The quantum spin systems ${\mathrm{Cu}}_2{M}^{\prime }{\mathrm{BO}}_5$ $(M^{\prime }=\mathrm{Al},\mathrm{Ga})$ with the ludwigite crystal structure consist of a structurally ordered ${\mathrm{Cu}}^{2+}$ sublattice in the form of three-leg ladders, interpenetrated by a structurally disordered sublattice with a statistically random site occupation by magnetic ${\mathrm{Cu}}^{2+}$ and nonmagnetic ${\mathrm{Ga}}^{3+}$ or ${\mathrm{Al}}^{3+}$ ions. A microscopic analysis based on density-functional-theory calculations for ${\mathrm{Cu}}_2{\mathrm{GaBO}}_5$ reveals a frustrated quasi-two-dimensional spin model featuring five inequivalent antiferromagnetic exchanges. A broad low-temperature ${}^{11}\mathrm{B}$ nuclear magnetic resonance points to a considerable spin disorder in the system. In zero magnetic field, antiferromagnetic order sets in below $T_{\text{N}}\approx 4.1$ K and $\sim 2.4$ K for the Ga and Al compounds, respectively. From neutron diffraction, we find that the magnetic propagation vector in ${\mathrm{Cu}}_2{\mathrm{GaBO}}_5$ is commensurate and lies on the Brillouin-zone boundary in the $\left(H0L\right)$ plane, ${\mathbf{q}}_{\text{m}}=(0.45,0,-0.7)$, corresponding to a complex noncollinear long-range ordered structure with a large magnetic unit cell. Muon spin relaxation is monotonic, consisting of a fast static component typical for complex noncollinear spin systems and a slow dynamic component originating from the relaxation on low-energy spin fluctuations. Gapless spin dynamics in the form of a diffuse quasielastic peak is also evidenced by inelastic neutron scattering. Most remarkably, application of a magnetic field above 1 T destroys the static long-range order, which is manifested in the gradual broadening of the magnetic Bragg peaks. We argue that such a crossover from a magnetically long-range ordered state to a spin-glass regime may result from orphan spins on the structurally disordered magnetic sublattice, which are polarized in magnetic field and thus act as a tuning knob for field-controlled magnetic disorder.

In the present work we have performed an ab initio calculation of vibrational properties of CuTe₂O₅ by means of density functional theory (DFT) method. One has compared calculated values with known experimental data on Raman and infrared spectroscopy in order to verify the obtained results. Lattice contribution to the heat capacity obtained from the ab initio simulations was added to magnetic contribution calculated from the simple spin Hamiltonian model in order to obtain total heat capacity. Obtained results are in good agreement with the experimental data. Thus, the DFT methods could complement the experimental and theoretical studying of low-dimensional magnetic systems such as CuTe₂O₅.

This work is devoted to the study of the magnetic properties and Electron Paramagnetic Resonance (EPR) spectroscopy of TiO₂:Fe nanoparticles doped with Al in different structural states. The sol-gel methods have been used to obtain the particles in both crystalline (average size from 3 to 20 nm) and X-ray amorphous states. The electron paramagnetic resonance spectra of crystalline samples TiO₂:Fe doped with aluminum besides a resonance line with g-factor ~2 exhibit a small signal with a g-factor of 4.3 from Fe³⁺ ions with rhombohedral distortions. The fraction of Fe³⁺ with rhombohedral distortions increases with increasing aluminum content. For the amorphous state at Al doping, the resonance with a g-factor of 4.3 is completely dominant in the electron paramagnetic resonance spectrum. The density functional theory calculation shows that aluminum prefers to be localized near iron ions, distorting the nearest Fe³⁺ environment. The complex integral electron paramagnetic resonance spectrum of all samples was fitted with sufficient accuracy by three separate resonance lines with different widths and intensities. The temperature behavior of the electron paramagnetic resonance spectrum can be described by the coexistence of paramagnetic centers (isolated Fe³⁺ ions including dipole-dipole interactions) and iron clusters with negative exchange interactions.