Magnetic Study of Phase Transitions in Magnetite

Transcription

1 WDS'07 Proceedings of Contributed Papers, Part III, 42 47, ISBN MATFYZPRESS Magnetic Study of Phase Transitions in Magnetite Z. Švindrych Charles University in Prague, Faculty of Mathematics and Physics, Ke Karlovu 3, , Prague 2, Czech Republic. Z. Janů Institute of Physics of the ASCR, v.v.i., Na Slovance 2, , Prague 8, Czech Republic. J. Hadač Czech Technical University in Prague, Faculty of Nuclear Sciences and Engineering, Břehová 7, , Prague 1, Czech Republic. Abstract. We have measured low field dc and low frequency ac magnetic properties of high quality magnetite single crystals with continuously reading high resolution SQUID magnetometer in a temperature range of K. In these data several features can be observed: the anisotropy point around 130 K, Verwey transition near 122 K, glass-like transition around 40 K and finally anomalous magnetic behaviour at lowest temperatures (below 30 K). Introduction Verwey transition, first observed in magnetite (Fe 3 O 4 ) as a magnetic anomaly [Reneger, 1913], is one of not-yet-fully-understood phase transitions in condensed matter physics. Since its discovery it has attracted much attention from both theoretical and experimental physicists. Especially the sharp drop in electrical conductivity on cooling through the transition temperature (T V ), as was precisely studied by Verwey et al. [1941], and its sensitivity to sample stoichiometry led to a variety of theories narrating metal-insulator transitions. Our high sensitivity, high resolution magnetic measurements on high quality samples can also be of considerable interest, especially when compared with other magnetic measurements (e.g. Balanda et al. [2005]), NMR measurements and Magnetic After Effect (MAE) results [Walz, 2002]. Present status Since the first measurements of Bragg [1915] magnetite at ambient temperature and pressure is known to crystallize in a cubic spinel structure. In normal spinel (general formula AB 2 O 4 ) the unit cell consists of 8 formula units, thus contains 56 atoms. Oxygen atoms form nearly fcc lattice with a number of interstitial positions partially occupied by A and B atoms. Eight A atoms occupy position which are tetrahedrally coordinated with oxygens, sixteen B atoms reside in octahedral positions (details e.g. in Wright et al., [2002]). Inverse spinel differs from the normal one only in the distribution of A and B species among tetrahedral and octahedral sublattices, namely eight B atoms occupy tetrahedral positions and the remaining eight B atoms and eight A atoms share sixteen octahedral sites. Also any linear combination of these two pure types may exist, thereby mixing A and B atoms in both sublattices (so called mixed spinel). One would think that in magnetite, where both A and B atoms are Fe, the situation is largely simplified. That s not the case, as in magnetite the question of valence electron distribution (Fe 3+ and Fe 2+ differ just by an electron) needs to be answered. Verwey et al. [1941] proposed inverse structure for magnetite, i.e. Fe 3+ ions occupy tetrahedrally coordinated sites and 1:1 mixture of Fe 3+ and Fe 2+ shares octahedral sites. This proposal was based on a good electrical conductivity compared to other spinels. It was also supported by magnetisation measurements, where Weiss et al. [1929] found a moment of 4.07 µ B per formula unit. This is in accordance with antiferromagnetic sublattice picture, where spins of Fe 3+ ions cancel mutually and remaining Fe 2+ ion gives a spin moment 4 µ B / f.u. However, Rakhecha et al. [1978] have shown that this ionic picture is not valid and the agreement between Weiss s measurements and Néel s theory is rather incidental. Finally, Mack et al. [2000] measured (using Mössbauer spectroscopy) the degree of 42

2 inversion of magnetite in the temperature range K and he demonstrated that Verwey s assumption was basically right. The departure from ideal inverse spinel is measurable only above room temperature, whereas at room temperature, according to their data, the amount of normal component in magnetite should be much less than 0.05% and of the order of 10-9 at T V. Second important proposal of Verwey was a model of Verwey transition. Based on resistivity data, they identified Verwey transition with charge order-disorder transition. In this model Fe 3+ and Fe 2+ ions are randomly distributed on octahedral sites above T V and charge transfer is permitted by means of electron exchange, implying good electrical conductivity. By contrast below T V the Fe ions in octahedral sublattice are ordered and conductivity drops. However, the actual ordering scheme, despite enormous effort, has not been found yet. Third important conclusion drawn from Verwey s [1941] measurements is the strong influence of sample stoichiometry on the transition. In magnetite of composition Fe 3(1-δ) O 4 the transition temperature T V is markedly depressed with increasing nonstiochiometry δ: the transition is of first order for δ = ; of higher order for δ = ; and for larger deviation the transition actually doesn t take place at all [Aragón, 1993]. But the colossal importance of sample quality has not been emphasized until In this year Sir Nevil Mott [1980] arranged the The Verwey Transition conference which is considered a milestone in the story of Verwey transition and stimulated oncoming research. There are two detailed reviews on this topic: Walz [2002] tries to find evidence of particular charge ordering; Garcíaet al. [2004] dispute the bare existence of such ordering. Both these points of view are supported by latest experiments. Whereas Wright [2002] found partial charge ordering of magnitude 0.2 electron among octahedral Fe sites below T V, a result further supported by x-ray resonant measurements by Goff et al. [2005]; Subías et al. [2004] shows no indication of charge ordering using the same technique. Also NMR experiments below T V of Novák et al. [2000] show that the states of iron ions on the octahedral sites are mixed so strongly that the notion of 2+ and 3+ values may lose its meaning. High pressure measurements (well above 100 GPa) of magnetite resulted in new set of valuable data. Care must be taken of sample quality (as always) and hydrostatic pressure conditions (see Môri s [2002] discussion of previous results). The electric resistivity measurements by Môri et al. [2002] on various synthetic magnetite crystals revealed that Verwey temperature decreases with increasing pressure, being entirely suppressed at critical pressure p C 8 GPa; p C decreases with departure from sample stoichiometry. The nonmetallic phase thus exists in a relatively small portion of the p,t diagram of magnetite. Rozenberg et al. [2006] studied the structural change (distortion from cubic to monoclinic structure) of magnetite in p,t diagram using powder x-ray diffraction. Simple conclusion can be drawn from these results: the sudden drop of electrical conductivity on cooling through T V (p) is caused by a band splitting due to structural distortion and associated unit-cell doubling. Finally, Rozenberg et al. [2007] completed phase diagram of magnetite around Verwey transition with their Mössbauer spectroscopy measurements on synthetic samples enriched by 57 Fe, where they observed a second order phase transition from inverse to normal spinel at higher pressure. An intermediate region between inverse and normal spinel phase is probably caused by local inhomogeneities, see Figure 1. All these high pressure results show that there is no ionic ordering of Fe ions. However, the role of nonstiochiometry and the origin of high electrical conductivity in normal spinel phase of magnetite are still unclear. Experiment and discussion The data presented here were recorded using noncommercial continuously reading high resolution SQUID magnetometer which reads both spontaneous and induced magnetic moments of the sample as a function of temperature T (in the range K) and applied fields H dc (up to ±20 mt) and H ac (0.1 to 100 µt) with frequency f (0 to 100 Hz). The frequency response of the magnetometer is perfectly flat in this frequency range. Details can be found in Janů et al. [2006]. 43

3 Figure 1. p,t phase diagram of magnetite at low temperatures and pressures up to 15 GPa: straight lines Mössbauer spectroscopy measurements [Rozenberg et al., 2007]; big circles x-ray diffraction measurements of structural phase transition [Rozenberg et al., 2006]; hatched area high resistivity phase of magnetite [Môri et al., 2002]. Verwey transition The sample measured is stoichiometric single-crystal slab 2 mm thick and of roughly rectangular shape with surface area of 2 cm 2, T V = 122 K, grown by skull melter technique [Harrison et al., 1978] and properly annealed. Sample was mounted on thermally insulated holder, so the thermodynamic aspect of the transition (latent heat) can be studied. During the transition the sample temperature is nearly constant due to release or absorbtion of latent heat, while the spontaneous magnetic moment of the sample varies wildly (Figure 2). The behavior of the magnetic moment is not reproducible, no magnetic field was applied during this measurement. We connect these variations to changes of magnetic domain structure (and possibly also crystal domain structure) due to changes in magnetocrystalline anisotropy [Bickford, 1950]. Glass-like transition Second set of magnetic measurements was taken on stoichiometric Fe 3 O 4 single crystal previously studied by NMR [Novák et al., 2000], TV = 123 K, grown by floating zone technique [Brabers, 1971] and properly annealed. The sample is cylinder-shaped, 4 mm in diameter and 5 mm high with cylinder axis parallel to crystallographic [100] direction. Also in this sample Verwey transition is indicated by changes in dc magnetization. Additional features were found at lower temperatures. In the temperature range K a glass-like transition occurs, a smooth decrease of ac susceptibility upon cooling (Figure 3). The transition temperature depends on frequency of ac field but does not depend on ac or dc field magnitude and cooling/warming rate. The transition can be quite accurately described as a Debye relaxation process with Arhenius temperature dependence of relaxation time [Janů et al., 2007]. The glass-like transition coincides fairly well with a minimum in NMR spin-spin relaxation time measured on this sample [Novák et al., 2000], similar anomalous effects were found by MAE spectroscopy [Walz, 2002]. 44

4 Figure 2. Thermodynamic (upper curve) and magnetic (lower curve) manifestation of Verwey transition during heating and cooling (0.5 to 2.0 K/min) measured simultaneously on thermally insulated sample in zero magnetic field. Shadow columns are guides for the eye they represent intervals in that the transition occurs. Figure 3. Temperature dependence of ac susceptibility of magnetite at glass-like transition for frequency from 1 to 60 Hz (rising to the right, roughly equidistant on logarithmic scale): upper curve - imaginary part, lower curve - real part; zero dc field, ac field 5 µt Low temperature anomaly At temperatures just below the glass-like transition an anomalous behavior of ac susceptibility appears (see Figure 4). It is expressed as a dramatic increase of ac susceptibility at lowest temperatures (5 K) induced by a step change of applied dc field. The sequence of measurement was following: when the sample was cooled or warmed in constant dc field and weak ac field (5 µt), curve (A) low ac susceptibility was recorded; on the other hand if step change of dc field was applied at low temperature then the ac susceptibility increased instantly and on subsequent warming curve (B) was recorded. Magnitude of the dc step (±2 mt) is several orders higher than magnitude of measuring ac field. As opposed to glass-like transition, this anomaly does not depend on the frequency of ac field but depends on the magnitude of dc step and also on warming rate. This anomaly can be explained as caused by displacing domain walls from their stabilized positions. At temperature 30 K the excited high-susceptibility state relaxes back to low susceptibility (a dip on curve (A) in Figure 4), which means that the stabilizing effects accommodate to the new domain wall positions. 45

5 Figure 4. Anomaly of ac susceptibility in magnetite at temperatures below glass-like transition: curves (A) warming or cooling in constant dc field down to 5 K; curves (B) at lowest temperatures a step change of applied dc field induced dramatic increase of ac susceptibility, warming. Measured in ac field of magnitude 5 µt. We also studied nonstiochiometric samples, one of these was annealed to obtain a deviation δ = in formula Fe 3(1-δ) O 4 and T V = 120K. In this sample, the glass-like transition extended down to 10 K and low temperature anomaly was not observed down to 5 K. Conclusion Our sensitive measuring methods to study low-frequency low-field magnetic properties of solids can also bring valuable results concerning the problem of magnetite. Exceptional resolution in field and temperature allows us to study the details of Verwey transition. Also the other effects observed in magnetite, namely the glass-like transition and the anomaly below 30 K can be important for understanding the physics of magnetite. Although they occur at much lower temperatures than Verwey transition, they have one major property in common the transition temperature of all these events is strongly suppressed by doping or nonstoichiometry of the sample. Our results compare with results of other magnetic measurements (MAE, NMR) and the sensitivity of squid magnetometer is far superior. As a result, we can use extremely weak measuring fields, several orders weaker than demagnetising pulses needed for MAE or RF pulses used in NMR, our studied system then can be closer to its equilibrium state and we are able to study the low temperature anomaly that is difficult to be observed using rougher magnetic techniques. References Aragón R., Gehring P.M. and Shapiro S.M., Stoichiometry, Percolation and Verwey Ordering in Magnetite, Phys. Rev. Lett , 1993 Balanda M. et al., Magnetic AC susceptibility of stoichiometric and low zinc doped magnetite single crystals, Eur. Phys. J. B , 2005 Bickford L.R. Jr., Ferromagnetic Resonance Absorption in Magnetite Single Crystals, Phys. Rev , 1950 Brabers V.A.M., Preparation of tetragonal single crystals in the Mn x Fe 3-x O 4 system, J. Cryst. Growth 8 26, 1971 Bragg W.H., Bragg W.L., The diffraction of X-rays by crystals, Nobel lecture, 1915 Goff R.J. et al., Resonant x-ray diffraction study of the charge ordering in magnetite, J. Phys.: Cond. Matter , 2005 Harrison H.R., Aragón R., Skull Melter Growth of Magnetite, Mater. Res. Bull , 1978 Janů Z., Soukup F. and Tichý R., Contact-less high-resolution magnetic measurement of electron transport, Int. J. of Material & Product Technology , 2006 Janů Z., Hadač J. and Švindrych Z., Glass-like and Verwey transition in magnetite in details, J.of Magn. And Magn. Mat , 2007 Mack D.E., Wissmann S., Becker K.D., High-temperature Mössbauer spectroscopy of electronic disorder in complex oxides, Solid State Ionics , 2000 Mott N., The Verwey Transition, Phil. Mag. 42 (special issue),

6 Môri N. et al., Metallization if magnetite at high pressures, Physica B , 2002 Néel L., Ann. Phys. Fr , 1948 Novák P., Štěpánková H., Englich J., Kohout J. and Brabers V.A.M., NMR in magnetite below and around the Verwey transition, Phys. Rev. B , 2000 Novák P. et al., Temperature Dependence of NMR in Magnetite, Ferrites: Proceedings of The Eighth International Conference on Ferrites, p.131, Japan 2000 Rakhecha V.C. et al., Spin transfer due to covalency for the tetrahedral-site Fe 3+ ions in Fe 3 O 4, J. Phys. C: Solid State Phys , 1978 Reneger K., Die anfängliche Suszeptibilität von Eisen und Magnetit in Abhängigkeit von der Temperatur, Thesis, Zürich 1913 Rozenberg G. Kh. et al., Origin of the Verwey Transition in Magnetite, Phys. Rev. Lett , 2006 Rozenberg G. Kh. et al., Structural characterization of pressure- and temperature-induced inverse normal spinel transformation in magnetite, Phys. Rev. B (R), 2007 Sir Nevil Mott, 1980: see Mott [1980] Subías G. et al., Magnetite, a Model System for Mixed-Valence Oxides, Does Not Show Charge Ordering, Phys. Rev. Lett , 2004 Vargas M. et al., Microbiological evidence for Fe(III) reduction on early Earth, Nature , 1998 Verwey E.J.W. and Haayman P.W., Electronic conductivity and transition point of magnetite ( Fe 3 O 4 ), Physica 8 979, 1941 Walz F., The Verwey transition a topical review, J. Phys.:Condens matter 14 R285, 2002 Weiss P. and Forrer R., Ann. Phys , 1929 Wright J.P. et al., Charge ordered structure of magnetite Fe 3 O 4 below the Verwey transition, Phys. Rev. B ,