Simultaneous investigation of thermal, acoustic, and magnetic emission during martensitic transformation in single-crystalline ${\text{Ni}}_2\text{MnGa}$

Simultaneous thermal, acoustic, and magnetic emission (AE and ME) measurements during thermally induced martensitic transformation in ${\text{Ni}}_2\text{MnGa}$ single crystals demonstrate that all three types of the above noises display many coincident peaks and the same start and finish temperatures. The amplitude and energy distribution functions for AE and ME avalanches satisfy power-law behavior, corresponding to the symmetry of the martensite. At zero external magnetic field asymmetry in the exponents was obtained: their value was larger for heating than for cooling. Application of constant, external magnetic fields (up to $B=722$ mT) leads to the disappearance of the above asymmetry, due to the decrease of the multiplicity of the martensite variants. Time correlations (i.e., the existence of nonhomogeneous temporal processes) within AE as well as ME emission events are demonstrated by deviations from the uncorrelated behavior on probability distributions of waiting times as well as of a sequence of number of events. It is shown that the above functions collapse on universal master curves for cooling and heating as well as for AE and ME noises. The analysis of the existence of temporal correlations between AE and ME events revealed that at short times the acoustic signals show a time delay relative to the magnetic one, due to the time necessary for the propagation of the ultrasound. At intermediate times, as expected, the magnetic signal is delayed, i.e., the magnetic domain rearrangement followed the steps of structural transformation. At much longer times the deviation from an uncorrelated (Poisson-type) behavior is attributed to the nonhomogeneity of the avalanche statistics.

Figure 1

Experimental arrangement. 1: Al-block; 2: sample with detector coils; 3: AE sensor with steel waveguide; 4: halogen lamp; 5: magnet poles.

Figure 2

Magnetic and acoustic activity during heating (a) and cooling (b) with rate 0.06 ${}^{\circ }$ C/min.

Figure 3

Acoustic activity and DSC during heating (a) and cooling (b) with rate 0.06 ${}^{\circ }$ C/min. The inset of (b) shows the enlarged part of acoustic activity below the DSC $M_f(\approx 44.63{}^{\circ }\text{C})$ temperature.

Figure 4

Acoustic activity as function of martensite ratio $\eta$ from simultaneous AE and DSC measurements during heating and cooling.

Figure 5

Energy probability distribution function from ME at $B=19$ mT, during cooling (2 ${}^{\circ }$ C/min). $P\left(E\right)=8.6\times {10}^{-8}\times E^{-1.55}\times \text{exp}(-E/9\times {10}^{-6})$.

Figure 6

ME amplitude (a) and energy (b) exponents as function of magnetic field.

Figure 7

AE amplitude (a) and energy (b) exponents as function of magnetic field (the curves for heating correspond to the case when the preceding cooling was made in magnetic field: see curves A in Fig. 6).

Figure 8

Probability distribution function of waiting times $\tau$ for acoustic and magnetic events at $B=0$ T. The horizontal and vertical axes are normalized by $1/〈\tau 〉$ and $〈\tau 〉$ respectively, where $〈\tau 〉\approx 0.1–0.5\text{s}$ is the mean waiting time. The dashed (Poisson) line corresponds to $\lambda =1.5{\text{s}}^{-1}$.

Figure 9

Probability distribution of a sequence of $n$ acoustic and magnetic events at $B=0$ T, belonging to the same burst with $\tau <{\tau }_m=0.5\text{s}$. Dashed line shows Eq. (5) with $a=0.6$ and the solid line shows the power-law behavior with $\beta =-1.9$.

Figure 10

Probability density function of the ${\delta }_{AE\to ME}$ and ${\delta }_{ME\to AE}$ delays for heating and cooling with 0.06 ${}^{\circ }$ C/min heating/cooling rate at $B=0$ mT (a) and $B=600$ mT (b). The dashed lines indicate the exponential function for uncorrelated signals.