Thermodynamic limit of the XXZ central spin model with an arbitrary central magnetic field

The U(1)symmetry of the X X Z central spin model with an arbitrary central magnetic field B is broken,since its total spin in the z-direction is not conserved.We obtain the exact solutions of the system by using the off-diagonal Bethe ansatz method.The thermodynamic limit is investigated based on the solutions.We find that the contribution of the inhomogeneous term in the associated T-Q relation to the ground state energy satisfies an N^(-1)scaling law,where N is the total number of spins.This result makes it possible to investigate the properties of the system in the thermodynamic limit.By assuming the structural form of the Bethe roots in the thermodynamic limit,we obtain the contribution of the direction of B to the ground state energy.It is shown that the contribution of the direction of the central magnetic field is a finite value in the thermodynamic limit.This is the phenomenon caused by the U(1)symmetry breaking of the system.

High current limits in chemical vapor deposited graphene spintronic devices

Understanding the stability and current-carrying capacity of graphene spintronic devices is key to their applications in graphene channel-based spin current sensors,spin-torque oscillators,and potential spin-integrated circuits.However,despite the demonstrated high current densities in exfoliated graphene,the current-carrying capacity of large-scale chemical vapor deposited(CVD)graphene is not established.Particularly,the grainy nature of chemical vapor deposited graphene and the presence of a tunnel barrier in CVD graphene spin devices pose questions about the stability of high current electrical spin injection.In this work,we observe that despite structural imperfections,CVD graphene sustains remarkably highest currents of 5.2×10^(8)A/cm^(2),up to two orders higher than previously reported values in multilayer CVD graphene,with the capacity primarily dependent upon the sheet resistance of graphene.Furthermore,we notice a reversible regime,up to which CVD graphene can be operated without degradation with operating currents as high as 108 A/cm^(2),significantly high and durable over long time of operation with spin valve signals observed up to such high current densities.At the same time,the tunnel barrier resistance can be modified by the application of high currents.Our results demonstrate the robustness of large-scale CVD graphene and bring fresh insights for engineering and harnessing pure spin currents for innovative device applications.