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Saturation of the anomalous Hall effect at high magnetic fields in altermagnetic RuO2
Observations of the anomalous Hall effect in RuO2 and MnTe have demonstrated unconventional time-reversal symmetry breaking in the electronic structure of a recently identified new class of compensated collinear magnets, dubbed altermagnets. While in MnTe, the unconventional anomalous Hall signal accompanied by a vanishing magnetization is observable at remanence, the anomalous Hall effect in RuO2 is excluded by symmetry for the Néel vector pointing along the zero-field [001] easy-axis. Guided by a symmetry analysis and ab initio calculations, a field-induced reorientation of the Néel vector from the easy-axis toward the [110] hard-axis was used to demonstrate the anomalous Hall signal in this altermagnet. We confirm the existence of an anomalous Hall effect in our RuO2 thin-film samples, whose set of magnetic and magneto-transport characteristics is consistent with the earlier report. By performing our measurements at extreme magnetic fields up to 68 T, we reach saturation of the anomalous Hall signal at a field Hc ≃ 55 T that was inaccessible in earlier studies but is consistent with the expected Néel-vector reorientation field.
Using internal strain and mass to modulate Dy⋯Dy coupling and relaxation of magnetization in heterobimetallic metallofullerenes DyM2N@C80 and Dy2MN@C80 (M = Sc, Y, La, Lu)
Endohedral clusters inside metallofullerenes experience considerable inner strain when the size of the hosting cage is comparably small. This strain can be tuned in mixed-metal metallofullerenes by combining metals of different sizes. Here we demonstrate that the internal strain and mass can be used as variables to control Dy⋯Dy coupling and relaxation of magnetization in Dy-metallofullerenes. Mixed-metal nitride clusterfullerenes DyxY3−xN@Ih-C80 (x = 0-3) and Dy2LaN@Ih-C80 combining Dy with diamagnetic rare-earth elements, Y and La, were synthesized and characterized by single-crystal X-ray diffraction, SQUID magnetometry, ab initio calculations, and spectroscopic techniques. DyxY3−xN clusters showed a planar structure, but the slightly larger size of Dy3+ in comparison with that of Y3+ resulted in increased elongation of the nitrogen thermal ellipsoid, showing enhancement of the out-of-plane vibrational amplitude. When Dy was combined with larger La, the Dy2LaN cluster appeared strongly pyramidal with the distance between two nitrogen sites of 1.15(1) Å, whereas DyLa2N@C80 could not be obtained in a separable yield. Magnetic studies revealed that the relaxation of magnetization and blocking temperature of magnetization in the DyM2N@C80 series (M = Sc, Y, Lu) correlated with the mass of M, with DySc2N@C80 showing the fastest and DyLu2N@C80 the slowest relaxation. Ab initio calculations predicted very similar g-tensors for Dy3+ ground state pseudospin in all studied DyM2N@C80 molecules, suggesting that the variation in relaxation is caused by different vibrational spectra of these compounds. In the Dy2MN@C80 series (M = Sc, Y, La, Lu), the magnetic and hysteretic behavior was found to correlate with Dy⋯Dy coupling, which in turn appears to depend on the size of M3+. Across the Dy2MN@C80 series, the energy difference between ferromagnetic and antiferromagnetic states changes from 5.6 cm−1 in Dy2ScN@C80 to 3.0 cm−1 in Dy2LuN@C80, 1.0 cm−1 in Dy2YN@C80, and −0.8 cm−1 in Dy2LaN@C80. The coupling of Dy ions suppresses the zero-field quantum tunnelling of magnetization but opens new relaxation channels, making the relaxation rate dependent on the coupling strengths. DyY2N@C80 and Dy2YN@C80 were found to be non-luminescent, while the luminescence reported for DyY2N@C80 was caused by traces of Y3N@C80 and Y2ScN@C80