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Crystal and magnetic structure temperature evolution in Ni–Mn–Ga magnetic shape memory martensite
Materials Science and Engineering A 481–482 (2008) 298–301
Crystal and magnetic structure temperature evolution in Ni–Mn–Ga magnetic shape memory martensite I. Glavatskyy a,∗ , N. Glavatska a , I. Urubkov a , J.-U. Hoffman b , F. Bourdarot c a
Institute for Metal Physics, NAS of Ukraine, 36 Vernadsky blvd., Kiev, UA-03142, Ukraine Hahn-Meitner-Institut, Abt. NE/Gastgruppe T¨ubingen, Glienicker Str. 100, BENSC, D-14109 Berlin, Germany c D´ epartement de Recherche Fondamentale sur la Mati`ere Condens´ee, SPSMS, CEA Grenoble, 38054 Grenoble Cedex 9, France b
Received 22 May 2006; received in revised form 30 January 2007; accepted 5 February 2007
Abstract The current work presents the original results concerning the temperature evolution of the magnetic and crystal structure of Ni–Mn–Ga magnetic shape memory alloys within the entire temperature interval of the martensite phase. The atomic positions and the correct space group of the 5M martensite unit cell has been derived, which is crucial for the electronic structure calculations. Neutron diffraction studies of the Ni–Mn–Ga alloy, possessing a large magnetic shape memory effect (>5% shear strain), revealed that there are several magnetic transitions in the martensite phase due to the smooth strongly anisotropic temperature dependence of the martensite lattice parameters. © 2007 Published by Elsevier B.V. Keywords: Ni–Mn–Ga; Magnetic shape memory; Martensite; Magnetic structure
1. Introduction The structure of Ni–Mn–Ga intermetallics has been studied intensively during last years because some of these alloys exhibit a large magnetic shape memory effect (MSM) in martensite phase, which makes these materials unique [1]. It is thought that the magnetic shape memory effect is observed only in alloys having five-layered modulated structure of martensite. Thus, it is of particular importance to study the atomic and magnetic ordering of this type of martensites in Ni–Mn–Ga. For the possible technical application of the MSM effect, it is important to study the temperature stability of the magnetic and crystal structure of the Ni–Mn–Ga martensites exhibiting the effect, since previous experimental studies shows the strong and nonmonotonous temperature dependence of magnetic field-induced strains (MFIS) [2]. 2. Experimental The off-stoichiometric Ni50.5 Mn28.2 Ga21.3 (at.%) alloy, possessing large magnetic shape memory effect (over 5%) at room ∗
Corresponding author. Tel.: +380 44 4246427; fax: +380 44 4243310. E-mail address: [email protected] (I. Glavatskyy).
0921-5093/$ – see front matter © 2007 Published by Elsevier B.V. doi:10.1016/j.msea.2007.02.139
temperature was studied using the D15 neutron diffractometer (ILL, Grenoble, France). The Curie and martensite phase transformation temperatures as determined using dilatometric and low-field magnetic susceptibility measurements are TC = 374 K, TM = 303 K, TA = 310 K, respectively. During preliminary studies by neutron scattering methods (E2, BENSC, HMI), the crystal structure of martensite was determined as orthorhombic (a = 0.421 nm, b = 0.562 nm, and c = 2.105 nm at 296 K) with five-layered modulation along [1 0 1] and [1 0 −1] directions and remains stable within temperature range 300–4 K [3]. Before the studies, the single crystal was cooled under applied magnetic field of H = 0.5 T from the austenite phase, producing single variant non-twinned martensite. Then, the specimen was mounted on a 4-circle cradle with “Displex” refrigerator on ˚ At T = 300 K some 700 the D15 diffractometer with λ = 1.17 A. reflections were collected and the UB-matrix for the unit cell was determined, also a temperature dependence of the strongest reflections were studied in steps of 20 K from 300 K down to 20 K, giving 14 temperature points in martensite phase, allowing the evolution of the magnetic structure of martensite to be studied. Some “residual” (less then 10%) twinning was treated using “PREWASH” program. The integral intensity of the reflection is 2 , while proportional to the square of the scattering factor ≈ Fhkl for non-polarized neutrons nuclear and magnetic scattering are 2 = F 2(nucl) + F 2(magn) , where F magn = phase independent: Fhkl hkl hkl hkl
I. Glavatskyy et al. / Materials Science and Engineering A 481–482 (2008) 298–301
magn
fν
299
Qhkl,ν e[2πi(hxν +kyν +lzν )] —magnetic scattering factor,
ν
Qhkl,ν = mν − (ehkl mν )ehkl , mv is the magnetic moment of individual atom in unit cell, eh k l the elementary scattering vectors, v the atom number in unit cell and h k l are the Miller indices. This allowed for a separation of the nuclear and magnetic contribution since magnetic contribution is absent when Q = 0, i.e. magnetic moment is normal to the scattering plane [8]. Electronic structure calculations were carried out using the WIEN2k program [4] in LAPW approach with local spin density approximation (LSDA). All modeling calculations are made in stoichiometric approximation Ni2 MnGa. To compare the real 5M martensite structure with the austenite FCC modification, we used the FCT martensite approximation as it is conventional for this type of calculations in the literature for the moment. 3. Results Fig. 1 represents the temperature dependence of the low-field magnetic susceptibility of the studied alloy single crystal used for the determination of the temperatures of direct and reverse martensite transformation (TM , TA ) and Curie point of austenite (TC ). Though the crystal lattice of the martensite is stable in the entire range of martensite (305–4 K) [2] and martensite lattice parameters develops smoothly (Fig. 2), the low-field magnetic susceptibility experiences a sharp jump with narrow temperature hysteresis near 200 K (Fig. 1). The martensite lattice parameters possess the strong anisotropic temperature dependence, bringing to the significant change of the tetragonal lattice distortion (a/b − 1) of the martensite with temperature. Tetragonality ratio of the martensite monotonously increases over whole temperature range of martensite with cooling from TM down to 4 K. Fig. 3b presents the temperature dependence of the critical switching field needed for the martensite twin variant rearrangement (as shown in Fig. 3a, an example of the magnetic shape memory effect in the martensite phase of the studied
Fig. 1. Temperature dependence of the low-field magnetic susceptibility (in arbitrary units, a.u.).
Fig. 2. Relative change of the a- and b-lattice parameters of the martensite with temperature calculated after the neutron diffraction studies.
alloy). In the temperature interval from TM down to T = 210 K, the switching field linearly increases with temperature. Thus, using the Arrhenius equation for the thermally-induced process v = v0 exp(−(EA /kT )), assuming the martensite twin boundary mobility: v ∼ 1/HC we obtain EA = 0.925 meV, the enthalpy of the martensite twin boundary activation. Though, in the temperature range 210–200 K, the dependence abruptly breaks as the critical field magnitude sharply falls off, i.e., the martensite twin boundary mobility steeply rises back to values as those at 270–280 K. This can be explained only if there is some transition taking place at these temperatures. But, since the crystal lattice of the martensite develops smoothly, we may only suppose some magnetic substructure transition to occur. To clear the nature of the observed intermartensitic transition, a series of neutron diffraction studies was conducted. From the refinement of the measured reflections by the full profile Rietveld analysis (using FullProf [5]), the unit cell, atomic positions (at T = 300 K) and the correct space group were Table 1 5M martensite structure parameters (stoichiometric approximation) and local magnetic moments directly after martensite transition (T = 300 K) Atom
No.
x
y
z
μB
Mn Mn Mn Mn Mn Mn Ni Ni Ni Ni Ni Ni Ga Ga Ga Ga Ga Ga
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
0 0.948 0.044 0.552 0.456 0.5 0.5 0.052 0.544 0.956 0.448 0 0 0.552 0.044 0.456 0.948 0.5
0 0 0 0.5 0.5 0.5 0.25 0.25 0.25 0.25 0.25 0.25 0.5 0 0.5 0 0.5 0
0 0.4 0.2 0.1 0.3 0.5 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5
3.42 3.4 3.41 3.42 3.41 3.42 0.43 0.45 0.43 0.43 0.45 0.43 −0.05 −0.05 −0.05 −0.05 −0.05 −0.05
˚ b = 5.62 A, ˚ Space group 10 (P2m); unique axis b; lattice parameters: a = 4.21 A, ˚ β = 90.07◦ . Total moment in unit cell: 42.54μB . c = 20.99 A,
300
I. Glavatskyy et al. / Materials Science and Engineering A 481–482 (2008) 298–301
Fig. 3. (a) Example of the MSM effect at T = 290 K. Directions p1 and p2 correspond to the possible magnetization axes. (b) Temperature dependence of the critical “switching” field (HC ) magnitude.
determined (Table 1). The monoclinic distortion of the martensite lattice is very small (β = 90.07◦ ) though it is temperature dependent. Thus, it is significant for the correct space group determination and cannot be neglected. It is also significant for precise, further ab initio studies of the electronic structure. It is clearly seen from Table 1 that local magnetic moment modulation of Mn and Ni atoms takes place in the 5M modulated martensite. According to the performed ab-initio calculations using WIEN2k package in stoichiometric FCT martensite approximation, the valence band of Ni–Mn–Ga consists of two sub-bands. The first, pre-Fermi, is situated at ∼10 eV from the Fermi level for the FCC-modification and ∼7 eV for FCTapproximation of the martensite lattice. The second, narrow band of deep states has binding energy near −14 to −16 eV and formed by gallium 3d-electrons. Pre-Fermi band is mainly formed by hybridized states of nickel and manganese atoms. Ni 3d-electrons dominate on the Fermi level. As a result of martensite transition, the magnetic moment of nickel atoms increases by 0.04μB , and the magnetic moment of manganese atoms decreases by 0.03μB . Consequently, the magnetic moment of whole cell increases by 0.11μB (Table 2). As it can be seen from Fig. 4a, integrated intensity of the strongest magnetic (1 0 5)5M reflection has strong peculiarities at T = 200 K, 140 K and 40 K, while the purely nuclear (0 1 0)5M
peak has smooth monotonic temperature dependence; as well as the lattice parameters themselves. Thus, it can be concluded that we observe some magnetic spin-reorientation transitions, namely at 200 K, 140 K and at the low temperature narrow “cusp-like” feature at 40 K. The 200 K and 140 K peculiarities concords with those observed independently by Runov et al. by the polarized neutron scattering studies [6,7]. In 5M-martensite Ni–Mn–Ga alloys, the magnetic system consists of two subsystems, related to Ni and Mn atoms, which Table 2 Magnetic moments of individual atoms and unit cell in FCC and FCT modifications according to the original ab-initio calculations Atom
Magnetic moment (μB )
FCC austenite Mn Ni Ga Unit cell
3.46 0.35 −0.05 4.13
FCT martensite Mn Ni Ga Unit cell
3.43 0.39 −0.05 4.24
I. Glavatskyy et al. / Materials Science and Engineering A 481–482 (2008) 298–301
301
[12], which is metastable and collapses back to the ferrimagnetic state further cooling. 4. Conclusions A series of a sharp magnetic transitions at T = 200 K, 140 K and 40 K has been observed, while the crystal structure of martensite remains stable with temperature. The observed transitions are due to the strongly anisotropic temperature dependence of the lattice parameters of the martensite. The magnetic structure becomes more correlated. Also, the crystal and magnetic structures becomes more commensurate, resulting in the sudden rise of the martensite twin boundary mobility at T = 200 K. At 40 K, the signs of narrow ∼10 K metastable spin-glass state are observed, which collapses with further cooling to the ferrimagnetic state. Acknowledgements Authors would like to acknowledge the BENSC, HMI (Berlin, Germany) and ILL (Grenoble, France) for the provided experimental facilities for neutron scattering studies. Authors also greatly acknowledge the support of European Office of Airspace Research Division (EOARD), STCU project P-137. I. Glavatskyy also greatly appreciates the financial support by NATO Reintegration grant NUKR.RIG.981327. Fig. 4. Temperature dependence of the: (a) integral intensities of the strongest magnetic (1 0 5)5M and nuclear (0 1 0)5M reflections; (b) magnetic scattering contribution to (1 0 5)5M , calculated after the experimental data.
are the carriers of the magnetic moment. Thus, the magnetic substructure evolves due to Ni–Ni, Ni–Mn and Mn–Mn exchange interaction. Anisotropic lattice parameter change brings to the strong changes in the atomic layer distances and angles and so to the changes of the electronic structure and directions and strength of the exchange interactions of magnetic Ni–Ni, Ni–Mn and Mn–Mn subsystems of the martensite [9–11]. This results in a realignment of the magnetic structure of the martensite at 200 K, as it is proved by the temperature dependence of the lowfield magnetic susceptibility (Fig. 1) and observed in the neutron magnetic scattering anomalies (Fig. 4a and b). From the temperature dependence of the magnetic contribution we suggest that with cooling T = 200 K, there occurs a transition from a ferromagnetic to a low temperature incommensurate ferrimagnetic phase with Mn–Mn and Ni–Ni magnetic sublattices. A narrow (∼10 K) low temperature (T = 40 K) magnetic neutron scattering anomaly with a “cusp-like” character gives grounds to suggest the spin-glass transition, in agreement with
References [1] O. S¨oderberg, A. Sozinov, Y. Ge, S.-P. Hannula, V.K. Lindroos, in: K.H.J. Buschow (Ed.), Handbook of Magnetic Materials, vol. 16, Elsevier B.V., Amsterdam, 2006, pp. 1–39. [2] N. Glavatska, G. Mogylnyy, I. Glavatsky, V. Gavriljuk, Scripta Mater. 46/8 (2002) 605–610. [3] N. Glavatska, G. Mogylnyy, S. Danilkin, D. Hohlwein, Mat. Sci. Forum 443–444 (2002) 397–400. [4] G.K.H. Madsen, P. Blaha, K. Schwarz, E. Sj¨ostedt, L. Nordstrom, Phys. Rev. B 64 (2001) 195102–195108. [5] J. Rodriguez-Carvajal, Phys. B 192 (1993) 55–69. [6] V.V. Runov, Yu.P. Cherenkov, M.R. Runova, V.G. Gavriljuk, N.I. Glavatska, Phys. B 335 (2003) 109–113. [7] V. Runov, M. Runova, V. Gavriljuk, N. Glavatska, Phys. B 350 (2004) E87–E89. [8] F. Mezei, Solid State Phenom. 56 (1997) 133–144. [9] A. Ayuela, J. Enkovaara, K. Ullakko, R.M. Nieminen, J. Phys.: Condens. Matter 11 (1999) 2017–2026. [10] J. Enkovaara, A. Ayuela, J. Jalkanen, L. Nordstrom, R.M. Nieminen, Phys. Rev. B 67 (2003) 054417–054421. [11] O.I. Velikokhatnyi, I.I. Naumov, Fiz. Tverd. Tela 41 (1999) 684– 690. [12] V.G. Gavriljuk, A. Dobrinsky, B.D. Shanina, S.P. Kolesnik, J. Phys.: Condens. Matter 18 (2006) 7613–7627.
Crystal and magnetic structure temperature evolution in Ni–Mn–Ga magnetic shape memory martensite I. Glavatskyy a,∗ , N. Glavatska a , I. Urubkov a , J.-U. Hoffman b , F. Bourdarot c a
Institute for Metal Physics, NAS of Ukraine, 36 Vernadsky blvd., Kiev, UA-03142, Ukraine Hahn-Meitner-Institut, Abt. NE/Gastgruppe T¨ubingen, Glienicker Str. 100, BENSC, D-14109 Berlin, Germany c D´ epartement de Recherche Fondamentale sur la Mati`ere Condens´ee, SPSMS, CEA Grenoble, 38054 Grenoble Cedex 9, France b
Received 22 May 2006; received in revised form 30 January 2007; accepted 5 February 2007
Abstract The current work presents the original results concerning the temperature evolution of the magnetic and crystal structure of Ni–Mn–Ga magnetic shape memory alloys within the entire temperature interval of the martensite phase. The atomic positions and the correct space group of the 5M martensite unit cell has been derived, which is crucial for the electronic structure calculations. Neutron diffraction studies of the Ni–Mn–Ga alloy, possessing a large magnetic shape memory effect (>5% shear strain), revealed that there are several magnetic transitions in the martensite phase due to the smooth strongly anisotropic temperature dependence of the martensite lattice parameters. © 2007 Published by Elsevier B.V. Keywords: Ni–Mn–Ga; Magnetic shape memory; Martensite; Magnetic structure
1. Introduction The structure of Ni–Mn–Ga intermetallics has been studied intensively during last years because some of these alloys exhibit a large magnetic shape memory effect (MSM) in martensite phase, which makes these materials unique [1]. It is thought that the magnetic shape memory effect is observed only in alloys having five-layered modulated structure of martensite. Thus, it is of particular importance to study the atomic and magnetic ordering of this type of martensites in Ni–Mn–Ga. For the possible technical application of the MSM effect, it is important to study the temperature stability of the magnetic and crystal structure of the Ni–Mn–Ga martensites exhibiting the effect, since previous experimental studies shows the strong and nonmonotonous temperature dependence of magnetic field-induced strains (MFIS) [2]. 2. Experimental The off-stoichiometric Ni50.5 Mn28.2 Ga21.3 (at.%) alloy, possessing large magnetic shape memory effect (over 5%) at room ∗
Corresponding author. Tel.: +380 44 4246427; fax: +380 44 4243310. E-mail address: [email protected] (I. Glavatskyy).
0921-5093/$ – see front matter © 2007 Published by Elsevier B.V. doi:10.1016/j.msea.2007.02.139
temperature was studied using the D15 neutron diffractometer (ILL, Grenoble, France). The Curie and martensite phase transformation temperatures as determined using dilatometric and low-field magnetic susceptibility measurements are TC = 374 K, TM = 303 K, TA = 310 K, respectively. During preliminary studies by neutron scattering methods (E2, BENSC, HMI), the crystal structure of martensite was determined as orthorhombic (a = 0.421 nm, b = 0.562 nm, and c = 2.105 nm at 296 K) with five-layered modulation along [1 0 1] and [1 0 −1] directions and remains stable within temperature range 300–4 K [3]. Before the studies, the single crystal was cooled under applied magnetic field of H = 0.5 T from the austenite phase, producing single variant non-twinned martensite. Then, the specimen was mounted on a 4-circle cradle with “Displex” refrigerator on ˚ At T = 300 K some 700 the D15 diffractometer with λ = 1.17 A. reflections were collected and the UB-matrix for the unit cell was determined, also a temperature dependence of the strongest reflections were studied in steps of 20 K from 300 K down to 20 K, giving 14 temperature points in martensite phase, allowing the evolution of the magnetic structure of martensite to be studied. Some “residual” (less then 10%) twinning was treated using “PREWASH” program. The integral intensity of the reflection is 2 , while proportional to the square of the scattering factor ≈ Fhkl for non-polarized neutrons nuclear and magnetic scattering are 2 = F 2(nucl) + F 2(magn) , where F magn = phase independent: Fhkl hkl hkl hkl
I. Glavatskyy et al. / Materials Science and Engineering A 481–482 (2008) 298–301
magn
fν
299
Qhkl,ν e[2πi(hxν +kyν +lzν )] —magnetic scattering factor,
ν
Qhkl,ν = mν − (ehkl mν )ehkl , mv is the magnetic moment of individual atom in unit cell, eh k l the elementary scattering vectors, v the atom number in unit cell and h k l are the Miller indices. This allowed for a separation of the nuclear and magnetic contribution since magnetic contribution is absent when Q = 0, i.e. magnetic moment is normal to the scattering plane [8]. Electronic structure calculations were carried out using the WIEN2k program [4] in LAPW approach with local spin density approximation (LSDA). All modeling calculations are made in stoichiometric approximation Ni2 MnGa. To compare the real 5M martensite structure with the austenite FCC modification, we used the FCT martensite approximation as it is conventional for this type of calculations in the literature for the moment. 3. Results Fig. 1 represents the temperature dependence of the low-field magnetic susceptibility of the studied alloy single crystal used for the determination of the temperatures of direct and reverse martensite transformation (TM , TA ) and Curie point of austenite (TC ). Though the crystal lattice of the martensite is stable in the entire range of martensite (305–4 K) [2] and martensite lattice parameters develops smoothly (Fig. 2), the low-field magnetic susceptibility experiences a sharp jump with narrow temperature hysteresis near 200 K (Fig. 1). The martensite lattice parameters possess the strong anisotropic temperature dependence, bringing to the significant change of the tetragonal lattice distortion (a/b − 1) of the martensite with temperature. Tetragonality ratio of the martensite monotonously increases over whole temperature range of martensite with cooling from TM down to 4 K. Fig. 3b presents the temperature dependence of the critical switching field needed for the martensite twin variant rearrangement (as shown in Fig. 3a, an example of the magnetic shape memory effect in the martensite phase of the studied
Fig. 1. Temperature dependence of the low-field magnetic susceptibility (in arbitrary units, a.u.).
Fig. 2. Relative change of the a- and b-lattice parameters of the martensite with temperature calculated after the neutron diffraction studies.
alloy). In the temperature interval from TM down to T = 210 K, the switching field linearly increases with temperature. Thus, using the Arrhenius equation for the thermally-induced process v = v0 exp(−(EA /kT )), assuming the martensite twin boundary mobility: v ∼ 1/HC we obtain EA = 0.925 meV, the enthalpy of the martensite twin boundary activation. Though, in the temperature range 210–200 K, the dependence abruptly breaks as the critical field magnitude sharply falls off, i.e., the martensite twin boundary mobility steeply rises back to values as those at 270–280 K. This can be explained only if there is some transition taking place at these temperatures. But, since the crystal lattice of the martensite develops smoothly, we may only suppose some magnetic substructure transition to occur. To clear the nature of the observed intermartensitic transition, a series of neutron diffraction studies was conducted. From the refinement of the measured reflections by the full profile Rietveld analysis (using FullProf [5]), the unit cell, atomic positions (at T = 300 K) and the correct space group were Table 1 5M martensite structure parameters (stoichiometric approximation) and local magnetic moments directly after martensite transition (T = 300 K) Atom
No.
x
y
z
μB
Mn Mn Mn Mn Mn Mn Ni Ni Ni Ni Ni Ni Ga Ga Ga Ga Ga Ga
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
0 0.948 0.044 0.552 0.456 0.5 0.5 0.052 0.544 0.956 0.448 0 0 0.552 0.044 0.456 0.948 0.5
0 0 0 0.5 0.5 0.5 0.25 0.25 0.25 0.25 0.25 0.25 0.5 0 0.5 0 0.5 0
0 0.4 0.2 0.1 0.3 0.5 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5
3.42 3.4 3.41 3.42 3.41 3.42 0.43 0.45 0.43 0.43 0.45 0.43 −0.05 −0.05 −0.05 −0.05 −0.05 −0.05
˚ b = 5.62 A, ˚ Space group 10 (P2m); unique axis b; lattice parameters: a = 4.21 A, ˚ β = 90.07◦ . Total moment in unit cell: 42.54μB . c = 20.99 A,
300
I. Glavatskyy et al. / Materials Science and Engineering A 481–482 (2008) 298–301
Fig. 3. (a) Example of the MSM effect at T = 290 K. Directions p1 and p2 correspond to the possible magnetization axes. (b) Temperature dependence of the critical “switching” field (HC ) magnitude.
determined (Table 1). The monoclinic distortion of the martensite lattice is very small (β = 90.07◦ ) though it is temperature dependent. Thus, it is significant for the correct space group determination and cannot be neglected. It is also significant for precise, further ab initio studies of the electronic structure. It is clearly seen from Table 1 that local magnetic moment modulation of Mn and Ni atoms takes place in the 5M modulated martensite. According to the performed ab-initio calculations using WIEN2k package in stoichiometric FCT martensite approximation, the valence band of Ni–Mn–Ga consists of two sub-bands. The first, pre-Fermi, is situated at ∼10 eV from the Fermi level for the FCC-modification and ∼7 eV for FCTapproximation of the martensite lattice. The second, narrow band of deep states has binding energy near −14 to −16 eV and formed by gallium 3d-electrons. Pre-Fermi band is mainly formed by hybridized states of nickel and manganese atoms. Ni 3d-electrons dominate on the Fermi level. As a result of martensite transition, the magnetic moment of nickel atoms increases by 0.04μB , and the magnetic moment of manganese atoms decreases by 0.03μB . Consequently, the magnetic moment of whole cell increases by 0.11μB (Table 2). As it can be seen from Fig. 4a, integrated intensity of the strongest magnetic (1 0 5)5M reflection has strong peculiarities at T = 200 K, 140 K and 40 K, while the purely nuclear (0 1 0)5M
peak has smooth monotonic temperature dependence; as well as the lattice parameters themselves. Thus, it can be concluded that we observe some magnetic spin-reorientation transitions, namely at 200 K, 140 K and at the low temperature narrow “cusp-like” feature at 40 K. The 200 K and 140 K peculiarities concords with those observed independently by Runov et al. by the polarized neutron scattering studies [6,7]. In 5M-martensite Ni–Mn–Ga alloys, the magnetic system consists of two subsystems, related to Ni and Mn atoms, which Table 2 Magnetic moments of individual atoms and unit cell in FCC and FCT modifications according to the original ab-initio calculations Atom
Magnetic moment (μB )
FCC austenite Mn Ni Ga Unit cell
3.46 0.35 −0.05 4.13
FCT martensite Mn Ni Ga Unit cell
3.43 0.39 −0.05 4.24
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301
[12], which is metastable and collapses back to the ferrimagnetic state further cooling. 4. Conclusions A series of a sharp magnetic transitions at T = 200 K, 140 K and 40 K has been observed, while the crystal structure of martensite remains stable with temperature. The observed transitions are due to the strongly anisotropic temperature dependence of the lattice parameters of the martensite. The magnetic structure becomes more correlated. Also, the crystal and magnetic structures becomes more commensurate, resulting in the sudden rise of the martensite twin boundary mobility at T = 200 K. At 40 K, the signs of narrow ∼10 K metastable spin-glass state are observed, which collapses with further cooling to the ferrimagnetic state. Acknowledgements Authors would like to acknowledge the BENSC, HMI (Berlin, Germany) and ILL (Grenoble, France) for the provided experimental facilities for neutron scattering studies. Authors also greatly acknowledge the support of European Office of Airspace Research Division (EOARD), STCU project P-137. I. Glavatskyy also greatly appreciates the financial support by NATO Reintegration grant NUKR.RIG.981327. Fig. 4. Temperature dependence of the: (a) integral intensities of the strongest magnetic (1 0 5)5M and nuclear (0 1 0)5M reflections; (b) magnetic scattering contribution to (1 0 5)5M , calculated after the experimental data.
are the carriers of the magnetic moment. Thus, the magnetic substructure evolves due to Ni–Ni, Ni–Mn and Mn–Mn exchange interaction. Anisotropic lattice parameter change brings to the strong changes in the atomic layer distances and angles and so to the changes of the electronic structure and directions and strength of the exchange interactions of magnetic Ni–Ni, Ni–Mn and Mn–Mn subsystems of the martensite [9–11]. This results in a realignment of the magnetic structure of the martensite at 200 K, as it is proved by the temperature dependence of the lowfield magnetic susceptibility (Fig. 1) and observed in the neutron magnetic scattering anomalies (Fig. 4a and b). From the temperature dependence of the magnetic contribution we suggest that with cooling T = 200 K, there occurs a transition from a ferromagnetic to a low temperature incommensurate ferrimagnetic phase with Mn–Mn and Ni–Ni magnetic sublattices. A narrow (∼10 K) low temperature (T = 40 K) magnetic neutron scattering anomaly with a “cusp-like” character gives grounds to suggest the spin-glass transition, in agreement with
References [1] O. S¨oderberg, A. Sozinov, Y. Ge, S.-P. Hannula, V.K. Lindroos, in: K.H.J. Buschow (Ed.), Handbook of Magnetic Materials, vol. 16, Elsevier B.V., Amsterdam, 2006, pp. 1–39. [2] N. Glavatska, G. Mogylnyy, I. Glavatsky, V. Gavriljuk, Scripta Mater. 46/8 (2002) 605–610. [3] N. Glavatska, G. Mogylnyy, S. Danilkin, D. Hohlwein, Mat. Sci. Forum 443–444 (2002) 397–400. [4] G.K.H. Madsen, P. Blaha, K. Schwarz, E. Sj¨ostedt, L. Nordstrom, Phys. Rev. B 64 (2001) 195102–195108. [5] J. Rodriguez-Carvajal, Phys. B 192 (1993) 55–69. [6] V.V. Runov, Yu.P. Cherenkov, M.R. Runova, V.G. Gavriljuk, N.I. Glavatska, Phys. B 335 (2003) 109–113. [7] V. Runov, M. Runova, V. Gavriljuk, N. Glavatska, Phys. B 350 (2004) E87–E89. [8] F. Mezei, Solid State Phenom. 56 (1997) 133–144. [9] A. Ayuela, J. Enkovaara, K. Ullakko, R.M. Nieminen, J. Phys.: Condens. Matter 11 (1999) 2017–2026. [10] J. Enkovaara, A. Ayuela, J. Jalkanen, L. Nordstrom, R.M. Nieminen, Phys. Rev. B 67 (2003) 054417–054421. [11] O.I. Velikokhatnyi, I.I. Naumov, Fiz. Tverd. Tela 41 (1999) 684– 690. [12] V.G. Gavriljuk, A. Dobrinsky, B.D. Shanina, S.P. Kolesnik, J. Phys.: Condens. Matter 18 (2006) 7613–7627.