5. NEW PHENOMENA UNDER HIGH PRESSURE
5.3 Negative MR of the magnetic multilayer Fe/Tb
shown inFigure 148. They increase with increasing pressure which is in contrast to the case for a-Ce58Ru42 in Figure 146. The origin of these discrepancies is not clear at present. The values of d(m/m0)/dP are evaluated to be 4104and 1102GPa1forc- anda-CeCu6, respec- tively. The value ofa-CeCu6is about 25 times larger than that ofc-CeCu6, which indicates that the Kondo effect ina-CeCu6is enhanced strongly by pressure.
In summary, a-CexRu100x alloys (x¼67 and 80) exhibit HF-like behavior characterized by large g and A. The ratios of A/g2 for those alloys show about 0.5106mOcm(Ce mol K2/mJ)2which is located in between the KW relation (full line) and generalized KW relation with N¼6(dotted line) as shown in Figure 144. By applying pressure, trans- port properties ina-Ce58Ru42anda-CeCu6are drastically changed andTK decreases ina-Ce58Ru42, but it increases ina-CeCu6.
of metals and alloys. There have been a few reports for the pressure effect on the GMR. Recently, it has been reported that a large enhancement of GMR occurs in Fe/Cr magnetic multilayers (Suenaga et al., 2007), where the GMR is observed when the antiparallel arrangement of Fe layer spins changes to parallel one by applying magnetic field. This investigation sheds new light on the basic mechanism of the transport properties and GMR in Fe/Cr magnetic multilayers. Since only a few examples of such enhancements of GMR in magnetic multilayers have been reported until now (Sakai et al., 1998), it is worthwhile to explore such pressure-induced phenomena in novel magnetic systems.
Magnetic multilayer systems including heavy rare earth metals are known to have various magnetic properties, such as antiferromagnetic, spiral magnetic, or twisted magnetic structures. These magnetic struc- tures can be realized in magnetic exchange spring multilayers. The mag- netic exchange springs can tailor artificial domain walls. It has been argued that domain walls in a ferromagnet should give rise to MR
a-CeCu6 30
⫻10–3
20
10
00 10
P (GPa)
20 1 2 3
m/m0
m
c-CeCu6
FIGURE 148 The value of the slope,m(¼@r/@logT), fora-CeCu6as a function of pressure. The pressure dependence of normalized valuesm/m0is plotted fora- and c-CeCu6(Kagayama et al., 1994a).
(Levy and Zhang, 1997).Mibu et al. (1998)studied the effect of exchange springs in the SmCo/NiFe system. However, MR here is small (1.5%) and dominated by anisotropic magnetoresistance (AMR). Gordeev et al.
(2001)demonstrated that the formation of short exchange springs in the YFe2/TbFe2superlattice results in a large magnitude of MR, as high as 32%. In general, the directions of magnetization in consecutive layers can be switched when a magnetic field is applied, and MR changes dramati- cally as a whole.
The Fe/Tb multilayer system is expected to have some kind of twisted magnetic structure, caused by the competition among the exchange cou- pling, the Zeeman energy, and the anisotropy energy. Takanod et al.
(2004)considered a twisting model where Fe magnetic moment and Tb magnetic moment make an angle with one another under the assumption that Fe magnetic moment is always aligned parallel to the magnetic field and that Tb magnetic moments are parallel coupled in the Tb layer.
Figure 149 shows an M–T magnetic phase diagram of [Fe(12 nm)/Tb (15 nm)]25 multilayer with long artificial period. In all regions, Fe mag- netic moment is magnetically dominant. In the region ‘‘Fe-aligned,’’ only Fe magnetic moments survive above 320 K which is the estimated Curie temperature of Tb in this multilayer. In the region ‘‘FerriI,’’ Tb magnetic moment and Fe magnetic moment are ferrimagnetically coupled in the rangeH < HC. This is due to the ordinary exchange coupling between Fe
2.0
1.0
00 100 200 300
T (K) m0H (T)
400 500
Ferro
Twisted Fe-aligned
Fe:
Tb:
FerriII
FerriI
FIGURE 149 Magnetic phase diagram of [Fe(12 nm)/Tb(15 nm)]25multilayer (Takanod et al., 2004).
and Tb magnetic moments, which is always negative. With increasing the magnetic field, twisted magnetic structure appears when the sample temperature is low, particularly below 150 K in this Fe/Tb multilayer, in the region ‘‘Twisted.’’ This magnetic structure comes from the compe- tition among the exchange coupling, the Zeeman energy, and the anisot- ropy energy. Further increase in the magnetic field beyond 1.5 T results in the ‘‘Ferro’’ phase where Fe and Tb magnetic moments are parallel to the magnetic field. ‘‘FerriII’’ phase appears in the middle range of tempera- ture and the field exceeding the HC. The magnetic moments of the Tb layers depend upon the temperature, and they finally disappear at the boundary temperature 320 K. This magnetic phase generally comes from the condition that the total energy of the sample, which consists of the exchange coupling, the Zeeman energy, and the anisotropic energy, should be at the minimum. Computer simulations are necessary, taking into account these energies, to explain the magnetic phase diagram shown inFigure 149. The phenomenon of twisted state needed to be considered in detail that the magnitude and the direction of the magnetic moment of every atomic layer are estimated by molecular field from nearest neighbor interactions. Those magnitudes and directions can be different in each atomic layer. And it is also predicted that Tb magnetic moments have some spiral states, that is, the directions of Tb magnetic moments at the interface are opposite to the applied magnetic field and those inside of the Tb layer are aligned with the applied magnetic field.
Figure 150A shows the MR curve of Tb single layer at 4.2 K (Ohashi et al., 2008). Here, the magnitude of MR ratio is defined as
MRðHÞ ¼Rð Þ 0 R Hð Þ
Rð Þ0 : (40)
The slope dMR/dHis negative in the region of high magnetic field of up to 30 T, and no anomalies is observed in the MR(H) curve.
The magnitude of the negative MR ratio is MR(30 T)¼9.9%. Such a large MR of a heavy rare earth metal was reviewed byMcGuire and Potter (1975), in which the giant magnitude of MR was obtained in Ho metal to be 32% at 4.2 K. Taking into account that Tb metal has very high magnetic anisotropy, the negative MR of Tb can also be due to an AMR effect. This suggestion is supported by the fact that the slope |dMR/dH| of Tb decreases slightly with increasing magnetic field. As shown in Figure 150A, the MR curve tends to saturate above 10 T but has a long tail at high magnetic field. As for the Fe/Tb multilayer, MR is symmetrical with respect the change of sign of the magnetic fieldH, while theM–H curve shows a hysteresis loop (Takanod et al., 2004).Figure 150B shows the MR curve of [Fe(12 nm)/Tb(15 nm)]25at 4.2 K. Here, the giant nega- tive MR is obtained to beMR(30 T)¼24.6%. Such a large negative MR has
never been reported in a multilayer system consisting of a transition metal and a rare earth metal. Moreover, it is found that MR is not saturated completely even at 30 T which is largely different from Fe/Cr case.
Apparently, the MR of the Fe/Tb multilayer has been enhanced com- pared with that of the Tb monolayer film. Since the AMR effect is enhanced by spin polarization and spin–orbit interactions (Campbell et al., 1970), it is reasonable to assume that the AMR effects on the Tb layer is enhanced by spin polarization of the Fe layers.
At room temperature, R of [Fe(12 nm)/Tb(15 nm)]25 multilayer is almost independent of pressure. The pressure coefficient |R1@R/@P|
is less than 1103 GPa1, which is one order of magnitude smaller than those of Fe/Cr and Co/Cu multilayers (Oomi et al., 1997).Figure 151 shows the electrical resistanceRof [Fe(12 nm)/Tb(15 nm)]25as a function of temperature at several pressures. At 0.1 GPa,Rdecreases with decreas- ing temperature, showing good linearity from room temperature down to 220 K, but R deviates from linearity at low temperature. The slope
0.00 A
B –0.10
0.00
–0.05
0 –0.001 –0.002 –0.003 –0.004
–0.4 –0.2 0.0 H (T)
0.2 0.4
–0.10
–0.15
–0.20
–0.25
0 5 10
[Fe(12 nm)/Tb(15 nm)]25 4.2 K
–MR(H) –MR (H)
–MR(H)
4.2 K Tb
H (T)
15 20 25 30
FIGURE 150 The MR curves of (A) Tb at 4.2 K and (B) [Fe(12 nm)/Tb(15 nm)]25as a function of the magnetic field applied parallel to the plane. Inset shows the MR curve of Fe/Tb from0.5 to 0.5 T (Ohashi et al., 2008).
@R/@T tends to increase with decreasing temperature slightly from 220 K down to 50 K. It is caused by the ferromagnetic order of Tb at TC219 K.Figure 152shows a sharp change in the slope of the resistivity curve of metallic Tb at 229 K for a weak antiferromagnetic state and at 219 K for a ferromagnetic one (Ohashi et al., 2009).
R of Fe/Cr multilayer is almost independent of pressure aboveTC, indicating that the scattering process between conduction electrons and phonons is not changed by pressure up to 3.2 GPa. BelowTC, on the other hand, we note a general increase in the total resistance of Tb with increas- ing pressure. It means that the spin-dependent scattering is enhanced with increasing pressure, since the ferromagnetic order of the Tb layer is suppressed. Indeed, the residual resistivity ratio R(280 K)/R(4.2 K) decreases with increasing pressure. The ratio R(280 K)/R(4.2 K) is obtained to be 1.28 at ambient pressure and that at 3.2 GPa is 1.26. This suggestion is consistent with the previous report that the spontaneous magnetization of Tb is suppressed by applying pressure (Bloch and Pauthenet, 1964).R–Tcurves show a minimum aroundTmin21 K and a maximum around Tmax 4 K, which is not observed in multilayers made from 3d transition metals such as Fe/Cr and Co/Cu (Oomi et al., 1997). Some of magnetic phase boundaries may exist nearTmaxandTmin,
3.2 Gpa 1.1 Gpa 0.1 Gpa
[Fe(12 nm)/Tb(15 nm)]25
R (mW)
110
105
100
95
90
85
800 50 100 150
T (K)
200 250 300
FIGURE 151 The electrical resistance of [Fe(12 nm)/Tb(15 nm)]25as a function of the temperature at several pressures (Ohashi et al., 2008).
but the reason is unknown in detail. BothTmaxandTminare independent of pressure.
Figure 153shows MR ratios up to 8.5 T at 4.2 K at several pressures.
It is already shown in Figure 150B that MR is not saturated completely even at 30 T. Further, the magnitude of MR decreases with increasing pressure. The effect of pressure on the magnitude of MR ratio, MR(8.5 T), is estimated by substitutingH¼8.5 T in Eq.(40).Figure 154A shows the magnitude of MR ratio at 8.5 T, MR(8.5 T), as a function of pressure. MR (8.5 T) decreases proportionally to the applied pressure. The pressure coefficient is (1/MR)d(MR)/dP 0.025 GPa1. In order to explain this result, we defined the magnitude of MR as DR¼ R(0)R(8.5 T).
By substitutingDRinto Eq.(40)at the magnetic field of 8.5 T, the MR ratio is obtained as MR(8.5 T)¼DR/R(0). By differentiating the equation with respect to pressure, we obtain
1 ðMRÞ
@ðMRÞ
@P ¼ 1
DR
@DR
@P 1
Rð Þ0
@Rð Þ0
@P : (41)
It means that the effect of pressure on MR consists of two terms: one is the effect of pressure onDRand the other is that on R(0). As shown in
140
120
100 Tb
0.4
0.3
0.2
dp/dT (mWcm/K)
0.1
0
160 180 200 220 T (K)
240 260
80
60
40
200 50 100 150
r (mWcm)
T (K)
200 250 300
FIGURE 152 The electrical resistivity of Tb single layer as a function of the tempera- ture. Inset shows temperature derivative of the resistivity (Ohashi et al., 2009).
Figure 154B,R(0) at 4.2 K increases at the rate of [1/R(0)][dR(0)/dP]¼ 6.0103GPa1. Qualitatively, this result is consistent with the sugges- tion that the spin-dependent scattering is enhanced because of the sup- pression of the ferromagnetic order of the Tb layer. Indeed, as shown in Figure 151, theR(T) curve increases with increasing pressure belowTC.
Further, as shown inFigure 154C,DRdecreases at the rate of (1/DR) (dDR)/dP ¼ 0.020 GPa1 at 4.2 K. Since pressure suppresses the ferromagnetic order of the Tb layer, AMR effects can also be suppressed.
Then DR decreases with increasing pressure. By substituting the values of [1/R(0)][dR(0)/dP] and (1/DR)(dDR/dP) into Eq.(41), (1/MR) (dMR/dP) is estimated to be0.026 GPa1, which is almost the same as 0.025 GPa1obtained by using the experimental results inFigure 154A.
In Fe/Cr magnetic multilayers,Suenaga et al. (2007)reported that the MR of [Fe(2 nm)/Cr(3 nm)]20is enhanced strongly by an application of pres- sure. This result is different from the case of Fe/Tb multilayers as men- tioned above. This may be resulted from a difference in spin structure and the interlayer coupling.
In summary, the suppression of MR of Fe/Tb multilayers is caused by both the effects of pressure onDRandR(0). Both effects are caused by the same origin, that is, by the change in magnetic states in the Tb layers. This is related to the suppression of the magnitude of MR by applying pressure.
0
–0.02
–0.04
–0.06
– MR(H)
–0.08
–0.10 2 4 6
H (T) [Fe(12 nm)/Tb(15 nm)]25
4.2 K
3.2 GPa 2.1 GPa 1.1 GPa 0.1 GPa
8 10
FIGURE 153 MR curve of [Fe(12 nm)/Tb(15 nm)]25at 4.2 K as a function of the magnetic field applied parallel on the plane. The value of MR is obtained by using Eq.(41)(Ohashi et al., 2008).