Magnetic field induced random pulse trains of magnetic and acoustic noises in martensitic single-crystal ${\mathrm{Ni}}_2\mathrm{MnGa}$

Jerky magnetic and acoustic noises were evoked in a single variant martensitic ${\mathrm{Ni}}_2\mathrm{MnGa}$ single crystal (produced by uniaxial compression) by application of an external magnetic field along the hard magnetization direction. It is shown that after reaching the detwinning threshold, spontaneous reorientation of martensite variants (twins) leads not only to acoustic emission but magnetic two-directional noises as well. At small magnetic fields, below the above threshold, unidirectional magnetic emission is also observed and attributed to a Barkhausen-type noise due to magnetic domain wall motions during magnetization along the hard direction. After the above first run, in cycles of decreasing and increasing magnetic field, at low-field values, weak, unidirectional Barkhausen noise is detected and attributed to the discontinuous motion of domain walls during magnetization along the easy magnetization direction. The magnetic noise is also measured by constraining the sample in the same initial variant state along the hard direction and, after the unidirectional noise (as obtained also in the first run), a two-directional noise package is developed and it is attributed to domain rotations. From the statistical analysis of the above noises, the critical exponents, characterizing the power-law behavior, are calculated and compared with each other and with the literature data. Time correlations within the magnetic as well as acoustic signals lead to a common scaled power function (with $\beta =-1.25$ exponent) for both types of signals.

Figure 1

Experimental setup, schematically (M and A refer to magnetic and acoustic signals respectively; see also the text).

Figure 2

Magnetic emission, ME, acoustic emission, AE, and relative deformation, $\mathrm{\Delta }L/L_0$, as a function of increasing magnetic field. The insert shows the shapes of the magnetic signals in the enlarged part of the unidirectional noise package.

Figure 3

Coincidence between magnetic and acoustic emission peaks (ME and AE, respectively). The insert shows the shapes of two coinciding MA and AE signals: see also the text.

Figure 4

Magnetic emission, ME, acoustic emission, AE, and relative deformation, as a function of decreasing magnetic field in the second cycle.

Figure 5

Magnetic emission, ME, acoustic emission, AE and relative deformation $\mathrm{\Delta }L/L_0$, as a function of increasing magnetic field in the second cycle.

Figure 6

Magnetization curves during the first (open symbols) and the following cycles (full dots). The arrow shows the beginning of detwinning (see also Fig. 2).

Figure 7

Change of the twin and magnetic domain structure (see also Ref. [30]) with increasing external magnetic field $B$ under a small compression due to the measuring force ($0.9\text{N}\sim 0.4\text{MPa}$): (a) single variant structure (produced by compression), the easy axis of magnetization (c axis) is vertical, the magnetic domains are aligned along the easy axis and separated by ${180}^{\circ }$ domain walls if $B=0$, (b) with increasing $B$ there are rotations inside the magnetic domains and domain wall motions, (c) at a certain $B$ value new twin nucleates, with c axis along the field, and thus within this the magnetization is parallel with $B$, (d) further increase of $B$ leads to the increase of the volume fraction of the new twin, during which there are sudden slips in the magnetization as the twin boundary experiences intermittent slips, (e) effect of decreasing the field to zero: one arrives at a variant structure, with a magnetic domain structure similar to (a) but rotated by ${90}^{\circ }$ (and containing a small fraction of a second variant, remained). Starting from (e) and cycling the field (increasing/decreasing the field), the system switches between (e) and (d).

Figure 8

Change of the magnetization, schematically during the first run (A-B-C path) and during the decrease (C-A path) or increase (A-C path) of the magnetic field after the first run. B corresponds to the start of detwinning. It can be seen that the A-B path is along the hard magnetization curve, while the low-field part of the A-C cycle lies along the easy magnetization curve (after Refs. [27] and [30]). The upper part of our experimental curves in Fig. 6 corresponds to this scheme.

Figure 9

Magnetic noise detected during increasing and decreasing the magnetic field between 0 and 0.3 T, i.e., stopping the increase of B before the deformation started (see Fig. 2) and decreasing it from this value.

Figure 10

Unidirectional Barkhausen signals, followed by two-directional peaks if the sample was constrained (detwinning is not allowed). The arrows indicate the direction of the change of the field.

Figure 11

Changes of the vertical components of magnetizations of neighboring domains schematically, if there is a small misalignment, ${\phi }_0$, from the exactly perpendicular position of domain magnetizations as compared to the direction of the field (see also the text).

Figure 12

Probability density functions of the peak energy, amplitude, and the scaling relation between the area $S$ and duration $T$ of magnetic emission signals in the low-field range [see Figs. 2 and 9, (a), (b), and c)], respectively. The straight lines indicate the fits with straight lines, i.e., neglecting the points in the cutoff range [see Eq. (1)].

Figure 13

Probability density function of peak durations for the Barkhausen noises obtained from magnetization along hard directions (see Figs. 2 and 9 and the first row in Table 1).

Figure 14

Probability density functions of the peak energy for acoustic emission (a) and magnetic emission (b) signals in the high field range in Fig. 2.

Figure 15

$P(n;t_m)$ distributions of a sequence of $n$ acoustic and magnetic events belonging to the same burst with $t<1s$ and $P_{\mathrm{ind}}(n;t_m)$ distributions of randomized data sets (shuffled data). The solid lines show a power-law with $\beta =-1.25$ and the dashed lines show Eq. (2) (independent events) with $a=0.976$ for AE and $a=0.988$ for ME.