magnetic phase competition in off-stoichiometric heusler...

Magnetic Phase Competition in Off-Stoichiometric HeuslerAlloys: The Case of Ni50-xCoxMn25+ySn25-y

K. P. Bhatti, D.P. Phelan, C. LeightonChemical Engineering and Materials Science, University of Minnesota

V. Srivastava, R.D. JamesAerospace Engineering and Mechanics, University of Minnesota

S. El-KhatibPhysics, American University of Sharjah

NIST Center for Neutron Research

S. Yuan, P.L. Kuhns, A.P. Reyes, J.S. Brooks, M.J.R. HochNational High Magnetic Field Laboratory

Multiferroic alloys (ferroelastic + magnetic)

> Magnetoelasticity, magnetic shape memory,field-induced phase transformations, magnetocaloric and barocaloric effects

> Actuators/sensors, magnetic refrigeration, energy conversion, heat-assisted recording?

Thermal hysteresis: Vital for applications, but fundamentals elusive….

Introduction: Martensitic (Magnetic) Alloys

T

TM(first-order

MPT)

AusteniteMartensite

T (K)

Krenke et al.Nat. Mater. (2005)

Introduction: Minimization of Thermal Hysteresis

Recent theoretical work by James et al.: Geometrical compatibility between austenite and martensite unit cells vital for T.

An invariant plane occurs at their interface if, 2 = 1, where 1,2,3 are the ordered eigenvalues of the transformation stretch matrix, U.

Cui et al. Nat. Mater. (2006)Zhang et al. Acta. Mat. (2009)

Experiment: Remarkable correlations between T and2. Direct observation of “ideal” interface by HRTEM

T

Application to Magnetic Alloys: The Route to Ni50-xCoxMn40Sn10

Step I Full Heusler alloys Ni2MnZ, Z = Sn, In, Ga, etc. (e.g. Ni2MnSn, F, TC = 350 K)

[ ]

[ ]

[ ]



Step II Ni50Mn25+yZ25-y:Tunable magnetic interactions (F vs. AF)*MPT for y > 52 1. [ ]

[ ]

[ ]

(001) plane

excess Mn*Krenke, Acet, Wasserman, Moya, Manosa, Planes, PRB (2005, 2006)



Step II Ni50Mn25+yZ25-y:Tunable magnetic interactions (F vs. AF)*MPT for y > 52 1.

*Krenke, Acet, Wasserman, Moya, Manosa, Planes, PRB (2005, 2006)

?




Step III Ni50-xCoxMn40Sn10: Enhanced TC, MSConvenient TM2 1 (1.0051 @ x = 6)


?




Step III Ni50-xCoxMn40Sn10: Enhanced TC, MSConvenient TM2 1 (1.0051 @ x = 6)

Ni46Co6Mn40Sn10: TC 440 K TM 380 K M 1000 emu/cm3

T < 10 K


?

Magnetism in Ni50-xCoxMn40Sn10 (and Related Systems)

High TC, high M, convenient TM, low T

F austenite, non-F martensite (AF or P?)

Nominally non-F martensite reveals some significant surprises:

> Superparamagnetic-like behavior at low T (in a bulk solid!)> Exchange bias in blocked low T state (in a single phase)> Collective freezing. Super-spin-glass?> ZFC exchange bias

Acute sensitivity of magnetism to composition

Nanoscale MagneticInhomogeneity?

Experimental Details

0

100

200

300

400

Data

Model

Residual

(a) T = 410K

cubic, Fm-3m

Inte

nsity [

arb

. u

nits]

Ni44Co6Mn40Sn10

20 30 40 50 60 70 80 90 100

0

200

400

(b) T = 300K

5M monoclinic, P21

2[deg]

Arc-melted polycrystalline bulk ingots [Srivastava et al APL (2010);Bhatti et al PRB (2012)]

Characterized by:

> DSC

> T-dependent XRD

> T-dependent Neutron PowderDiffraction (NPD)

> Magnetometry

> Small-Angle Neutron Scattering (SANS)

> 55Mn zero-field NMR

Ni50-xCoxMn40Sn10 Phase Diagram

0 2 4 6 8 10 12 14

0

100

200

300

400

500

600

0 5 10 15 20 25

0

100

200

300

400

500

600

700

(b)

F (Aust.)

TB

TC

TM

P (Aust.)

x

AF/SP (Mart.)

EB Clustered

(Mart.)

Clustered

(Mart.)

e/a

T [K

]

e/a

Ni50-x

CoxMn

40Sn

10

TC

TM

P (Aust.)

T [K

]

y

F (Aust.)

AF (Mart.)

Ni50

Mn25+y

Sn25-y

(a)

8.20 8.15 8.10 8.067.8 8.0 8.2 8.4

?

0 100 200 300 400 5000

10

20

30

0 100 200 300 400 5000.00

0.02

0.04

0.06

0.08

M

[e

mu

/cm

3]

T [K]

Ni48

Co2Mn

40Sn

10

H = 5000 Oe

M [em

u/c

m3]

FCW

FCC

ZFCW

T [K]

H = 10 Oe

M vs. T (x = 2)

0 2 4 6 8 10 12 14

0

100

200

300

400

500

600

0 5 10 15 20 25

0

100

200

300

400

500

600

700

(b)

F (Aust.)

TB

TC

TM

P (Aust.)

x

AF/SP (Mart.)

EB Clustered

(Mart.)

Clustered

(Mart.)

e/a

T [K

]

e/a

Ni50-x

CoxMn

40Sn

10

TC

TM

P (Aust.)

T [K

]

y

F (Aust.)

AF (Mart.)

Ni50

Mn25+y

Sn25-y

(a)

8.20 8.15 8.10 8.067.8 8.0 8.2 8.4

M vs. T (x = 6)

?

0 100 200 300 400 500 6000

2

4

6

8

10

0 100 200 3000.00

0.05

0.10

0.15

0.20

FCC

ZFCW

M [

em

u/c

m3]

T [K]

H = 10 Oe

Ni44

Co6Mn

40Sn

10

M [

em

u/c

m3]

T [K]

M vs. T (x = 6)

0 2 4 6 8 10 12 14

0

100

200

300

400

500

600

0 5 10 15 20 25

0

100

200

300

400

500

600

700

(b)

F (Aust.)

TB

TC

TM

P (Aust.)

x

AF/SP (Mart.)

EB Clustered

(Mart.)

Clustered

(Mart.)

e/a

T [K

]

e/a

Ni50-x

CoxMn

40Sn

10

TC

TM

P (Aust.)

T [K

]

y

F (Aust.)

AF (Mart.)

Ni50

Mn25+y

Sn25-y

(a)

8.20 8.15 8.10 8.067.8 8.0 8.2 8.4

M vs. T (x = 14)

?

-75 -50 -25 0 25 50 75

-900

-600

-300

0

300

600

900

0 100 200 300 400 500 6000

2

4

6

8

10

5 K

300 K

550 K

H [kOe]

M [

em

u/c

m3]

FCC

FCW

ZFCW

T [K]

Ni36

Co14

Mn40

Sn10

M [

em

u/c

m3] H = 10 Oe

M vs. T (x = 14)

0 2 4 6 8 10 12 14

0

100

200

300

400

500

600

0 5 10 15 20 25

0

100

200

300

400

500

600

700

(b)

F (Aust.)

TB

TC

TM

P (Aust.)

x

AF/SP (Mart.)

EB Clustered

(Mart.)

Clustered

(Mart.)

e/a

T [K

]

e/a

Ni50-x

CoxMn

40Sn

10

TC

TM

P (Aust.)

T [K

]

y

F (Aust.)

AF (Mart.)

Ni50

Mn25+y

Sn25-y

(a)

8.20 8.15 8.10 8.067.8 8.0 8.2 8.4

M vs. H (x = 2)

?

M vs. H (x = 2)

-30 -15 0 15 30-80

-40

0

40

80-60 -40 -20 0 20 40 60

-50

0

50

-30

0

30

(c)

5 K

50 K

H [kOe]

Langevin fit

M [

em

u/c

m3]

(b)

200 K

175 K

150 K

125 K

M [

em

u/c

m3]

500 K

400 K

Ni48

Co2Mn

40Sn

10

(a)

M vs. H (x = 2)

-30 -15 0 15 30-80

-40

0

40

80-60 -40 -20 0 20 40 60

-50

0

50

-30

0

30

(c)

5 K

50 K

H [kOe]

Langevin fit

M [

em

u/c

m3]

(b)

200 K

175 K

150 K

125 K

M [

em

u/c

m3]

500 K

400 K

Ni48

Co2Mn

40Sn

10

(a)

T > TM: P

T < TM: AF/P

M vs. H (x = 2)

-30 -15 0 15 30-80

-40

0

40

80-60 -40 -20 0 20 40 60

-50

0

50

-30

0

30

(c)

5 K

50 K

H [kOe]

Langevin fit

M [

em

u/c

m3]

(b)

200 K

175 K

150 K

125 K

M [

em

u/c

m3]

500 K

400 K

Ni48

Co2Mn

40Sn

10

(a)

T > TM: P

T < TM: AF/P

300 - 100 K: Langevin-like M(H)

HTHT

Tk

Tk

HTTTnTHM BG

C

B

B

C

CC )()(

)(coth)()(),(

M vs. H (x = 2)

-30 -15 0 15 30-80

-40

0

40

80-60 -40 -20 0 20 40 60

-50

0

50

-30

0

30

(c)

5 K

50 K

H [kOe]

Langevin fit

M [

em

u/c

m3]

(b)

200 K

175 K

150 K

125 K

M [

em

u/c

m3]

500 K

400 K

Ni48

Co2Mn

40Sn

10

(a)

T > TM: P

T < TM: AF/P


T < 100 K: M(H) gradually opens“Static” FZFC exchange bias*

HTHT

Tk

Tk

HTTTnTHM BG

C

B

B

C

CC )()(

)(coth)()(),(

*Wang et al PRL (2011)

0 2 4 6 8 10 12 14

0

100

200

300

400

500

600

0 5 10 15 20 25

0

100

200

300

400

500

600

700

(b)

F (Aust.)

TB

TC

TM

P (Aust.)

x

AF/SP (Mart.)

EB Clustered

(Mart.)

Clustered

(Mart.)

e/a

T [K

]

e/a

Ni50-x

CoxMn

40Sn

10

TC

TM

P (Aust.)

T [K

]

y

F (Aust.)

AF (Mart.)

Ni50

Mn25+y

Sn25-y

(a)

8.20 8.15 8.10 8.067.8 8.0 8.2 8.4

M vs. H (x = 6)

?

M vs. H (x = 6)

-75 -50 -25 0 25 50 75

-100

0

100

-0.6

0.0

0.6

-100

0

100

-0.6

0.0

0.6

-1000

-500

0

500

1000

-5.6

-2.8

0.0

2.8

5.6

-500

0

500

-2.8

0.0

2.8

-0.1 0.0 0.1-100

-50

0

50

100

(d)

H [kOe]

5K

30K

(c)M

[

B/f

.u.]

M [

em

u/c

m3]

80K

100K

150K

200K

300K

370K

(b)

400K

395K

390K

415K

550K

(a)

415K

M vs. H (x = 6)

-75 -50 -25 0 25 50 75

-100

0

100

-0.6

0.0

0.6

-100

0

100

-0.6

0.0

0.6

-1000

-500

0

500

1000

-5.6

-2.8

0.0

2.8

5.6

-500

0

500

-2.8

0.0

2.8

-0.1 0.0 0.1-100

-50

0

50

100

(d)

H [kOe]

5K

30K

(c)M

[

B/f

.u.]

M [

em

u/c

m3]

80K

100K

150K

200K

300K

370K

(b)

400K

395K

390K

415K

550K

(a)

415K

T > TC: P

T < TC: Soft F

M vs. H (x = 6)

-75 -50 -25 0 25 50 75

-100

0

100

-0.6

0.0

0.6

-100

0

100

-0.6

0.0

0.6

-1000

-500

0

500

1000

-5.6

-2.8

0.0

2.8

5.6

-500

0

500

-2.8

0.0

2.8

-0.1 0.0 0.1-100

-50

0

50

100

(d)

H [kOe]

5K

30K

(c)M

[

B/f

.u.]

M [

em

u/c

m3]

80K

100K

150K

200K

300K

370K

(b)

400K

395K

390K

415K

550K

(a)

415K

T > TC: P

T < TC: Soft F

400 - 380 K: Hysteresis region(H-induced MPT)

M vs. H (x = 6)

-75 -50 -25 0 25 50 75

-100

0

100

-0.6

0.0

0.6

-100

0

100

-0.6

0.0

0.6

-1000

-500

0

500

1000

-5.6

-2.8

0.0

2.8

5.6

-500

0

500

-2.8

0.0

2.8

-0.1 0.0 0.1-100

-50

0

50

100

(d)

H [kOe]

5K

30K

(c)M

[

B/f

.u.]

M [

em

u/c

m3]

80K

100K

150K

200K

300K

370K

(b)

400K

395K

390K

415K

550K

(a)

415K

T > TC: P

T < TC: Soft F



M vs. H (x = 6)

-75 -50 -25 0 25 50 75

-100

0

100

-0.6

0.0

0.6

-100

0

100

-0.6

0.0

0.6

-1000

-500

0

500

1000

-5.6

-2.8

0.0

2.8

5.6

-500

0

500

-2.8

0.0

2.8

-0.1 0.0 0.1-100

-50

0

50

100

(d)

H [kOe]

5K

30K

(c)M

[

B/f

.u.]

M [

em

u/c

m3]

80K

100K

150K

200K

300K

370K

(b)

400K

395K

390K

415K

550K

(a)

415K

T > TC: P

T < TC: Soft F



T < 60 K: M(H) gradually opens“Static” F

Superparamagnetic-like Behavior

102

103

104

50 100 150 200 250 300

1017

1018

1019

x = 2

x = 3

x = 4

x = 6

c [

B]

(a)

Ni50-x

CoxMn

40Sn

10

(b)

nc [

cm

-3]

T [K]

c 200-250 B

nc 2-3 x 1019 cm-3

dc 2-6 nm

Implication: Dense ensemble ofnm-scale spin clusters

HTHT

Tk

Tk

HTTTnTHM BG

C

B

B

CCC )(

)(

)(coth)()(),(

Exchange Bias

0

1000

2000

0 50 100 150 2000

200

400

600

800 Ni48

Co2Mn

40Sn

10

Ni44

Co6Mn

40Sn

10

Hc

[Oe]

HFC

= 70 kOe

(a)

(b)

HE [O

e]

T [K]

x = 2:

> SP blocking at 100-150 K> EB blocking at 60 K> Large HC peak

x = 6:

> SP blocking at 60 K> EB blocking at 60 K> No HC peak

Phase Diagram

SANS (NIST)

Detectorchamber

ReactorNeutronguide

Cryostat/magnet

0.01 0.1

0.1

1

10

100

q [Å-1]

(a) 500 K

d/d

[cm

-1]

n

P

q

Td

d

Tqd

d)(

,

2

2

)(

1

)(

,

Tq

Td

d

Tqd

d L

Low q (large length-scale)Porod Scattering

High q (short length-scale)Lorentzian Scattering

SANS (x = 6)

0.01 0.10.01

0.1

1

10

100

0.1

1

10

100

0.1

1

10

100

0.1

1

10

100

0.1

1

10

100

(e) 30 K

q [Å-1]

(d) 380 K

Ni44

Co6Mn

40Sn

10

(c) 390 K

(b) 425 K

(a) 500 K

d/d

[cm

-1]

SANS: q Dependence

0.01 0.10.01

0.1

1

10

100

0.1

1

10

100

0.1

1

10

100

0.1

1

10

100

0.1

1

10

100

(e) 30 K

q [Å-1]

(d) 380 K

Ni44

Co6Mn

40Sn

10

(c) 390 K

(b) 425 K

(a) 500 K

d/d

[cm

-1]

SANS: q Dependence

Low q Porod scattering:

> Increases below TC> Magnetic domain scattering > Proof of long-range F order (>> 100 nm)

High q Lorentzian scattering:

> Peaks at TC> F spin correlations

Intermediate q scattering:

> A peak develops! 2/q 120-200 Å> Structure factor peak. Liquid-like spatial

distribution of magnetic clusters.

2

2

)(2

))((exp)(

)(

),(T

TqqT

d

d

q

Td

d

Tqd

d G

G

n

P

Tot

2

2

)(

1

)(

Tq

Td

d

L

SANS: T Dependence

100 200 300

0.02

0.03

0.03

0 100 200 300 400 500

0.0

0.1

0.2

0.3

0

50

100

150

d/d

[cm

-1]

T [K]

(b) q = 0.1 Å-1

d/d

[cm

-1]

T [K]

Ni44

Co6Mn

40Sn

10

d/d

[cm

-1]

Heating

Cooling

(a) q = 0.005 Å-1 q = 0.005 Å

-1 (1200 Å):

> Sharp onset of domainscattering at TC

> Hysteretic loss at TM

q = 0.1 Å-1 (60 Å):

> Critical scattering peak at TC

SANS: T Dependence

100 200 300

0.02

0.03

0.03

0 100 200 300 400 500

0.0

0.1

0.2

0.3

0

50

100

150

d/d

[cm

-1]

T [K]

(b) q = 0.1 Å-1

d/d

[cm

-1]

T [K]

Ni44

Co6Mn

40Sn

10

d/d

[cm

-1]

Heating

Cooling

(a) q = 0.005 Å-1 q = 0.005 Å

-1 (1200 Å):

> Sharp onset of domainscattering at TC

> Hysteretic loss at TM

q = 0.1 Å-1 (60 Å):

> Critical scattering peak at TC

> 130 K transition (!), clearly associated with clusters

> Blocking at 10-12 s time-scales!

SANS T Dependence: Porod

0 100 200 300 400 500

2

3

410

-9

10-6

10-3

T [K]

n (d/d

) P

[cm

-1]

Scattering in martensite strong, T-dependent

Paramagnetic, n = 4 (grains); Ferromagnetic, n = 2 (pinned domains); Martensitic, n = 3 (AF domains?)

Additional (indirect) evidence for AF order in the martensite

0

1

0 100 200 300 400 500

0.03

0.04

0.05

(d/d

) G

[cm

-1]

[cm

-1]

qG[c

m-1]

T [K]

0.02

0.04

SANS T Dependence: Gaussian

Gaussian peak intensity actually emerges at high T (even above TC?)

Peak position weakly T-dependent. Peak width decreases on cooling

Correlation length > 5 inter-particle spacings! Collective response*?

*Cong et al APL (2010); APL (2010) and Wang et al PRL (2011)

Å Å

0

1

2

3

0 100 200 300 400 5000

20

40

(d

/d

) L

[cm

-1]

T [K]

[Å

-1]

SANS T Dependence: Lorentzian

Only present in significant intensities in paramagnetic phase

Magnetic correlation length diverges as T TC+

Qualitative Model

Qualitative Model

P

Qualitative Model

P

F

Qualitative Model

P

F

AF?

Qualitative Model

P

F

AF?

AF?

AF in the Martensite: Neutron Diffraction Problems

AF known at Ni50Mn50, suspected in someform in Ni50Mn25+ySn25-y

Indirect evidence:

> (T)> Exchange bias> SANS (Porod scattering)

Why not just do neutron diffraction?

> Texture an issue> Looking for the onset of AF order

simultaneous with MPT to lowsymmetry state (very challenging refinement)

AF in the Martensite: Neutron Diffraction Problems

AF known at Ni50Mn50, suspected in someform in Ni50Mn25+ySn25-y

Indirect evidence:

> (T)> Exchange bias> SANS (Porod scattering)

Why not just do neutron diffraction?

> Texture an issue> Looking for the onset of AF order

simultaneous with MPT to lowsymmetry state (very challenging refinement)

Weak evidence for an AF order parameter?

Polarized neutrons…….

AF in the Martensite: 55Mn Zero Field NMR (/2 = 10.5 MHz/T)

150 200 250 300 350 400 450 500

Frequency f (MHz)

Ni50-xCoxMn40Sn10

x=14

x=7

x=0

AF F

AF x 0.1 F

F

T = 1.6 K

48 T14 T

NMR signal enhancement factor, , measured by calibration to 19F

Typically: High in Fs, low in AFs

225 10

AF in the Martensite: 55Mn Zero Field NMR (/2 = 10.5 MHz/T)

Unambiguous F/AF assignment

The martensite indeed has ordered AF, decreasing with Co substitution

-10.5 MHz / TNi50Mn40Sn10 (x = 0)

AF in the Martensite: 55Mn Zero Field NMR

AF/F phase coexistence at low T

Volume fractions

Conclusions

Bhatti, El-Khatib, Srivastava, James, Leighton, Phys. Rev. B. 85, 134450 (2012)

Bhatti, Srivastava, Phelan, James, Leighton, Heusler Alloys, Eds. Hirohata and Felser, Springer (2015)

Yuan, Kuhns, Reyes, Brooks, Hoch, Srivastava, James, El-Khatib, Leighton, Phys. Rev. B. 91, 214421 (2015)

Yuan, Kuhns, Reyes, Brooks, Hoch, Srivastava, James and Leighton, Phys. Rev. B., submitted (2015)

Ni50-xCoxMn25+ySn25-y: Physically very interesting, potentially useful set of alloys

High TC, convenient TM, exceptionally low T, high M

Nanoscale magneto-electronic inhomogeneity:

> SP-like freezing of nm-scale spin clusters> Exchange bias in a nominally single-phase system> First direct observation by SANS

(liquid-like distribution, dc 2-6 nm, dc-c = 12 nm, strong interactions)> First observation by zero-field 55Mn NMR

(proof of short-range AF order, dc 8.5 4.0 nm)

New magnetic phase diagram

Qualitative model based on (unavoidable) compositional fluctuations

magnetic phase competition in off-stoichiometric heusler...

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