fe g = 0 · conclusions • the dilution of ls co3+ in ndfe 1-xco xo 3 is equivalent to the...

x > 0 : distribution of internal fieldsx > 0 : distribution of internal fields

Relevant parameter: G = level of uncompensationRelevant parameter: G = level of uncompensation

Fe

Co

Nd

G = 0G = 0



Fe

Co

Nd

G = 1G = 1



Fe

Co

Nd

G = 2G = 2



Fe

Co

Nd

G = 0G = 0



Fe

Co

Nd

G = 4G = 4


0

20

40

60

80

100

0 1 2 3 4

x = 0.03, x = 0.97

x = 0.1, x = 0.9

x = 0, x = 1

x = 0.2, x = 0.8

0.5

% d

e io

nes

Nd

G (en iones Fe3 + descompensados)

Relevant parameter: level of uncompensationRelevant parameter: level of uncompensation

x > 0 : sum of Schottky contributionsx > 0 : sum of Schottky contributions

x > 0 : sum of Schottky contributionsx > 0 : sum of Schottky contributions

0 1 2 3 4 5 60.0

0.2

0.4

ConclusionsConclusions

• The dilution of LS Co3+ in NdFe1-xCoxO3 is equivalent to theinclusion of magnetic vacancies in the system

• The vacancies uncompensate the AF Fe ordered sublattice,increasing the Fe-Nd interaction and

inhibiting Nd cooperative order for x ≥ 0.1

• A mean field model for the parent compound has beenmodified to take account for low doping NdFe1-xCoxO3 (x ≤

0.1)

• It is appealing to suggest that this is the mechanism fornegative magnetization in manganites (isntead of

ferrimagnetism)

RMORMO33 : Model systems : Model systemsM-M, M-R, R-R interactions.M-M, M-R, R-R interactions.

• M-M

• M-R

•R-R

1000 K

100 K

10 K

1 K

M antiferro order (Cr, Fe, Ni, ...)

M SRT’s, ...

R induced order: M-RR cooperative order: R-R

(Nd, Sm, Gd, Er, ...)

NdNiONdNiO33 : Peculiar : Peculiar systemsystem

TN = TM-I = 200 K

Ni AF order(a very unusual one!)M-I transition &Orbital order

1000 K

100 K

10 K

1 K

TNd = 20 K Nd induced order(very unusual one, too!)

0.1 KT = 0.2 K Enhancement of the

diffracted neutron intensities(unclear origin)

for a review, see M. Medarde, J. Phys.:Condens Martter 9, 1679 (1997)J.L. García Muñoz et al., Phys. Rev. B 50, 978 (1994)

S. Rosenkranz, Ph.D. Thesis ETH Zürich, 11853 (1996)

NdNiONdNiO33 : : crystal structurecrystal structure

•• Pbnm Pbnm orthorhombicorthorhombic perovskite

Ni

O

Nd

Each Nd ion is placed at theEach Nd ion is placed at thecenter of a Ni cubecenter of a Ni cube

Ni occupies Ni occupies abab planes : planes :A planesA planes

b

c

a

Ni Ni magnetic order inmagnetic order in NdNiONdNiO33 : : ““Model 1Model 1””

Stacking of alternating ab layers A+ A- A- A+A+ A- A- A+ A+...

AntiferroAntiferroNi spinsNi spins

ddxx22-y-y22

ddzz22

b

b’a’

aA+A+

A+A+

A-A-

A-A-J.L. García Muñoz et al., Phys. Rev. B 50, 978 (1994)

J.L. García Muñoz et al., Phys. Rev. B 51, 15197 (1995)

TTN N = 200 K= 200 K

Model 1 hypothesisModel 1 hypothesis

““Model 1Model 1””: Two kind of magnetic Nd ions: Two kind of magnetic Nd ions

--Nd BNd B++

Ni ANi A++

Nd BNd B00

Uncompensatedenvironment:

Strong polarization

Ni ANi A++

Ni ANi A--

Compensatedenvironment:

Zero polarization

J.L. García Muñoz et al., Phys. Rev. B 50, 978 (1994)J.L. García Muñoz et al., Phys. Rev. B 51, 15197 (1995)

““Model 1Model 1””: Diffracted intensity: Diffracted intensityfrom polarized Ndfrom polarized Nd

Macroscopic Experimental test of Macroscopic Experimental test of ““Model 1Model 1””::

Low-temperature specific heat Low-temperature specific heat

However...However... Nd compensated environments :

non-zero Zeeman splittings

NdCrO3 : Δ = 27 K ;NdFeO3 : Δ = 5.7 KNdMnO3: Δ ~ 25 K

J.L. García Muñoz et al., Phys. Rev. B 50, 978 (1994)

Low-temperature contributionLow-temperature contribution

Model 1

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 1 2 3 4

Specific heat (R)

T (K)

NdNiO3

Schottky-like maximumSchottky-like maximumTTN2 = 0.77 K = 0.77 K

0

1

2

3

4

5

-0.2 0 0.2 0.4 0.6

INS intensity (arb. units)

Ei (meV)

Two channels evidenced by HR-INS:Two channels evidenced by HR-INS:

ΔΔ00 = 4.1 K ; = 4.1 K ; ΔΔ±± = 5.2 K = 5.2 K

T = 2K

A microscopic probe:A microscopic probe:high resolution Inelastic Neutron Scatteringhigh resolution Inelastic Neutron Scattering

ΔΔ±±

ΔΔ±±

ΔΔ00

ΔΔ0 0 = 0= 0

The Ni Nx magnetic modePOLARIZES

the Nd subsystem in a mode (let’s call it nx)

belonging to the same irep of the magnetic group than Nx

Nd-Nd cooperative orderwill favour another mode

(let’s call it r) belonging to another irep

b a

c

Quadruple Magnetic unit cell, TQuadruple Magnetic unit cell, TN N = 200 K= 200 K

Mean field model: Mean field model: specific heatspecific heat

2 2 ˆH ˆ 2 ˆ 2 2

p2

cexcB !"#"µ!"#" $$$$$= xxxpc g nnrH

Self interaction terms Self interaction terms Ni-Nd Zeeman term (eff. exchange field)Ni-Nd Zeeman term (eff. exchange field) Nd-Nd exchange of the polarized component N Nd-Nd exchange in cooperative mode

ˆ 2

1- r=!

where...

ˆ 2

1- xn=!

are mean field order parameters for the cooperative and induced order modesand

c! p!and are the Nd-Nd exchange constants

in cooperative and polarized modes

Spin Hamiltonian for the Nd system:Spin Hamiltonian for the Nd system:

< > < >

Free energy :Free energy :

If we impose:If we impose: 0

excexc HH >± , the free energy splits into two terms:, the free energy splits into two terms:

!"#

$%&

''(

)**+

, -.+= /

±= TT

2cosh2ln

2

1

2

1

á2

p2

c0,á

á 0121F

with

( ) ( )2pá2

cá

!"µ#" ++=$ excBx Hg

being the exchange splittings of the Nd3+ (±, 0) ground doublets.

áF !!By minimizingBy minimizing andand , we get the , we get the

characteristic equations of the system, which gives thecharacteristic equations of the system, which gives theordered net Néel moments ordered net Néel moments as a function of as a function of T.T.!! andand

with respect to with respect to

Ecuaciones características :Ecuaciones características :

!!"

#$$%

& '

'=

T2 tanh

2

á

á

c())

!!"

#$$%

& '

'

+=

T

Hg excBx

2 tanh

2

á

á

pá ()µ

(

0 =!

!!"

#$$%

& '=

'

T2tanh

2

á

c

á

(

Fase ordenadaFase ordenadacooperativamentecooperativamente

FaseFaseparamagnética conparamagnética conorden inducidoorden inducido

Transición de FaseTransición de Fase0

0.2

0.4

0.6

0.8

1

0 1 2 3 4

!

T (K)

"

Mom

ento

net

o no

rmal

izad

o

Entropy...Entropy...

!!"

#$$%

& ''()

*

+,-

.!!"

#$$%

& '+= /

±= TTTS

2 tanh

2

2 cosh ln 2ln

ááá

0,á

C (R

) and specific heat : and specific heat :

0

0.1

0.2

0.3

0 1 2 3 4

B+-

B0

T (K)

Δ0t = 2.6 K ≅ Δ0

e = 4.1 K

Δ±t = 5.3 K Ζ Δ±

e = 5.2 K

TNt = TNe = 0.77 K

0

0.1

0.2

0.3

0.4

0.5

0.6

0

Cp

/ R

2 4 6 8 10

ra = 3

rb = 0

a

b

t

0

0.25

0.5

0.75

0 2 4 6 8

Cp

/ R

10

a

b

ra = 1.5

rb = 0

t

0

0.2

0.4

0.6

0.8

1

0

Cp

/ R

2 4 6 8 10

t

ra = 1

rb = 0

a

b

0

0.5

1

1.5

0 2 4 6 8

Cp

/ R

10

ra = 0.5

rb = 0

a

b

t

Results for HResults for H00excexc = 0 : = 0 :

HH±± = 0.5 = 0.5

HH00 = 0 = 0

HH±± = 1 = 1

HH00 = 0 = 0

HH±± = 1.5 = 1.5

HH00 = 0 = 0

H± = 3

H0 = 0C

(R)

C (R

)C

(R)

C (R

)

C (R

)C

(R)

C (R

)C

(R)

0.4

0

ra = 2

rb = 1

a

0.1b

0.2

Cp

/ R

0.3

0 2 4

t

6 8 10

0

0.1

0.2

0.3

0.4

0.5

0

Cp

/ R

2 4 6 8 10

ra = r

a = 2

a = b

t

0

0.1

0.2

0.3

Cp

/ R

0 2 4 6 8 10

t

ra = 3

rb

= 1

ab

Results for HResults for H00excexc > 0 : > 0 :

HH±± = H = H00 = 2 = 2

HH±± = 3 = 3

HH00 = 1 = 1

HH±± = 2 = 2

HH00 = 1 = 1 Only intermediate (though different)Only intermediate (though different)

values for both, Hvalues for both, H±±excexc and H and H00

excexc

reproduce the experimental resultsreproduce the experimental resultsC

(R)

C (R

)

C (R

)C

(R)

C (R

)C

(R)

0.2

CCpp best fit best fit

C (R

)

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20

T (K)

!

!1!2

Nor

mal

ized

net

mom

ent

0

0.1

0.2

0.3

0 1 2 3 4

B+-

B0

T (K)

ΔΔ00tt = 3.6 K = 3.6 K

ΔΔ±±tt = 5.6 K = 5.6 K

TTNtNt = 0.81 K = 0.81 K

fe g = 0 · conclusions • the dilution of ls co3+ in ndfe 1-xco xo 3 is equivalent to the...

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