Magnetic Gold; Structure Dependent Ferromagnetism in Au4V

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A description of the ferromagnetic interactions found in crystallographic Au4V is investigated through high pressure (P<35 GPa) electrical resistivity measurements. The results suggest an intimate connection between crystallographic structure and ferromagnetism for this material.

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  • Magnetic Gold; Structure Dependent Ferromagnetism in Au4V

    1. 1. Structure-dependent ferromagnetism in Au 4 V studied under high pressure Investigations into Magnetic Gold D. D. Jackson et al. , PRB 74 , 174401, 2006 This work was performed under the auspices of the U.S. Department of Energy by University of California, Lawrence Livermore National Laboratory under Contract W-7405-Eng-48. Lawrence Livermore National Laboratory University of California Livermore, CA 94550 Damon D Jackson Chantel Aracne Sam T. Weir Wei Qiu Joel D. Griffith Yogesh Vohra University of Alabama at Birmingham Department of Physics Birmingham, AL 35294 Jason Jeffries * Brian Maple University of California, San Diego Department of Physics San Diego, CA 92093 * Now at LLNL
    2. 2. Overview <ul><li>Au 1-x V x is a “Kondo” system </li></ul><ul><ul><li>resistance minimum due to magnetic impurity </li></ul></ul><ul><li>If prepared correctly, V crystallographically order to form Au 4 V </li></ul><ul><ul><li>FM at T C = 43 K </li></ul></ul><ul><li>Applying pressure increases magnetic coupling </li></ul><ul><ul><li>T C increases </li></ul></ul><ul><li>Pressure also pushes Au 4 V back to Au-20%V </li></ul>Magnetic Phase Diagram Au 4 V Au - 20% V
    3. 3. Electrical Resistivity of Metals
    4. 4. Electrical Resistivity vs Temperature for Metals <ul><li>Behavior of ρ( T ) depends on dominant electron scattering mechanism </li></ul><ul><ul><li>T due to phonons ( T > θ D ) </li></ul></ul><ul><ul><li>T 5 due to phonons ( T ≈ θ D ) </li></ul></ul><ul><ul><li>T 2 due to electron-electron scattering (low temperatures) </li></ul></ul><ul><ul><li>saturates to a constant due to impurities (low temperatures) </li></ul></ul><ul><li>Matthiessen’s Rule says that the various mechanisms can be summed up to get total temperature dependence </li></ul>ρ( T )=ρ 0 +ρ electrons ( T )+ρ phonons ( T ) ρ( T )=ρ 0 + a T 2 + b T 5 + c T Typical Metallic Behavior
    5. 5. Good Metals with Magnetic Impurities <ul><li>improvement in sample quality lead to interesting new phenomena </li></ul><ul><ul><li>semiconductors </li></ul></ul><ul><ul><li>upturn at low T with very small concentrations of magnetic impurities </li></ul></ul><ul><li>Magnetic impurity concentrations < 1% resulted in resistance minima at large temperatures (10-20 K) </li></ul>Magnetic Impurities cause ρ( T )to increase at low T Jun Kondo, Prog. Theor. Phys. 32 , 37, 1964
    6. 6. Kondo Effect <ul><li>Metals with dilute magnetic impurities exhibit the “Kondo Effect” </li></ul><ul><ul><li>depth of minimum (ρ( T =0) - ρ( T min )) proportional to impurity concentration </li></ul></ul><ul><li>Electrons get trapped by magnetic impurity </li></ul>
    7. 7. Kondo Effect <ul><li>Metals with dilute magnetic impurities exhibit the “Kondo Effect” </li></ul><ul><ul><li>depth of minimum (ρ( T =0) - ρ( T min )) proportional to impurity concentration </li></ul></ul><ul><li>Electrons get trapped by magnetic impurity </li></ul>Ziman, “Electrons and Phonons”
    8. 8. Kondo’s Theory of the Resistance Minima <ul><li>explained concentration dependence on T min </li></ul><ul><li>log( T ) behavior below T min </li></ul><ul><li>Kondo temperature </li></ul><ul><ul><li>Δρ( T K ) / Δρ(0) ) = 0.8 </li></ul></ul><ul><ul><li>energy scale, not minimum </li></ul></ul>Kondo Resistance Schilling, Adv. Phys. 28 , 657, 1979 T K ≈ T F exp(-1/| J N ( E F ) | ) ρ spin ( T )=Δρ( T )=ρ imp ( T ) - ρ host ( T ) Jun Kondo, Prog. Theor. Phys. 32 , 37, 1964
    9. 9. Kondo’s Theory of the Resistance Minima <ul><li>explained concentration dependence on T min </li></ul><ul><li>log( T ) behavior below T min </li></ul><ul><li>Kondo temperature </li></ul><ul><ul><li>Δρ( T K ) / Δρ(0) ) = 0.8 </li></ul></ul><ul><ul><li>energy scale, not minimum </li></ul></ul>Kondo Resistance Schilling, Adv. Phys. 28 , 657, 1979 T K ≈ T F exp(-1/| J N ( E F ) | ) ρ spin ( T )=Δρ( T )=ρ imp ( T ) - ρ host ( T ) Jun Kondo, Prog. Theor. Phys. 32 , 37, 1964
    10. 10. Kondo’s Theory of the Resistance Minima <ul><li>explained concentration dependence on T min </li></ul><ul><li>log( T ) behavior below T min </li></ul><ul><li>Kondo temperature </li></ul><ul><ul><li>Δρ( T K ) / Δρ(0) ) = 0.8 </li></ul></ul><ul><ul><li>energy scale, not minimum </li></ul></ul>Example ρ( T ) for Various T K Schilling, Adv. Phys. 28 , 657, 1979 T K ≈ T F exp(-1/| J N ( E F ) | ) ρ spin ( T )=Δρ( T )=ρ imp ( T ) - ρ host ( T ) Jun Kondo, Prog. Theor. Phys. 32 , 37, 1964
    11. 11. Kondo Under Pressure <ul><li>Exponential dependence on magnetic exchange parameter result in </li></ul><ul><ul><li>T K increase with Pressure </li></ul></ul><ul><ul><ul><li>due to: </li></ul></ul></ul><ul><ul><li>increase in |- J | </li></ul></ul>Schilling, Adv. Phys. 28 , 657, 1979 T K ≈ T F exp(-1/| J N ( E F ) | ) Kondo Resistance with Pressure
    12. 12. Kondo Under Pressure <ul><li>Exponential dependence on magnetic exchange parameter result in </li></ul><ul><ul><li>T K increase with Pressure </li></ul></ul><ul><ul><ul><li>due to: </li></ul></ul></ul><ul><ul><li>increase in |- J | </li></ul></ul>Magnetic Exchange with Pressure Schilling, Adv. Phys. 28 , 657, 1979 T K ≈ T F exp(-1/| J N ( E F ) | )
    13. 13. Electrical Resistivity of Au-V Alloys
    14. 14. Electrical Resistivity of Au-V Alloys <ul><li>Kume (JPSJ, 22 , 1116, 1967) found “quite peculiar” electrical resistivity for Au-V alloys </li></ul><ul><li>Creveling investigated Au-V alloys in depth (PR, 176 , 614, 1968) and found </li></ul><ul><ul><li>V has a local moment for concentration ≤ 30% </li></ul></ul>Au-V Resistance Kondo Resistance ρ spin ( T )=Δρ( T )=ρ Au-V ( T ) - ρ Au ( T )
    15. 15. Kondo Behavior in Au-V Alloys <ul><li>Creveling found V has a local moment in Au-V alloys for concentration ≤ 30% </li></ul><ul><li>Jeffries investigated Au-V up to 10% and found Kondo behavior for x <1% </li></ul><ul><li>Au-0.5%V has deep Kondo min. </li></ul><ul><li>Measured for P ≤2.8 GPa </li></ul><ul><ul><li>T K increases with pressure </li></ul></ul>
    16. 16. Kondo Behavior in Au-V Alloys <ul><li>Creveling found V has a local moment in Au-V alloys for concentration ≤ 30% </li></ul><ul><li>Jeffries investigated Au-V up to 10% and found Kondo behavior for x <1% </li></ul><ul><li>Au-0.5%V has deep Kondo min. </li></ul><ul><li>Measured for P ≤2.8 GPa </li></ul><ul><ul><li>T K increases with pressure </li></ul></ul>
    17. 17. Kondo Behavior in Au-V Alloys <ul><li>Creveling found V has a local moment in Au-V alloys for concentration ≤ 30% </li></ul><ul><li>Jeffries investigated Au-V up to 10% and found Kondo behavior for x <1% </li></ul><ul><li>Au-0.5%V has deep Kondo min. </li></ul><ul><li>Measured for P ≤2.8 GPa </li></ul><ul><ul><li>T K increases with pressure </li></ul></ul>dT K /d P ≈ 6.5 K/GPa
    18. 18. Au-V Kondo Behavior Review <ul><li>Magnetic impurities in a non-magnetic host </li></ul><ul><li>Resistance minimum </li></ul><ul><li>Pressure increases the Kondo temperature </li></ul><ul><li>T K increases for Au-V </li></ul><ul><ul><li>d T K /d P ≈ 6.5 K/GPa </li></ul></ul>
    19. 19. Au-V Kondo Behavior Review <ul><li>Magnetic impurities in a non-magnetic host </li></ul><ul><li>Resistance minimum </li></ul><ul><li>Pressure increases the Kondo temperature </li></ul><ul><li>T K increases for Au-V </li></ul><ul><ul><li>d T K /d P ≈ 6.5 K/GPa </li></ul></ul>Ziman, “Electrons and Phonons”
    20. 20. Au-V Kondo Behavior Review <ul><li>Magnetic impurities in a non-magnetic host </li></ul><ul><li>Resistance minimum </li></ul><ul><li>Pressure increases the Kondo temperature </li></ul><ul><li>T K increases for Au-V </li></ul><ul><ul><li>d T K /d P ≈ 6.5 K/GPa </li></ul></ul>Schilling, Adv. Phys. 28 , 657, 1979
    21. 21. Au-V Kondo Behavior Review <ul><li>Magnetic impurities in a non-magnetic host </li></ul><ul><li>Resistance minimum </li></ul><ul><li>Pressure increases the Kondo temperature </li></ul><ul><li>T K increases for Au-V </li></ul><ul><ul><li>d T K /d P ≈ 6.5 K/GPa </li></ul></ul>T K vs P for Au-0.5%V
    22. 22. Au 4 V and its properties
    23. 23. Discovery of Ferromagnetism in Ordered Au 4 V <ul><li>Creveling, Luo, and Knapp annealed Au-20%V at 500 C for a week </li></ul><ul><ul><li>V atoms become crystallographically ordered </li></ul></ul><ul><li>Au 4 V alloy is FM at T C =43 K </li></ul><ul><li>Paramagnetic state shows Curie-Weiss behavior with p eff =1.43 µ B </li></ul><ul><ul><li>indicates local moment, S =½ </li></ul></ul>L. Creveling et al., Phys Rev. Lett., 18 , 851 (1967)
    24. 24. Discovery of Ferromagnetism in Ordered Au 4 V <ul><li>Creveling, Luo, and Knapp annealed Au-20%V at 500 C for a week </li></ul><ul><ul><li>V atoms become crystallographically ordered </li></ul></ul><ul><li>Au 4 V alloy is FM at T C =43 K </li></ul><ul><li>Paramagnetic state shows Curie-Weiss behavior with p eff =1.43 µ B </li></ul><ul><ul><li>indicates local moment, S =½ </li></ul></ul>Magnetization of Au 4 V L. Creveling et al., Phys Rev. Lett., 18 , 851 (1967)
    25. 25. Discovery of Ferromagnetism in Ordered Au 4 V <ul><li>Creveling, Luo, and Knapp annealed Au-20%V at 500 C for a week </li></ul><ul><ul><li>V atoms become crystallographically ordered </li></ul></ul><ul><li>Au 4 V alloy is FM at T C =43 K </li></ul><ul><li>Paramagnetic state shows Curie-Weiss behavior with p eff =1.43 µ B </li></ul><ul><ul><li>indicates local moment, S =½ </li></ul></ul>Curie-Weiss behavior of Au 4 V L. Creveling et al., Phys Rev. Lett., 18 , 851 (1967)
    26. 26. Crystal Structure <ul><li>Vanadiums ordered in Au 4 V </li></ul><ul><li>Space Group I 4/m </li></ul><ul><li>Body-centered tetragonal </li></ul><ul><ul><li>a=6.40 Å </li></ul></ul><ul><ul><li>c=3.98 Å </li></ul></ul>• Gold crystal structure is the basis for Au-V alloys • fcc (F m-3m ) • a=4.08 Å
    27. 27. Crystal Structure <ul><li>Vanadiums ordered in Au 4 V </li></ul><ul><li>Space Group I 4/m </li></ul><ul><li>Body-centered tetragonal </li></ul><ul><ul><li>a=6.40 Å </li></ul></ul><ul><ul><li>c=3.98 Å </li></ul></ul>• Gold crystal structure is the basis for Au-V alloys • fcc (F m-3m ) • a=4.08 Å
    28. 28. X-Ray Analysis <ul><li>Qiu and Griffith from Vohra’s group at UAB performed XRD </li></ul><ul><ul><li>energy dispersive </li></ul></ul><ul><ul><li>angle dispersive </li></ul></ul><ul><li>tetragonal peak intensities reduce with P </li></ul>Angle Dispersive XRD Energy Dispersive XRD
    29. 29. EOS for Au 4 V <ul><li>Between 18 and 27 GPa, can be indexed to fcc gold structure </li></ul><ul><li>Gold structure maintained during downloading </li></ul><ul><li>3rd-order Birch-Murnaghan EOS gives: </li></ul><ul><ul><li>B 0 = 207.11 GPa </li></ul></ul><ul><ul><li>B 0 ́ = 3.62 </li></ul></ul>Au 4 V EOS
    30. 30. <ul><li>typical sample size is 75 µm in diameter, 50 µm thick </li></ul><ul><li>“ Center-of-Earth” type pressures (360 GPa) are possible </li></ul><ul><li>wonderful tool for optical measurements (x-ray, Raman) </li></ul>Diamond Anvil Cell: The tool for ultra-high pressure research DAC capabilities are limited for electrical transport, magnetic properties, etc.
    31. 31. Designer Diamond Anvils <ul><li>lithographically fabricated thin-film tungsten microprobes </li></ul><ul><li>completely encased within epitaxial diamond </li></ul><ul><li>embedded leads provide electrical insulation so that metal gaskets can still be used </li></ul><ul><li>diamond-encapsulated probes remain functional to multi-Mbar pressures </li></ul>60-250 µm 4-12 µm
    32. 32. <ul><li>“ 3D” Lithography required for fabrication onto the non-flat surfaces </li></ul><ul><ul><li>projection lithography for the diamond flat </li></ul></ul><ul><ul><li>laser pantography for the contact pads </li></ul></ul><ul><ul><ul><li>Tungsten probes have a width of 5-10 µm and 0.5 µm thick </li></ul></ul></ul>1st Step: Lithography onto Diamond Anvils Electrical Contact Pads
    33. 33. <ul><li>2% methane and 98% hydrogen gas mixture </li></ul><ul><li>plasma generated by a 1.2 kW magnetron, operating at 2.45 GHz </li></ul><ul><li>epitaxial diamond onto diamond substrates at a growth rate of about 10 µm/hr </li></ul>2nd Step: Microwave Plasma Chemical Vapor Deposition Yogesh Vohra, Univ. of Alabama, Birmingham Plasma Heated Substrate (1000 C) Diamond Growth H 2 CH 4 Microwave Power
    34. 34. <ul><li>a new single-crystal diamond anvil with diamond-embedded electrodes </li></ul>3rd Step: Polishing rate of diamond nucleation and growth on clean metal films is low electrical contact pads
    35. 35. <ul><li>Lithographic Fabrication of Microprobes </li></ul><ul><ul><li>laser pantography (electrical pads) and projection lithography (diamond flat) </li></ul></ul><ul><ul><li>linewidths down to 1 µm </li></ul></ul><ul><li>Epitaxial Diamond Deposition </li></ul><ul><ul><li>Univ. of Alabama CVD process </li></ul></ul><ul><ul><li>diamond film is typically 10-50 µm thick </li></ul></ul><ul><li>Final Polishing and Completion </li></ul><ul><ul><li>microprobes are now completely encapsulated in diamond, except for the exposed ends. </li></ul></ul>Designer Diamond Anvil Fabrication 300 µm
    36. 36. Broad Range of Techniques 300 µm I I I I I I V Heating element in operation at ≈10 GPa Electrical Resistivity Magnetic Susceptibility Internal Ohmic Heating 10  m
    37. 37. Electrical Resistance of Au 4 V <ul><li>In 1967, Maple et al. found a kink in R ( T ) at T C </li></ul><ul><ul><li>We analyzed the same batch of samples! </li></ul></ul><ul><li>Can use the kink to identify T C and track its pressure dependance </li></ul>M.B. Maple et al., Phys. Lett. A, 25 , 121 (1967)
    38. 38. Au 4 V Resistivity Under Pressure <ul><li>Kink broadens as pressure increases </li></ul><ul><li>T C increases with pressure </li></ul><ul><li>Why not use magnetic susceptibility? </li></ul><ul><ul><li>Chin et al. (1968) found M sat (4.2K) quickly decreased with increasing strain </li></ul></ul><ul><ul><li>M ( T,P ) signal too small </li></ul></ul>G.Y. Chin et al., Solid State Comm., 6 , 153 (1968)
    39. 39. T C vs Pressure Phase Diagram <ul><li>Bridgeman (hydrostatic) and DAC (non-hydrostatic) results are consistent </li></ul><ul><li>P ≤18 GPa, d T C /d P = 2.7 K/GPa </li></ul><ul><li>Above 18 GPa, indication of T C became washed out </li></ul><ul><ul><li>not possible to accurately pinpoint T C </li></ul></ul><ul><li>No indication of magnetic ordering during downloading </li></ul>Magnetic Phase Diagram
    40. 40. <ul><li>Au-0.5%V exhibits the Kondo effect, indicating </li></ul><ul><ul><li>T K ↑ with pressure </li></ul></ul><ul><ul><li>| J K | ↓ with volume </li></ul></ul><ul><li>Au 4 V is tetragonal with V ordered on the Au sites </li></ul><ul><li>18 < P < 27 GPa, structure goes to fcc gold </li></ul><ul><li>Au 4 V is FM with T C = 43 K </li></ul><ul><li>T C ↑ with pressure ( P <18 GPa) </li></ul>Review of Experimental Results
    41. 41. <ul><li>Au-0.5%V exhibits the Kondo effect, indicating </li></ul><ul><ul><li>T K ↑ with pressure </li></ul></ul><ul><ul><li>| J K | ↓ with volume </li></ul></ul><ul><li>Au 4 V is tetragonal with V ordered on the Au sites </li></ul><ul><li>18 < P < 27 GPa, structure goes to fcc gold </li></ul><ul><li>Au 4 V is FM with T C = 43 K </li></ul><ul><li>T C ↑ with pressure ( P <18 GPa) </li></ul>Review of Experimental Results
    42. 42. <ul><li>Au-0.5%V exhibits the Kondo effect, indicating </li></ul><ul><ul><li>T K ↑ with pressure </li></ul></ul><ul><ul><li>| J K | ↓ with volume </li></ul></ul><ul><li>Au 4 V is tetragonal with V ordered on the Au sites </li></ul><ul><li>18 < P < 27 GPa, structure goes to fcc gold </li></ul><ul><li>Au 4 V is FM with T C = 43 K </li></ul><ul><li>T C ↑ with pressure ( P <18 GPa) </li></ul>Review of Experimental Results
    43. 43. <ul><li>Au-0.5%V exhibits the Kondo effect, indicating </li></ul><ul><ul><li>T K ↑ with pressure </li></ul></ul><ul><ul><li>| J K | ↓ with volume </li></ul></ul><ul><li>Au 4 V is tetragonal with V ordered on the Au sites </li></ul><ul><li>18 < P < 27 GPa, structure goes to fcc gold </li></ul><ul><li>Au 4 V is FM with T C = 43 K </li></ul><ul><li>T C ↑ with pressure ( P <18 GPa) </li></ul>Review of Experimental Results
    44. 44. Theoretical Description of Au 4 V Ferromagnetism
    45. 45. Kondo Coupling ⇔ T C increase <ul><li>For free electron: N ( E F ) ∝ V ⅔ </li></ul><ul><ul><li>d ln N ( E F )/ d ln V = 2/3 </li></ul></ul><ul><li>Data implies d ln| J K | /d ln V </li></ul><ul><li>Heisenberg interaction depends on local moment exchange </li></ul><ul><li>Exchange mediated through indirect exchange </li></ul><ul><ul><li>ℐ ∝ N ( E F ) J RKKY 2 </li></ul></ul><ul><li>Data implies d ln| J RKKY | /d ln V </li></ul>✓ ✓ ✓ ≈ -1.8 d ln T K /d ln V ≈ -7
    46. 46. Kondo Coupling ⇔ T C increase <ul><li>For free electron: N ( E F ), ∝ V ⅔ </li></ul><ul><ul><li>d ln N ( E F )/ d ln V = 2/3 </li></ul></ul><ul><li>Data implies d ln| J K | /d ln V </li></ul><ul><li>Heisenberg interaction depends on local moment exchange </li></ul><ul><li>Exchange mediated through indirect exchange </li></ul><ul><ul><li>ℐ ∝ N ( E F ) J RKKY 2 </li></ul></ul><ul><li>Data implies d ln| J RKKY | /d ln V </li></ul>✓ ✓ ✓ ✓ ≈ -1.8 ≈ -5.3 d ln T K /d ln V ≈ -7 d ln T C /d ln V ≈ -9.9 ?
    47. 47. Structure and Magnetism <ul><li>Au 4 V has bct structure </li></ul><ul><li>Au-20%V has fcc structure </li></ul><ul><li>Broad transition between them </li></ul><ul><ul><li>and </li></ul></ul><ul><li>FM ordering not found in fcc </li></ul>
    48. 48. Magnetic Nearest Neighbors <ul><li>Au 4 V has 2 magnetic nearest neighbors </li></ul><ul><li>fcc gold has </li></ul><ul><ul><li>12 1 st nearest neighbors </li></ul></ul><ul><ul><li>6 2 nd nearest neighbors </li></ul></ul><ul><li>Due to random arrangement of V in Au-20%V, there are, on average, </li></ul><ul><li>18 ✕ 0.2= 3.6 nearest V neighbors within the same distance </li></ul>
    49. 49. Magnetic Nearest Neighbors <ul><li>Au 4 V has 2 magnetic nearest neighbors </li></ul><ul><li>fcc gold has </li></ul><ul><ul><li>12 1 st nearest neighbors </li></ul></ul><ul><ul><li>6 2 nd nearest neighbors </li></ul></ul><ul><li>Due to random arrangement of V in Au-20%V, there are, on average, </li></ul><ul><li>18 ✕ 0.2= 3.6 nearest V neighbors within the same distance </li></ul>
    50. 50. Magnetic Nearest Neighbors <ul><li>Au 4 V has 2 magnetic nearest neighbors </li></ul><ul><li>fcc gold has </li></ul><ul><ul><li>12 1 st nearest neighbors </li></ul></ul><ul><ul><li>6 2 nd nearest neighbors </li></ul></ul><ul><li>Due to random arrangement of V in Au-20%V, there are, on average, </li></ul><ul><li>18 ✕ 0.2= 3.6 nearest V neighbors within the same distance </li></ul>
    51. 51. Magnetic Nearest Neighbors <ul><li>Au 4 V has 2 magnetic nearest neighbors </li></ul><ul><li>fcc gold has </li></ul><ul><ul><li>12 1 st nearest neighbors </li></ul></ul><ul><ul><li>6 2 nd nearest neighbors </li></ul></ul><ul><li>Due to random arrangement of V in Au-20%V, there are, on average, </li></ul><ul><li>18 ✕ 0.2= 3.6 nearest V neighbors within the same distance </li></ul>
    52. 52. Magnetic Nearest Neighbors <ul><li>Au 4 V has 2 magnetic nearest neighbors </li></ul><ul><li>fcc gold has </li></ul><ul><ul><li>12 1 st nearest neighbors </li></ul></ul><ul><ul><li>6 2 nd nearest neighbors </li></ul></ul><ul><li>Due to random arrangement of V in Au-20%V, there are, on average, </li></ul><ul><li>18 ✕ 0.2= 3.6 nearest V neighbors within the same distance </li></ul>
    53. 53. Magnetic Nearest Neighbors <ul><li>Au 4 V has 2 magnetic nearest neighbors </li></ul><ul><li>fcc gold has </li></ul><ul><ul><li>12 1 st nearest neighbors </li></ul></ul><ul><ul><li>6 2 nd nearest neighbors </li></ul></ul><ul><li>Due to random arrangement of V in Au-20%V, there are, on average, </li></ul><ul><li>18 ✕ 0.2= 3.6 nearest V neighbors within the same distance </li></ul>
    54. 54. Magnetic Nearest Neighbors <ul><li>Au 4 V has 2 magnetic nearest neighbors </li></ul><ul><li>fcc gold has </li></ul><ul><ul><li>12 1 st nearest neighbors </li></ul></ul><ul><ul><li>6 2 nd nearest neighbors </li></ul></ul><ul><li>Due to random arrangement of V in Au-20%V, there are, on average, </li></ul><ul><li>18 ✕ 0.2= 3.6 nearest V neighbors within the same distance </li></ul>
    55. 55. Magnetic Nearest Neighbors <ul><li>Au 4 V has 2 magnetic nearest neighbors </li></ul><ul><li>fcc gold has </li></ul><ul><ul><li>12 1 st nearest neighbors </li></ul></ul><ul><ul><li>6 2 nd nearest neighbors </li></ul></ul><ul><li>Due to random arrangement of V in Au-20%V, there are, on average, </li></ul><ul><li>18 ✕ 0.2= 3.6 nearest V neighbors within the same distance </li></ul>
    56. 56. Magnetic Nearest Neighbors <ul><li>Au 4 V has 2 magnetic nearest neighbors </li></ul><ul><li>fcc gold has </li></ul><ul><ul><li>12 1 st nearest neighbors </li></ul></ul><ul><ul><li>6 2 nd nearest neighbors </li></ul></ul><ul><li>Due to random arrangement of V in Au-20%V, there are, on average, </li></ul><ul><li>18 ✕ 0.2= 3.6 nearest V neighbors within the same distance </li></ul>
    57. 57. Must Account for Structure Changes d ln z /d ln V ≈ -7 d ln T K /d ln V ≈ -7 d ln T C /d ln V ≈ -9.9 d ln| J|/d ln V ≈ -1.8 ℐ ∝ N ( E F ) J 2 Au-0.5%V Au 4 V
    58. 58. Must Account for Structure Changes <ul><li>Au 4 V has 2 magnetic nearest neighbors within a unit cell lattice spacing </li></ul><ul><li>Au-20%V has on average 3.6 magnetic nearest neighbors (within same distance) </li></ul><ul><li>Using derived pressure dependencies, one finds </li></ul>d ln| J|/d ln V ≈ -1.8 d ln z /d ln V ≈ -7 d ln T C /d ln V ≈ -9.9 Au 4 V • P ( z =3.6) = 21 GPa
    59. 59. Must Account for Structure Changes <ul><li>Au 4 V has 2 magnetic nearest neighbors within a unit cell lattice spacing </li></ul><ul><li>Au-20%V has on average 3.6 magnetic nearest neighbors (within same distance) </li></ul><ul><li>Using derived pressure dependencies, one finds </li></ul>Au 4 V Phase Diagram • P ( z =3.6) = 21 GPa
    60. 60. Structure- Dependent Ferromagnetism in Au 4 V
    61. 61. <ul><li>Au 1-x V x is a Kondo material for x<1% </li></ul><ul><li>Increasing Pressure results in increasing Kondo exchange parameter </li></ul><ul><li>With careful annealing, V order crystallographical in Au 4 V </li></ul><ul><li>Pressure gradually transforms Au 4 V into disordered alloy </li></ul><ul><li>Au 4 V is FM and T C increases with pressure due to | J | and V nn’s </li></ul><ul><li>Intimate connection between structure and magnetism for Au 4 V </li></ul>Structure-dependent ferromagnetism in Au 4 V studied under high pressure Au-.5%V Kondo Behavior
    62. 62. <ul><li>Au 1-x V x is a Kondo material for x<1% </li></ul><ul><li>Increasing Pressure results in increasing Kondo exchange parameter </li></ul><ul><li>With careful annealing, V order crystallographical in Au 4 V </li></ul><ul><li>Pressure gradually transforms Au 4 V into disordered alloy </li></ul><ul><li>Au 4 V is FM and T C increases with pressure due to | J | and V nn’s </li></ul><ul><li>Intimate connection between structure and magnetism for Au 4 V </li></ul>Structure-dependent ferromagnetism in Au 4 V studied under high pressure Au-.5%V Kondo Behavior
    63. 63. Structure-dependent ferromagnetism in Au 4 V studied under high pressure <ul><li>Au 1-x V x is a Kondo material for x<1% </li></ul><ul><li>Increasing Pressure results in increasing Kondo exchange parameter </li></ul><ul><li>With careful annealing, V order crystallographical in Au 4 V </li></ul><ul><li>Pressure gradually transforms Au 4 V into disordered alloy </li></ul><ul><li>Au 4 V is FM and T C increases with pressure due to | J | and V nn’s </li></ul><ul><li>Intimate connection between structure and magnetism for Au 4 V </li></ul>T K vs P for Au-0.5%V
    64. 64. <ul><li>Au 1-x V x is a Kondo material for x<1% </li></ul><ul><li>Increasing Pressure results in increasing Kondo exchange parameter </li></ul><ul><li>With careful annealing, V order crystallographical in Au 4 V </li></ul><ul><li>Pressure gradually transforms Au 4 V into disordered alloy </li></ul><ul><li>Au 4 V is FM and T C increases with pressure due to | J | and V nn’s </li></ul><ul><li>Intimate connection between structure and magnetism for Au 4 V </li></ul>Structure-dependent ferromagnetism in Au 4 V studied under high pressure Au 4 V Crystal Structure
    65. 65. <ul><li>Au 1-x V x is a Kondo material for x<1% </li></ul><ul><li>Increasing Pressure results in increasing Kondo exchange parameter </li></ul><ul><li>With careful annealing, V order crystallographical in Au 4 V </li></ul><ul><li>Pressure gradually transforms Au 4 V into disordered alloy </li></ul><ul><li>Au 4 V is FM and T C increases with pressure due to | J | and V nn’s </li></ul><ul><li>Intimate connection between structure and magnetism for Au 4 V </li></ul>Structure-dependent ferromagnetism in Au 4 V studied under high pressure bct to fcc Transformation
    66. 66. Structure-dependent ferromagnetism in Au 4 V studied under high pressure <ul><li>Au 1-x V x is a Kondo material for x<1% </li></ul><ul><li>Increasing Pressure results in increasing Kondo exchange parameter </li></ul><ul><li>With careful annealing, V order crystallographical in Au 4 V </li></ul><ul><li>Pressure gradually transforms Au 4 V into disordered alloy </li></ul><ul><li>Au 4 V is FM and T C increases with pressure due to | J | and V nn’s </li></ul><ul><li>Intimate connection between structure and magnetism for Au 4 V </li></ul>Magnetic Phase Diagram
    67. 67. <ul><li>Au 1-x V x is a Kondo material for x<1% </li></ul><ul><li>Increasing Pressure results in increasing Kondo exchange parameter </li></ul><ul><li>With careful annealing, V order crystallographical in Au 4 V </li></ul><ul><li>Pressure gradually transforms Au 4 V into disordered alloy </li></ul><ul><li>Au 4 V is FM and T C increases with pressure due to | J | and V nn’s </li></ul><ul><li>Intimate connection between structure and magnetism for Au 4 V </li></ul>Structure-dependent ferromagnetism in Au 4 V studied under high pressure Au 4 V Phase Diagram Au 4 V Au - 20% V
    68. 68. <ul><li>Au 1-x V x is a Kondo material for x<1% </li></ul><ul><li>Increasing Pressure results in increasing Kondo exchange parameter </li></ul><ul><li>With careful annealing, V order crystallographical in Au 4 V </li></ul><ul><li>Pressure gradually transforms Au 4 V into disordered alloy </li></ul><ul><li>Au 4 V is FM and T C increases with pressure due to | J | and V nn’s </li></ul><ul><li>Intimate connection between structure and magnetism for Au 4 V </li></ul>Structure-dependent ferromagnetism in Au 4 V studied under high pressure Au 4 V Phase Diagram Au 4 V Au - 20% V
    69. 70. Discovery of Ferromagnetism in Ordered Au 4 V <ul><li>Creveling, Luo, and Knapp report on magnetization measurements showing FM at T C =43 K in ordered phase </li></ul><ul><li>paramagnetic state shows Curie-Weiss behavior with p eff =1.43 µ B </li></ul><ul><li>large magnetic anisotropy </li></ul><ul><li>when field cooled, M sat =0.414 µ B at 4.2 K </li></ul>L. Creveling et al., Phys Rev. Lett., 18 , 851 (1967) G.Y. Chin et al., Solid St. Comm., 6 , 153 (1968) High T suggests local moment picture ( S =1/2) and low T suggests itinerant ferromagnetic picture
    70. 71. S =1/2 moment at V site <ul><li>Luo et al. (1967) found specific heat anomaly, but show large density of states </li></ul><ul><li>Mössbauer measurements on Au 197 by Cohen et al. (1969) indicated a moment of 1µ B /V </li></ul><ul><li>Paramagnetic moment is about 1.73µ B /V </li></ul><ul><li>Pulsed high field results by Kido et al. (1983) up to 30 T give M sat =1µ B /V </li></ul>H.L. Luo et al., Phys. Lett. A, 28 , 740 (1967) R.L. Cohen et al., Phys. Rev., 188 , 684 (1969) G. Kido et al., J. Magn. Magn. Mater., 31-34 , 283 (1983) V has S =1/2 local moment as long as nearest neighbors are Au
    71. 72. <ul><li>lithographically fabricated thin-film tungsten microprobes completely encased within epitaxial diamond </li></ul><ul><li>overcome the problem of introducing wires into gasket hole </li></ul><ul><li>usable up to 100’s of GPa </li></ul>Designer Diamond Anvils D.D. Jackson et al., Rev. Sci. Instrum., 74 , 2467 (2003) diamond-encapsulated probes remain functional to multi-Mbar pressures
    72. 73. Designer Diamond Anvils for Electrical Resistivity <ul><li>Capabilities allow for 4-probe electrical resistivity measurements </li></ul><ul><li>Resistivity can be measured up to megabar pressures </li></ul><ul><li>Temperature ranges: 2< T <330K </li></ul><ul><li>Magnetic fields up to 16 T </li></ul>
    73. 74. Kondo’s Solution <ul><li>Kondo explained using the Hamiltonian: </li></ul><ul><ul><li>H = -J( r ) S •s( r ) + v( r ) </li></ul></ul>Jun Kondo, Prog. Theor. Phys. 32 , 37, 1964
    74. 75. Kondo’s Solution <ul><li>Kondo explained using the Hamiltonian: </li></ul><ul><ul><li>H = - J( r ) S •s( r ) + v( r ) </li></ul></ul>Jun Kondo, Prog. Theor. Phys. 32 , 37, 1964 Exchange Interaction
    75. 76. Kondo’s Solution <ul><li>Kondo explained using the Hamiltonian: </li></ul><ul><ul><li>H = -J( r ) S •s( r ) + v( r ) </li></ul></ul>Jun Kondo, Prog. Theor. Phys. 32 , 37, 1964 Spin due to the Magnetic Impurity
    76. 77. Kondo’s Solution <ul><li>Kondo explained using the Hamiltonian: </li></ul><ul><ul><li>H = -J( r ) S • s( r ) + v( r ) </li></ul></ul>Jun Kondo, Prog. Theor. Phys. 32 , 37, 1964 Spin Density of Host Metal Conduction Electrons
    77. 78. Kondo’s Solution <ul><li>Kondo explained using the Hamiltonian: </li></ul><ul><ul><li>H = -J( r ) S •s( r ) + v( r ) </li></ul></ul>Jun Kondo, Prog. Theor. Phys. 32 , 37, 1964 Scattering Potential

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