Thermally or Magnetically Induced Polarization Reversal in the Multiferroic
CoCr
2O
4Y. J. Choi,1J. Okamoto,2D. J. Huang,2,3K. S. Chao,2,4H. J. Lin,2C. T. Chen,2M. van Veenendaal,5 T. A. Kaplan,6and S-W. Cheong1
1Rutgers Center for Emergent Materials and Department of Physics and Astronomy,
136 Frelinghuysen Road, Piscataway, New Jersey 08854, USA
2National Synchrotron Radiation Research Center, Hsinchu 30076, Taiwan 3Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan 4Department of Electrophysics, National Chiao Tung University, Hsinchu 30010, Taiwan
5Department of Physics, Northern Illinois University, De Kalb, Illinois 60115, USA,
and Advanced Photon Source, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA
6Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
(Received 28 May 2008; published 9 February 2009)
We report the unexpected evolution, with thermal and magnetic-field (H) variations, of the interrelation between the polarization P, magnetization M, and spiral wave vector Q in CoCr2O4, which has a ferrimagnetic conical-spiral magnetic order. For example,P suddenly jumps and changes its sign at the magnetic lock-in transition (TL) with thermal variation, or with isothermal variation of H (without
changing its direction) at TL, which surprisingly occurs without change in spiral handedness (i.e., the sign
ofQ). The presence of multiple spiral sublattices may be behind this unusual behavior.
DOI:10.1103/PhysRevLett.102.067601 PACS numbers: 77.80.e, 77.22.Ej, 75.80.+q, 78.70.Ck
Magnetically driven ferroelectrics where magnetic order with broken inversion symmetry accompanies the occur-rence of ferroelectric polarization have been of great recent interest [1,2], the first example of which was reported by Newnham et al. [3]. Recently, the high tunability of di-electric properties by applied magnetic fields (H), such as reversibly flipping ferroelectric polarization or a drastic change of dielectric constant, has been found in such materials [4]. Spinel CoCr2O4, which shows a complex conical-spiral ferrimagnetic spin order [5], is unique among such materials [3,6–10] in that it has a spontaneous magnetization M; the spiral component induces the ob-served electric polarization P [8] in common with the others. In addition to M and P, a multiferroic domain is characterized by the spiral wave vectorQ, and single such
domains can be produced by poling. Here we report the first comprehensive study of the switching behavior of these domains under a variation of applied H, and tem-perature (T). We find that Q dependence of P differs from that expected from previous simpler spiral orderings, where a change in sgnðPÞ accompanies a change in sgnðQÞ. CoCr2O4 crystallizes in a cubic spinel structure, mag-netic Co2þand Cr3þions occupying the tetrahedral (A) and octahedral (B) sites, respectively [Fig.1(a)]. For nearest-neighbor and isotropic antiferromagnetic A-B and B-B exchange interactions (JAB and JBB), with JBB=JAB>
2=3, an approximate, variational solution for the ground state was found, a "ferrimagnetic spiral," where the spins lie on conical surfaces [11–13]: The spins on the 6 fcc sublattices containing the magnetic sites are given by Sn ¼ sin½ ^x cosðQ rnþ Þ þ ^y sinðQ rnþ Þ þ ^z cos; 0 ; ¼ 1; ; 6: (1)
For fixed , rn goes over the sites of sublattice , the
values of the cone12-angle and phase depend on ,
and the wave vectorQ ffi 0:6 ½110, in units of 2=lattice constant, is along the crystallographic ½110; ^x, ^y, ^z are orthonormal vectors [11–13] [see Fig.1(a)].
A state approximately of this form was found from neutron diffraction in CoCr2O4 [5,14], with ^z the ½001 crystal direction when Q is in the þ or ½110 direc-tion, ‘‘½110 Q domains’’ (with the same relative ori-entation for the cubically equivalent Q’s). In ½110 do-mains, the z components produce the magnetization M (along ½001). According to Yamasaki et al. [8], the spiral components give rise to ferroelectricity, whereP / e12 ðS1 S2Þ for a pair of spins S1 and S2 with
rela-tive displacement e12 [15–17]. For the spiraling
compo-nents of the Cr spins lying along the ½110 chains, shown in Fig. 1(a), this gives the same contribution for every nearest-neighbor pair, namely P / Q ½001 / ½110, as seen in Fig.1(a)and as observed [8].
Magnetic measurement was performed in a SQUID magnetometer, specific heat was measured using a Quantum Design PPMS, and the dielectric constant, ", was measured using an LCR meter at f ¼ 44 kHz. The T (H) dependence of electric polarization, P, was obtained by the integration of a pyroelectric (magnetoelectric) cur-rent measured using an electrometer with the T (H) varia-tion of 4 K= min (0:01–0:02 T=s). While poling in E 10 kV=cm, a small static H (H ¼ 0:5 T for Fig. 2) PRL 102, 067601 (2009) P H Y S I C A L R E V I E W L E T T E R S 13 FEBRUARY 2009week ending
was also applied along the magnetic easy axis, along½001, so this magnetoelectric cooling procedure with E and H fixes the directions of the possibleM, P, and Q; i.e., the procedure chooses a single (M, P, Q) domain.
The T dependence of physical properties of our single-crystalline CoCr2O4, grown with a vapor-transport method
[18], exhibits sharp features, indicative of three phase transitions, as displayed in Fig.1(b). The long-range ferri-magnetic collinear spin order appears below TC¼ 95 K. A
sharp but continuous increase of MðTÞ at TS¼ 27 K is
ascribed to the conical-spiral order of spins, going along with a sharp peak in the specific heat, CðTÞ, and a peaky anomaly in "ðTÞ along the ½110 direction where the elec-tric polarization emerges. A steplike jump of MðTÞ at TL ¼
14 K [see also Fig.2(a)], accompanied by a small feature in CðTÞ and "ðTÞ, is associated with a small but clear thermal hysteresis (not shown), indicating the 1st order nature of this transition.
The onset of ferroelectricity along the ½110 direction, matches the spiral magnetic ordering transition at TS¼
27 K [Fig.2(a)]. At the 14 K transition, whenM is kept in one direction with H, P suddenly flips its direction, in contrast to the previous finding [8]. But in agreement with [8], when H, and therefore M, is reversed at fixed T, we find P to be reversed, as seen in Figs.2(b)and2(c). This correlation between M and P was attributed [8] to Bloch domain wall motion involved in reversingM. Such an essentially uniform rotation of the spin state character-izing the wall, takingM to M, can be seen to take a Q domain to aQ domain [19]. We have observed directly this sign change of Q upon H reversal by our circularly polarized resonant magnetic x-ray scattering experiment. Thus, M, P, and Q change to M, P, Q in H, respectively [Fig.2(b)]. Furthermore, at 10 K (below TL),
H reversal also induces the 180 flipping ofM, P, and Q [Fig.2(c)].
In contrast to this behavior, we find that the sign flip ofP across the 14 K transition is not accompanied by a change of sgnðQÞ; rather our results indicate that the sign of Q (or spiral handedness) is invariant at the 14 K transition (dis-cussed further below). The low-temperature state is
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H (kOe) M 00 1 (10 -1 µ B /f.u.) M 001 (10 -1 µ B /f.u.)20 K
H (kOe)(a)
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FIG. 2 (color online). (a) T dependence of electric polariza-tion, P, along the ½110 direction, and M along the ½001 direction below 30 K. P suddenly switches sign when cooling across 14 K without changing the signs of M and Q. (b) and (c) H dependence of M and P at 20 K and 10 K, respectively. The reversal of all ofM, P, and Q is achieved by H reversal. Co Cr O M//[001] Q//[110] P//[110] CrO6 CoO4 A1 A2 B3 B1 B2 B4 A1 A2 B1 B3 B2 B4
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FIG. 1 (color online). (a) Crystallographic and low-T magnetic structure of spinel CoCr2O4. Co2þand Cr3þ ions are located at
the center of tetrahedral and octahedral O2cages, respectively. Conical-spiral spins of Co2þand Cr3þ ions for only 3 of the 6 sublattices (A2, B1, and B2) are shown for clarity. Cone angles
shown are from [12], which, with [13], should be consulted for more details. Also shown are the directions ofM, P, and Q. (b) T dependence of magnetization,M, along the ½001 direction in H ¼ 0:5 T upon cooling, specific heat divided by temperature in H ¼ 0 T upon cooling, and dielectric constant in H ¼ 0 T at 44 kHz upon warming. The existence of three phase transitions is evident, and TC, TS, and TL denote temperatures for
ferrimag-netic transition, conical spin ordering, and lock-in transition, respectively.
PRL 102, 067601 (2009) P H Y S I C A L R E V I E W L E T T E R S 13 FEBRUARY 2009week ending
ciated with a slight increase of the magnitude ofM as well asP, as shown in Fig.2(a). Note that in a multiferroic with a spiral magnetic order with only one magnetic sublattice, switching ofP results from a sign change of Q [20]. (This is the usual behavior found in other multiferroics with spiral magnetism.)
Our resonant magnetic soft x-ray scattering experiment was performed with the elliptically polarized-undulator beam line at the National Synchrotron Radiation Research Center in Taiwan. With photon energy tuned at the Co L3edge, the scattering results reveal that there is an
abrupt change in magnetic modulations at14 K. Unlike earlier neutron results [5,14,21], we found two incommen-surate magnetic modulations Qþ and Q at 15 K, a temperature above TL, while, for T below TL, there are
one commensurate modulation QC¼ 2=3½110 and two incommensurate ones,Q0þandQ0, with a separation along ½110 much larger than that between Qþ and Q, as
illustrated in the contour plots [Fig.3(a)]. The intensities of theQ0peaks are 1 to 2 orders of magnitude smaller than theQCpeak, and the three vectors are approximately equal in direction as well as magnitude; similarly, the vectors Qþ, Q are approximately equal [Fig. 3(a)]. The x-ray
scattering intensity can distinguish between spirals with wave vectorQ and Q, if the incident beam is circularly polarized [22]. This is similar to the scattering of polarized neutrons [20,23]. Figures3(b),3(d), and3(e)show that the measured scattering intensities with circularly polarized light indeed change upon the reversal of magnetization along ½001, disclosing the expected flip of Q with H reversal. Figure 3(c) also illustrates conical-spiral spins above and below the 14 K transition where M corre-spond toQ, respectively. Strikingly, the scattering results also reveal that the sign of theQ of the largest peak at each T (QC andQ) remains unchanged as T changes across
TL: The H dependences of the intensities of these peaks do
not reverse. Thus, to the extent that we can consider a single-wave-vector spiral as a good approximation to the observed state, this is solid evidence of sgn (Q) invariance across TL. In addition, the only one of the smaller peaks
(Q0þ) that has an observable intensity change on H reversal also shows this invariance, and further, the wave vectors of all the peaks are approximately equal. Therefore, even considering the complexity of having multiple Fourier components in the spin configuration, the data strongly suggest that the sign of Q (for each Fourier component) does not change across the 1st order transition.
A plausible interpretation for the switch in the sign ofP across 14 K without sign change ofQ and M (despite its impossibility for a single sublattice conical spiral, as noted above) is found in a ‘‘ferrielectric’’-type scenario. Now, Co2þhas a more-than-half-filled d shell, while Cr3þhas a
less-than-half-filled shell, suggesting that Co-Cr and Cr-Cr bonds have the opposite sign of spin-orbit interaction, resulting in the opposite directions of electric dipole mo-ments,PCoCrandPCrCrfrom the different bonds of form Eq. (1) [24]. Furthermore, the bond charges that give rise to
the dipole moments are interionic overlap charge densities [15,16], and are therefore very sensitive to small changes in interionic distances expected to occur through the 1st order phase transition at TL. Then, it is conceivable that the
delicately balanced net polarization can change its sign at TL without a change in sgnðQÞ (the directions of each
contribution PCoCr and PCrCr do not change, but their magnitudes do).
Repeated switching of electric polarization direction is achieved by varying temperature step-linearly with time between 8 K and 20 K as shown in Fig. 4(a). The mea-surement of the pyroelectric current began at 8 K in the ðþ; ; þÞ state defined as [sgnðMÞ, sgnðPÞ, sgnðQÞ] after poling in H ¼ 0:1 T and E 10 kV=cm. Upon warming, this state switches to the ðþ; þ; þÞ state, but the initial state is recovered by cooling back to 8 K. Because of the 1st order nature of the TL transition, the temperatures at
which P flips differ by 1:6 K between warming and cooling. Figure 4(b) displays howPðTÞ depends on large
(d)
Q+ -0.03 0.00 0.03 0 4 8 12 -0.01 0.00 0.01 0 2 4 ⎯10 Q1 0.663 0.666 0.669 0.672 0 3 6 ⎯10 Inte nsity (arb. unit s)Intensity (arb. units)
Q1 Q 110 Inte nsity (a rb. units ) Q -Q+ Q -QC Q'- Q' + 2/3
(a)
10 K
10 K
15 K
Q'+ Q' -QC(c)
(b)
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+H, +Q -H, -Q10 K
15 K
+H -HFIG. 3 (color online). (a) Contour plots of the Co L3 edge
magnetic soft x-ray scattering intensity in the plane defined by Q110 andQ110 recorded at temperatures above and below TL
(14 K) with photon energy of 778.4 eV. TheE vector of incident x-rays was parallel to the½001 axis. The contour plots are shown in a logarithmic scale with its order of magnitude expressed by means of color. (b), (d), and (e) Scattering intensity ofQ scans along½110 and ½110 under þM (solid curves) and M (open circles) with circularly polarized x-rays. (c) Depiction of conical-spiral spins where M go with Q above and below TL, respectively.
PRL 102, 067601 (2009) P H Y S I C A L R E V I E W L E T T E R S 13 FEBRUARY 2009week ending
cooling H, showing a slight increasing tendency of TLwith
increasing H. At exactly 14.0 K, the phase cooled in 0.1 T is in theðþ; þ; þÞ state, whereas cooling in 3 T puts the phase in the ðþ; ; þÞ state. The black downward arrow denotes the possible switching of the physical state with increasing H at 14.0 K. As demonstrated in Fig.4(c), the isothermal polarization reversal is, indeed, achieved by varying H at 14.0 K. After cooling down to 14.0 K in 0.1 T, the phase is initially in the ðþ; þ; þÞ state. The isothermal increase of H results in changing the state to ðþ; ; þÞ by reversing P, but keeping the direction of M and Q fixed. Because of the 1st order nature of the TL transition, theðþ; ; þÞ state does not go back to the initial state of ðþ; þ; þÞ when H is reduced to zero (or the original 0.1 T). When the H direction is reversed, M flips, so doP and Q, and thus the ðþ; ; þÞ state becomes the ð; þ; Þ state.
In summary, the conical-spiral ferroelectricity in CoCr2O4 can be described by the interrelationship among
ferroelectric polarization (P), magnetization (M), and spi-ral wave vector (Q). Our results demonstrate that sponta-neous electric polarization induced by the noncollinear spin order shows a discontinuous jump with a change in sign across the magnetic lock-in transition temperature (TL¼ 14 K); furthermore the sign change occurs while
keeping fixed the spin rotation direction, i.e., spiral hand-edness or sgnðQÞ. This differs from the usual behavior wherein for a simple spiral, change in sgnðPÞ requires the handedness to change sign, and we give a possible mecha-nism for such unusual behavior. We also recover the pre-vious finding wherein P ! P when M ! M [8], but further show experimentally that this is accompanied by Q ! Q, consistent with the Bloch wall mechanism [8] for switching M. We further show that P reverses its direction in 3 T at exactly 14.0 K, due to a slight in-creasing trend of TLwith increasing H.
We thank S. D. Mahanti for his close following of this work and for many helpful discussions. Work at Rutgers is supported by NSF-DMR-0520471.
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applied H (0.1, 0.5, and 3 T), indicating that TLincreases slightly
with increasing H. (c) P at 14.0 K vs H after poling the specimen in H ¼ 0:1 T and E 10 kV=cm. The initial ðþ; þ; þÞ state which is defined as [sgnðMÞ, sgnðPÞ, sgnðQÞ] changes to the ðþ; ; þÞ state in H 3 T. Negative H scan, reversing M, induces switching ofP and Q, i.e., resulting in the ð; þ; Þ state.
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