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Journal Club
New Spin Mechanism forNegative Magnetoresistance in
Hopping RegimePRB 89, 100201(R) 2014
Thuong T. Nguyen
April 16, 2014
Outline
1 Overview of Magnetoresistance (MR) in Hopping Regime
♠ Orbital Mechanism
♠ Spin Mechanism
2 New Spin Mechanism
♠ Qualitative picture
♠ Simple Model
Overview of Magnetoresistance
in Hopping Regime
Hopping ConductionStrongly localized systems at low temperatureThe main contribution to electrical conductivity comes from
electrons hopping between impurities (tunneling).
MR in hopping regime NOT well understood.
Orbital-related mechanisms Spin-related mechanisms
Orbital Mechanism
Metallic regime: Negative MR is explained by weaklocalization theory (back-scattering).
∝ 1kF l
Orbital MechanismHopping regime: anomalously large negative MR1.
∝ B4/5
Characteristics• field: H0 ∼ Φ0/S = ~c/eS.
• ANISOTROPY in two dimension.
1Ioffe & Spivak, JETP 117, 551 (2013)
Absence of interference effects for free spins2
(more on Shumilin and Kozub, PRB 85,115203 (2012))
2Shklovskii & Spivak, in Hopping Transport in Solid, 1991
Spin Mechanism
{ISOTROPIC + POSITIVE} Magnetoresistance 3
3Kamimura et. al, 1985
Spin Mechanism
{ISOTROPIC + POSITIVE} Magnetoresistance 3
3Kamimura et. al, 1985
Spin Mechanism
{ISOTROPIC + POSITIVE} Magnetoresistance 3
3Kamimura et. al, 1985
Summary
Orbital Mechanism
• Negative
∝ B4/5
• Anisotropy
Spin Mechanism
• Positive
∝ B2
• Isotropy
New Spin Mechanism
New Spin Mechanism
• Characters: NEGATIVE + ISOTROPIC
• Ingredients: fluctuation of g factor in space; long memory of
non-equilibrium spin correlation.
Qualitative PictureHopping rate of an electron i→ j depends on the relative spin
configuration of hoping electron and a spin nearby.
Qualitative Picture1 Spin-memory ←− nonequilibrium electric current: decreases
conductivity for H = 0
2 Strong disordered system: random g factor: increases
conductivity.
Qualitative Picture1 Spin-memory ←− nonequilibrium electric current: decreases
conductivity for H = 0
2 Strong disordered system: random g factor: increases
conductivity.
Qualitative Picture
1 Spin-memory ←− nonequilibrium electric current
2 Strong disordered system: random g factor
Characteristic field:
δgµBH∗τ ∼ 1
with τ � τsEstimation: R ∼ 10−9Ω, δg ∼ 0.01 −→ µBnH∗/T ∼ 10−4, i.e
field of order of gauss at T ∼ 1K .
Simple model
• Main assumptions:� indirect transition rate: γij � 1 - perturbation parameter.� link spins are rare.
• Parametrize states: P 0i + TrP̂ 1i = 1
ni = TrP̂1i , Si = Tr(σP̂
1i )
Simple model
d 〈ni〉dt
= −∑j
[〈ni〉+ γij (〈ni〉 − 〈Si · sij〉)
τi→j− (i↔ j)
]d 〈Si〉dt
= hi × 〈Si〉 −∑j
[〈Si〉+ γij (〈Si〉 − 〈nisij〉)
τi→j− (i↔ j)
]d 〈sij〉dt
= hij × 〈sij〉
Simple modelNon-equilibrium variables:
〈ni〉 → neqi (1 + ψi) , Si → neqi S̃i, sij → sij
=⇒
neqidψidt
=∑j
1
τij
[ψj − ψi − γij
〈(S̃j − S̃i
)· sij
〉]neql
[(d
dt+
1
τs
)Cαβl;ij − �αγδh
γl C
αβl;ij − �βγδh
γijC
αδl;ij
]= −
∑k 6=l
Cαβl;ij − Cαβk;ij
τlk+ γijδαβ (δil − δjl)
ψi − ψjτij
γij
〈(S̃j − S̃i
)· sij
〉= Qij (H) (ψj − ψi)
Gij =e2
Tτij[1−Qij (H)]
Simple model: Resultσ(H →∞)− σ(0)
σ(0)∼ A = ργ2ij !Small
δσ(H)
Aσ(0)∼ −Γ
(−ds
2
) 1∑l=−1
[(ilH
H∗+τ
τs
)ds/2+
(τ
τs
)ds/2]
Conclusion
Negative Magnetoresistance
Spin memory effect Strongly disordered systems
Thanks for Your Attention!
Overview of Magnetoresistance (MR) in Hopping Regime Orbital Mechanism Spin Mechanism
New Spin Mechanism Qualitative picture Simple Model