Thermal demagnetization due to spin waves in nanocrystalline Ni

• Thermal demagnetization in nanocrystalline Ni is solely due to spin waves.
• Stoner single-particle excitations do not contribute.
• Magnon–magnon interactions cause thermal renormalization of spin wave stiffness.
• Crystallite size is the relevant length for spin waves in nanocrystalline nickel.
• Spin-fluctuation-to-spin-wave crossover in 10 nm nickel nanoparticles.

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 10kOe≤H≤70kOe and temperatures T≤350K, (ii) demonstrate that spin-wave (SW) excitations alone account for the observed MH(T  ) and (iii) the thermal renormalization of spin-wave stiffness is primarily due to the magnon–magnon interactions. For fields H≥20kOe, the spin-wave stiffness at 0K,D(T=0,H), is found to decrease with field as D(T=0,H)∼H1/2D(T=0,H)∼H1/2 for all the nanocrystalline samples. Extrapolation of the D(T=0,H)−H1/2D(T=0,H)−H1/2 straight line to H  =0 yields D0≡D(T=0,H=0)D0≡D(T=0,H=0) for a sample of given d. D0 varies with d   as d4/3d4/3. This power law behavior of D0 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†T≤T†(H) in nc-Ni with d=10 nm. Such departures, marked by the T4/3T4/3 power law behavior of [MH(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 H1/2H1/2 power law.