FeCr2O4 and CoCr2O4 spinels: Multiferroicity in the

FeCr2O4 and CoCr2O4 spinels: Multiferroicity in the collinear magnetic state? Kiran Singh, Antoine Maignan, Charles Simon, and Christine Martin Citation: Appl. Phys. Lett. 99, 172903 (2011); doi: 10.1063/1.3656711 View online: http://dx.doi.org/10.1063/1.3656711 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v99/i17 Published by the American Institute of Physics.

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APPLIED PHYSICS LETTERS 99, 172903 (2011)

FeCr2O4 and CoCr2O4 spinels: Multiferroicity in the collinear magnetic state? Kiran Singh, Antoine Maignan,a) Charles Simon, and Christine Martin Laboratoire CRISMAT, CNRS UMR 6508, ENSICAEN, 6 Bd. du Mare´chal Juin, 14050 Caen Cedex, France

(Received 5 July 2011; accepted 7 October 2011; published online 26 October 2011) Dielectric permittivity (e0 ) and electrical polarization (P) have been measured as a function of temperature for two polycrystalline ACr2O4 spinels (A ¼ Fe and Co). Anomalies on the e0 (T) curves are detected at the characteristic magnetic transition temperatures (TC, TS, and Tlock-in) for FeCr2O4 and CoCr2O4 and also at the Jahn-Teller (JT) transition for FeCr2O4. The P(T) curves of both spinels exhibit transitions at TC showing that polar and ferrimagnetic states coexist in these oxides. The link between the distortion of the spinel structure due to the Jahn-Teller Fe2þ and the larger polarization value at 8 K, P ¼ 35 lC/m2, against P ¼ 3.5 lC/m2 for CoCr2O4, is also C 2011 American Institute of Physics. [doi:10.1063/1.3656711] discussed. V The transition-metal spinels of AB2X4 general formula form a large class of materials with very rich orbital/charge/ spin ordering phenomena.1 In this structure, the B-cations form a pyrochlore lattice well known for its geometric frustration leading to reentrant spin glass, like in CoCr2O4.2 Recently, magnetic spinel oxides have been reported to exhibit dielectric anomaly and/or ferroelectric properties, both related to their magnetism.3–9 In that respect, the ACr2O4 normal spinels, where A is a divalent magnetic cation (Mn, Fe, Co, Ni) occupying the tetrahedral site and Cr3þ (S ¼ 3/2) lying at the octahedral site, are attracting much attention.2–5,7,8,10 For the Jahn-Teller cations (A ¼ Fe2þ, Ni2þ, Cu2þ) the magnetism remains rather complex,10,11 as illustrated by FeCr2O4.10 Upon cooling from room temperature, the JahnTeller effect leads to a tetragonal distortion (TJT % 140 K) and then two successive magnetic transitions occur: the ferrimagnetic transition (TC % 80 K) which is followed by a transition towards a conical spiral magnetic ordering (TS % 35 K). These characteristic temperatures slightly differ from one report to another.12–14 A lowering of the symmetry (from tetragonal to orthorhombic), associated with the ferrimagnetic transition, is also proposed in Ref. 11, in contrast to CoCr2O4 which remains cubic.11 The latter exhibits a ferrimagnetic transition at TC % 93 K and a conical spin order below TS % 25 K that induces ferroelectricity.3 In that respect, the CoCr2O4 spinel belongs to the class of spin induced ferroelectrics for which the centrosymmetry is locally broken by the conical spin structure. For CoCr2O4, in the T region where spontaneous magnetization plus transverse spiral spin state, with incommensurate propagation vector, coexist, the spin current model predicted the occurrence of a polarization.16 Generally, for these type-II multiferroics, the electrical polarization is smaller than in type-I multiferroics (such as BiFeO3 or YMnO3) where TCurie (ferroelectric) is much larger than the magnetic ordering temperature.17 More recently, a multiferroic behavior was also reported in the collinear magnetic structure of the CdV2O4 spinel9 i.e., for which the spin current model cannot be invoked to explain the spin induced ferroelectricity. These a)

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0003-6951/2011/99(17)/172903/3/$30.00

reports on spinels have motivated us to investigate the electrical behavior of FeCr2O4 in comparison with CoCr2O4 and to elucidate the possible existence of an electrical polarization in the collinear magnetic state. Polycrystalline samples of FeCr2O4 and CoCr2O4 were prepared by solid-state reaction at high temperature. Room temperature structures were analyzed from X-ray diffraction data: both samples are single phased and crystallize in the centrosymmetric Fd-3m space group with cell parameters consistent with those reported in the literature.5,12 Magnetic properties were measured during warming, in zero field cooling and field cooling modes, in different magnetic fields within a quantum design superconducting quantum interference device (SQUID) magnetometer and in a physical property measurement system (PPMS) by an extraction technique. Dielectric permittivity was measured on a small plate with parallel capacitor geometry. Silver paste was used to make the electrodes. Dielectric measurements were performed using Agilent 4284 A LCR meter; the control of the sample temperature and external magnetic field was ensured by using a PPMS. For FeCr2O4, dielectric permittivity and tan d were measured between 8 and 300 K during cooling and warming (2 K/min) at 1 V ac bias field with several frequencies (from 1 to 100 kHz). The polarization was measured with a Keithley 6517 A electrometer in a coulombic mode. A poling static electric field of 6200 kV/m was applied at 85 K during cooling to align electric dipoles. At 8 K, the poling electric field (E) was removed and the polarization vs. time was recorded for 5000 s before measuring polarization (P) vs. temperature, i.e., during warming (5 K/min) under zero electric field. To test the effect of the magnetic field upon polarization, the sample was also cooled with a magnetic field (14 T and 200 kV/m) always applied at 85 K and the same measurement procedure as mentioned above was used (keeping 14 T and removing the electric field). Upon magnetic field application, in every case, the magnetic and electric fields were perpendicular to each other. Polarization vs. temperature was also measured for CoCr2O4 using similar procedure but with a poling electric field E ¼ 120 kV/m. For both spinel samples, attempts to collect P(E) loops were also made by using maximum E values of 400 kV/m.

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The T-dependence of the dielectric permittivity (e0 ) at f ¼ 100 kHz during warming is shown in Fig. 1(a) for FeCr2O4. Below 160 K, the curve exhibits several changes of slope which are correlated to the characteristic structural and/or magnetic transitions of that spinel. A clear signature is observed at the cubic to tetragonal structural transition (TJT % 140 K). Then a concave cusp is observed at the ferrimagnetic temperature (TC % 80 K). Finally, a sharp decrease of dielectric permittivity is detected at the conical magnetic transition (TS % 38 K). All these anomalies are magnetic field independent up to 5 T (not shown), and they are consistent with the transitions observed in the magnetic susceptibility curve (Fig. 1(a)). The variation of the dielectric permittivity vs. temperature (8 K T 180 K) is very small reaching a De0 /e0 maximum of only 3%. The characteristic temperatures of the dielectric anomalies are found to be frequency independent (not shown). There is one additional anomaly around 10 K which is only observed for frequencies 50 kHz. The exact origin of this anomaly is still unclear but the comparison of this e0 (T) curve with the CoCr2O4 shows interesting similarities (Fig. 1(b)). For the Cochromite spinel, clear changes of slope are observed at %93 K (TC) and %25 K (TS) and %15 K (Tlock-in), in agreement with the results reported for CoCr2O4 single crystals.3 From this comparison, it appears reasonable to ascribe the change of slope at 15 K in FeCr2O4 to a lock-in transition. The e0 variation vs. T is even smaller for CoCr2O4 (%0.4% for 8 K T 120 K). In dielectric studies, the imaginary part (tan d) is the signature of the losses. This important factor to qualify a capac-

FIG. 1. (Color online) (a) FeCr2O4: temperature dependence of the dielectric permittivity at 100 kHz (left y-axis) and of the magnetic susceptibility (right y-axis). (b) CoCr2O4: temperature dependence of the dielectric permittivity at 100 kHz (left y-axis) and of the magnetic susceptibility (right y-axis).

Appl. Phys. Lett. 99, 172903 (2011)

FIG. 2. (Color online) FeCr2O4: low temperature dielectric permittivity (left y-axis) and corresponding losses (tand, right y-axis), all measured at 100 kHz.

itor corresponds to the deviation from tan d ¼ 0. At the scale of the capacitor, to be intrinsic, the dielectric anomaly for both real and imaginary parts should occur at the same temperature, whereas the losses magnitude should remain small enough. To check for the nature of the dielectric change at TN, the low temperature part of both e0 and tand of FeCr2O4 collected at 100 kHz are given in Fig. 2. For both curves, a clear anomaly is observed at the same temperature corresponding to the spiral magnetic ordering T, TS % 38 K. The tan d value, remaining lower than 103 in the TC region, indicates a behavior expected for a real capacitor, with lack of both conducting contribution and relaxor behavior. For the first time, polarization is observed in FeCr2O4 up to TC, as shown in Fig. 3. Upon warming from 8 K, the polarization is first rather constant up to 60 K, with P values close to 35 lC/m2, then from 60 to 80 K it decreases and becomes %0 at TC, and its sign changes with the sign of the poling electric field. These results show that P exists in both non collinear (T < TS) and collinear (TS < T < TC) magnetic states and thus prove that spiral order is not indispensable to have polarization in FeCr2O4. Interestingly, the P value is about 15 times higher than in a single crystal of CoCr2O4 measured with a poling electric field of 400 kV/m.3 It must be emphasized that due to the granular nature of our sample, the P measurements made by averaging over all directions might lead to underestimated P values. Also, the polycrystallinity could act against the dipole alignment during the poling process. All our attempts made to measure P(E) loops below TS by using electrical fields up to 400 kV/m were not conclusive. The possible charge injection in the grain boundaries might explain why the applied voltage had to be limited to smaller values. Similarly, no P(E) loop was reported for the CdV2O4 spinel in Ref. 9. To check for a possible contribution of the spiral magnetic ordering to the P value, measurements were also performed on the FeCr2O4 sample according to the procedure derived from that used in Ref. 3, but with a much larger magnetic field, 14 T instead of 0.3 T. After poling with an applied magnetic field of 14 T perpendicular to the electric field, E is removed at low T prior to measurements made in 14 T upon warming. As shown in Fig. 3, the corresponding P(T) curve exhibits a small anomaly at about 40 K, which can be attributed to the spiral ordering at TS % 38 K. As shown by the


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FIG. 3. (Color online) FeCr2O4: temperature dependent polarization after poling with static electric field cooling (E ¼ 200 kV/m) and after magnetoelectric cooling (E ¼ 200 kV/m and l0 H ¼ 14 T). Right-up inset: enlargement of the polarization curve measured in magnetic field. Left-down inset: temperature dependent polarization for CoCr2O4 after magnetoelectric cooling (E ¼ 120 kV/m, l0 H ¼ 14 T).

enlargement in the inset, a corresponding extra polarization of %3 lC/m2 can be estimated, i.e., about 10% of the total P value. The magnitude of this additional component of polarization due to the spiral magnetic state (T < TS) is comparable to the observed polarization value for a CoCr2O4 single crystal.3 Thus, as the main part of the electrical polarization persists above TS, it confirms that the conical spin ordering is not a necessary condition to observe a polar state in FeCr2O4. The existence of an electrical polarization below TC in FeCr2O4 has motivated polarization measurements to be performed for a CoCr2O4 polycrystalline sample (Fig. 3). As for FeCr2O4, a transition is also observed at TC % 93 K on the P(T) curve, which maximal value reaches about 3.5 lC/m2, i.e., ten times smaller than that found in FeCr2O4 and similar to the one reported for a CoCr2O4 single crystal.3 The most important result of the present study comes from the persistence in both spinels of a polarization up to TC. Clearly, FeCr2O4 and CoCr2O4 spinels do exhibit polarization in their collinear magnetic state, with a maximal value ten times larger for the former. However, in Ref. 3, the polarization measurements made along c in a CoCr2O4 crystal did not reveal the existence of a significant P value in the collinear state TS < T < TC. Thus the existence of polarization in the polycrystalline sample suggests that additional measurements in a CoCr2O4 crystal have to be performed along different directions and up to TC. This study shows that both spinels exhibit a polar state in their collinear magnetic state. This indicates that the conical spin order found below %25 K in CoCr2O4 and %38 K in FeCr2O4 is not the unique state to observe a polarization in spinel chromites, independently of the existence or not of the Jahn-Teller (JT) character. In fact, despite their different space groups below TC, resulting from the presence or absence of a Jahn-Teller cation at the A-site, FeCr2O4 and CoCr2O4 exhibit rather similar magnetic/electric properties. As T is decreased from T> TC, anomalies on the e0 (T) curves are detected at TC, TS, and Tlock-in. Similarly, the P(T) curves exhibit a similar shape with a transition temperature, taken at the inflection point, corresponding to TC. Such a resem-

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blance for either cubic or distorted spinels emphasizes the importance of the pyrochlore network of magnetic cations which is responsible for competing interactions. The magnetic situation is rather complex as nearest neighbor Cr3þ– Cr3þ and A2þ–A2þ interactions are similar to A2þ–Cr3þ ones.15 As for the ferroelectricity reported for CdV2O4,9 the existence of different exchange pathways might break the inversion symmetry, as along some particular directions chains of up-up and down-down spins (""##) can be found. As shown for ACr2O4 spinels in Ref. 11, by using a local probe technique, a local symmetry breaking was evidenced below TC. In the light of these data, to elucidate the mechanism responsible for the local symmetry breaking explaining the P appearance in the collinear magnetic state of the present chromite spinels, more theoretical and experimental work will be needed. Interestingly, the structural distortion of the spinel induced by the presence at the A-site of Fe2þ that is a JahnTeller cation amplifies the polarization value of FeCr2O4 as compared to CoCr2O4. More detailed studies are necessary to discriminate the structural effect (inter-atomic distances and angles) from the magnetic one, since electronic configurations of Co2þ and Fe2þ are different, and magnetic structures complex. Anyway, polarization in the different magnetic states of spinels containing a Jahn-Teller cation at the A-site—such as NiCr2O4 or CuCr2O4—will deserve to be measured. K.S. would like to acknowledge CNRS for providing financial support in the form of post doctoral fellowship. 1

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