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1 This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier s archiving and manuscript policies are encouraged to visit:

Solid State Communications 149 (2009) 759 762 Contents lists available at ScienceDirect Solid State Communications journal homepage: www.elsevier.

Ovsyannikov a,b, Alexander E. Karkin a, Sakae Todo b, Yoshiya Uwatoko b a Institute of Metal Physics of Russian Academy of Sciences, Urals Division, GSP-170, 18 S.

2 Solid State Communications 149 (2009) Contents lists available at ScienceDirect Solid State Communications journal homepage: Galvanomagnetic properties of fast neutron bombarded Fe 3 O 4 magnetite: A case against charge ordering mechanism of the Verwey transition Vladimir V. Shchennikov a,, Sergey V. Ovsyannikov a,b, Alexander E. Karkin a, Sakae Todo b, Yoshiya Uwatoko b a Institute of Metal Physics of Russian Academy of Sciences, Urals Division, GSP-170, 18 S. Kovalevskaya Street, Yekaterinburg , Russia b Division of Physics in Extreme Conditions, The Institute for Solid State Physics, The University of Tokyo, Kashiwanoha, Kashiwa, Chiba , Japan a r t i c l e i n f o a b s t r a c t Article history: Received 14 January 2009 Received in revised form 27 February 2009 Accepted 3 March 2009 by E.V. Sampathkumaran Available online 9 March 2009 PACS: Lw Kz Ks Pa Ey i Ks Vw Synthetic single-crystalline samples of Fe 3 O 4 magnetite were subjected to fast neutron bombardment with a fluency Φ = cm 2. A comparative study of the electrical resistivity ρ, normal (ordinary) and anomalous (extraordinary) Hall effects, and the magnetoresistance in a temperature range from 50 to 400 K (i.e across the Verwey transition (VT) at T V 125 K) was performed on both as grown and irradiated samples. The galvanomagnetic properties were investigated in magnetic fields B up to 13.6 T. From the normal (ordinary) Hall effect the concentration of charge carriers was determined. The activation energy was also estimated. On the Verwey transition the conductivity type was changed form electronic to hole. Contrary to expectations, the fast neutron irradiation resulted only in a minor decrease in T V by 4 K. The results gathered evidence against a distributed opinion that the charge ordering on the octahedral sites in the spinel structure of Fe 3 O 4 is a major driving factor of the Verwey transition Elsevier Ltd. All rights reserved. Keywords: A. Magnetically ordered materials A. Semiconductors D. Galvanomagnetic effects E. Neutron scattering 1. Introduction Magnetite, Fe 3 O 4 is a natural ferromagnetic mineral. At ambient conditions it adopts a cubic spinel structure (space group Fd3m) with an inverse electronic configuration, [Fe 3+ ] A [Fe 2+ + Fe 3+ ] B O 4, i.e. the Fe 2+ ions are in the octahedral (B) sites and the Fe 3+ ions are in both the octahedral and the tetrahedral (A) sites [1 3]. Upon cooling below T V K magnetite undergoes a metal-insulator phase transition ( Verwey transition VT) at which the electrical resistivity jumps by approximately two orders [4]. On this transition an energy gap of about mev appears [5 7]. After the original addressing of the VT Corresponding author. addresses: vladimir.v@imp.uran.ru (V.V. Shchennikov), sergey2503@gmail.com (S.V. Ovsyannikov). to a charge (i.e. Fe 2+ ion) ordering at the B-sites [4], many studies were undertaken to understand this phenomenon and to develop a model of it [8 19]. At the moment the charge ordering mechanism of the VT is the most distributed viewpoint. Meanwhile, the existent models are not completely fitted with experimental data and hence they need further specification [8 19]. In short, a current view is that magnetite exhibits a unique metal-insulator transition which differs from the all known cases. Therefore, understanding of the VT would greatly advance the condensed matter physics [12,20 25]. A number of structural studies [26 33] established the difference in crystal lattices of the low- and the high-temperature phases (i.e. respectively below and above T V ). It was found that the Verwey phase crystallizes in a low-symmetric monoclinic lattice, for which several possible space groups were proposed as following: Pmca or Pmc2 1 [30], P2/c [12], and Pmca [33]. However, an exact crystal structure of the low temperature /$ see front matter 2009 Elsevier Ltd. All rights reserved. doi: /j.ssc

3 760 V.V. Shchennikov et al. / Solid State Communications 149 (2009) phase still remains unrefined. Recently, Rozenberg et al. [33] has established that a pressure (P) temperature (T ) boundary of this structural transition coincides well with a one for the VT found by the electrical resistivity ρ technique [34]. Hence, it was proclaimed that the structural transformation is an actual driving mechanism of the VT [33]. A number of experimental studies reported observations of the charge ordering below T V [32,35 37], while, some others could not detect any trace of it [38,39]. A modern theory (for example, [24]) suggests this charge ordering effect to be rather weak, and therefore, it hardly can drive the VT. The above vagueness in the nature of a leading factor of the VT (charge ordering or structural distortion) could be resolved with assistance of a technique permitting a partial disordering of a crystal structure in the whole bulk of a sample. For example, by using a technique of irradiation with high-energy electricallyneutral particles, i.e. fast neutron bombardment. Irradiation with fast neutrons is known to lead to atom displacements and thereby results in modifications in electronic, magnetic and structural properties [40]. Usually, a series of anneals can partly or completely recover the original properties [40]. Then, if the VT is driven by the charge ordering, an effect from the disordering should be significant. In the opposite case of the dominant role of a structural distortion factor, the effect may be minor. To the present, no such studies were reported. Thus, in the present work a comparative study of the electrical and the galvanomagnetic properties on as-grown and fast-neutron-bombarded Fe 3 O 4 is carried out. 2. Experiments High-quality single-crystalline ingots of stoichiometric magnetite were synthesized by the floating zone method [34]. The as-grown ingots were characterized by the X-ray diffraction and Raman studies [41]. The fast neutron bombardment was performed at a temperature of 330 ± 10 K. A neutron source employed generated neutrons possessing an average energy about 1 MeV. Only the particles having energies higher than 0.1 MeV were accounted for in the neutron fluency. The irradiation was two-staged, at the first one with a fluency of Φ = cm 2 and at the second one of Φ = cm 2. Hence, the total fluency was equal to Φ = cm 2. Since after the first stage no changes in the transport properties were found, here we present results gathered only after the second one. The irradiated samples were highly radioactive owing to a dramatic increase in the amount of radioactive iron isotopes. For this reason their examination was limited to a transport study in a special cryostat. The measurements of electrical resistivity ρ and Hall effect R H were performed by a conventional Montgomery method (a modification of a Van der Pauw one, which even allows determining anisotropy of galvanomagnetic properties) [40]. The comparative experiments were carried out on the same samples before and after the irradiation. The samples were parallelepipedshaped of sizes mm 3. The Hall R H and the magnetoresistance effects were measured in a stationary magnetic field B up to 13.6 T in an Oxford Instruments setup [42,43]. The measurements were performed for both two opposite signs of an electrical current through a sample, and two directions of magnetic field. A variation in magnetic field B assisted in a separation of the ordinary and the extraordinary Hall effects [44 48]. At room temperature the as-grown samples were characterized by a typical for magnetite value of the electrical resistivity, ρ = 4.3 m cm and by the electron concentration n = cm Results and discussion The results gathered are shown at Figs The temperature dependencies of both the electrical resistivity ρ(t) and the Hall resistivity ρ H (T) (Fig. 1) behave similarly and exhibit an abrupt metal insulator transition near T V = 125 K for the as-grown samples. This T V value evidences no deviation in the stoichiometry [49]. On the transition the electrical resistivity jumps by approximately two orders of magnitude (Fig. 1) in accordance with previous reports [4,34]. The fast-neutron bombardment results in only minor effects (Fig. 1). Hall resistivity in ferromagnets comprises two components, namely, ordinary (normal) Hall resistivity which related to conventional Hall effect, and an extraordinary (anomalous) one which arises due to magnetization M under applied magnetic field [44,47]: ρ H = R O B + R A µ 0 M, (1) where R O is the ordinary and R A the extraordinary Hall coefficients, and µ 0 is the magnetic susceptibility. Therefore, the coefficient R O of the normal Hall effect may be determined from a linear slope of a dependence of the Hall resistivity on magnetic field B, ρ H (B) after the magnetization M has saturated (Figs. 2 and 3(a)) [44,47, 50,51]. In order to separate the normal and the anomalous Hall effects, the ρ H (B) dependencies were measured to 13.6 T at fixed temperatures (Fig. 2). In our case, the magnetization completely saturates to 1 T (Fig. 2), in agreement with previous studies [44, 47,50,51]. Meanwhile, the magnetization saturation may depend on a mesostructure of a sample [47,50,51]. Note, that Siratori et al. supposed that higher order terms, those proportional to cubic and higher power of B and M could be also important in separation of ordinary and extraordinary Hall effects [45]. Using the well known one-band expressions for Hall concentration n and mobility µ H (n = 1/(eR O ), where e is the electron charge and a Hall-factor was assumed to be equal to 1; µ H = R O /ρ) one can estimate n and µ H (Fig. 3(b, c)). Thus, at 305 K for the as-grown sample we find n cm 3 and µ H 0.07 cm 2 /(V s). This mobility value is essentially lower than the found upper limit for ambient Hall mobility, 0.45 cm 2 /(V s) [44]. The magnetoresistance effect ρ/ρ (Fig. 4) gives much higher mobility values: µ MR 50 cm 2 /(V s) at 305 K in low magnetic fields ( ρ/ρ (µb) 2 ) [52]. A reason of this divergence consists in a fact that the Hall mobility strongly depends on electrical barriers (such as dislocations) in materials, and, for instance, for elemental selenium µ H and µ MR differ in magnitude by two orders [52]. Notice, that the estimated value of the electron concentration (n cm 3 ) is somewhat higher than the concentration of Fe 3 O 4 molecules (the lattice parameter of the cubic spinel equals 8.39 Å [8]; this gives unit cells or molecules in 1 cm 3 as each unit cell consists of eight molecules). The theory of polaron hopping in magnetite, [Fe 3+ ] A [Fe 2+ + Fe 3+ ] B O 4 [8] states that each molecule supplies precisely one charge carrier (the Fe 2+ ion), and hence ideally the carrier concentration should be near cm 3. Our estimation is closer to this value than those of previous studies suggesting only carrier per molecule [44,47]. From the temperature dependence of the electron concentration (Fig. 3(b)), an activation energy E a for the as-grown sample may be roughly estimated as E a 14 mev. It is interesting to note that bringing this value in the known formula for the thermopower S (S (k 0 /e)[e a /(k 0 T)]), where k 0 is the Boltzmann s constant [8]), one can obtain the thermopower value of S 50 µv/k that is close to experimental data, S (40 60)µV/K [41,53 55]. The differences in estimations of E a values of Fe 3 O 4 in previous studies were discussed in detail in Ref. [41]. In any case, the calculated semiconductor gap is less or comparable with k 0 T ; this explains

4 V.V. Shchennikov et al. / Solid State Communications 149 (2009) Fig. 1. The temperature (T ) dependencies of (a) the electrical resistivity (ρ) and of (b) the Hall resistivity (ρ H ) for the maximal magnetic field 13.6 T of (1) as-grown and (2) fast-neutron-bombarded single-crystalline Fe 3 O 4 magnetite, across the Verwey transition near K (marked by the arrow). Fig. 2. The dependencies of the Hall resistivity (ρ H ) on magnetic field B for (a) as-grown and (b) fast-neutron-bombarded single-crystalline Fe 3 O 4 magnetite. The insets show (a) large-scale parts of the ρ H (B) and (b) ρ H (B) curves at 110 K. Fig. 3. The plot (a) shows a separation of ordinary and extraordinary Hall resistivity. A linear slope of the ρ H (B) curve at low magnetic fields B depends on both R A and R O coefficients (Eq. (1)). At high B after the magnetization has saturated, a slope depends only on R O. The plots (b) and (c) show the temperature dependencies of the carrier concentration and mobility estimated from the ordinary Hall effect for (1) as-grown and (2) fast-neutron-bombarded Fe 3 O 4. The vertical dashed lines indicate the Verwey transition. Fig. 4. The dependencies of the magnetoresistance effect ( ρ/ρ) on magnetic field B for (a) as-grown and (b) fast-neutron-bombarded single-crystalline Fe 3 O 4 magnetite. The inset in (b) shows the ρ/ρ (B) curve at 110 K. The lines are the guides for the eye. the nearly metallic character of conductivity at ambient temperature [34]. The fast neutron bombardment reduces T V by 4 K (Fig. 1). After the irradiation the Hall electron concentration at 305 K drops to n cm 3 (Fig. 3(b)), while the Hall mobility slightly raises, µ H cm 2 /(V s) (Fig. 3(c)). This increases (decreases) the electrical resistivity above (below) T V (Fig. 1(a)). For the irradiated sample we find E a 13 mev, i.e. a bit lower than for the as-grown one. Below T v the ordinary Hall effect in the irradiated sample inverts its sign (Fig. 3(b), inset) suggesting an inversion in the type of the dominant charge carries. Earlier, at the Verwey phase the hole conductivity was already established [53,54]. In the case of as-grown sample strong noise below T v prevented the Hall measurements. The magnetoresistance effect before the irradiation is mostly negative (Fig. 4(a)) in accordance with previous reports [51,56]. Increase in magnetic ordering degree is known to reduce electron scattering (and hence the electrical resistivity) [8]. Near T v a positive contribution to the magnetoresistance starts prevailing at high magnetic fields (Fig. 4); supposedly, this results from the appearance of mobile charge carriers. Irradiation leads to only marginal changes in this effect (Fig. 4(b)). Below T V the absolute value of the magnetoresistance effect grows in accordance with the higher mobility of holes found in the low-temperature phase (Fig. 3(b)). The main effect from irradiation with high-energy electrically-neutral particles consists in radiation-induced distortions (displacements) in the bulk of a material, while a swelling of it may be negligible [40]. Usually, irradiation drastically modifies the electronic properties of semiconductors and insulators [40]. The average neutron energy of 1 MeV exceeds the known typical critical energies of defect formation. After similar neutron bombardment the electrical resistivity of PbSe increased by several orders of magnitude [43], and a superconductive transition T c in MgB 2 shifted from 38 K to 5 K [58]. In previous work [57] after the fast neutron bombardment with energies above 1 MeV a tiny swelling of the cubic spinel structure of magnetite was found. Thus, an irradiation with a fluency of Φ = cm 2 neutrons increased the lattice parameter by 0.03% [57] owing to a formation of stable defects. After the irradiation the ambient electrical resistivity of Fe 3 O 4 rises by 50% (Fig. 1). The moderate changes in transport properties of Fe 3 O 4 (Figs. 1 4) are likely owing to the high carrier concentration. In other words a limited number of radiationinduced defects which supply either carriers or traps cannot

5 762 V.V. Shchennikov et al. / Solid State Communications 149 (2009) drastically shift the charge balance in Fe 3 O 4. A weak effect of the irradiation on T V (Fig. 1) is apparently not consistent with the charge ordering mechanism of the VT [4,9 19]. The found changes in both the carrier concentration and mobility across the VT (Fig. 3(b, c)) also do not correspond to the case of the charge ordering, at which the carrier mobility would expected to significantly drop. On the other hand, T V strongly depends on an iron deficiency δ in Fe 3(1 δ) O 4 [49,59,60]. Upon an increase in δ to , T v shifts from 125 to 82 K [49,59,60] and exhibits a discontinuity by 10 K at δ [49]; the discontinuity was explained by a change in the nature of the VT [49,59]. In our case of neutrondisordered magnetite the stoichiometry is preserved, and the shift in T v is only 4 K (Fig. 1). This supports the hypothesis of the structural-distortion origin of the VT [33]. The majority of structural studies of the VT established that below T v the unit cell symmetry diminishes to monoclinic and a doubling of the cubic unit cell parameter along the c axis occurs [12,26 32]. It was also shown that below T V the unit cell consists of four rhombohedral-distorted initial cubic unit cells [12, 30 32]. Likewise, the charge fluctuations of both the Fe ions at the B sites and the 2p-orbitals of the O atoms have a period which is equal to a double lattice constant along the c axis [12,30 32]. Raman spectra measured across the VT revealed that a number of phonon peaks increases from four at the cubic spinel [41] to thirteen at the low-temperature phase [61]. This multiplication of the Raman modes suggests at least a double folding of the Brillouin zone. Then, one may surmise that the VT is driven by the Peierls distortion, which is known to lead to multiple folding of Brillouin zone as well as to opening of an energy gap at Fermi level. The Peierls mechanism is realized in both crystalline, and amorphous and liquid materials [62] and hence it appears to be tolerant to a lattice disordering. 4. Conclusion A comparative study of galvanomagnetic and electrical properties of as-grown and fast-neutron irradiated magnetite across the Verwey transition has been performed. The charge carrier parameters have been estimated. A weak influence of the irradiation on the transition temperature appears to be not consistent with the claimed charge ordering origin of the VT. Meanwhile, it tolerates the structural-distortion transition mechanism. The Peierls distortion, for instance, might be considered as a possible driving mechanism of the VT. Acknowledgements The authors thank B.N. Goshchitskii (IMP) for useful comments and discussion. The work was partly supported by the RFBR (Gr. # ), by the Quantum macro-physics Program (State contract # /Ï-3/ / , project # 4 Urals Div. 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Studies of the Verwey Transition in Magnetite

Vol. 106 (2004) ACTA PHYSICA POLONICA A No. 5 Proceedings of the School Superconductivity and Other Phenomena in Perovskites, Warsaw 2004 Studies of the Verwey Transition in Magnetite Z. Tarnawski, A.