Learning crystal field parameters using convolutional neural networks

We present a deep machine learning algorithm to extract crystal field (CF) Stevens parameters from thermodynamic data of rare-earth magnetic materials. The algorithm employs a two-dimensional convolutional neural network (CNN) that is trained on magnetization, magnetic susceptibility and specific heat data that is calculated theoretically within the single-ion approximation and further processed using a standard wavelet transformation. We apply the method to crystal fields of cubic, hexagonal and tetragonal symmetry and for both integer and half-integer total angular momentum values JJ of the ground state multiplet. We evaluate its performance on both theoretically generated synthetic and previously published experimental data on CeAgSb_22, PrAgSb_22 and PrMg_22Cu_99, and find that it can reliably and accurately extract the CF parameters for all site symmetries and values of JJ considered. This demonstrates that CNNs provide an unbiased approach to extracting CF parameters that avoids tedious multi-parameter fitting procedures.

Temperature-Independent Cuprate Pseudogap from Planar Oxygen NMR

Planar oxygen nuclear magnetic resonance (NMR) relaxation and shift data from all cuprate superconductors available in the literature are analyzed. They reveal a temperature-independent pseudogap at the Fermi surface, which increases with decreasing doping in family-specific ways, i.e., for some materials, the pseudogap is substantial at optimal doping while for others it is nearly closed at optimal doping. The states above the pseudogap, or in its absence are similar for all cuprates and doping levels, and Fermi liquid-like. If the pseudogap is assumed exponential it can be as large as about 1500 K for the most underdoped systems, relating it to the exchange coupling. The pseudogap can vary substantially throughout a material, being the cause of cuprate inhomogeneity in terms of charge and spin, so consequences for the NMR analyses are discussed. This pseudogap appears to be in agreement with the specific heat data measured for the YBaCuO family of materials, long ago. Nuclear relaxation and shift show deviations from this scenario near Tc, possibly due to other in-gap states.

Magnetic studies of monoclinic Cu4O(SeO3)3, a copper-oxo-selenite derivative

Cu4O(SeO3)3 is a copper-oxo-selenite belonging to the CuxO(SeO3)(x–1) family of the topological chiral magnet Cu2OSeO3. We report magnetometry and specific heat data measured in a monoclinic Cu4O(SeO3)3 single crystal grown through a Chemical Vapour Transport (CVT) reaction. Our study shows a typical antiferromagnetic behaviour, with a Néel temperature TN = 58 K, similar to that of the Cu2OSeO3 and an additional transition at 13 K. The effective magnetic moment per Cu atom is 1.84 μB, close to the expected theoretical value for Cu2+. The low-temperature M(H) curves, show a transition starting at Hc1 ~ 400 Oe at 1.8 K shifting to a lower value of ~ 280 Oe at 30 K, likely from a helical into a conical intermediate phase, and a second transition at Hc2 ~ 1 kOe, above which the net moment increases linearly with applied field. The magnetisation moment value in a 90 kOe field is 0.053 μB/Cu at 1.8 K and attains a maximum value of 0.061 μB at 13 K. Low-temperature specific heat measurements confirm the presence of the magnetic transition at 13 K, slightly shifting to lower temperatures under an applied magnetic field.

Magnetocaloric and Thermal Properties of Ho(Co1–xSix)2 Compounds

The specific heat and thermal conductivity of HoCo2 and Ho(Co0.95Si0.05)2 were measured as functions of temperature in several constant magnetic fields up to 8 T. From a specific-heat data analysis the isothermal entropy change and the magnetocaloric effect (MCE) have been evaluated in a wide temperature range for several values of the applied magnetic field. The considerable values of the magnetocaloric effect in the vicinity of the magnetic ordering transition are qualifying both compounds as suitable for magnetic refrigeration purposes. The magnetic phase transition temperature (TC) increases from 77 K for HoCo2 to 103 K for Ho(Co0.95Si0.05)2 while the large MCE in the vicinity of TC is maintained, which demonstrates ways of tuning the operating temperatures of the magnetic refrigerant.