Rock-magnetic properties

1. Titanomagnetite series and Low-temperature properties

 1.1 Crystal structure of magnetite and its antiferrimagnetism

 Figure 1. A part of the spinel structure for magnetite showing two types of cation sites (Redraw from O’Reilly, 1984).

Magnetite, (Fe³⁺)_A (Fe³⁺Fe²⁺)_BO₄, is a cubic mineral with spinel structure (Fig. 1). The cations are distributed on both A (tetrahedral) and B (Octahedral) sites. A unit cell consists of four A and four B sites with lattice constant a=8.396Å. The easy-axis is along the diagonal [111] of the cubic cell. Because there are unbalanced numbers of Fe³⁺ and Fe²⁺ spins at these two sites, the net magnetization will be not zero, resulting in strongly antiferrimagnetism.

The major interaction is between A and B sites, and the A-A and B-B interactions are much weaker. By neglecting the A-A and B-B interactions, the total interaction energy (or Curie temperature, which is a measure how strong the interactions is) is determined by T_c ~ (z_Az_B)^1/2, where, z_A is the number of the nearest A-sublattice neighbors to a B site. Apparently, with increase of substitution of cations on B site, T_c will decrease. For example, for titanomagnetite Fe_3-xTi_xO4, with increase x, Tc will linearly decrease from ~585^oC for magnetite (x=0) to less than –100^oC for ülvospinel (x=1). 

1.2 Verwey transition (~122K)

The first report that magnetite exhibits a low-temperature transition was by Millar (192). However, detailed studies on the crystal structure and electrical properties were conducted by Verwey (1939). He found that the crystal lattice of magnetite is distorted slightly from the cubic spinel structure above Tv to a simpler structure below, which was further demonstrated to be a monoclinic structure (Yoshida and Iida, 1979; Zuo et al., 1990) (Fig. 2).

The Verwey transition is an ionic order-disorder transition. Above Tv, the Fe³⁺ and Fe²⁺ B-site cations hop freely. Therefore, the average of Fe³⁺ and Fe²⁺ on the B-site can be regarded as Fe^2.5+.  However, below Tv, the B-site Fe²⁺ and Fe³⁺ cations are ordered, causing distortion of the crystal lattice.

Figure 2. Crystal shapes above (cubic) and below (monoclinic) the Verwey transition (~122K).

It has been well documented that the Verwey transition temperature (Tv) of magnetite (Fe_3(1-d)O₄) and titanomagnetite (Fe_3-xTi_xO₄) system is strongly affected by both variations in oxygen stoichiometry and by substitutions of iron with other cations (e.g. Ti⁴⁺). Generally, increase of non-stoichiometry will not only shift the Tv to a lower temperature, but also depress and broaden the transition. The effects of oxidation and Titanium substitution on Tv are analogous with the correspondence relationship x=3d.

A number of studies have independently demonstrated that in the range of –0.0005<d<0.0039ºdc variation in Verwey transition is of first (I) order, with the Tv linearly decreasing from 122 K to 108 K with increasing cation vacancy density. Whereas, just above the critical dc, Tv plummets to about 100 K, and follows a second or higher order (II) variation in the range dc <d<3dc. When 3d (or x) >9dc, no transition can be observed.

The phenomena observed above can be successfully explained by the microscopic order-disorder model proposed by Honing and Spalek (1992) and Honing (1995). In this model, the non-stoichiometric cation fraction (d) can be expressed as d=(8N_S)^-1(N₃₊-2N₂₊), where N_S, N₂₊ and N₃₊ are the summation of cation and vacant sites, number of the Fe²⁺ and Fe³⁺, respectively (Aragón et al., 1993; Honing, 1995). The oxidation of one Fe²⁺ to Fe³⁺ increases the difference between N₃₊ and 2N₂₊ by 3. Because N_S equals 96 in a unit cell, then dc is 0.0039 by substituting these constant into the equation above, in agreement well with the experimental obs  ervation. Thus the discontinuity of the Tv change at x=3d=0.017 corresponds to the conversion of exactly one Fe²⁺ out of 96 cations to Fe³⁺. The critical point 3d (or x) >9dc, at where Tv are completely suppressed, corresponds to a loss of three electrons or one cation per vertex.

 Figure 3. Variations in Tv with compositions of Fe_3(1-d)O₄ and Fe_3-xTi_xO4 (redraw from Kozlowshi et al., 1995).

 However, such model is based on homogeneous oxidation of the magnetic particles. For natural samples, partially oxidized magnetite or titanomagnetite are prevalent. The latter exhibits very different low-temperature properties (Liu et al., 2004), therefore, cautions have to be made before applying the model in Fig. 3 to natural samples.

Based on Fig. 3, we conclude that Verwey transition will disappear only for a small x values (0.04), corresponding to TM₄. This has been demonstrated by Moskovitz et al. (1998) (Fig. 4). When x>0.04, the low-temperature behaviors of TM can be further divided into two groupd with x<0.4 and x>0.4, respectively. For x<0.4, SIRM warming-curves display sharp remanence transitions below 100 K with little change above. However, this transition is not a suppressed Verwey transition because the lowest Tv is ~80K. This transition is related to the magnetic isotropic points where K1 is zero. Therefore, for a natural sample with a sharp drop in intensity below 50 K may not exclusively caused by pyrrhotite (a well-known transition at 34 K), but also can be caused by TM20-30. For X>0.4, SIRM is almost temperature-independent below 50 K, and then rapidly decrease between 50 and 80 K, and then continue to decrease more gradually up to 300 K.

1.3 Changes in SIRM through Tv

Özdemir and Dunlop (1999) measured temperature dependence of SIRM for a 1.5-mm single crystal of magnetite. Results (Fig. 4) show that large changes in SIRM across Tv. For SIRM acquired at 300 K, there is a reversible large jump in SIRM  Tv when the cubic [001] hard direction becomes the monoclinic c-axis, but above Tv on warming, more than 90% of the initial SIRM has been demagnetized. For the SIRM acquired at 20 K, the SIRM almost totally lose at Tv. Also we note that SIRM_20K is about 30 times higher than SIRM_300K. This can be interpreted in the following way.

Because [001] is the hard axis above Tv, the domains will have a choice of four equivalent <111> easy axes, which make identical angles of 54.7^o and are arranged symmetrically about [001]. This pattern will be mutually canceled to some extend, resulting in relatively smaller SIRM. In contrast, below Tv, [001] becomes the monoclinic easy axis and all the domain magnetizations rotate into this direction, then the bulk remanence increases substantially. In recrossing  Tv, the domain magnetizations rotate back to [111] directions and the remanence drops back to its original level.

 Figure 4. Low-temperature dependence of SIRM acquired 5 K for synthetic titanomagnetites. (a) TM0-TM41, and (b) TM55-TM61. (redraw from Moskowitz et al., 1998).

When the crystal is aligned along [001], one of <111> directions is closer to the field direction. This will yield a larger SIRM_300K than SIRM_300K//[111]. Meanwhile, when crossing Tv to lower temperature, it is not certain only one set of [001] axes will be selected as the c-axes. There are so many competing directions are available. Then the net magnetization will be small. Then we will not observe the large increase SIRM in Fig. 5a.

 1.4 Changes in the domain states

Submicron magnetites undergo significant changes in their domain state in crossing the Verwey transition (Özdemir and Dunlop, 2002). For a sample (37 nm) at the SP/SD boundary becomes totally thermally stable SD grains. A larger sample (100 nm) of the fine-grained PSD region also become SD at 15 K, probably contain a mixture of SD and 2D/vortex states (Fig. 6). Coercivity force Hc increases by a factor of 3-40 between 120 and 100 K. Above 100 K, changes in these properties are small.

 Figure 5. Temperature dependence of SIRM by a 2.5 T acquired at 300 K (a) and 20 K (b). Arrows show the heating and cooling processes (redraw from Özdemir and Dunlop, 1999). M_SIRM//[001] is the SIRM acquired along the direction [001].

Figure 6. Low-temperature hysteresis parameters for the 100 and 220 nm magnetites on a Day plot (redraw from Özdemir et al., 2002).

1.5 Grain size and coercivity dependence of SIRM, TRM, ARM, and susceptibility carried by magnetite

Figure 7. Grain size dependence of low temperature SIRM acquired at 300 K. (redraw from Özdemir et al., 2002).

SIRM  For stable SD grains (37 nm), the SIRM cooling curve is almost flat between 300 and 150 K. When crossing Tv, about 5% of remanence is lost. When returning back to 300 K,m about ~85% of remanence remain (Fig. 7). This indicates that SD grains have fairly stable low-T behavior compared to the other PSD/MD grains. Furthermore, because low-temperature oxidation can sufficiently oxidized the SD magnetites into SD maghemites. Thus, it is usually valid to claim that SD SIRM is independent of temperature. With increasing grain sizes, the remanences decreases more and more between 300 and 150 K, and less and less remanence can remain after the LTD ccylce.

TRM  Systematic low-temperature behaviors of TRM were conducted by Muxworthy and McClelland (2000) (Fig. 8). On cooling through Tv, for smaller samples, their TRMs display large increase. This intensity increase gradually muted for intermediate grain size PSD (13 mm) sample (Fig. 8c), and then begin to drop for MD grains (Figs 8e and 8f). However, for even larger particles >190 mm, TRM increases again when crossing Tv. Therefore, additional criteria are needed to clarify the general grain size by Day-plot and the direct SEM observations. Once the grain size can be determined to be less than several tens of mm, Fig. 8 can be a calibration to determine the grain sizes of TRM carried magnetites. However, there are no systematic investigations of the low-temperature behavior of TRM carried by titanomagnetites with different x values. One possible project to is to use natural igneous rocks.

The large increase of remanence when crossing Tv for fine-grained PSD samples (Figs 8a and 8b) might be different from that of the coarse-grained magnetites (Figs. 8g-8i) and also different from the SIRM behavior for the 1.2 mm magnetite. Muxworhty and McClleland (2000) proposed that the remanence jumps for TRM is due to removal or destruction of “screening” or “soft” domain walls, revealing a “hard” domain structure which carries a net remanence in the direction of the initial remanence. At room temperature, closure domains are highly favourable for large grains of magnetic with many domains, however, in the monoclinic phase closure domains become much less important.

Figure 8. Low-temperature cycling of TRM induced in a field of 100 mT in synthetic hydrothermal samples. (a) 3 mm, (b) 7.5 mm, (c), 13 mm, (d) 18 mm, (e) 24 mm, (f) 59 mm. (g) –(I) are for natural samples with size of 190 mm (g), 250 mm (h) and 3 mm (i).

ARM   ARM sometimes can be an analogue of TRM.

Figure 9. Comparison of the low temperature behaviors of different fraction of remanences. (a) remanence after AF demagnetization of SIRM acquired at 300K; (b) pARM; and (c) ARM with different DC fields.

Muxworthy et al. (2003) revealed that the low-temperature behaviors of SIRM and ARM is not only grain size dependent, but also coercivity dependent (Fig. 9). Fig. 9a shows the results for a 7 mm magnetite. With increasing the AF demagnetization peak fields, first, the demagnetization on cooling associated with domain re-ordering decreases, and second, the sudden increase of intensity on cooling through Tv increases. Finally, the memory ratio also increases. Similar features are also observed for pARM of a 1.7 mm magnetite (Fig. 9b) that the higher-coercivity fraction of remanence exhibit larger intensity jumps on cooling thorough Tv. The effects of the biasing DC fields are shown in Fig. 9c. Clearly, the LTD of ARM acquired with a 200 mT DC field resembles the SIRM behavior.

1.6 Oxidation of titanomagnetite

The oxidized titanomagnetite can be expressed as (FeTið)₃O₄, where ð is vacancy on the B-site. The oxidation can be realized by two different processes: addition of oxygen and loss of iron (Marshall and Cox, 1972; Rayll and Hall, 1980; Worm an Banerjee, 1984; Kelso et al., 1991; Zhou et al., 1999).

Addition of oxygen  In this mechanism, oxygen atoms are adsorbed at the surface of the crystal. The local Fe²⁺ will be oxidized into Fe³⁺ to reduce oxygen to become part of the O-Fe chemical bonds. A formula stoichiometric Fe_3-xTi_xO₄ contains (1-x) Fe²⁺ and (2-2x) Fe³⁺. After oxidation, vacancies are introduced, Fe_(3-x)RTi_xRð_(3-x)RO₄, where R is used to quantify the degree of oxidation. R is between 1 (stoichiometry) and 8/(9+x) when no Fe²⁺ remains. For a whole system, the oxidation process is:

Fe_3-xTi_xO₄ + (z/2)(1+x) O à (1/R) Fe_(3-x)RTi_xRð_(3-x)RO₄

Where z shows partial oxidation. When z=0, no oxidation, and z=1 corresponds to the maximum degree of oxidation. The (3-x)R Fe consists of (1-z)(1+x)R Fe²⁺ and {2-2x+z(1+x)}R Fe³⁺ per formula.

Removes of iron   When no oxygen is available at the surface of the crystal, addition of oxygen is inhibited. However, local accumulation of electron eventually will change a Fe²⁺ to a free iron atom, then could be leached away. Of course, for both two mechanisms, diffusion inside is required to form a homogeneous crystal. The maximum loss of iron for TM with (1+x) Fe²⁺ is (1+x)/3 per formul because the production of a one Fe atom requires the loss 3Fe²⁺ and the gain of 2Fe³⁺.  For a general process,

Fe³⁺_2-2x0Fe²⁺_1+x0Ti_x0O₄ à

                      Fe³⁺_{2-2x0+2/3(1+x0)}Fe²⁺_1+x0-z(1+x0)Ti_x0ð_z/3(1+x0)

                      + Fe²⁺_z/3(1+x0)+e_2/3z(1+x0)

where x0 is the original Ti composition. Clearly, oxidation does not change Ti composition.

To accurate determine x0, z, we need to quantify both oxygen contents and Fe/Ti ratio (e.g., by Zhou et al., 1999).

Zhou et al. (1999) also defined a parameter x=3Ti/(Ti+Fe). For addition of oxygen, x remains constant. However, for removal of iron, x will increase with increase of z, especially for ocean-floor basalt.

The relationship between the lattice parameter and the oxidation degree z for TM60 and the other TMx is shown in Fig. 10.

Figure 10. Relationship between the lattice parameter and the oxidation for TM60 (left, data from Zhou et al., 1999 and TM70, TM50 and TM30 (right, data from Nishitani and Kono, 1983).

 1.7 Effects of oxidation on Curie temperature of TM

Figure 11. Curie temperature against oxidation state. (data from Nishitani and Kono, 1983).