Cumulative minor loop growth in Co/Pt and Co/Pd multilayers

The behavior of minor hysteresis loops in perpendicular anisotropy [Co/Pt] and [Co/Pd] multilayers has been investigated. Upon applying a succession of identical magnetic field cycles, we observe a very substantial cumulative growth of the minor loop area. For the [Co/Pt] multilayers this effect only saturates near complete magnetization reversal while the behavior is slightly more limited for [Co/Pd] multilayers. We also find this cumulative growth to occur even if the minor loop field cycles are made asymmetric by means of a positive bias field. The cumulative behavior persists up to a sample-dependent threshold value above which this effect disappears. In all samples, the cumulative minor loop growth is correlated with a small reduction in the maximum magnetization value in each cycle. Magneto-optical Kerr microscopy studies correlate the minor loop growth with the memory and cumulative expansion of lateral domain cycling. All experimental observations can be consistently explained as an accumulation of small nucleation domains that aid subsequent reversals and facilitate the cumulative minor loop growth.

Figure 1

Field dependence of the magnetization for a ${\left(\text{Co}/\text{Pt}\right)}_8$ multilayer. The thick solid line represents the major loop behavior while the thin solid line shows a sequence of successive minor loops upon applying a symmetric field amplitude of $H_{\text{max}}=-H_{\text{min}}=290\text{Oe}$. The first, third, and fifth minor loop are labeled. The inset is a schematic of the $H$ vs $t$ dependence, which was applied for this measurement.

Figure 2

(a) $M\left(t\right)$ dependence for successive minor loop cycles measured for a ${\left(\text{Co}/\text{Pt}\right)}_8$ multilayer. The different curves were measured for different peak values of the magnetic field $H_{\text{max}}\left(=-H_{\text{min}}\right)$. The time is given in units of the cycle period $T=80\text{s}$, which was held constant for all experiments. The experimental data are shown as (●) while the solid lines represent least-squares fits of Eq. (2); (b) relaxation time constant $\tau$, derived from the least-squares fits of Eq. (2) to the experimental data, as a function of $-H_{\text{min}}$. The squares are the results of the individual fits while the dashed line illustrates exponential field dependence according to Eq. (4).

Figure 3

$M\left(t\right)$ dependence for successive minor loop cycles measured for a ${\left(\text{Co}/\text{Pt}\right)}_8$ multilayer. The solid line, corresponding to the left-hand scale, shows the complete time evolution upon applying a field sequence with $H_{\text{max}}=-H_{\text{min}}=280\text{Oe}$. The open circles (○) show the maximum magnetization $M_{\text{max}}$ reached in every cycle and correspond to the right-hand scale.

Figure 4

(a) $\Delta M\left(t\right)$ dependence for successive minor loop cycles measured for a ${\left(\text{Co}/\text{Pd}\right)}_8$ multilayer upon applying symmetric field sequences of varying strength $H_{\text{max}}=-H_{\text{min}}$; (b) relaxation time constant $\tau$, derived from the least-squares fits of Eq. (5) to the experimental data, as a function of $-H_{\text{min}}$. The circles are the results of the individual fits while the line illustrates exponential field dependence according to Eq. (4).

Figure 5

$\Delta M\left(t\right)$ dependence for successive minor loop cycles measured for a ${\left(\text{Co}/\text{Pd}\right)}_8$ multilayer upon applying asymmetric field sequences: (a) $H_{\text{max}}=450\text{Oe}$ for different values of $H_{\text{min}}$; (b) $-H_{\text{min}}=370\text{Oe}$ for different values of $H_{\text{max}}$.

Figure 6

(a) Relaxation time constant $\tau$, derived from the least-squares fits of Eq. (5) to experimental data from a ${\left(\text{Co}/\text{Pd}\right)}_8$ multilayer, as a function of $-H_{\text{min}}$ for different values of $H_{\text{max}}=500\text{Oe}$ (◼), 450 Oe (○), 400 Oe (△), and $H_{\text{max}}=-H_{\text{min}}$ $(★)$; (b) $M_{\text{max}}$ vs $\Delta M$ data for successive minor loop cycles with $-H_{\text{min}}=360\text{Oe}$ (○), 370 Oe (●), and 380 Oe (△) and fixed $H_{\text{max}}=500\text{Oe}$.

Figure 7

$\Delta M\left(t\right)$ dependence for successive minor loop cycles measured for a ${\left(\text{Co}/\text{Pd}\right)}_8$ multilayer upon applying asymmetric field sequences for different values of $H_{\text{max}}$ and $-H_{\text{min}}=370\text{Oe}$.

Figure 8

Sequence of Kerr-effect microscopy images taken on a ${\left(\text{Co}/\text{Pd}\right)}_8$-multilayer sample at different points of an asymmetric field sequence $\left(H_{\text{max}}=500\text{Oe},-H_{\text{min}}=380\text{Oe}\right)$ during consecutive cycles. Columns 1, 2, and 3 correspond to the negative remanent state, the positive remanent state, and the initial negative reversal state at $H=-240\text{Oe}$, respectively. Rows (a)–(d) show pictures taken in four subsequent minor loop cycles. The schematic insets in (a1)–(a3) indicate at which point on the minor loop cycle the observation was made.

Figure 9

Schematic of the underlying physical process: the sequence of images shows the domain evolution during consecutive minor loop cycles. Columns 1, 2, and 3 correspond to the negative remanent state, the positive remanent state, and the initial negative reversal state for $H>H_{\text{min}}$, respectively. Rows (a)–(c) illustrate the behavior of three subsequent minor loop cycles. The schematic insets in (a1)–(a3) indicate, which point on the minor loop cycle is represented in every column.

Figure 10

Sequence of Kerr-effect microscopy line scans taken on a ${\left(\text{Co}/\text{Pd}\right)}_8$-multilayer sample at different points of an asymmetric field sequence $\left(H_{\text{max}}=500\text{Oe},-H_{\text{min}}=380\text{Oe}\right)$ during the same cycle: $\left(\text{b}1\right)\to \left(\text{b}2\right)\to \left(\text{b}3\right)$ as shown in Fig. 8.