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Synthesis and magnetic propertiesof 2-D frustrated materials

Praneeth Chilakalapudi

Guide: Prof. S SrinathIn collaboration with: Dr. B Koteswara Rao

University of Hyderabad

May 05, 2016

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Praneeth C S

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Overview

Introduction magnetic frustration

Magnetic Order: FM, AFMMagnetic frustrationGeomerical frustrationPbCuTeO5

Literature Survey

Motivation

Progress

SynthesisXRDMagnetic data analysis

Future plans

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Types of Magnetic Order

Model Hamiltonian:H = −

∑i,j JijS

ni · Sn

j′n′ is the spin dimensionality.

Ferromagnetism

↑↑↑↑J, θCW ≥ 0

Anti-ferromagnetism

↑↓↑↓J, θCW ≤ 0

Spin dim Model Type

1 Ising model2 XY model3 Heisenberg model

Figure: χ behaviour for AFMmaterial

θCW ∼ Tc only for conventional cases casesθCW : exchange interaction, ∼ Tc : transition

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Magnetic Frustration

Definition

Frustration is a generic term that encapsulates

numerous phenomena where two or more types of

microscopic interactions compete in driving the

development of correlations in a system.

1

1Magnetic Frustration, La Physique au Canada, Vol. 68, No. 2, Pg 67

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Magnetic Frustration

1 OriginExchange energies can not be satisfied simultaneouslyArise due to incompatibility of magnetic ◦ of freedomwith crystal geometry

Figure: GFM in triangular AFM lattice with Ising spins

QM fluctuations exist. Spin ordering disturbed not just bythermal excitation.

2 Consequences → exotic properties:Accidental degeneracy in ground stateThis violates 3rd law of thermodynamicsLarge f− parameter. f = θCW /T

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Geometric Frustration

First theoretical expectations in AFM 4lar lattice with Isingspins (Only � and � states) and N.N. interactions 2

Large ground state entropyEven at low T, no static orderNo discontinuity in power law behaviour of Cp

f = 0 f = 5 f =∞

Conventional Multiferroricity QuantumFM, AFM spin liquid

2G H Wannier, Phys. Rev, Vol 79, No 2 July 15, 1950

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2-D planar kagome system

4lar system with cornershared lattice!

Basket structure

Figure: ZnCu3(OH)6Cl2:Herberthsmithite structure No LRO down to 20mK, despite its

θCW ∼ 300K

Broad-maximum in χ(T )

f > 15000 as Tc ≤ 20mK

33F. Bert1 et. al, Journal of Physics: Conference Series 145 (2009) 0120046 / 28

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Motivation and Plan

To experimentally understand GF in a 2-D checkboard lattice

Synthesis and Structurecharacterization

Analysis of magneticproperties

Figure: Unit Cell

PbCuTeO5 is a candidatematerial

Figure: 2-D distorted checkboardlattice

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Progress: Synthesis and XRD characterization

Synthesized PbCuTeO5

PbO,CuO,Te mixture

Heat treatment:

Intermittent grinding

XRD (SEST, UoH).

λ11.54060 A, λ2 had beenstripped

Scan 10◦ - 80◦ for 1 hour

P -1 space group, Tricliniclattice. Maximumasymmetry

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Progress: XRD, Rietveld refinement

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XRD, Rietveld refinment

Unit cell parameters, before and after refinementParameter Before refinement After refinement

a 6.43 A 6.39Ab 11.32 A 11.26Ac 12.31 A 12.25Aα 107.92◦ 107.857◦

β 90.94◦ 90.96◦

γ 90.38◦ 90.468◦

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Progress: DC χ measurement - χ vs T

SQUID VSM (Measured at IIT-B, Prof Avinash Mahajan’s lab)

Figure: PbCuTeO5 χvsT

χmol =M · χvolume

ρ

At 1 Tesla,Curie-Weissbehaviour

Low fields, FMbehaviour is notsuppressed

Inset graph - FMtransition

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Progress: DC χ measurement - χ−1 vs T

We know that:χ = χ◦ + C

T−θχ◦ = χdia + χVV

Non-linear fit to:

χ−1 =1

χ◦ + CT−θ

Frustration parameter:f = θCW

Tc= 165K

6K∼ 27

Note that f−parameter was calculated for 100 Oe readings

Maybe at 1 Tesla, since transition is suppressed, it has a very highvalue?

If so at fields >> 1 T, its a potential candidate for QSL12 / 28

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Some info for the reader:

This marks end of slides from Midterm Presentation(Skipping concluding remarks)

Beginning Final Presentation slides(Skipping preliminary remarks)

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Discussing somequestions

Figure: 2-D checkboard lattice

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Recapitulation

Magnetic frustration

Motivation

Procedures followed

SynthesisXRDMagnetic dataanalysis

Figure: GFM in triangular AFM lattice

θCW ∼ Tc only forconventional cases cases

f = θcwT

f = 0 f = 5 f =∞

Conventional Multiferroricity QuantumFM, AFM spin liquid

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Recapitulation

(a) Macroscopic χ(T ) (b) χ(T )−1 vs T

Figure: PbCuTeO5: DC Magnetic susceptibility plots

θCW ∼ 6KTc ∼ 166K

f ∼ 28

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Previous Questions

Necessity of Pb inPbCuTeO5?A: Allows for 2-D magneticbehaviour

Are Oxygen molecules in thesame plane as Cu2+ ions?A: No, but CuO4 squares arepresent

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Previous Questions

Q: Give information about particle size from Rietveld?A: FullProf requires instrument resolution file, which isunavailable.Alternative: Scherrer Equation (Rough estimate) :

τ =Kλ

β cos θ, λ = Cu − Kα(1.5456A)

τ : domain size,K : Shape factor (0.9), β: FWHM

Figure: XRD pattern (zoomed in)

τ =∼ 8.95A

However, not agood estimate

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Heat Capacity

Quantum Design PPMS at Prof A Mahajan’s lab, IIT-B

Thermal relaxation method

Zero Field measurement

Figure: Heat Capacity measurement apparatus

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Heat Capacity

CTotal is the sum of only the lattice and magnetic contributions

Cmagnetic(T ) = CTotal(T )− Clattice(T )

PbCuTeO5 is an insulator, ∴ no electronic contribution

Measured data was fitted at high temperatures (100K to 300 K)

Two Debye model

Clattice(T ) = C1

∫ θ1/T

0

x3

ex − 1dx + C2

∫ θ2/T

0

x3

ex − 1dx

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Heat Capacity

Plot of CP vs T for various θD

For Clattice(T ) fit, χ2 minimization for various θD at every T

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Heat Capacity

(a) CP(T ) with fit at high T (b) Cmag (T )

Figure: PbCuTeO5: Heat Capacity measurements

The Cmagnetic data indicates possibility of erroneousmeasurement

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Heat Capacity

(a) Cmag (T )

T(b) ∆Smagnetic

Figure: PbCuTeO5: Heat Capacity measurements

Higher temperature states above TC are not saturating to Rln(2)

∴ Short-range correlations more favoured above TC

Frustration suppresses LRO

∴ Frustration is present in sample

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Conclusions

PbCuTeO5 is a frustrated magnetic material

Verified through two independent experiments

f-parameter ∼ 28

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Accurate phonon DOS measurements using NMR, or Neutrondiffraction

In-field χ(T ) and Cp(T ) experiments

Single crystal growth and study

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Extra - Spin Ice

The residual (ground state) entropy in these structures can beexplained using Linus Pauling’s estimate for water ice.

W = (3/8)N2N ;S = kB lnW . Also, structure analogous to H2O

4

Spins ’freeze’ below a certain temperature 5

Excitations can be thought of as magnetic monopoles

In excited state, ∇ · ~B 6= 04Picture taken from: C. Castelnovo, R. Moessner and S. L. Sondhi, Annu.

Rev. Condens. Matter Phys. 3, 35 (2012)5Leon Balents, Spin liquids in frustrated magnets, doi:10.1038/nature08917

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Extra - Quantum Spin Liquids

Highly disordered system

f =∞QM fluctuations persist all the way till T = 0 Kelvin

No phase transitions, and all symmetries are possible

Are theoretically predicted to show ’exotic excitations withfractional quantum numbers’ (beyond scope of this talk)

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References

Pavlina Choleva PhD thesis, 2004

B.D. Cullity and S.R. Stock, Elements of X-Ray Diffraction, 2ndEd.,Addison-Wesley, 1978, p 102

Moessner and Ramirez, Geometrical Frustration, Physics Today,February 2006

Leon Balents, Spin liquids in frustrated magnets,doi:10.1038/nature08917

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