Neutron Diffraction Study of Antiferromagnetic Phase Transitions in an Ordered Pt 3 Fe(111) Film

Transcription

1 Neutron Diffraction Study of Antiferromagnetic Phase Transitions in an Ordered Pt 3 Fe(111) Film G. J. Mankey, V. V. Krishnamurthy, and I. Zoto MINT Center, The University of Alabama, Tuscaloosa, AL J. L. Robertson Oak Ridge National Laboratory, Oak Ridge, TN S. Maat and Eric E. Fullerton Hitachi Global Storage Systems, San Jose Research Center 650 Harry Road, California I. Nwagwu and J. K. Akujieze Department of Chemistry and Physics, Chicago State University Chicago, Illinois Acknowledgements: DOE/EPSCoR - grant no. DE-FG02-02ER45966 and NSF MRSEC program - grant no. DMR at UA DOE grant no. DE-AC05-00OR22725 at ORNL

2 Motivation Magnetic thin films exhibit structural and magnetic properties that are different from bulk due to the strain and the changes in the grain sizes induced by the substrate. Antiferromagnetically ordered pinning layers are used to induce unidirectional magnetic anisotropy of ferromagnetic layers used in devices. Neutron diffraction measurements directly measure antiferromagnetic structure, spin ordering phase transitions and the order parameter. These measurements are used to study the correlation between the structural and magnetic properties of antiferromagnetically ordered epitaxial thin films. The study of antiferromagnetic thin films using these methods has just begun.

3 Antiferromagnetic Structures of Chemically Ordered Pt 3 Fe L1 2 type crystal structure Sites Fe at (0, 0, 0) Pt at (0.5, 0.5, 0) (0.5, 0, 0.5) (0, 0.5,0.5) Bulk lattice constant nm Single Crystals: Bacon & Crangle 1963 Epitaxial Films on Sapphire: S. Maat et al., PRB (2001)

4 Pt 73 Fe 27 Film Growth and Characterization Magnetron sputtering Base Pressure: 2 x 10-7 mbar Characterization: Pt 73 Fe 27 (111) 280nm Pt 3 Cr (111) 2nm Fe (110) 1nm a-axis cut Sapphire (1) Rutherford Backscattering composition: (within 1%) film thickness: 280 nm (2) X-ray Diffraction in-plane lattice constant nm out-of-plane lattice constant nm (Pt 3 Fe in bulk : nm) S. Maat et al., PRB 63, (2001)

5 Magnetic Neutron Diffraction The differential cross-section for elastic magnetic neutron scattering: 3 dσ 1 2π ( ) = δ ( Q τ ) ( TM M F M τ M dω N ν 0 Magnetic structure factor F M = Q F M Q ) 2 The integrated intensity for a magnetic Bragg reflection: I B (hkl) = C j A(θ Β ) γ χ <O M2 > F M 2 F M µ

6 Bragg Diffraction The Bragg equation states that constructive interference occurs when the path length difference associated with reflections from adjacent crystal planes is an integral number of wavelengths: 2d sin Θ = nλ This basic equation is the starting point for understanding crystal diffraction of x-rays, electrons, neutrons and any other particle which has a DeBroglie wavelength less than an interatomic spacing. Θ n Θ d

7 Reciprocal Space A Bravais lattice is an infinite array of discrete points with an arrangement an orientation which appears exactly the same, from whichever of the points the array is viewed. There are 14 Bravais lattices with primitive vectors a1, a2, and a3. The set of all wave vectors k that yield plane waves with the periodicity of a given Bravais lattice is known as the reciprocal lattice. The primitive vectors of the reciprocal lattice are r r found from: r b i = 2π ( a a ) Where cyclic permutations of i, j, and k generate the three primitive vector components. Ref: Ashcroft and Mermin, Solid State Physics (1976). r a i a j a r j k r k a 2 a 1 b 2 =2π/a 2 REAL b 1 =2π/a 1 RECIPROCAL

8 Period Doubling in Reciprocal Space Doubling the periodicity in real space produces twice as many diffraction spots in reciprocal space. This effect can be produced chemically with an ordered binary alloy or magnetically with antiparallel spins in and antiferromagnet.. The primitive vectors of the reciprocal lattice are found from: r b i = π r a i r r a j a r ( a a ) j k 2 REAL A doubling of the periodicity in real space due to antiferromagnetism will produce half-order spots in reciprocal space. The magnetic scattering of neutrons gives them a unique property of scattering from antiferromagnetic ordered structures. Ref: Ashcroft and Mermin, Solid State Physics (1976). r k a 2 a 1 2a 2 2a 1 b 2 =π/a 2 b 1 =π/a 1 RECIPROCAL

9 Q 1 = 2π/a [½ ½ 0] Bragg Peak 280 nm thick Pt 73 Fe 27 film on α-al 2 O 3 Counts/120 sec Q 1 =2π/a(1/2 1/2 0) K 119 K 139 K 155 K q (r. l. u.) Pt 73 Fe 27 The onset of long range antiferromagnetic order is seen at T~160 K. I B is Bragg peak intensity M is sublattice magnetization The order parameter is proportional to the square root of the intensity I B I B 1/2 ~ M = M 0 (1-T/T N ) β β is the phenomenological power law exponent. Neutron Diffraction Measurements: HB1 Instrument at HFIR, ORNL

10 Critical Behavior of the Q 1 Phase 280 nm thick Pt 73 Fe 27 film on α-al 2 O 3 I B 1/2 (arb. units) Pt 73 Fe 27 I B 1/2 (arb. units) Q 1 = 2π/a(1/2 1/2 0) t = (1-T/T N ) β =0.368(13) T N = (20) K t β Temperature (K) The onset of long range antiferromagnetic order is seen at T~160 K. The order parameter, which is proportional to the square root of the intensity (I B ), has been fitted to a power law function of reduced temperature, t = 1-T/T N. The value of the exponent, β = ± , corresponds to the exponent of the 3d Heisenberg model.

11 Q 2 = 2π/a [½ 0 0] Bragg Peak 280 nm thick Pt 73 Fe 27 film on α-al 2 O 3 Counts/120 sec K 78.8 K 90.2 K 94.2 K Q 2 =2π/a(1/2 0 0) Pt 73 Fe 27 The onset of long range antiferromagnetic order is seen at T~95 K. The order parameter is proportional to the square root of the intensity (I B ) I B 1/2 ~ M = M 0 (1-T/T N ) β 100 β is the phenomenological power law exponent q (r. l. u.)

12 Critical Behavior of the Q 2 Phase I B 1/2 (arbitary units) 280 nm thick Pt 73 Fe 27 film on α-al 2 O Pt 73 Fe 27 I B 1/2 (arb. units) Q 2 = 2π/a(1/2 0 0) Temperature (K) t β t = (1-T/T N ) β = 0.37(2) T N = 95.0(2) K The onset of the spin reorientation transition has been observed at T~ 95 K. The order parameter, which is proportional to the square root of the intensity (I B ), has been fitted to a power law function of reduced temperature, t = 1-T/T N. The value of the exponent β=0.37 ± 0.02, corresponds to the exponent of the 3D Heisenberg model.

13 Critical Exponents: Experiment vs. Theory Reference Model Method Critical exponent β this work Neutron Diffraction, (½, ½, 0) ± (Pt 3 Fe) Neutron Diffraction, (½, 0, 0) 0.37 ± 0.02 Ref. 1 3d Heisenberg Monte Carlo ± High Temp. Expansion Ref. 2 3d Heisenberg Continuous Renormalization 0.37 Group Ref. 3 3d Heisenberg Field Theory: d = 3 expansion ± Ref. 4 3d Ising Field Theory [1] M. Compostrini, et al., Phys. Rev. B 65, (2002). [2] G. v. Gersdorff and C. Wetterich, Phys. Rev. B 64, (2001). [3] F. Jasch and H. Kleinert, J. Math. Phys. 42, 52 (2001). [4] J. C. Le Guillou and J. Zinn-Justin, Phys. Rev. B 21, 3976 (1980).

14 Critical Exponents and T N : Film vs. Bulk Reference Method T N (K) Critical exponent β this work Neutron Diffraction, (½, ½, 0) ± ± Pt 73 Fe 27 Film Neutron Diffraction, (½, 0,0) 95.0 ± ± 0.02 on Sapphire Bacon & Crangle Neutron Diffraction, (½, ½, 0) ± ± 0.03 Pt 73.3 Fe 26.7 Single Crystal Neutron Diffraction, (½, 0, 0) ± ± 0.03 Ref. 6 Neutron Diffraction 0.38 NiO bulk 5. G. E. Bacon and J. Crangle, Proc. R. Soc. London A 272, 387 (1963) 6. C. F. von Doorn and P. de V. Du Plessis, Phys. Lett. A 66, 141 (1978)

15 Summary Neutron diffraction was used to measure antiferromagnetic order of an epitaxial film of chemically ordered Pt 73 Fe 27 grown on a-axis oriented sapphire (α-al 2 O 3 ). The critical behavior of the two antiferromagnetic phase transitions having the propagation vectors Q 1 = 2π/a(½ ½ 0) and Q 2 = 2π/a(½ 0 0) has been investigated. The exponent β of 0.368(13) for Q 1 = 2π/a(½ ½ 0) phase as well as the exponent β of 0.37(2) for Q 2 = 2π/a(½ 0 0) phase agree with the critical exponent of the 3D Heisenberg model and with the critical exponents of a Pt 73 Fe 27 single crystal. The agreement between the critical exponents of the film and the bulk can be explained by the absence of epitaxial strain for Pt 73 Fe 27 on sapphire.