a stimulated emission, fast transport and reabsorption of photons by creation of electron-hole pairs. Theoretical quantitative model, based on the above interpretation, shows a very good agreement with the experimental data, gives a valuable insight into the system dynamics and predicts conditions at which the effect should be observable. At temperatures below 100 K, further increase of the propagation speed of electron-hole plasma surface (up to $\sim c/10$) is observed. This effect is interpreted as the direct observation of the optical soliton propagation in the crystal.

Complex frustrated magnetic structures in multiferroic hexaferrites are well tunable by temperature, magnetic field and doping. We investigated the influence of strong THz pulses generated by superradiant THz sources on magnetic structure and related electromagnons’ absorption in Y- and Z-type multiferroic hexaferrites. While in Z-type hexaferrite (Ba0.2Sr0.8)3Co2Fe24O41 polycrystal, the observed changes in transmission spectra were fully described by sample heating, a blue-shift of the electromagnon frequency observed in Y-type hexaferrite Ba0.2Sr1.8Co2(Fe0.96Al0.04)12O22 single-crystal could be possibly ascribed to the transition from the alternating longitudinal conical to the transverse conical magnetic structure. We elaborated a nonlinear model which explained absence of nonlinearity in Z-type hexaferrite (Ba0.2Sr0.8)3Co2Fe24O41. For Y-type hexaferrite Ba0.2Sr1.8Co2(Fe0.96Al0.04)12O22, we discuss possible transient or even permanent effects of both THz electric and magnetic fields on its magnetic structure.

Optical conductivity of a moderately disordered superconducting NbN film was investigated by terahertz time-domain spectroscopy in external magnetic field applied along the film plane. The film thickness of about 5 nm was comparable with the coherence length, so vortices should not form. This was confirmed by the fact that no marked difference between the spectra with terahertz electric field set perpendicular and parallel to the external magnetic field was observed. Simultaneous use of Maxwell-Garnett effective medium theory and the model of optical conductivity by Herman and Hlubina proved to correctly reproduce the terahertz spectra obtained experimentally in a magnetic field of up to 7 T. This let us conclude that the magnetic field tends to suppress the superconductivity, resulting in an inhomogeneous state where superconducting domains are enclosed within a normalstate matrix. The scattering rate due to pair-breaking effects was found to linearly increase with magnetic field.

Lawsonite is a water-containing mineral occurring in the Earth’s crust and mantle, exhibiting low-temperature ferroelectricity linked to water molecules. Using broad-band polarized electromagnetic spectroscopy, we studied the lattice dynamics of a single crystal between 1Hz and 20THz at temperatures from 20 to 500K. We identified three anomalies associated with the two phase transitions occurring at 270 and 124K—a critical GHz relaxation, a soft THz phonon, and an overdamped sub-THz excitation in the $\mathbf{E} \|a, \mathbf{E} \|b$ and $\mathbf{E} \|c$ permittivity spectra, respectively. The fact that the soft mode is polarized perpendicularly to the ferroelectric axis is very unusual.

The complex conductivity of an ultrathin superconducting NbN film was investigated by terahertz time-domain spectroscopy under an in-plane magnetic field. Simultaneous use of Maxwell-Garnett effective medium theory and the model of optical conductivity by Herman and Hlubina [Phys. Rev. B 96, 014509 (2017)] assuming linear dependence of pair-breaking scattering rate on the magnetic field proved to correctly reproduce the terahertz spectra obtained experimentally in a magnetic field of up to 7 T.

Lattice dynamics of a single crystal of lawsonite were studied over a broad range of frequencies (1 Hz to 20 THz) using impedance, THz time-domain and infrared spectroscopies. Based on polarized spectra of complex permittivity ε̂ measured as a function of temperature between 10 K and 500 K, we analyzed the properties of the two known phase transitions—an antiferrodistortive one near Tc1 = 270 K and a ferroelectric one, occurring at Tc2 = 124 K. The former one is accompanied by a flat maximum in the THz-range permittivity ε̂c near Tc1, which is due to a polar excitation in the E || c spectra reflecting the dynamics of water and hydroxyl groups. The strength of this mode decreases on cooling below Tc1, and the mode vanishes below Tc2 due to hydrogen ordering. At the pseudoproper ferroelectric phase transition, two independent anomalies in permittivity were observed. First, ε̂a exhibits a peak at Tc2 = 124 K due to critical slowing down of a relaxation in the GHz range. Second, infrared and THz spectra revealed an optical phonon softening towards Tc2 which causes a smaller but pronounced maximum in ε̂b. Such anomaly, consisting in a soft mode polarized perpendicularly to the ferroelectric axis, is unusual in ferroelectrics.

We have studied the radio frequency dielectric response of a system consisting of separate polar water molecules periodically arranged in nanocages formed by the crystal lattice of the gemstone beryl. Below T = 20-30 K, quantum effects start to dominate the properties of the electric dipolar system as manifested by a crossover between the Curie-Weiss and the Barrett regimes in the temperature-dependent real dielectric permittivity ε'(T). When analyzing in detail the temperature evolution of the reciprocal permittivity (ε')-1 down to T ≈ 0.3 K and comparing it with the data obtained for conventional quantum paraelectrics, like SrTiO3, KTaO3, we discovered clear signatures of a quantum-critical behavior of the interacting water molecular dipoles: Between T = 6 and 14 K, the reciprocal permittivity follows a quadratic temperature dependence and displays a shallow minimum below 3 K. This is the first observation of "dielectric fingerprints" of quantum-critical phenomena in a paraelectric system of coupled point electric dipoles.

Herein, in situ temperature‐dependent THz and DC conductivity measurements in the crystalline states of Ge2Sb2Te5(GST225) are performed at relatively high temperatures (>300 K). As observed in many nanomaterials, a non‐Drude type of THz conductivity is found in the crystalline state of phase‐change (PC) materials. Both the intra‐ and intergrain effects can be separated in the THz and DC conductivity. It is shown that grain boundaries significantly affect the THz and DC conductivities of the crystalline phase (distorted rock salt structure). The experimentally observed DC Hall mobility is different from the intragrain mobility extracted from the THz conductivity, suggesting that a series sequence of intra‐ and intergrain transport mechanisms controls the electronic transport in the crystalline state of GST225.

Due to their outstanding dielectric and magnetic properties, hexaferrites are attracting ever-increasing attention for developing electronic components of next-generation communication systems. The complex crystal structure of hexaferrites and the critical dependences of their electric and magnetic properties on external factors, such as magnetic/electric fields, pressure, and doping, open ample opportunities for targeted tuning of these properties when designing specific devices. Here we explored the electromagnetic properties of lead-substituted barium hexaferrite, Ba 1− x Pb x Fe 12 O 19 , a compound featuring an extremely rich set of physical phenomena that are inherent in the dielectric and magnetic subsystems and can have a significant effect on its electromagnetic response at terahertz frequencies. We performed the first detailed measurements of the temperature-dependent (5–300 K) dielectric response of single-crystalline Ba 1− x Pb x Fe 12 O 19 in an extremely broad spectral range of 1 Hz–240 THz. We fully analyzed numerous phenomena with a corresponding wide distribution of specific energies that can affect the terahertz properties of the material. The most important fundamental finding is the observation of a ferroelectric-like terahertz excitation with an unusual temperature behavior of its frequency and strength. We suggest microscopic models that explain the origin of the excitation and its nonstandard temperature evolution. Several narrower terahertz excitations are associated with electronic transitions between the fine-structure components of the Fe 2+ ground state. The discovered radio-frequency relaxations are attributed to the response of magnetic domains. Gigahertz resonances are presumably of magnetoelectric origin. The obtained data on diverse electromagnetic properties of Ba 1− x Pb x Fe 12 O 19 compounds provide information that makes the entire class of hexaferrites attractive for manufacturing electronic devices for the terahertz range.

We present results of a multimethod investigation of the polar antiferromagnets Ni2CoTeO6 and NiCo2TeO6, inspired by the colossal magnetoelectric effect present in Ni3TeO6. Both compounds crystalize in the same polar space group R3 as Ni3TeO6, preserving the crystal symmetry at least from room temperature down to 2 K. Ni2CoTeO6 and NiCo2TeO6 undergo antiferromagnetic phase transitions at T-N = 55 and 52 K, and spin-flop transitions at an external magnetic field of approximately 8 and 4 T, respectively. Both compounds present an incommensurate antiferromagnetic helical structure with spins lying in the ab plane, in contrast to the collinear one along the c axis in Ni3TeO6. Moreover, dielectric anomalies are observed at their antiferromagnetic phase transitions, suggesting a magnetoelectric behavior. Spin and lattice dynamics studies by a combination of infrared, Raman, and terahertz spectroscopies were performed. Below T-N, in both Ni2CoTeO6 and NiCo2TeO6, low-frequency spin excitations extremely sensitive to external magnetic field were observed. At least one of these magnons was simultaneously seen in Raman and THz spectra of both compounds, therefore we propose to assign them to electromagnons.

EuTiO 3 is an incipient ferroelectric antiferromagnet showing an anomalously strong spin-phonon coupling. We studied EuTiO 3 ceramics by terahertz (THz) time-domain spectroscopy upon varying temperature and magnetic field. We observed a large anisotropy which is due to the shift from the microwave to the sub-THz region of a ferromagnetic resonance appearing only when the external magnetic field is applied perpendicular to the magnetic component of the THz radiation.