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Magnetism, Electronic Transport and Magneto-Structural Coupling in Sr2IrO4

Ashim Kr. Pramanik

School of Physical Sciences Jawaharlal Nehru University

JNU, Frustrated Magnetism, Feb 13, 2015

Our ¡Group ¡at ¡JNU ¡

q Work in experimental condensed matter physics. q Most work in low temperature regime. q Do prepare materials, characterize them and study physical properties. q At present group of 7 people: 3 Ph.D students and 3 M.Sc students. q Transition metal oxides (4d & 5d) based materials.

q Sr2

2+Ir4+O4 2- is 5d based Transition Metal Oxide

q Electronic configuration: Ir4+ 4ƒ145d5 q Significant Crystal Field effect Low spin state eg t2g q Half filled t2g band. q Extended nature of 5d orbitals. q Reduced electronic correlation effect than 3d and 4d counterpart. q Therefore, 5d oxides expected to be metallic. q Heavy character of Ir (77) atom. q Significant spin-orbit coupling (SOC) effect (∝ z4, atomic number) q Comparable energy scale of Coulomb interaction and SOC ∼ 0.5 eV

Sr2IrO4 ¡(214) ¡: ¡Overview ¡

Importance ¡of ¡Structure ¡

Sr2IrO4 (214) : Structural Overview

q Member of Ruddlesden-Popper series Srn+1IrnO3n+1 with n = 1. q Layered (K2NiF4) structure. q Crystalizes in tetragonal structure Space group : I41/acd. q Alternate tilting of IrO6 octahedra along c-axis (θOct ∼ 11o) . q Iso-structural with La2CuO4 and Sr2RuO4 q Possible superconductivity !!! Wang, PRL, 106, 136402 (2011) Yang, PRB 89, 094518 (2014)

θOct ¡

Sr2IrO4 (214) : Magnetic Overview

Ye, PRB, 87, 140406, (2013) Cao, PRB, 57, 11039, (1998)

q Canted Antiferromagnet with TN ∼ 240 K. q Structural distortion induced Dzyaloshinsky-Moriya (DM) interaction. q Weak ferromagnetism with much lower moment than spin-only value (1 µB/f.u) for S = ½

Sr2IrO4 (214) : Electronic Transport

Sr2IrO4 Korneta, PRB, 82, 115117 (2010) Sr2RhO4 Perry, JPCM, 8, 175 (2006)

Sr2IrO4 (214) : Insulating behaviour

• B. J. Kim, PRL 101, 076402 (2008); Science, 323, 1329 (2009)

q Interplay between SOC, W and U gives novel ground state. q SOC splits t2g band onto Jeff = 1/2 and Jeff = 3/2 band. q Jeff = 1/2 band is half-filled and narrow. q Moderate U can lead to Mott gap.

Jeff Mott Insulator : Electronic correlation driven

Sr2IrO4 (214) : Insulating behaviour

Slater Insulator : Magnetic Order driven Time resolved optical study Hsieh, PRB, 86, 035128(2012) STM/STS investigation. Li, Scientific Reports, 3, 3073 (2013)

Sr2IrO4 (214) : Material Synthesis

10 20 30 40 50 60 70 80 90 0.0 0.5 1.0 1.5

Observed Calculated Difference

Intensity (10

3 a. u.)

2θ (Deg)

T = 298 K

q Single-phase polycrystalline material prepared using solid state method. q Materials are characterized using XRD and allied Rietveld analysis. q Sample crystallizes in tetragonal structure with I4/acd symmetry. q Lattice parameters; a = 5.4980(2) Å and c = 25.779(1) Å.

Bhatti, AKP , JPCM, 27, 016005 (2014)

50 100 150 200 250 300 50 100 150 200

150 200 250 300 0.0 0.5 1.0 1.5

M (emu/mole) T (K)

H = 10 kOe ZFC FC

χ

• 1 (10

3)

T (K)

Sr2IrO4 (214) : Magnetic Properties

q Weak FM transition around 238 K (dM/dT). q Steep decrease in MZFC(T) below ∼ 95 K. q Curie-Weiss behaviour in limited temperature. q Estimated θP = 233 K and µeff = 0.56 µB/f.u. q Expected µeff = 0.57 and µH = 0.33 µB/f.u (gJ = 2/3)

• 80 -60 -40 -20

20 40 60 80

• 0.06
• 0.04
• 0.02

0.00 0.02 0.04 0.06

2 4 6 8 10 12 14 1 2 3

T = 5 K T = 5 K

M (µB/f.u) H (kOe) Μ

2 (µB/f.u) 2

H/M (10

5 Oe f.u µB

• 1)

×10

• 3

Ge, ¡PRB, ¡84, ¡100402 ¡(2011). ¡

Sr2IrO4 (214) : Temperature Dependent Structure

10 20 30 40 50 60 70 80 90 0.0 0.5 1.0 1.5 2.0

20 K 200 K

Intensity (10

3 a.u.)

2θ (Deg)

298 K

q Representative XRD data in PM, FM and low temperature state. q No structural phase transition down to 20 K.

Sr2IrO4 (214) : Temperature Dependent Structure

Temperature dependent changes in structural parameters.

5.480 5.485 5.490 5.495 5.500 25.775 25.780 25.785 25.790 25.795 4.690 4.695 4.700 4.705 50 100 150 200 250 300 774 776 778 780

Tc

a (A

0)

(a) TM (b)

c (A

0)

(c)

c/a

(d)

V (A

03)

T (K)

Unit Cell

158 159 160 10.0 10.5 11.0 11.5 1.970 1.975 1.980 50 100 150 200 250 300 2.06 2.08 2.10 2.12 2.14

Tc

<Ir-O2-Ir> (Deg)

(a) TM (b)

θOct (Deg)

(c)

dIr-O2 (A

0)

(d)

dIr-O1 (A

0)

T (K)

IrO6 Octahedra

Sr2IrO4 (214) : Prediction for Magneto-Structural correlation

Jackeli, PRL, 102, 017205 (2009)

q Magnetism is linked to IrO6 octahedra distorsion. q α - IrO6 octahedra distortion angel. q Φ - spin canting angle. q θ - tetragonal distortion parameter.

Sr2IrO4 (214) : Electronic Transport

q Resistivity shows insulating behaviour (dρ/dT < 0). q Resistivity increases by five orders at low temperature. q Electronic transport can be understood using 2D Mott variable range hopping model.

50 100 150 200 250 300 10 10

1

10

2

10

3

10

4

10

5

ρ (Ohm-cm) T (K)

0.2 0.3 0.4 0.5 0.6 2 4 6 8 10 TM

ln ρ T

• 1/3 (K
• 1/3)

ρ = ρ0exp(T0/T)

1/3

TC

10 20 30 40 50 60 70 80

• 0.05
• 0.04
• 0.03
• 0.02
• 0.01

0.00

ρ(H) - ρ(0) / ρ(0) H (kOe)

5 K 150 K 180 K

Sr2IrO4 (214) : Magneto-transport

1 2 3 4 5 6 7

• 0.05
• 0.04
• 0.03
• 0.02
• 0.01

0.00

ρ(H) - ρ(0) / ρ(0) H

2 (10 8 Oe 2)

Magnetoresistance (MR) =

) ( ) ( ) ( ) ( ρ ρ ρ ρ ρ − = Δ H

q Positive MR (weak antilocalization) in strong SOC systems, Bi2Se3, Bi2Te3, Na2IrO3 films. q Negative MR at low T in VRH regime – weak localization – quantum interference effect – Quadratic field dependence.

Sr2IrO4 (214) : Critical Analysis

50 100 150 200 250 300 0.0 0.1 0.2 0.3 0.4 FM

M (emu g

• 1)

T (K)

PM

10 20 30 40 50 0.0 0.1 0.2 0.3 0.4

ΔT = 2 K

T = 238 K T = 218 K

M (emu g

• 1)

H (kOe)

q Magnetic isotherms across FM transition

10 20 30 40 50 0.0 0.5 1.0 1.5 2.0

dM/dH (emu g

• 1 Oe
• 1)

H (kOe)

226 K

Sr2IrO4 (214) : Critical Analysis

0.0 0.5 1.0 1.5 0.00 0.02 0.04 0.06

M

1/β (emu g

• 1)

1/β

(H/M)

1/γ (10 4 Oe emu

• 1 g)

1/γ

3D Ising Model β = 0.325 γ = 1.24

2 4 6 8 10 12 14 16 0.00 0.04 0.08 0.12 0.16

M

β (emu g

• 1)

β

(H/M)

1/γ (10 4 Oe emu

• 1 g)

1/γ

Mean Field Model β = 0.5 γ = 1.0

0.0 0.2 0.4 0.6 0.00 0.03 0.06 0.09

M

1/β (emu g

• 1)

1/β

(H/M)

1/γ (10 4 Oe emu

• 1 g)

1/γ

3D Heisenberg Model β = 0.365 γ = 1.386

Sr2IrO4 (214) : Critical Analysis

Modified ¡ArroA ¡plot: ¡

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.00 0.04 0.08 0.12 0.16 0.20

M

1/β (emu g

• 1)

1/β

(H/M)

1/γ (10 4 Oe emu

• 1 g)

1/γ

β = 0.55 γ = 1.15

216 220 224 228 232 236 240 0.04 0.06 0.08 0.10 0.12

T (K) MS (emu g

• 1)

2 4 6 8

Tc = 225 K β = 0.57(2) Tc = 225 K γ = 1.147(1)

χ0

−1 (10 4 Oe emu g

• 1)

216 220 224 228 232 236 240

• 15
• 12
• 9
• 6
• 3

TC = 225 K γ = 1.14(3)

T (K) MS(dMS/dT)

• 1 (K)

TC TC

TC = 225 K β = 0.5517(1)

2 4 6 8 10 12

χ0

• 1(dχ0
• 1/dT)
• 1 (K)

Sr2IrO4 (214) : Critical Analysis

10 20 30 40 50 0.0 0.1 0.2 0.3 0.4

3.0 3.5 4.0 4.5 5.0

• 2.4
• 2.2
• 2.0
• 1.8

M (emu g

• 1)

H (kOe)

T = 226 K

δ = 3.090(2)

Log(M) Log(H)

Kouvel-Fisher Plot Critical Plot Critical isotherm: M ∝ H1/δ

0.01 0.1 1 10 0.1 1 10

15 30 45 60 2 4 6 8

M|ε|

• β (emu g
• 1)

H|ε|

• (γ+β) (10

6 Oe)

218 K 220 K 222 K 224 K 226 K 228 K 230 K 232 K

M|ε|

• β (emu g
• 1)

H|ε|

• (γ+β) (10

6 Oe)

Exponents ¡ β ¡ γ ¡ δ ¡ This ¡Work ¡ 0.55 ¡ 1.15 ¡ 3.03 ¡ Mean ¡Field ¡ 0.5 ¡ 1.0 ¡ 3.0 ¡ 3D ¡Heisenberg ¡ 0.365 ¡ 1.386 ¡ 4.8 ¡ 3D ¡Ising ¡ 0.325 ¡ 1.241 ¡ 4.82 ¡

Sr2IrO4 (214) : Critical Analysis

Scaling ¡analysis ¡

Sr2IrO4 (214) : Thermal Demagnetization

Thermal Demagnetization ΔM : Spin-wave (SW) excitation (Bloch) : Stoner single-particle (SP) excitation: ΔMTotal = ΔMSW + ΔMSP

2 / 3

) ( ) ( ) ( ) ( BT M M T M M M = − = Δ

) exp( ) ( ) ( ) ( ) (

2 / 3

T k CT M M T M M M

B

Δ − = − = Δ

50 100 150 200 250 300

• 1.5

0.0 1.5 3.0 4.5 6.0

7 T 5 T 3 T 2 T 1 T

• ΔS (10
• 2 Jkg
• 1K
• 1)

T (K)

Sr2IrO4 (214) : Magnetocaloric Effect (MCE)

Magnetic Entropy change: ΔSM(T,H) = SM(T,H) – SM(T,0) =

( )

dH T H T M

H H

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∫ δ δ ,

Relative cooling power: ΔSM(T,H) × δTFWHM

20 40 60 80 0.0 0.2 0.4 0.6 0.8 M (emu/g) H (kOe)

5 K - 300 K

Sr2IrO4 (214) : Field dependence of MCE

0.02 0.04 0.06 0.08 0.10 0.000 0.015 0.030 0.045 0.060

Experimental data Linear fit of data

• ΔSM (J kg
• 1 K
• 1)

(H/TC)

2/3

Nice linear field dependence For both ΔSM and RCP . Linear dependence of ΔSM and (H/Tc)2/3 shows mean Field nature.

150 200 250 300

• 0.12
• 0.10
• 0.08
• 0.06
• 0.04
• 0.02

0.00

dρ/dT T (K)

TN

Sr2IrO4 (214) : Resistivity derivative

50 100 150 200 250 300 10 10

1

10

2

10

3

10

4

10

5

ρ (Ohm-cm) T (K)

Mott OR Slater OR Both !!!

Acknowledgement

Institute : AIRF – JNU for low temperature XRD data. UGC-DAE CSR for Magnetization and Transport data. Collaborator : Imtiaz Noor Bhatti, Ph.D student Alok Banerjee, UGC-DAE CSR Rajeev Rawat, UGC-DAE CSR Funding : UGC, Govt of India DST, Govt of India

!!! Thank you !!!