Tunable scaling behaviour observed in Barkhausen criticality of a ferromagnetic film

Abstract

A ferromagnetic material shows a sequence of discrete and jerky domain jumps, known as the Barkhausen avalanche 1,2 , in the presence of an external magnetic field. Studies of Barkhausen avalanches reveal power-law scaling behaviour that suggests an underlying criticality 3-8 , as observed in a wide variety of systems such as superconductor vortices 9 , microfractures 10 , earthquakes 11 , lung inflations 12 , mass extinctions 13 , financial markets 14 and charge-density waves 15 . The most interesting unsolved fundamental question is whether the universality in the scaling exponent holds regardless of the material and its detailed microstructure. Here we show that the scaling behaviour of Barkhausen criticality in a given ferromagnetic film is experimentally tunable by varying the temperature (not dimensionality). We observe for the first time that the scaling behaviour in the Barkhausen criticality of a given system crosses over between two universality classes when the relative contributions from the dipolar interaction and domain-wall energies are altered by an experimental parameter.All theoretical works so far predict that the universality of the scaling exponent depends only on the dimensionality of a system, even though the value of the scaling exponent varies according to the theory [16][17][18][19][20][21][22] . However, the measured scaling exponents reported in the literature span a relatively wide range of values despite the same dimensionality 3-8 . Thus, the universality has been questioned, and our understanding is far from complete. To test the validity of the universality of Barkhausen criticality, a desirable approach is to make systematic measurements of the scaling exponent under well-controlled experimental conditions with reliable statistics in a given system while maintaining the same dimensionality. A ferromagnetic (FM) MnAs film on GaAs(001) substrate is considered an ideal system for such purposes: it reveals a systematic variation of domain-evolution patterns with temperature during a Barkhausen avalanche, a variation that results from the decrease in the saturation magnetization M S with temperature 23 . Thus, scaling behaviour in different domain-evolution patterns in a given system can be investigated in an experimentally controllable manner. Figure 1 shows representative domain-evolution patterns of the 50 nm MnAs film observed three consecutive times by means of a magneto-optical microscope magnetometer (MOMM) at each designated temperature in a range of 20−35 • C. In Fig. 1, we can clearly see that the domain evolution patterns at each temperature show a sequence of discrete and jerky domain jumps during the magnetization reversal. Also, we found that the domain jumps proceed with randomness of interval, size and location for the repeated experiments, as clearly seen from the three representative domain images at each temperature. From this evidence, it Figure 1 Representative domain-evolution patterns at several temperatures in the temperature range of 20−35 • C. These pattern...

Universality classes and crossover scaling of Barkhausen noise in thin films

“…To mimic the experiments of Ruy et al [10], we simulate the system by integrating Eq. (3) numerically for a lateral system size L = 512, fixing the external force F ext to a constant value below the critical depinning force F c (above which the DW would keep moving continuously with a nonzero time-averaged velocity), and monitor the dynamics of the DW.…”

“…In three-dimensional bulk ferromagnetic materials, the scaling behavior of the Barkhausen effect is understood theoretically in terms of the depinning transition of domain walls [3] with two distinct universality classes for amorphous and polycrystalline materials [4]. A similar clear-cut classification does not exist in lower dimensions, despite Barkhausen avalanches having been studied experimentally for decades in several ferromagnetic thin films with in-plane [5][6][7][8][9][10] or out-of-plane anisotropy [11,12]. This issue is particularly important because these lowdimensional magnetic structures have become increasingly relevant for various technological applications [13,14].…”

“…An important step towards understanding the different universality classes in thin films was achieved by the magnetooptical experiments of Ryu et al [10], who observed a crossover between two different avalanche size exponents τ as temperature T was varied close to but below the Curie temperature T c of a 50-nm MnAs film. This crossover was accompanied by changes in DW morphology, such that the DW structure evolves from rough for high T to DW's with a pronounced tendency to form zigzag or sawtoothlike patterns for lower T .…”

Model for domain wall avalanches in ferromagnetic thin films

“…Recently, experimental results show that the critical exponent of the size distribution decreases with increasing temperature, a fact attributed to a transition between the universality classes of long-to short-range interactions. [21] However, theoretically, this is an argument that can be sustained only for 3-dimensional systems. [22] The paper is organized as follows.…”

“…Magnetic thin films (bellow 200 nm) have exponents belonging to a new universality classes different from the 3-dimensional magnets. [19][20][21] The usual theoretical approach to these thin films are 2-dimensional models. Recently, experimental results show that the critical exponent of the size distribution decreases with increasing temperature, a fact attributed to a transition between the universality classes of long-to short-range interactions.…”