Thermal demagnetization due to spin waves in nanocrystalline Ni

Abstract An elaborate analysis of the decline of magnetization with increasing temperature, observed in nanocrystalline (nc-) Ni samples with average crystallite size, d , varying from d =10 nm to 40 nm, permits us to (i) completely rule out a possible Stoner single-particle contribution to the thermal demagnetization, M ( T ), at external magnetic fields 10 kOe ≤ H ≤ 70 kOe and temperatures T ≤ 350 K , (ii) demonstrate that spin-wave (SW) excitations alone account for the observed M H ( T ) and (iii) the thermal renormalization of spin-wave stiffness is primarily due to the magnon–magnon interactions. For fields H ≥ 20 kOe , the spin-wave stiffness at 0 K , D ( T = 0 , H ) , is found to decrease with field as D ( T = 0 , H ) ∼ H 1 / 2 for all the nanocrystalline samples. Extrapolation of the D ( T = 0 , H ) − H 1 / 2 straight line to H =0 yields D 0 ≡ D ( T = 0 , H = 0 ) for a sample of given d. D 0 varies with d as d 4 / 3 . This power law behavior of D 0 asserts that the crystallite size is the relevant length scale for spin waves. Strong departures from the spin-wave behavior are observed at low temperatures T ≤ T † ( H ) in nc-Ni with d =10 nm. Such departures, marked by the T 4 / 3 power law behavior of [ M H ( T )] 2 , are a manifestation of damped spin waves, which act as non-propagating spin fluctuations and get suppressed by magnetic field in accordance with the H 1 / 2 power law.