Constrained Monte Carlo method and calculation of the temperature dependence of magnetic anisotropy

Abstract

We introduce a constrained Monte Carlo method which allows us to traverse the phase space of a classical spin system while fixing the magnetization direction. Subsequently we show the method's capability to model the temperature dependence of magnetic anisotropy, and for bulk uniaxial and cubic anisotropies we recover the low-temperature Callen-Callen power laws in M .We also calculate the temperature scaling of the 2-ion anisotropy in L1 0 FePt, and recover the experimentally observed M 2.1 scaling. The method is newly applied to evaluate the temperaturedependent effective anisotropy in the presence of the Néel surface anisotropy in thin films with different easy axis configurations. In systems having different surface and bulk easy axes, we show the capability to model the temperature-induced reorientation transition. The intrinsic surface anisotropy is found to follow a linear temperature behavior in a large range of temperatures. PACS numbers: 75.30.Gw, 75.70.Rf, 75.10.Hk, 75.70.Ak Recently, the high temperature behavior of magnetic anisotropy has become important due to the applications in heat-assisted magnetic recording (HAMR) 5-7 . The idea of HAMR is based on the heating of the recording media to decrease the writing field of the high anisotropy media (such as FePt) to values compatible with the writing fields provided by conventional recording heads. Since the writing field is proportional to the anisotropy field H k = 2K eff u (T )/M(T ), the knowledge of the scaling behavior of the anisotropy K u with the magnetization M has become a paramount consideration for HAMR 8 . It should be noted that even in relatively simple systems, a simple scaling behavior predicted by the Callen-Callen theory is only valid at temperatures far from the Curie temperature. The systems proposed for HAMR applications can also include more complex composite media such as soft/hard bilayers 9 , FePt/FeRh with metamagnetic phase transition 10,11 , or exchange-bias systems 12 .The evaluation of the temperature dependence of magnetic anisotropy is also important for the modeling of the laser-induced demagnetization processes. The thermal decrease of the anisotropy during the laser-induced demagnetization has been shown to be responsi-

Temperature-dependent exchange stiffness and domain wall width in Co

“…The simulated temperature dependence of the domain wall width allows the temperature dependence of the exchange stiffness parameter A to be calculated via the formula δ DW = π A/K. For this purpose we first evaluate the temperature dependence of the macroscopic anisotropy K using the constrained Monte Carlo method [40], implemented in the VAMPIRE code. The evaluation shows that the macroscopic anisotropy closely follows the Callen-Callen law K(m) ∼ m 3 practically up to 1200 K. Using the temperature dependent values of the anisotropy and the domain wall width resulting from our simulations we calculate the exchange stiffness for the whole temperature range, as shown in Fig.…”

Quantitative simulation of temperature-dependent magnetization dynamics and equilibrium properties of elemental ferromagnets

“…(4). Secondly, it allows a direct and more accurate determination of the temperature dependence of all the parameters needed for numerical micromagnetics at elevated temperatures from first principles when combined with atomistic spin model simulations [18][19][20] . We also expect the same form is applicable to other technologically important composite magnets such as CoFeB, NdFeB or FePt alloys.…”

“…Understanding the complex interaction of these physical effects often requires numerical simulations such as those provided by micromagnetics [12][13][14] or atomistic spin models 15 . Micromagnetic simulations at elevated temperatures 16,17 in addition need the temperature dependence of the main parameters 18 such as the magnetization, micromagnetic exchange 19 and effective anisotropy 20 . Although analytical approximations for these parameters exist, multiscale ab-initio/atomistic simulations 18,21 have been shown to more accurately determine them.…”

Non-Collinear Magnetic Configurations at Finite Temperature in Thin Films

“…At finite temperature it is well known that the temperature-dependent anisotropy energy decreases faster than the magnetization -see for example [15] -, while the temperature-dependent exchange generally decreases at the same rate as the magnetization as can be obtained in the random phase approximation method [16]. Therefore it may be expected that the system turns into the spin spiral state at finite temperature when the temperature-dependent parameters begin to favor this type of order, before reaching a paramagnetic state.…”