Morphotropic phase boundary in ferromagnets- a way leading to large magnetostriction 54 Materials Science : Structure The morphotropic phase boundary (MPB), a phase boundary separating two ferroelectric phases of different crystallographic symmetries in the composition-temperature phase diagram, is crucial in ferroelectric materials, because MPB can lead to a great enhancement of piezoelectricity, the most useful property of this large class of functional materials. The current workhorse of piezoelectric materials, i.e., PZT (PbZrO 3 -PbTiO 3 ) and PMN-PT (PbMg 1/3 Nb 2/3 O 3 -PbTiO 3 ), is designed to have a composition close to the MPB to achieve a maximum piezoelectric effect. Figure 1(a) shows a typical ferroelectric MPB in PZT, which separates a ferroelectric rhombohedral (R) phase on the PbZrO 3 side and a ferroelectric tetragonal (T) phase on the PbTiO 3 side. The R and T ferroelectric phases share a common cubic paraelectric phase at high temperatures. Theoretical and experimental studies have shown that, at the MPB composition, P s can be easily rotated under a small external field, thereby causing a high piezoelectric effect. Ferromagnetic systems are physically parallel to ferroelectric ones; the former involve an ordering of magnetic moment and the latter involve an ordering of polarization below a critical temperature (Curie temperature) T c . In both systems, the order parameter is coupled to the lattice, respectively leading to the magnetoelastic and piezoelectric effects. From the physical parallelism between ferromagnetism and ferroelectricity, it is tempting to ask an interesting question: Can a similar MPB situation exist in ferromagnetic systems? If yes, can such magnetic MPB yield large magnetostriction (magnetic-field- induced distortion, an effect analogous to the piezoelectricity in ferroelectrics)? Following the definition of MPB in ferroelectrics, a magnetic MPB should be a phase boundary separating two different ferromagnetic states with different crystallographic symmetries. So far, the major obstacle to the existence of MPB in ferromagnets has been the general observation (by conventional X-ray diffractometry (XRD)) that a difference in M s direction does not result in a difference in crystal symmetry, differently from the ferroelectric case. Therefore, for ferromagnetic systems, the condition for MPB seems not satisfied. However, with the great enhancement in the structure resolution using synchrotron XRD ( BL15XU ), recent studies have proved that different ferromagnetic states indeed correspond to different crystal symmetries 0 0 0 50 0 20 40 60 80 30%DyCo 2 70%DyCo 2 90%DyCo 2 T C T C T M 100 150 200 20 40 60 80 100 18.04 18.08 18.12 42.56 42.64 42.72 40 80 120 160 200 240 280 0 20 40 60 80 100 100 200 300 400 500 P C MPB F R (Pm3m) (R3m) F T (P4mm) F R (R3c) Temperature (℃) Temperature (K) χ ’ (emu/g)×10 -3 PbZrO 3 mol% PbTiO 3 PbTiO 3 TbCO 2 DyCO 2 2 θ θ (deg) mol% DyCO 2 (a) (b) (c) (d) a a a a a a a a c P S P S a a a A o Cubic Cubic Rhombohedral Tetragonal Tetragonal 222 222 C 222 R 222 T 800 T 008 T 800 C 800 R 800 Rhombohedral a a a a a a a a c MS M S a a a MPB T C 222 R _ Intensity (arb. units) 50 100 150 200 50 100 150 200 Temperature (K) Fig. 1. (a) Phase diagram of PZT. (b) Phase diagram of TbCo 2 -DyCo 2 . (c) Temperature dependence of ac susceptibility χ ’. T c and T M denote the para-ferro and ferro-ferro transition temperatures, respectively. (d) Synchrotron XRD profiles of cubic paramagnetic, rhombohedral ferromagnetic and tetragonal ferromagnetic phases. 55 [1,2], the same as in the ferroelectric case; however, the lattice distortion due to a difference in crystal symmetry is usually too small to be detected by conventional XRD analysis. Now, we have a good reason to expect the existence of a magnetic MPB and therefore we propose to detect a magnetic MPB in a pseudo binary ferromagnetic system TbCo 2 -DyCo 2 , using of BL15XU beamline. The results are shown in detail in Fig. 1, Fig. 2, and Fig. 3. The MPB composition demonstrates a 3-6 times larger “figure of merit” of magnetostrictive response than the off-MPB compositions (Fig. 3). The finding of MPB in ferromagnets may help to discover novel high-performance magnetostrictive and even magnetoelectric materials [3]. 0 0 0 10 20 30 40 30 60 90 90 100 110 120 120 400 800 1200 1600 20 40 40 50 60 70 80 90 100 60 MPB Rhombohedral Tetragonal 110 K 110 K 110 K 110 K 110 K mol% DyCo 2 Figure of merit χ χ ' ' (emu/g) × 10 -3 |ε| |ε|(× 10 -6 ) | |ε ε| |/Η (1/ Oe) × 10 -6 M S (emu/g) H C (Oe) 7.176 80 18.04 18.08 18.12 42.56 42.64 42.72 90 100 110 120 130 140 150 89.90 89.92 89.94 89.96 89.98 7.182 7.188 7.194 7.200 7.206 Temperature (K) 2 θ (deg) Lattice Parameters (Å) Intensity (arb. units) (b) (a) Tetragonal (T) Tetragonal (T) Rhombohedral (R) Rhombohedral (R) R + T aT aR α R α (deg) c T MPB range R+T 150K 222 R 222 R _ 222 R _ 800 R 800 R 800 T 800 T 008 T 008 T 222 R 222 T 222 T 110K 90K 222 70%DyCo 2 800 Fig. 2. (a) XRD profiles of rhombohedral phase at 150 K (above MPB), a mixture of rhombohedral and tetragonal phase at 110 K (at MPB), and tetragonal phase at 90 K (below MPB). The red and blue peaks underneath the experimental peaks are Lorentzian rhombohedral and tetragonal peaks respectively, giving the best fit to the experimental profiles. (b) Temperature dependence of lattice parameters ( a R and α R stand for the lattice parameters of the R-phase with M s ||[111], and a T and c T for that of the T-phase with M s ||[001]); the MPB corresponds to a 2-phase mixture of rhombohedral and tetragonal phases. The error bars are determined by the fitting error in Fig. 2(a). Fig. 3. Composition dependences of Ac susceptibility χ ’, saturation magnetization M s , coercivity H c , magnetostriction ε (absolute value) at 10 kOe field, and figure of merit ε /H c , in relation to MPB composition at 110 K. Sen Yang a,†, * and Xiaobing Ren b a NIMS Beamline Station SPring-8, National Institute for Materials Science b Ferroic Physics Group, National Institute for Materials Science (NIMS) Email: yang.sen@mail.xjtu.edu.cn † Present address: Department of Materials Physics, Xi'an Jiaotong University, China References [1] S. Yang and X. Ren: Phys. Rev. B 77 (2008) 014407. [2] S. Yang, X. Ren and X. Song, Phys. Rev. B 78 (2008) 174427. [3] S. Yang, H. Bao, C. Zhou, Y. Wang, X. Ren, Y. Matsushita, Y. Katsuya, M. Tanaka, K. Kobayashi, X. Song and J. Gao: Phys. Rev. Lett. 104 (2010) 197201.
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