The magnetic phase diagram and Landau free energy of. CuO. R. Villarreal, G.
Quirion, M.L. Plumer. Department of Physics. Memorial University, St. John's, NL,
...
The magnetic phase diagram and Landau free energy gy of CuO
R. Villarreal, G. Quirion, M.L. Plumer Department of Physics Memorial University, St. John’s, NL, Canada
Collaborators M. Poirier Département de Physique Université de Sherbrooke Sherbrooke, Sherbrooke Sherbrooke, QC QC, Canada
T. Usui, T. Kimura Division of Materials Physics, Osaka University, Osaka, Japan
Spin--Driven Multiferroics Spin •Ferroelectric -> transition metal ions with empty d shell •Magnetism -> requires partially filled shell 10 years ago TbMnO3 and DyMnO3
DM interaction
->
ferroelectricity and magnetism exclude each other
ferroelectric order driven by spiral magnetic order renews the interest for the search of magnetoelectric materials
Wave vector Q Cycloidal
PQ
Other mechanism Proper Screw
P // Q CuFeO2, CuCrO2
F. Kagawa, PRL, 102, 057604, 2009.
Spin--Driven Multiferroics Spin As spiral magnetic orders
arise from spin frustration
CuO Mizuno, Tohyama, Maekawa et al. PRB 57, 5326 (1998); Shimizu et al. JPSJ 72, 2165 (2003),
monoclinic C2/c (2/m) Cu2+
150
low dimensional cuprates low-dimensional
(TN=243K) 243K)
FM 146o
o
109
[101]
The structure can be considered as being composed of Cu-O chains running along [101] and [101] directions.
Exchang ge constan nt J1
O
AFM
[101]
Nd2CuO4
90
O
100
La2CuO4
o
O
(320)
CuO (230)
Cu
YBa2Cu3O6 (410) 180
BaCu aCu 2Ge2O7
50
(8.5)
Ca2Y2 Cu5 O10 (30 ) CuGeO3 (14) BaCu Si O (9.2) 2 2 7
0 Li 2CuO2 (8)
90
LiCuVO4 (2.4) LiCu 2O4 (23)
O
Cu
O
AFM FM FM AF
120 150 180 Cu-O-Cu bond angle (deg)
Magnetic and Electric Properties Cu0 Spin Configuration AF2 (spiral)
TN1 = 213 K
Spontaneous P l i ti along Polarization l b-axis
TN2 = 230 K
TN2 = 230 K TN1
QICM = [0.506 0 -0.483] TN2
T. Kimura et al., Nature Materials, 7, 291 (2008) ( )
AF1 (collinear) TN1 = 213 K
AF Chains QCM = [0.5 0 -0.5]
Sound Velocity Measurements
V
dV df V f
Ceff
Ultrasonic interferometer hi h resolution higher l i )V/V ~ 10-6
2L t
Sound Velocity Measurements = 213 K
B // b
Magnetic Phase Diagram of CuO
Landau Model CuO Landau Free Energy: FL = F2I + F2A + F4 + FZ Second Order Isotropic Contribution:
F2 I
1 d r d r A ( r , r ) s ( r ) s ( r 1 2 1 2 1 2) 2 2V
Second Order Single-ion Anisotropic Contribution:
1 F2 A dr D y (r ) s y (r ) s y (r ) Dz (r ) s z (r ) s z (r ) Dxz (r ) s x (r ) s z (r ) 2V 2V Fourth Order Isotropic Contribution:
F4
1 d r d r d r d r B ( r , r , r , r ) s ( r ) s ( r ) s ( r ) s ( r 1 2 3 4 1 2 3 4 1 2 3 4) 4 4V
Spin Density V s (r ) N
Local Spin Density: Non-local Spin Density
(r ) (r R) R
( r ) m Se
iQ r
S e
* iQ r
S S1 i S2
where
S1 S cos β cosγ yˆ sin γ ρˆ 2 S 2 S sin β cos ˆ1 sin ((cos yˆ sin ρˆ 2 )
ˆ1 cos xˆ sin zˆ ˆ 2 sin xˆ cos zˆ
Q wave vector associated with the spin configuration Describes non-collinear spin configuration
two orthogonal unit vectors in the ac-plane
S1
S2
Wave Vector Q S Second dO Order d IIsotropic t i Contribution: C t ib ti
1 F2 I dr1dr2 A(r1 , r2 ) s (r1 ) s (r2 ) 2 2V 2V
1~ 2 F2 I A m AQ S 2 2
J1
J2
where AQ = a T + J(Q)
J(Q) = 2 [J1f1(Q) + J2f2(Q) + J3f3(Q) + J4f4(Q)] f1(Q) = cos (qa - qc) f2((Q)) = cos (q ( a + qc) f3(Q) = cos (qa – qb) + cos (qa + qb) f4(Q) = cos (qb – qc) + cos (qb + qc)
J3 J4
Wave Vector Q Antiferromagnetic g States (J1 = 1) QICM = [0.506 [0 506 0 − 0.483] 0 483]
J2/J1 = −0.3, J3/J1 = 0.017, 0 017 J4/J1 = 0 leading to JQ/J1 = −2.6
Magnetic Phase Diagram of CuO FL AQ S D yQQ S y 2
AQ = a (T −T TQ)
2
2 1 2 1 DzQQ S z DxzQQ S x S z B1S B2 S S BU S S c.c 4Q ,G 2 4 2 1 1 2 4 Ao m B3 m 2 B4 m S B5 m 2 S 2 H m 2 4 2
4
Numerical Predictions H // b
Experimental Results
Spin Configurations H // b HF1 (collinear)
HF2 (spiral)
HF3 (collinear)
H AF1 (collinear)
p ) AF2 ((spiral)
T
AF3 (collinear)
Conclusions •new collinear lli phase h (AF3) detected d t t d between b t the th PM and d the th spiral i l phase h (AF2). • for B // b,, we also observe a spin-flop p p phase p (HF1) ( ) at low temperatures. p • Complementary dielectric measurements confirm that magnetoelectric effects exist only in the spiral phase (AF2). the existence of the intermediate phase AF3 is supported by our Landau model . The model predicts additional phase transitions possibly at higher fields. •Finally, the proposed model is potentially useful for the description of other monoclinic multiferroic systems, systems such as MnWO4 and AMSi2O6. 6
References • R. Villarreal et al., cond-mat : arXiv:1205.5229v1 (2012) • T. Kimura et al., Nature Materials, 7, 291, (2008)
MnWO4 V Felea et al V. al., J J. Phys Phys.:: Cond Cond. Matter 23 23, 216001 (2011) (2011).
