Pressure Lag Effect Of The Spin Pumping In The Spin-transition Materials

The generation and detection of the spin current as a prerequisite of the spintronic devices is widely investigated.The applied pressure which can change obviously the crystal field energy in the spin-transition materials can result in the transition between the high-spin state and the low-spin state of the system.In this article,we consider a spin-transition material| normal metal Pt bilayer.When we applied an external magnetic field perpendicular to an excitation field,both in plane,the applied pressure on the bilayer modulates the spin state of the system and the magnetization magnitude,in turn changes the spin current pumped into the normal metal and the measurable DC and AC voltages induced by the inverse spin Hall effect in the normal metal.We find that under certain conditions,pressure lag effect exists in the pumped spin current in the normal metal during the increasing and decreasing pressure processes.Firstly,we investigate the effect of the applied pressure on the state of the system.Numerical results show that with the increase of the pressure the high spin mole fraction in the spin transition material decreases,and the spin transition material changes from the high-spin state into the low-spin state.When the enthalpy term describing the intermolecular interaction is small enough,the spin-transition material with the increase of the external pressure change gradually from the high-spin state into the low-spin state and the transition process is not abrupt.For the large enough enthalpy,the high spin mole fraction appears the lagged behavior,i.e.the pressure lag hysteresis,during the increasing and decreasing pressure processes.Secondly,we calculate the dependence of the pressure lag hysteresis on the intermolecular interaction parameter.We find that the width of the pressure lag hysteresis increases with the increase of the intermolecular interaction.Thirdly,we consider the modulation of the pressure on the measurable DC and AC voltages from the pumped spin current.Calculated results show that in the low pressure condition the pumped spin current and the measurable DC and AC voltages attain the maximum when the ferromagnetic resonance condition is satisfied.With the increase of the applied external pressure,the transition of the system spin state results in the decrease of the magnetization magnitude,in turn,the pumped spin current and the measurable DC and AC voltages decay rapidly with the departure of the resonance condition.For the small intermolecular interaction,the measurable DC and AC voltages change gradually and no abrupt behavior exists during the increasing and decreasing pressure processes.For the large enough intermolecular interaction,the measurable DC and AC voltages from the pumped spin current appear the lagged behavior,i.e.the pressure lag spin pumping,during the increasing and decreasing pressure processes.Finally,for different electrical conductivities of spin-transition materials and different thickness of paramagnetic metals we investigate the effect of the applied pressure on the measurable DC and AC voltages.Numerical results show that the pressure lag behavior or the pressure lag hysteresis still exists for large enough intermolecular interaction.