Proximity-Induced Fully Ferromagnetic Order with Eightfold Magnetic Anisotropy in Heavy Transition Metal Oxide CaRuO3

Ferromagnetic materials with a strong spin-orbit coupling (SOC) have attracted much attention in recent years because of their exotic properties and potential applications in energy-efficient spintronics. However, such materials are scarce in nature. Here, a proximity-induced paramagnetic to ferromagnetic transition for the heavy transition metal oxide CaRuO₃ in (001)-(LaMnO₃/CaRuO₃) superlattices is reported. Anomalous Hall effect is observed in the temperature range up to 180 K. Maximal anomalous Hall conductivity and anomalous Hall angle are as large as ∼15 Ω⁻¹ cm⁻¹ and ∼0.93%, respectively, by one to two orders of magnitude larger than those of the typical 3d ferromagnetic oxides such as La_0.67Sr_0.33MnO₃. Density functional theory calculations indicate the existence of avoid band crossings in the electronic band structure of the ferromagnetic CRO layer, which enhances Berry curvature thus strong anomalous Hall effects. Further evidences from polarized neutron reflectometry show that the CaRuO₃ layers are in a fully ferromagnetic state (∼0.8 μ_B/Ru), in sharp contrast to the proximity-induced canted antiferromagnetic state in 5d oxides SrIrO₃ and CaIrO₃ (∼0.1 μ_B/Ir). More than that, the magnetic anisotropy of the (001)-(LaMnO₃/CaRuO₃) superlattices is eightfold symmetric, showing potential applications in the technology of multistate data storage.     

Exact solutions for Belousov-Zhabotinskii reaction-diffusion system

Abstract. We consider the following simplified model for the Belousou-Zhabotinskii(B-Z)reaction:     

The occupation time of Brownian motion in a ball

LetW be a Wiener process of dimensiond3, starting from 0, and letX(t) be the total time spent byW in the ball centered at 0 with radiust. We give an affirmative answer to a conjecture of Taylor and Tricot⁽¹⁶⁾ on the tail distribution ofX(t). Lévy's lower functions ofX(t) are characterized by an integral test.