magnetic gold; structure dependent ferromagnetism in au4v

Structure-dependent ferromagnetism in Au4V 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 LaboratoryUniversity of CaliforniaLivermore, CA 94550

Damon D Jackson

Chantel AracneSam T. Weir

Wei QiuJoel D. GriffithYogesh Vohra

University of Alabama at BirminghamDepartment of Physics

Birmingham, AL 35294

Jason Jeffries*

Brian Maple

University of California, San DiegoDepartment of PhysicsSan Diego, CA 92093

* Now at LLNL

Overview

•Au1-xVx is a “Kondo” system

•resistance minimum due to magnetic impurity

•If prepared correctly, V crystallographically order to form Au4V

•FM at TC=43 K

•Applying pressure increases magnetic coupling

•TC increases

•Pressure also pushes Au4V back to Au-20%V

Magnetic Phase Diagram

Au4V Au - 20% V

Electrical Resistivity

ofMetals

Electrical Resistivity vs Temperature for Metals

•Behavior of ρ(T) depends on dominant electron scattering mechanism

•T due to phonons (T>θD)

•T5 due to phonons (T≈ θD)

•T2 due to electron-electron scattering (low temperatures)

•saturates to a constant due to impurities (low temperatures)

•Matthiessen’s Rule says that the various mechanisms can be summed up to get total temperature dependence

ρ(T)=ρ0+ρelectrons(T)+ρphonons(T)

ρ(T)=ρ0 + aT2 + bT5 + cT

Typical Metallic Behavior

Good Metals with Magnetic Impurities

•improvement in sample quality lead to interesting new phenomena

•semiconductors

•upturn at low T with very small concentrations of magnetic impurities

•Magnetic impurity concentrations < 1% resulted in resistance minima at large temperatures (10-20 K)

Magnetic Impurities cause ρ(T)to increase at low T

Jun Kondo, Prog. Theor. Phys. 32, 37, 1964

Kondo Effect

•Metals with dilute magnetic impurities exhibit the “Kondo Effect”

•depth of minimum (ρ(T=0) - ρ(Tmin)) proportional to impurity concentration

•Electrons get trapped by magnetic impurity

Kondo Effect

Ziman, “Electrons and Phonons”

•Metals with dilute magnetic impurities exhibit the “Kondo Effect”

•depth of minimum (ρ(T=0) - ρ(Tmin)) proportional to impurity concentration

•Electrons get trapped by magnetic impurity

Kondo Resistance

Kondo’s Theory of the Resistance Minima

•explained concentration dependence on Tmin

•log(T) behavior below Tmin

•Kondo temperature

‣Δρ(TK) / Δρ(0) ) = 0.8

‣energy scale, not minimum

Schilling, Adv. Phys. 28, 657, 1979

TK ≈ TF exp(-1/| J N(EF) | )

ρspin(T)=Δρ(T)=ρimp(T) - ρhost(T)

Jun Kondo, Prog. Theor. Phys. 32, 37, 1964

Kondo Resistance

Kondo’s Theory of the Resistance Minima

•explained concentration dependence on Tmin

•log(T) behavior below Tmin

•Kondo temperature

‣Δρ(TK) / Δρ(0) ) = 0.8

‣energy scale, not minimum

Schilling, Adv. Phys. 28, 657, 1979

TK ≈ TF exp(-1/| J N(EF) | )

ρspin(T)=Δρ(T)=ρimp(T) - ρhost(T)

Jun Kondo, Prog. Theor. Phys. 32, 37, 1964

Example ρ(T) for Various TK

Kondo’s Theory of the Resistance Minima

•explained concentration dependence on Tmin

•log(T) behavior below Tmin

•Kondo temperature

‣Δρ(TK) / Δρ(0) ) = 0.8

‣energy scale, not minimum

Schilling, Adv. Phys. 28, 657, 1979

TK ≈ TF exp(-1/| J N(EF) | )

ρspin(T)=Δρ(T)=ρimp(T) - ρhost(T)

Jun Kondo, Prog. Theor. Phys. 32, 37, 1964

Kondo Resistance with Pressure

Kondo Under Pressure

•Exponential dependence on magnetic exchange parameter result in

•TK increase with Pressure

•due to:

•increase in |-J |

Schilling, Adv. Phys. 28, 657, 1979

TK ≈ TF exp(-1/| J N(EF) | )

Magnetic Exchange with Pressure

Kondo Under Pressure

•Exponential dependence on magnetic exchange parameter result in

•TK increase with Pressure

•due to:

•increase in |-J |

Schilling, Adv. Phys. 28, 657, 1979

TK ≈ TF exp(-1/| J N(EF) | )

Electrical Resistivity

ofAu-V Alloys

Electrical Resistivity of Au-V Alloys

•Kume (JPSJ, 22, 1116, 1967) found “quite peculiar” electrical resistivity for Au-V alloys

•Creveling investigated Au-V alloys in depth (PR, 176, 614, 1968) and found

•V has a local moment for concentration ≤ 30%

Au-V Resistance Kondo Resistance

ρspin(T)=Δρ(T)=ρAu-V(T) - ρAu(T)

Kondo Behavior in Au-V Alloys

•Creveling found V has a local moment in Au-V alloys for concentration ≤ 30%

•Jeffries investigated Au-V up to 10% and found Kondo behavior for x<1%

•Au-0.5%V has deep Kondo min.

•Measured for P≤2.8 GPa

•TK increases with pressure

Kondo Behavior in Au-V Alloys

•Creveling found V has a local moment in Au-V alloys for concentration ≤ 30%

•Jeffries investigated Au-V up to 10% and found Kondo behavior for x<1%

•Au-0.5%V has deep Kondo min.

•Measured for P≤2.8 GPa

•TK increases with pressure

Kondo Behavior in Au-V Alloys

•Creveling found V has a local moment in Au-V alloys for concentration ≤ 30%

•Jeffries investigated Au-V up to 10% and found Kondo behavior for x<1%

•Au-0.5%V has deep Kondo min.

•Measured for P≤2.8 GPa

•TK increases with pressure

dTK/dP ≈ 6.5 K/GPa

Au-V Kondo Behavior Review

•Magnetic impurities in a non-magnetic host

•Resistance minimum

•Pressure increases the Kondo temperature

•TK increases for Au-V

•d TK/d P ≈ 6.5 K/GPa

Ziman, “Electrons and Phonons”

Au-V Kondo Behavior Review

•Magnetic impurities in a non-magnetic host

•Resistance minimum

•Pressure increases the Kondo temperature

•TK increases for Au-V

•d TK/d P ≈ 6.5 K/GPa

Schilling, Adv. Phys. 28, 657, 1979

Au-V Kondo Behavior Review

•Magnetic impurities in a non-magnetic host

•Resistance minimum

•Pressure increases the Kondo temperature

•TK increases for Au-V

•d TK/d P ≈ 6.5 K/GPa

TK vs P for Au-0.5%V

Au-V Kondo Behavior Review

•Magnetic impurities in a non-magnetic host

•Resistance minimum

•Pressure increases the Kondo temperature

•TK increases for Au-V

•d TK/d P ≈ 6.5 K/GPa

Au4V and its properties

Discovery of Ferromagnetism in Ordered Au4V

•Creveling, Luo, and Knapp annealed Au-20%V at 500 C for a week

•V atoms become crystallographically ordered

•Au4V alloy is FM at TC=43 K

•Paramagnetic state shows Curie-Weiss behavior with p

eff=1.43 µ

B

•indicates local moment, S=½

L. Creveling et al., Phys Rev. Lett., 18, 851 (1967)

Magnetization of Au4V

Discovery of Ferromagnetism in Ordered Au4V

•Creveling, Luo, and Knapp annealed Au-20%V at 500 C for a week

•V atoms become crystallographically ordered

•Au4V alloy is FM at TC=43 K

•Paramagnetic state shows Curie-Weiss behavior with p

eff=1.43 µ

B

•indicates local moment, S=½

L. Creveling et al., Phys Rev. Lett., 18, 851 (1967)

Curie-Weiss behavior of Au4V

Discovery of Ferromagnetism in Ordered Au4V

•Creveling, Luo, and Knapp annealed Au-20%V at 500 C for a week

•V atoms become crystallographically ordered

•Au4V alloy is FM at TC=43 K

•Paramagnetic state shows Curie-Weiss behavior with p

eff=1.43 µ

B

•indicates local moment, S=½

L. Creveling et al., Phys Rev. Lett., 18, 851 (1967)

Crystal Structure

• Vanadiums ordered in Au4V

•Space Group I4/m

•Body-centered tetragonal

•a=6.40 Å

•c=3.98 Å

• Gold crystal structure is the basis for Au-V alloys

• fcc (Fm-3m

)

• a=4.08 Å

Crystal Structure

• Vanadiums ordered in Au4V

•Space Group I4/m

•Body-centered tetragonal

•a=6.40 Å

•c=3.98 Å

• Gold crystal structure is the basis for Au-V alloys

• fcc (Fm-3m

)

• a=4.08 Å

X-Ray Analysis

•Qiu and Griffith from Vohra’s group at UAB performed XRD

•energy dispersive

•angle dispersive

•tetragonal peak intensities reduce with P

Angle Dispersive XRDEnergy Dispersive XRD

EOS for Au4V

•Between 18 and 27 GPa, can be indexed to fcc gold structure

•Gold structure maintained during downloading

•3rd-order Birch-Murnaghan EOS gives:

•B0 = 207.11 GPa

•B0 ́= 3.62

Au4V EOS

•typical sample size is 75 µm in diameter, 50 µm thick

•“Center-of-Earth” type pressures (360 GPa) are possible

•wonderful tool for optical measurements (x-ray, Raman)

Diamond Anvil Cell:The tool for ultra-high pressure research

DAC capabilities are limited for electrical transport,

magnetic properties, etc.

Designer Diamond Anvils

•lithographically fabricated thin-film tungsten microprobes

•completely encased within epitaxial diamond

•embedded leads provide electrical insulation so that metal gaskets can still be used

•diamond-encapsulated probes remain functional to multi-Mbar pressures60-250 µm

4-12 µm

•“3D” Lithography required for fabrication onto the non-flat surfaces

•projection lithography for the diamond flat

•laser pantography for the contact pads

•Tungsten probes have a width of 5-10 µm and 0.5 µm thick

Electrical Contact Pads

1st Step: Lithography onto Diamond Anvils

•2% methane and 98% hydrogen gas mixture

•plasma generated by a 1.2 kW magnetron, operating at 2.45 GHz

•epitaxial diamond onto diamond substrates at a growth rate of about 10 µm/hr

2nd Step: Microwave Plasma Chemical Vapor Deposition

Yogesh Vohra, Univ. of Alabama, Birmingham

Plasma

Heated Substrate (1000 C)

Diamond Growth

H2

CH4

Microwave Power

•a new single-crystal diamond anvil with diamond-embedded electrodes

3rd Step: Polishing

electrical contact pads

rate of diamond nucleation and growth on clean metal films is low

•Lithographic Fabrication of Microprobes

•laser pantography (electrical pads) and projection lithography (diamond flat)

•linewidths down to 1 µm

•Epitaxial Diamond Deposition

•Univ. of Alabama CVD process

•diamond film is typically 10-50 µm thick

•Final Polishing and Completion

•microprobes are now completely encapsulated in diamond, except for the exposed ends.

Designer Diamond Anvil Fabrication

300 µm

Broad Range of Techniques

300 µm

I

I

II

I

I

V

Heating element in operation at ≈10 GPa

ElectricalResistivity

Magnetic Susceptibility

InternalOhmicHeating

10 m

M.B. Maple et al., Phys. Lett. A, 25, 121 (1967)

Electrical Resistance of Au4V

•In 1967, Maple et al. found a kink

in R(T) at TC

•We analyzed the same batch

of samples!

•Can use the kink to identify TC and track its pressure dependance

Au4V Resistivity Under Pressure

•Kink broadens as pressure increases

• TC increases with pressure

•Why not use magnetic susceptibility?

•Chin et al. (1968) found M

sat(4.2K) quickly decreased

with increasing strain

•M(T,P) signal too small

G.Y. Chin et al., Solid State Comm., 6, 153 (1968)

TC vs Pressure Phase Diagram

• Bridgeman (hydrostatic) and DAC (non-hydrostatic) results are consistent

•P≤18 GPa, dTC/dP = 2.7 K/GPa

•Above 18 GPa, indication of TC became washed out

•not possible to accurately pinpoint TC

•No indication of magnetic ordering during downloading

Magnetic Phase Diagram

•Au-0.5%V exhibits the Kondo effect, indicating

•TK ↑ with pressure

•|JK| ↓ with volume

•Au4V is tetragonal with V ordered on the Au sites

•18 < P < 27 GPa, structure goes to fcc gold

•Au4V is FM with TC = 43 K

•TC ↑ with pressure (P<18 GPa)

Review of Experimental Results

•Au-0.5%V exhibits the Kondo effect, indicating

•TK ↑ with pressure

•|JK| ↓ with volume

•Au4V is tetragonal with V ordered on the Au sites

•18 < P < 27 GPa, structure goes to fcc gold

•Au4V is FM with TC = 43 K

•TC ↑ with pressure (P<18 GPa)

Review of Experimental Results

•Au-0.5%V exhibits the Kondo effect, indicating

•TK ↑ with pressure

•|JK| ↓ with volume

•Au4V is tetragonal with V ordered on the Au sites

•18 < P < 27 GPa, structure goes to fcc gold

•Au4V is FM with TC = 43 K

•TC ↑ with pressure (P<18 GPa)

Review of Experimental Results

•Au-0.5%V exhibits the Kondo effect, indicating

•TK ↑ with pressure

•|JK| ↓ with volume

•Au4V is tetragonal with V ordered on the Au sites

•18 < P < 27 GPa, structure goes to fcc gold

•Au4V is FM with TC = 43 K

•TC ↑ with pressure (P<18 GPa)

Review of Experimental Results

Theoretical Description of

Au4V Ferromagnetism

Kondo Coupling ⇔ TC increase

•For free electron: N(EF) ∝V⅔

‣dlnN(EF)/dlnV = 2/3

•Data implies dln|JK|/dlnV

•Heisenberg interaction depends on local moment exchange

•Exchange mediated through indirect exchange

‣ℐ ∝ N(EF) JRKKY2

•Data implies dln|JRKKY|/dlnV

✓ ✓ ✓

≈ -1.8dlnTK/dlnV ≈ -7

Kondo Coupling ⇔ TC increase

•For free electron: N(EF),∝V⅔

‣dlnN(EF)/dlnV = 2/3

•Data implies dln|JK|/dlnV

•Heisenberg interaction depends on local moment exchange

•Exchange mediated through indirect exchange

‣ℐ ∝ N(EF) JRKKY2

•Data implies dln|JRKKY|/dlnV

✓✓ ✓✓

≈ -1.8

≈ -5.3

dlnTK/dlnV ≈ -7

dlnTC/dlnV ≈ -9.9

??

Structure and Magnetism

•Au4V has bct structure

•Au-20%V has fcc structure

•Broad transition between them

•and

•FM ordering not found in fcc

Magnetic Nearest Neighbors

•Au4V has 2 magnetic nearest neighbors

•fcc gold has

•12 1st nearest neighbors

•6 2nd nearest neighbors

•Due to random arrangement of V in Au-20%V, there are, on average,

• 18✕0.2= 3.6 nearest V neighbors within the same distance

Magnetic Nearest Neighbors

•Au4V has 2 magnetic nearest neighbors

•fcc gold has

•12 1st nearest neighbors

•6 2nd nearest neighbors

•Due to random arrangement of V in Au-20%V, there are, on average,

• 18✕0.2= 3.6 nearest V neighbors within the same distance

Magnetic Nearest Neighbors

•Au4V has 2 magnetic nearest neighbors

•fcc gold has

•12 1st nearest neighbors

•6 2nd nearest neighbors

•Due to random arrangement of V in Au-20%V, there are, on average,

• 18✕0.2= 3.6 nearest V neighbors within the same distance

Magnetic Nearest Neighbors

•Au4V has 2 magnetic nearest neighbors

•fcc gold has

•12 1st nearest neighbors

•6 2nd nearest neighbors

•Due to random arrangement of V in Au-20%V, there are, on average,

• 18✕0.2= 3.6 nearest V neighbors within the same distance

Magnetic Nearest Neighbors

•Au4V has 2 magnetic nearest neighbors

•fcc gold has

•12 1st nearest neighbors

•6 2nd nearest neighbors

•Due to random arrangement of V in Au-20%V, there are, on average,

• 18✕0.2= 3.6 nearest V neighbors within the same distance

Magnetic Nearest Neighbors

•Au4V has 2 magnetic nearest neighbors

•fcc gold has

•12 1st nearest neighbors

•6 2nd nearest neighbors

•Due to random arrangement of V in Au-20%V, there are, on average,

• 18✕0.2= 3.6 nearest V neighbors within the same distance

Magnetic Nearest Neighbors

•Au4V has 2 magnetic nearest neighbors

•fcc gold has

•12 1st nearest neighbors

•6 2nd nearest neighbors

•Due to random arrangement of V in Au-20%V, there are, on average,

• 18✕0.2= 3.6 nearest V neighbors within the same distance

Magnetic Nearest Neighbors

•Au4V has 2 magnetic nearest neighbors

•fcc gold has

•12 1st nearest neighbors

•6 2nd nearest neighbors

•Due to random arrangement of V in Au-20%V, there are, on average,

• 18✕0.2= 3.6 nearest V neighbors within the same distance

Magnetic Nearest Neighbors

•Au4V has 2 magnetic nearest neighbors

•fcc gold has

•12 1st nearest neighbors

•6 2nd nearest neighbors

•Due to random arrangement of V in Au-20%V, there are, on average,

• 18✕0.2= 3.6 nearest V neighbors within the same distance

dlnz/dlnV ≈ -7

Must Account for Structure Changes

dlnTK/dlnV ≈ -7 dlnTC/dlnV ≈ -9.9

dln|J|/dlnV ≈ -1.8 ℐ ∝ N(EF) J2

Au-0.5%V Au4V

dln|J|/dlnV ≈ -1.8

dlnz/dlnV ≈ -7

Must Account for Structure Changes

dlnTC/dlnV ≈ -9.9

Au4V•Au4V has 2 magnetic nearest neighbors within a unit cell lattice spacing

•Au-20%V has on average 3.6 magnetic nearest neighbors (within same distance)

•Using derived pressure dependencies, one finds

• P(z=3.6) = 21 GPa

Au4V Phase Diagram

Must Account for Structure Changes

•Au4V has 2 magnetic nearest neighbors within a unit cell lattice spacing

•Au-20%V has on average 3.6 magnetic nearest neighbors (within same distance)

•Using derived pressure dependencies, one finds

• P(z=3.6) = 21 GPa

Structure- Dependent

Ferromagnetism in Au4V

•Au1-xVx is a Kondo material for x<1%

•Increasing Pressure results in increasing Kondo exchange parameter

•With careful annealing, V order crystallographical in Au4V

•Pressure gradually transforms Au4V into disordered alloy

•Au4V is FM and TC increases with pressure due to |J| and V nn’s

•Intimate connection between structure and magnetism for Au4V

Structure-dependent ferromagnetism in Au4V studied under high pressure

Au-.5%V Kondo Behavior

•Au1-xVx is a Kondo material for x<1%

•Increasing Pressure results in increasing Kondo exchange parameter

•With careful annealing, V order crystallographical in Au4V

•Pressure gradually transforms Au4V into disordered alloy

•Au4V is FM and TC increases with pressure due to |J| and V nn’s

•Intimate connection between structure and magnetism for Au4V

Structure-dependent ferromagnetism in Au4V studied under high pressure

Au-.5%V Kondo Behavior

Structure-dependent ferromagnetism in Au4V studied under high pressure

TK vs P for Au-0.5%V

•Au1-xVx is a Kondo material for x<1%

•Increasing Pressure results in increasing Kondo exchange parameter

•With careful annealing, V order crystallographical in Au4V

•Pressure gradually transforms Au4V into disordered alloy

•Au4V is FM and TC increases with pressure due to |J| and V nn’s

•Intimate connection between structure and magnetism for Au4V

•Au1-xVx is a Kondo material for x<1%

•Increasing Pressure results in increasing Kondo exchange parameter

•With careful annealing, V order crystallographical in Au4V

•Pressure gradually transforms Au4V into disordered alloy

•Au4V is FM and TC increases with pressure due to |J| and V nn’s

•Intimate connection between structure and magnetism for Au4V

Structure-dependent ferromagnetism in Au4V studied under high pressure

Au4V Crystal Structure

•Au1-xVx is a Kondo material for x<1%

•Increasing Pressure results in increasing Kondo exchange parameter

•With careful annealing, V order crystallographical in Au4V

•Pressure gradually transforms Au4V into disordered alloy

•Au4V is FM and TC increases with pressure due to |J| and V nn’s

•Intimate connection between structure and magnetism for Au4V

Structure-dependent ferromagnetism in Au4V studied under high pressure

bct to fcc Transformation

Magnetic Phase Diagram

Structure-dependent ferromagnetism in Au4V studied under high pressure

•Au1-xVx is a Kondo material for x<1%

•Increasing Pressure results in increasing Kondo exchange parameter

•With careful annealing, V order crystallographical in Au4V

•Pressure gradually transforms Au4V into disordered alloy

•Au4V is FM and TC increases with pressure due to |J| and V nn’s

•Intimate connection between structure and magnetism for Au4V

Au4V Phase Diagram

Au4V Au

- 20

% V

•Au1-xVx is a Kondo material for x<1%

•Increasing Pressure results in increasing Kondo exchange parameter

•With careful annealing, V order crystallographical in Au4V

•Pressure gradually transforms Au4V into disordered alloy

•Au4V is FM and TC increases with pressure due to |J| and V nn’s

•Intimate connection between structure and magnetism for Au4V

Structure-dependent ferromagnetism in Au4V studied under high pressure

•Au1-xVx is a Kondo material for x<1%

•Increasing Pressure results in increasing Kondo exchange parameter

•With careful annealing, V order crystallographical in Au4V

•Pressure gradually transforms Au4V into disordered alloy

•Au4V is FM and TC increases with pressure due to |J| and V nn’s

•Intimate connection between structure and magnetism for Au4V

Structure-dependent ferromagnetism in Au4V studied under high pressure

Au4V Phase Diagram

Au4V Au

- 20

% V