- Email: [email protected]
Spin order in FeV2O4 determined by single crystal Mössbauer spectroscopy in applied magnetic field
Physica B xxx (xxxx) xxx–xxx
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Spin order in FeV2O4 determined by single crystal Mössbauer spectroscopy in applied magnetic field ⁎
Shin Nakamuraa,b, , Yasuhiro Kobayashic, Shinji Kitaoc, Makoto Setoc a b c
Teikyo University, Department of Science and Engineering, Utsunomiya, Tochigi 320-8551, Japan Waseda University, Advanced Research Center of Science and Engineering, Shinjuku, Tokyo 169-8555, Japan Kyoto University, Research Reactor Institute, Kumatori, Osaka 590-0494, Japan
A R T I C L E I N F O
A BS T RAC T
Keywords: FeV2O4 57 Fe Mössbauer spectroscopy Orbital order Spin order Canted ferrimagnet
In order to clarify the spin order of FeV2O4, 57Fe Mössbauer spectroscopy has been conducted by using a single crystal specimen. A measurement in applied magnetic field has been also conducted. By applying a slight compression in the sample plane, almost single domain state was achieved in the low temperature phases. The spectra consist of Fe2+ spectra (~ 85%) and Fe2.5+ spectra (~ 15%), corresponding to the A- and B-site Fe ions, respectively. The B-site spectrum well represents the local structure and the magnetic structure of V3+ ion on the B-site. Notable changes in the Mössbauer parameters are recognized at 140, 110, and 65 K, where the successive phase transitions take place. The feature well represents the orbital and spin order. In the orthorhombic phase below 110 K, Fe2+ and V3+ spins form a collinear ferrimagnetic order along the a-axis. Below 65 K in the low temperature tetragonal phase, however, both spins incline from the c-axis to form a canted ferrimagnetic structure. The canting angles are about 17° and 52° at 4.2 K for Fe2+ and V3+ spins, respectively.
1. Introduction Iron vanadium spinel FeV2O4 is an interesting material where both Fe2+ and V3+ ions have spin and orbital degrees of freedom. The roomtemperature structure is cubic (space group Fd3m). The A-site (tetrahedral site, 8a) is occupied by the Fe2+ ion having a high-spin 3d6 configuration, where three electrons are in the doubly degenerate ground-state dγ orbital. On the other hand, the B-site (octahedral site, 16d) is occupied by the V3+ ion (3d2 configuration), where there are two electrons in the triply degenerate ground-state dε orbital. With decreasing temperature, successive phase transitions occur [1,2]. At 140 K, the cubic-to-tetragonal transition takes place. The tetragonal phase (I41/amd) has the lattice constants c/ 2 a < 1 (HT tetragonal). Then, at 110 K, a transition to the orthorhombic phase (Fddd) occurs (a > c > b). Finally, at 65 K, another tetragonal phase (I41/amd) appears again with the lattice constants c/ 2 a > 1 (LT tetragonal). Recent thermal conductivity measurement clearly shows that the orbital order takes place at 65 K [3]. Magnetically, a ferrimagnetic order develops below Tc = 110 K. The magnetic easy axis is always the longest axis, the a-axis in the orthorhombic phase or the c-axis in the LT tetragonal phase. Below 65 K, a canted ferrimagnetic order occurs, where Fe2+ spins remain aligning along the longest c-axis but V3+ spins incline toward the cubic < 111 > axis. The magnetic moments of Fe2+
⁎
and V3+ are estimated to be 4.0 and 0.85 μB, respectively, by the neutron powder diffraction [4]. The saturation magnetic moment is about 3 μB/f.u. at 20 K [5]. Thus, the lattice is strongly coupled with the electron configurations, the spin order, and the orbital order. That is, the three transitions at 140, 110, and 65 K are caused by the Jahn– Teller effect of the Fe2+ ion, the spin order, and the orbital order, respectively. Mössbauer studies of this compound were also conducted using powder specimens in the early stage of the investigation [6–10]. The orbital and spin order, however, have not been discussed in detail, presumably because of a lack of the information on the successive phase transition at low temperature. One of the present authors (S.N.) has found a distinct evidence of the orbital order by 57Fe Mössbauer spectroscopy using a powder specimen [11]. That is, the sign of the quadrupole coupling constant e2qQ/2 changes abruptly from negative to positive at 65 K. The change in the orbital state accompanies a sudden decrease in the hyperfine field Hhf. In the ferrimagnetic state below 110 K, the Fe2+ spins align along the orthorhombic a-axis, but seem to incline slightly from the tetragonal c-axis below 65 K. In the present research, in order to clarify the spin order of FeV2O4, we have conducted 57Fe Mössbauer spectroscopy using a single crystal specimen. A measurement in applied magnetic field has been also conducted. The spectra consist of major Fe2+ spectra corresponding to
Corresponding author at: Teikyo University, Department of Science and Engineering, Utsunomiya, Tochigi 320-8551, Japan. E-mail address: [email protected] (S. Nakamura).
http://dx.doi.org/10.1016/j.physb.2017.09.123 Received 29 June 2017; Received in revised form 19 September 2017; Accepted 27 September 2017 0921-4526/ © 2017 Elsevier B.V. All rights reserved.
Please cite this article as: Nakamura, S., Physica B (2017), http://dx.doi.org/10.1016/j.physb.2017.09.123
Physica B xxx (xxxx) xxx–xxx
S. Nakamura et al.
Fig. 1. Schematic view of the experimental setup of the specimen.
the A-site Fe ion and minor Fe2.5+ spectra originating from Fe ion substituted on the B-site. The latter well represents the local structure and the magnetic structure of V3+ ion on the B-site. We have successfully obtained not only spin order of Fe2+ ion on the A-site but also that of V3+ ion on the B-site. 2. Experiments A single crystal of FeV2O4 was prepared by a floating zone (FZ) method in a controlled oxygen atmosphere using a CO2 – H2 mixed gas (CO2/H2 = 0.7 at room temperature). As-grown specimen was heattreated at 1473 K in the same oxygen atmosphere for a week. A (001) plane disk specimen with approximately 5 mm diameter and 40 µm thick was fixed on the acryl plate with the edge surrounded by the epoxy resin. Thus [100] and [010] axes in the plane undergo slight compression during cooling to achieve a single domain state in the low temperature phases [12]. The schematic view of the experimental setup of the specimen is shown in Fig. 1. Mössbauer spectroscopy was conducted in conventional transmission geometry by using 57Co-in-Rh (25 and 50 mCi) as γ-ray source. The Doppler velocity scale was calibrated using an Fe metal foil at room temperature. The incident γ-ray was parallel to the [001] axis, which is supposed to be the longest axes in the low temperature phases (the a-axis in the orthorhombic phase and the c-axis in the LT tetragonal phase). The measurements were conducted in the temperature range from 4.2 to 291 K using a closed-cycle refrigerator, a liquid nitrogen cryostat, and a liquid helium cryostat. At 4.2 K, a measurement in applied magnetic field was also conducted. The magnetic field of 2 T was applied parallel to the [001] axis. For the magnetically ordered spectra, the major Fe2+ spectra were analyzed exactly using a mixture of magnetic and quadrupole Hamiltonians, while the minor Fe2.5+ spectra were analyzed by a perturbation method. Lorentzian line shapes were assumed for the analysis of the spectra.
Fig. 2. Paramagnetic spectra of the single crystal FeV2O4 at (a) 291, (b) 200, and (c) 130 K. A-site (red curve) and B-site (blue curve) denote A-site Fe2+ and B-site Fe2.5+, respectively.
cide well with the calculated values by a point charge model, 0.18 mm/ s in both the cubic and HT tetragonal region. The z-axis in the cubic phase is < 111 > axis since the B-site has site symmetry of 3m, and presumably almost the same local structure is retained in the HT tetragonal phase. Thus, the intensity ratio I1/I2 is always assumed to be 1 in the analysis. In Fig. 3, the magnetically ordered spectra at several temperatures are shown. The spectra consist of three subspectra corresponding to two types of A-site Fe2+ and a B-site Fe2.5+, denoted as A-0° (red curve), A-90° (green curve), and B (blue curve) in the figure, respectively. The intended single domain state, the longest crystallographic axis perpendicular to the sample plain, is attained 80– 85% for the A-site spectra (0°-domain, A-0°), whereas the rest is a domain with the longest axis in the plain (90°-domain, A-90°). For the B-site spectra, we assume only 0°-domain. The B-site spectrum is not clearly seen in the temperature range 100–110 K, because its hyperfine field is small and the spectrum overlaps with the A-site spectrum. The obtained Mössbauer parameters, isomer shifts (IS), quadrupole coupling constants (e2qQ/2), quadrupole shifts (εq), asymmetric parameters (η), hyperfine fields (Hhf), Euler angles between the z-axis and the direction of the hyperfine field (θ, φ), and line widths (W), are indicated in Table 1 for the temperatures corresponding to Figs. 2 and 3. The quadrupole shift is defined as εq = (Δ56 − Δ12)/4, where Δij represents the splitting between the ith and jth lines. For the A-site spectrum in the LT tetragonal phase, where η = 0 owing to the site symmetry of 4 m2, φ cannot be determined. The temperature dependences of some parameters for the A- and B-site spectra are shown in Figs. 4 and 5, respectively. It is clearly seen in Fig. 4(b) and (c) that the e2qQ/2 and Hhf change according to the structural and magnetic transition. Especially, the changes of the A-site parameters at the
3. Results and discussion The paramagnetic spectra at several temperatures are shown in Fig. 2. The spectra are composed of major Fe2+ spectra (about 85%) and minor Fe2.5+ spectra (about 15%). The major Fe2+ spectra correspond to the Fe2+ ion on the A-site (A-site spectra). At room temperature, the A-site spectrum is a singlet, reflecting the cubic symmetry (site symmetry 4 3m). With decreasing temperature, however, the singlet spectrum becomes broadened, and below 250 K, it splits into a doublet even in the cubic region. This is due to the local and dynamical Jahn–Teller effect. In the LT tetragonal region, the quadrupole splitting (QS) abruptly becomes large. At 130 K, The intensity ratio of the 1st to 2nd lines, I1/I2, is approximately 0.62. This indicates that the principal axis of the electric field gradient (EFG), z-axis (shortest crystallographic c-axis in the HT tetragonal phase) is almost in the sample plain. On the other hand, the minor Fe2.5+ spectra originate from a small amount of Fe ion on the B-site, approximately 8% substituted for V3+ (B-site spectra). The B-site spectra are always doublet with almost constant QS (0.11–0.21 mm/s). The values coin2
Physica B xxx (xxxx) xxx–xxx
S. Nakamura et al.
Fig. 3. Magnetically ordered spectra of the single crystal FeV2O4 at (a) 100, (b) 50, and (c) 18 K. A-0° (red curve), A-90° (green curve), and B (blue curve) denote A-site Fe2+ in 0°-domain, A-site Fe2+ in 90°-domain, and B-site Fe2.5+, respectively.
Fig. 4. Temperature dependences of (a) isomer shift IS, (b) quadrupole coupling constant e2qQ/2, (c) hyperfine field Hhf, and (d) canting angle θm of the Fe2+ spin from the longest axes for the A-site Fe2+ ion in FeV2O4.
orbital order (65 K) are notable. These features are well consistent with that observed for the powder specimen [11]. Here we discuss the spin order in the orthorhombic and LT tetragonal phases. Since the direction of Hhf is parallel to that of the spin (antiparallel to the magnetic moment), the spin order can be estimated by referring θ and φ for the A-site Fe2+. The spin direction in the 90°-domain seems to incline slightly toward the perpendicular direction, presumably because of the magnetic dipole field of the 0°domain spins. Hereafter, we only refer to the spin order in the 0°domain. In the orthorhombic phase, the EFG z-, y-, and x-axes coincide with the crystallographic b-, a-, and c-axes, respectively [11]. Thus, (θ,
φ) = (90°, 90°) is the direction of the a-axis (the longest axis). In the LT tetragonal phase, the z-axis coincides with the crystallographic c-axis. Therefore θ = 0° is the direction of the c-axis (the longest axis). In Fig. 4(d), the angle between the direction of Hhf and the longest crystallographic axis, θm, is plotted. The spins align along the a-axis in the orthorhombic phase, but with decreasing temperature they begin to incline, and finally reach θm = 17° at 4.2 K in the LT tetragonal phase. Note that the estimated angles in the orthorhombic phase may not be so precise, since the B-site spectra cannot be fitted well in this
Table 1 Isomer shifts (IS), quadrupole coupling constants (e2qQ/2), quadrupole shifts (εq), asymmetric parameters (η), hyperfine fields (Hhf), Euler angles between the z-axis and the direction of the hyperfine field (θ, φ), and line widths (W) of the A-site and B-site Fe in FeV2O4 at several temperatures (corresponding to the spectra in Figs. 2 and 3). A-0° and A-90° denote A-site 0°-domain and 90°-domain, respectively. The quadrupole shift is defined as εq = (Δ56 − Δ12)/4, where Δij represents the splitting between the ith and jth lines. T (K)
site
IS (mm/s)
e2qQ/2, εq (mm/s)
η
Hhf (T)
θ (°)
φ (°)
W (mm/s)
Ratio (%)
291
A B A B A B A-0° A-90° A-0° A-90° B A-0° A-90° B
0.909(10) 0.452(10) 0.987(10) 0.497(10) 1.025(10) 0.518(20) 1.014(20) 1.014(20) 1.054(20) 1.054(20) 0.507(20) 1.027(20) 1.027(20) 0.512(20)
0 0.113(10) −0.248(10) 0.145(10) −1.892(10) 0.195(10) −2.256(20) −2.256(20) 3.062(20) 3.062(20) −0.023(20) 3.087(20) 3.087(20) −0.044
0 0 0 0 0 – 0.48 0.48 0 0 – 0 0 –
0 0 0 0 0 0 10.68(10) 10.68(10) 8.39(10) 8.39(10) 41.15(10) 8.25(10) 8.25(10) 45.84(10)
– – – – – – 90(2) 108(2) 11(1) 35(1) – 15(1) 33(1) –
– – – – – – 90(2) 90(2) – – – – – –
0.376(10) 0.287(10) 0.369(10) 0.261(10) 0.365(10) 0.256(10) 0.482(20) 0.521(20) 0.371(20) 0.372(20) 0.731(20) 0.379(20) 0.379(20) 0.484(20)
86(1) 14(1) 87(1) 13(1) 86(1) 14(1) 84(1) 16(1) 70(1) 16(1) 14(1) 68(1) 16(1) 16(1)
200 130 100 50
18
3
Physica B xxx (xxxx) xxx–xxx
S. Nakamura et al.
Fig. 6. Mössbauer spectra of the single crystal FeV2O4 at 4.2 K (a) without and (b) with applied magnetic field of 2 T along the c-axis. A-0° (red curve), A-90° (green curve), and B (blue curve) denote A-site Fe2+ in 0°-domain, A-site Fe2+ in 90°-domain, and B-site Fe2.5+, respectively.
Here θm again represent the angle between the direction of spins and the longest crystallographic axis. Eq. (2) yields that θm is 0 in the orthorhombic phase, while it is about 47° in the LT tetragonal phase. This means that the V3+ spins align along the a-axis in the orthorhombic phase, but incline approximately toward the cubic < 111 > direction in the LT tetragonal phase. The spin order can be evaluated more precisely by a measurement in an applied magnetic field. The spectra at 4.2 K without and with applied magnetic field of 2 T along the c-axis are shown in Fig. 6(a) and (b), respectively. And the obtained parameters are indicated in Table 2. The observed field (Hobs) is a vector sum of the hyperfine field (Hhf) and the applied external magnetic field (Hex),
Fig. 5. Temperature dependences of (a) isomer shift IS, (b) hyperfine field Hhf, (c) quadrupole shift εq, and (d) intensity ratio of 2nd–5th lines to 1st–6th lines I25/I16 for the B-site Fe2.5+ ion in FeV2O4.
temperature range. On the other hand, the spin order of V3+ ion on the B-site is supposed to be well represented by that of Fe2.5+ ion on the Bsite [13–15]. Since the B-site spectra are analyzed by the perturbation method that does not give θ and φ, but we can roughly estimate the direction of the spins from Fig. 5(c) and (d). In Fig. 5(c), it is seen that εq changes its sign from positive to negative around 65 K. When η is small, the quadrupole shift is approximated as 2
εq ≈
Hobs = Hhf + Hex .
The difference ΔH = Hobs − Hhf is −1.83 and +1.24 T for the A- and Bsite spectra, respectively. This means that the spins of the A- and B-site ion form up- and down-moments, respectively, but clearly they both cant from the c-axis. According to Eq. (3), we can evaluate Hhf of the Asite in applied magnetic field. The result is Hhf = 8.80 T and θ = θm = 17°, which is well consistent with the value without magnetic field (see Table 2). On the other hand, for the B-site spectra, the values of Hobs and Hhf can deduce the canting angle as θm = 52° from the c-axis. This means that the V3+ spins are almost in the cubic < 111 > direction. In summary, Fe2+ and V3+ spins form a collinear ferrimagnetic order along the a-axis in the orthorhombic phase, whereas both of them incline from the c-axis to form a canted ferrimagnetic structure in the LT tetragonal phase. The feature is schematically shown in Fig. 7. In this experiment, the canting direction of Fe2+ spins cannot be determined because η = 0, but the direction toward the cubic < 111 > axes is probable. Using the vales of magnetic moments of Fe2+ and V3+ obtained by the neutron powder diffraction (4.0 and 0.85 μB, respectively) [4], the net magnetic moments are calculated as 2.30 and 2.78 μB/f.u. for the orthorhombic and LT tetragonal phases, respectively. The estimated values seem to be consistent with the experimental magnetization values.
2
e qQ 3cos θ − 1 ⋅ . 2 4
(1) 2
According to the point charge calculation, the values of e qQ/2 are 0.20 and 0.24 mm/s for the orthorhombic and LT tetragonal phases, respectively. That is, the local structures of the B-site remain almost unchanged from that of the cubic phase. Therefore the change in the sign of εq implies the change in θ. The angular factor in Eq. (1) becomes 0 when θ = 54.7°. Assuming that the z-axis is still in the vicinity of the cubic < 111 > axis, we can deduce that the spins aligning in the adirection (θ = 54.7°) in the orthorhombic phase begin to incline toward the rest of the three < 111 > directions (θ = 70.5°) in the LT tetragonal phase. This feature can be also explained by the intensity ratio of 2nd– 5th lines to 1st–6th lines, I25/I16, shown in Fig. 5(d). The value of I25/ I16 is almost 0 in the orthorhombic phase, while it is about 0.5 in the LT tetragonal phase. In this experiment, since the direction of the incident γ-ray is supposed to be parallel to the longest axes (the a- and c-axes for the orthorhombic and LT tetragonal phases, respectively), the intensity ratio is approximately given by
I25 4sin2θm ≈ . I16 3 + 3cos2θm
(3)
(2) 4
Physica B xxx (xxxx) xxx–xxx
S. Nakamura et al.
Table 2 Isomer shifts (IS), quadrupole coupling constants (e2qQ/2), quadrupole shifts (εq), asymmetric parameters (η), hyperfine fields (Hhf), observed fields (Hobs), Euler angles between the zaxis and the direction of the hyperfine field or observed field (θ), and line widths (W) of the A-site and B-site Fe in FeV2O4 at 4.2 K with and without applied magnetic field (Hex). Hex (T)
Site
IS (mm/s)
e2qQ/2, εq (mm/s)
η
Hhf, Hobs (T)
θ (°)
W (mm/s)
Ratio (%)
0
A-0° A-90° B A-0° A-90° B
1.059(20) 1.059(20) 0.515(20) 1.056(20) 1.056(20) 0.554(20)
3.139(20) 3.139(20) −0.08(20) 3.143(20) 3.143(20) −0.053
0 0 – 0 0 –
8.74(10) 8.74(10) 46.52(10) 6.91(10) 6.91(10) 47.76(10)
17(1) 35(1) – 22(1) 49(1) –
0.404(20) 0.443(20) 0.443(20) 0.433(20) 0.394(20) 0.491(20)
72(1) 13(1) 15(1) 76(1) 10(1) 15(1)
2
ferrimagnetic structure. The canting angles are about 17° and 52° at 4.2 K for Fe2+ and V3+ spins, respectively. The estimated canting angle of V3+ spins seems to be close to that reported by the powder neutron diffraction study. The canting of Fe2+ spins is our new finding, which has been also suggested by our powder Mössbauer measurement. Acknowledgement This work has been carried out in part under the Visiting Researchers Program of the Kyoto University Research Reactor Institute. References [1] T. Katsufuji, T. Suzuki, H. Takei, M. Shingu, K. Kato, K. Osaka, M. Takata, H. Sagayama, T. Arima, J. Phys. Soc. Jpn. 77 (2008) 053708. [2] Y. Nii, H. Sagayama, T. Arima, S. Aoyagi, R. Sakai, S. Maki, E. Nishibori, H. Sawa, K. Sugimoto, H. Ohsumi, M. Takata, Phys. Rev. B 86 (2012) 125142. [3] Y. Ishitsuka, T. Ishikawa, R. Koborinai, T. Omura, T. Katsufuji, Phys. Rev. B 90 (2014) 224411. [4] G.J. MacDougall, V.O. Garlea, A.A. Aczel, H.D. Zhou, S.E. Nagler, Phys. Rev. B 86 (2012) 060414. [5] H. Takei, T. Suzuki, T. Katsufuji, Appl. Phys. Lett. 91 (2007) 072506. [6] M. Tanaka, T. Tokoro, Y. Aiyama, J. Phys. Soc. Jpn. 21 (1966) 262. [7] F. Hartmann-Boutron, P. Imbert, J. Appl. Phys. 39 (1968) 775. [8] M. Abe, M. Kawachi, S. Nomura, J. Solid State Chem. 10 (1974) 351. [9] M.P. Gupta, H.B. Mathurt, J. Phys. C: Solid State Phys. 8 (1975) 370. [10] C.D. Spencer, P.A. Smith, R.P. Stillwell, J. Phys. Chem. Solids 39 (1978) 103. [11] S. Nakamura, A. Fuwa, J. Phys. Soc. Jpn. 85 (2016) 014702. [12] S. Nakamura, A. Fuwa, Phys. Procedia 75 (2015) 747. [13] I. Kagomiya, S. Nakamura, S. Matsumoto, M. Tanaka, K. Kohn, J. Phys. Soc. Jpn. 74 (2005) 450. [14] S. Nakamura, M. Sato, S. Morimoto, S. Nasu, Y. Tsunoda, Hyperfine Interact. 169 (2006) 1235. [15] Shin Nakamura, Akio Fuwa, Yorihiko Tsunoda, Hyperfine Interact. 208 (2012) 29.
Fig. 7. Spin order of FeV2O4 in (a) the orthorhombic and (b) the LT tetragonal phases.
4. Conclusion We have conducted 57Fe Mössbauer spectroscopy of the single crystal of FeV2O4 in order to clarify the spin order. A measurement in applied magnetic field has been also conducted. By applying a slight compression in the sample plane, almost single domain state was achieved in the low temperature phases. The spectra consist of major Fe2+ spectra corresponding to the A-site Fe ion and minor Fe2.5+ spectra originating from Fe ion substituted on the B-site. The B-site spectrum well represents the local structure and the magnetic structure of V3+ ion on the B-site. The Mössbauer parameters change according to the structural and magnetic transition. Especially, the changes of the A-site parameters at the orbital order (65 K) are notable. In the orthorhombic phase below 110 K, Fe2+ and V3+ spins form a collinear ferrimagnetic order along the a-axis. Below 65 K in the LT tetragonal phase, however, both spins incline from the c-axis to form a canted
5
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Spin order in FeV2O4 determined by single crystal Mössbauer spectroscopy in applied magnetic field ⁎
Shin Nakamuraa,b, , Yasuhiro Kobayashic, Shinji Kitaoc, Makoto Setoc a b c
Teikyo University, Department of Science and Engineering, Utsunomiya, Tochigi 320-8551, Japan Waseda University, Advanced Research Center of Science and Engineering, Shinjuku, Tokyo 169-8555, Japan Kyoto University, Research Reactor Institute, Kumatori, Osaka 590-0494, Japan
A R T I C L E I N F O
A BS T RAC T
Keywords: FeV2O4 57 Fe Mössbauer spectroscopy Orbital order Spin order Canted ferrimagnet
In order to clarify the spin order of FeV2O4, 57Fe Mössbauer spectroscopy has been conducted by using a single crystal specimen. A measurement in applied magnetic field has been also conducted. By applying a slight compression in the sample plane, almost single domain state was achieved in the low temperature phases. The spectra consist of Fe2+ spectra (~ 85%) and Fe2.5+ spectra (~ 15%), corresponding to the A- and B-site Fe ions, respectively. The B-site spectrum well represents the local structure and the magnetic structure of V3+ ion on the B-site. Notable changes in the Mössbauer parameters are recognized at 140, 110, and 65 K, where the successive phase transitions take place. The feature well represents the orbital and spin order. In the orthorhombic phase below 110 K, Fe2+ and V3+ spins form a collinear ferrimagnetic order along the a-axis. Below 65 K in the low temperature tetragonal phase, however, both spins incline from the c-axis to form a canted ferrimagnetic structure. The canting angles are about 17° and 52° at 4.2 K for Fe2+ and V3+ spins, respectively.
1. Introduction Iron vanadium spinel FeV2O4 is an interesting material where both Fe2+ and V3+ ions have spin and orbital degrees of freedom. The roomtemperature structure is cubic (space group Fd3m). The A-site (tetrahedral site, 8a) is occupied by the Fe2+ ion having a high-spin 3d6 configuration, where three electrons are in the doubly degenerate ground-state dγ orbital. On the other hand, the B-site (octahedral site, 16d) is occupied by the V3+ ion (3d2 configuration), where there are two electrons in the triply degenerate ground-state dε orbital. With decreasing temperature, successive phase transitions occur [1,2]. At 140 K, the cubic-to-tetragonal transition takes place. The tetragonal phase (I41/amd) has the lattice constants c/ 2 a < 1 (HT tetragonal). Then, at 110 K, a transition to the orthorhombic phase (Fddd) occurs (a > c > b). Finally, at 65 K, another tetragonal phase (I41/amd) appears again with the lattice constants c/ 2 a > 1 (LT tetragonal). Recent thermal conductivity measurement clearly shows that the orbital order takes place at 65 K [3]. Magnetically, a ferrimagnetic order develops below Tc = 110 K. The magnetic easy axis is always the longest axis, the a-axis in the orthorhombic phase or the c-axis in the LT tetragonal phase. Below 65 K, a canted ferrimagnetic order occurs, where Fe2+ spins remain aligning along the longest c-axis but V3+ spins incline toward the cubic < 111 > axis. The magnetic moments of Fe2+
⁎
and V3+ are estimated to be 4.0 and 0.85 μB, respectively, by the neutron powder diffraction [4]. The saturation magnetic moment is about 3 μB/f.u. at 20 K [5]. Thus, the lattice is strongly coupled with the electron configurations, the spin order, and the orbital order. That is, the three transitions at 140, 110, and 65 K are caused by the Jahn– Teller effect of the Fe2+ ion, the spin order, and the orbital order, respectively. Mössbauer studies of this compound were also conducted using powder specimens in the early stage of the investigation [6–10]. The orbital and spin order, however, have not been discussed in detail, presumably because of a lack of the information on the successive phase transition at low temperature. One of the present authors (S.N.) has found a distinct evidence of the orbital order by 57Fe Mössbauer spectroscopy using a powder specimen [11]. That is, the sign of the quadrupole coupling constant e2qQ/2 changes abruptly from negative to positive at 65 K. The change in the orbital state accompanies a sudden decrease in the hyperfine field Hhf. In the ferrimagnetic state below 110 K, the Fe2+ spins align along the orthorhombic a-axis, but seem to incline slightly from the tetragonal c-axis below 65 K. In the present research, in order to clarify the spin order of FeV2O4, we have conducted 57Fe Mössbauer spectroscopy using a single crystal specimen. A measurement in applied magnetic field has been also conducted. The spectra consist of major Fe2+ spectra corresponding to
Corresponding author at: Teikyo University, Department of Science and Engineering, Utsunomiya, Tochigi 320-8551, Japan. E-mail address: [email protected] (S. Nakamura).
http://dx.doi.org/10.1016/j.physb.2017.09.123 Received 29 June 2017; Received in revised form 19 September 2017; Accepted 27 September 2017 0921-4526/ © 2017 Elsevier B.V. All rights reserved.
Please cite this article as: Nakamura, S., Physica B (2017), http://dx.doi.org/10.1016/j.physb.2017.09.123
Physica B xxx (xxxx) xxx–xxx
S. Nakamura et al.
Fig. 1. Schematic view of the experimental setup of the specimen.
the A-site Fe ion and minor Fe2.5+ spectra originating from Fe ion substituted on the B-site. The latter well represents the local structure and the magnetic structure of V3+ ion on the B-site. We have successfully obtained not only spin order of Fe2+ ion on the A-site but also that of V3+ ion on the B-site. 2. Experiments A single crystal of FeV2O4 was prepared by a floating zone (FZ) method in a controlled oxygen atmosphere using a CO2 – H2 mixed gas (CO2/H2 = 0.7 at room temperature). As-grown specimen was heattreated at 1473 K in the same oxygen atmosphere for a week. A (001) plane disk specimen with approximately 5 mm diameter and 40 µm thick was fixed on the acryl plate with the edge surrounded by the epoxy resin. Thus [100] and [010] axes in the plane undergo slight compression during cooling to achieve a single domain state in the low temperature phases [12]. The schematic view of the experimental setup of the specimen is shown in Fig. 1. Mössbauer spectroscopy was conducted in conventional transmission geometry by using 57Co-in-Rh (25 and 50 mCi) as γ-ray source. The Doppler velocity scale was calibrated using an Fe metal foil at room temperature. The incident γ-ray was parallel to the [001] axis, which is supposed to be the longest axes in the low temperature phases (the a-axis in the orthorhombic phase and the c-axis in the LT tetragonal phase). The measurements were conducted in the temperature range from 4.2 to 291 K using a closed-cycle refrigerator, a liquid nitrogen cryostat, and a liquid helium cryostat. At 4.2 K, a measurement in applied magnetic field was also conducted. The magnetic field of 2 T was applied parallel to the [001] axis. For the magnetically ordered spectra, the major Fe2+ spectra were analyzed exactly using a mixture of magnetic and quadrupole Hamiltonians, while the minor Fe2.5+ spectra were analyzed by a perturbation method. Lorentzian line shapes were assumed for the analysis of the spectra.
Fig. 2. Paramagnetic spectra of the single crystal FeV2O4 at (a) 291, (b) 200, and (c) 130 K. A-site (red curve) and B-site (blue curve) denote A-site Fe2+ and B-site Fe2.5+, respectively.
cide well with the calculated values by a point charge model, 0.18 mm/ s in both the cubic and HT tetragonal region. The z-axis in the cubic phase is < 111 > axis since the B-site has site symmetry of 3m, and presumably almost the same local structure is retained in the HT tetragonal phase. Thus, the intensity ratio I1/I2 is always assumed to be 1 in the analysis. In Fig. 3, the magnetically ordered spectra at several temperatures are shown. The spectra consist of three subspectra corresponding to two types of A-site Fe2+ and a B-site Fe2.5+, denoted as A-0° (red curve), A-90° (green curve), and B (blue curve) in the figure, respectively. The intended single domain state, the longest crystallographic axis perpendicular to the sample plain, is attained 80– 85% for the A-site spectra (0°-domain, A-0°), whereas the rest is a domain with the longest axis in the plain (90°-domain, A-90°). For the B-site spectra, we assume only 0°-domain. The B-site spectrum is not clearly seen in the temperature range 100–110 K, because its hyperfine field is small and the spectrum overlaps with the A-site spectrum. The obtained Mössbauer parameters, isomer shifts (IS), quadrupole coupling constants (e2qQ/2), quadrupole shifts (εq), asymmetric parameters (η), hyperfine fields (Hhf), Euler angles between the z-axis and the direction of the hyperfine field (θ, φ), and line widths (W), are indicated in Table 1 for the temperatures corresponding to Figs. 2 and 3. The quadrupole shift is defined as εq = (Δ56 − Δ12)/4, where Δij represents the splitting between the ith and jth lines. For the A-site spectrum in the LT tetragonal phase, where η = 0 owing to the site symmetry of 4 m2, φ cannot be determined. The temperature dependences of some parameters for the A- and B-site spectra are shown in Figs. 4 and 5, respectively. It is clearly seen in Fig. 4(b) and (c) that the e2qQ/2 and Hhf change according to the structural and magnetic transition. Especially, the changes of the A-site parameters at the
3. Results and discussion The paramagnetic spectra at several temperatures are shown in Fig. 2. The spectra are composed of major Fe2+ spectra (about 85%) and minor Fe2.5+ spectra (about 15%). The major Fe2+ spectra correspond to the Fe2+ ion on the A-site (A-site spectra). At room temperature, the A-site spectrum is a singlet, reflecting the cubic symmetry (site symmetry 4 3m). With decreasing temperature, however, the singlet spectrum becomes broadened, and below 250 K, it splits into a doublet even in the cubic region. This is due to the local and dynamical Jahn–Teller effect. In the LT tetragonal region, the quadrupole splitting (QS) abruptly becomes large. At 130 K, The intensity ratio of the 1st to 2nd lines, I1/I2, is approximately 0.62. This indicates that the principal axis of the electric field gradient (EFG), z-axis (shortest crystallographic c-axis in the HT tetragonal phase) is almost in the sample plain. On the other hand, the minor Fe2.5+ spectra originate from a small amount of Fe ion on the B-site, approximately 8% substituted for V3+ (B-site spectra). The B-site spectra are always doublet with almost constant QS (0.11–0.21 mm/s). The values coin2
Physica B xxx (xxxx) xxx–xxx
S. Nakamura et al.
Fig. 3. Magnetically ordered spectra of the single crystal FeV2O4 at (a) 100, (b) 50, and (c) 18 K. A-0° (red curve), A-90° (green curve), and B (blue curve) denote A-site Fe2+ in 0°-domain, A-site Fe2+ in 90°-domain, and B-site Fe2.5+, respectively.
Fig. 4. Temperature dependences of (a) isomer shift IS, (b) quadrupole coupling constant e2qQ/2, (c) hyperfine field Hhf, and (d) canting angle θm of the Fe2+ spin from the longest axes for the A-site Fe2+ ion in FeV2O4.
orbital order (65 K) are notable. These features are well consistent with that observed for the powder specimen [11]. Here we discuss the spin order in the orthorhombic and LT tetragonal phases. Since the direction of Hhf is parallel to that of the spin (antiparallel to the magnetic moment), the spin order can be estimated by referring θ and φ for the A-site Fe2+. The spin direction in the 90°-domain seems to incline slightly toward the perpendicular direction, presumably because of the magnetic dipole field of the 0°domain spins. Hereafter, we only refer to the spin order in the 0°domain. In the orthorhombic phase, the EFG z-, y-, and x-axes coincide with the crystallographic b-, a-, and c-axes, respectively [11]. Thus, (θ,
φ) = (90°, 90°) is the direction of the a-axis (the longest axis). In the LT tetragonal phase, the z-axis coincides with the crystallographic c-axis. Therefore θ = 0° is the direction of the c-axis (the longest axis). In Fig. 4(d), the angle between the direction of Hhf and the longest crystallographic axis, θm, is plotted. The spins align along the a-axis in the orthorhombic phase, but with decreasing temperature they begin to incline, and finally reach θm = 17° at 4.2 K in the LT tetragonal phase. Note that the estimated angles in the orthorhombic phase may not be so precise, since the B-site spectra cannot be fitted well in this
Table 1 Isomer shifts (IS), quadrupole coupling constants (e2qQ/2), quadrupole shifts (εq), asymmetric parameters (η), hyperfine fields (Hhf), Euler angles between the z-axis and the direction of the hyperfine field (θ, φ), and line widths (W) of the A-site and B-site Fe in FeV2O4 at several temperatures (corresponding to the spectra in Figs. 2 and 3). A-0° and A-90° denote A-site 0°-domain and 90°-domain, respectively. The quadrupole shift is defined as εq = (Δ56 − Δ12)/4, where Δij represents the splitting between the ith and jth lines. T (K)
site
IS (mm/s)
e2qQ/2, εq (mm/s)
η
Hhf (T)
θ (°)
φ (°)
W (mm/s)
Ratio (%)
291
A B A B A B A-0° A-90° A-0° A-90° B A-0° A-90° B
0.909(10) 0.452(10) 0.987(10) 0.497(10) 1.025(10) 0.518(20) 1.014(20) 1.014(20) 1.054(20) 1.054(20) 0.507(20) 1.027(20) 1.027(20) 0.512(20)
0 0.113(10) −0.248(10) 0.145(10) −1.892(10) 0.195(10) −2.256(20) −2.256(20) 3.062(20) 3.062(20) −0.023(20) 3.087(20) 3.087(20) −0.044
0 0 0 0 0 – 0.48 0.48 0 0 – 0 0 –
0 0 0 0 0 0 10.68(10) 10.68(10) 8.39(10) 8.39(10) 41.15(10) 8.25(10) 8.25(10) 45.84(10)
– – – – – – 90(2) 108(2) 11(1) 35(1) – 15(1) 33(1) –
– – – – – – 90(2) 90(2) – – – – – –
0.376(10) 0.287(10) 0.369(10) 0.261(10) 0.365(10) 0.256(10) 0.482(20) 0.521(20) 0.371(20) 0.372(20) 0.731(20) 0.379(20) 0.379(20) 0.484(20)
86(1) 14(1) 87(1) 13(1) 86(1) 14(1) 84(1) 16(1) 70(1) 16(1) 14(1) 68(1) 16(1) 16(1)
200 130 100 50
18
3
Physica B xxx (xxxx) xxx–xxx
S. Nakamura et al.
Fig. 6. Mössbauer spectra of the single crystal FeV2O4 at 4.2 K (a) without and (b) with applied magnetic field of 2 T along the c-axis. A-0° (red curve), A-90° (green curve), and B (blue curve) denote A-site Fe2+ in 0°-domain, A-site Fe2+ in 90°-domain, and B-site Fe2.5+, respectively.
Here θm again represent the angle between the direction of spins and the longest crystallographic axis. Eq. (2) yields that θm is 0 in the orthorhombic phase, while it is about 47° in the LT tetragonal phase. This means that the V3+ spins align along the a-axis in the orthorhombic phase, but incline approximately toward the cubic < 111 > direction in the LT tetragonal phase. The spin order can be evaluated more precisely by a measurement in an applied magnetic field. The spectra at 4.2 K without and with applied magnetic field of 2 T along the c-axis are shown in Fig. 6(a) and (b), respectively. And the obtained parameters are indicated in Table 2. The observed field (Hobs) is a vector sum of the hyperfine field (Hhf) and the applied external magnetic field (Hex),
Fig. 5. Temperature dependences of (a) isomer shift IS, (b) hyperfine field Hhf, (c) quadrupole shift εq, and (d) intensity ratio of 2nd–5th lines to 1st–6th lines I25/I16 for the B-site Fe2.5+ ion in FeV2O4.
temperature range. On the other hand, the spin order of V3+ ion on the B-site is supposed to be well represented by that of Fe2.5+ ion on the Bsite [13–15]. Since the B-site spectra are analyzed by the perturbation method that does not give θ and φ, but we can roughly estimate the direction of the spins from Fig. 5(c) and (d). In Fig. 5(c), it is seen that εq changes its sign from positive to negative around 65 K. When η is small, the quadrupole shift is approximated as 2
εq ≈
Hobs = Hhf + Hex .
The difference ΔH = Hobs − Hhf is −1.83 and +1.24 T for the A- and Bsite spectra, respectively. This means that the spins of the A- and B-site ion form up- and down-moments, respectively, but clearly they both cant from the c-axis. According to Eq. (3), we can evaluate Hhf of the Asite in applied magnetic field. The result is Hhf = 8.80 T and θ = θm = 17°, which is well consistent with the value without magnetic field (see Table 2). On the other hand, for the B-site spectra, the values of Hobs and Hhf can deduce the canting angle as θm = 52° from the c-axis. This means that the V3+ spins are almost in the cubic < 111 > direction. In summary, Fe2+ and V3+ spins form a collinear ferrimagnetic order along the a-axis in the orthorhombic phase, whereas both of them incline from the c-axis to form a canted ferrimagnetic structure in the LT tetragonal phase. The feature is schematically shown in Fig. 7. In this experiment, the canting direction of Fe2+ spins cannot be determined because η = 0, but the direction toward the cubic < 111 > axes is probable. Using the vales of magnetic moments of Fe2+ and V3+ obtained by the neutron powder diffraction (4.0 and 0.85 μB, respectively) [4], the net magnetic moments are calculated as 2.30 and 2.78 μB/f.u. for the orthorhombic and LT tetragonal phases, respectively. The estimated values seem to be consistent with the experimental magnetization values.
2
e qQ 3cos θ − 1 ⋅ . 2 4
(1) 2
According to the point charge calculation, the values of e qQ/2 are 0.20 and 0.24 mm/s for the orthorhombic and LT tetragonal phases, respectively. That is, the local structures of the B-site remain almost unchanged from that of the cubic phase. Therefore the change in the sign of εq implies the change in θ. The angular factor in Eq. (1) becomes 0 when θ = 54.7°. Assuming that the z-axis is still in the vicinity of the cubic < 111 > axis, we can deduce that the spins aligning in the adirection (θ = 54.7°) in the orthorhombic phase begin to incline toward the rest of the three < 111 > directions (θ = 70.5°) in the LT tetragonal phase. This feature can be also explained by the intensity ratio of 2nd– 5th lines to 1st–6th lines, I25/I16, shown in Fig. 5(d). The value of I25/ I16 is almost 0 in the orthorhombic phase, while it is about 0.5 in the LT tetragonal phase. In this experiment, since the direction of the incident γ-ray is supposed to be parallel to the longest axes (the a- and c-axes for the orthorhombic and LT tetragonal phases, respectively), the intensity ratio is approximately given by
I25 4sin2θm ≈ . I16 3 + 3cos2θm
(3)
(2) 4
Physica B xxx (xxxx) xxx–xxx
S. Nakamura et al.
Table 2 Isomer shifts (IS), quadrupole coupling constants (e2qQ/2), quadrupole shifts (εq), asymmetric parameters (η), hyperfine fields (Hhf), observed fields (Hobs), Euler angles between the zaxis and the direction of the hyperfine field or observed field (θ), and line widths (W) of the A-site and B-site Fe in FeV2O4 at 4.2 K with and without applied magnetic field (Hex). Hex (T)
Site
IS (mm/s)
e2qQ/2, εq (mm/s)
η
Hhf, Hobs (T)
θ (°)
W (mm/s)
Ratio (%)
0
A-0° A-90° B A-0° A-90° B
1.059(20) 1.059(20) 0.515(20) 1.056(20) 1.056(20) 0.554(20)
3.139(20) 3.139(20) −0.08(20) 3.143(20) 3.143(20) −0.053
0 0 – 0 0 –
8.74(10) 8.74(10) 46.52(10) 6.91(10) 6.91(10) 47.76(10)
17(1) 35(1) – 22(1) 49(1) –
0.404(20) 0.443(20) 0.443(20) 0.433(20) 0.394(20) 0.491(20)
72(1) 13(1) 15(1) 76(1) 10(1) 15(1)
2
ferrimagnetic structure. The canting angles are about 17° and 52° at 4.2 K for Fe2+ and V3+ spins, respectively. The estimated canting angle of V3+ spins seems to be close to that reported by the powder neutron diffraction study. The canting of Fe2+ spins is our new finding, which has been also suggested by our powder Mössbauer measurement. Acknowledgement This work has been carried out in part under the Visiting Researchers Program of the Kyoto University Research Reactor Institute. References [1] T. Katsufuji, T. Suzuki, H. Takei, M. Shingu, K. Kato, K. Osaka, M. Takata, H. Sagayama, T. Arima, J. Phys. Soc. Jpn. 77 (2008) 053708. [2] Y. Nii, H. Sagayama, T. Arima, S. Aoyagi, R. Sakai, S. Maki, E. Nishibori, H. Sawa, K. Sugimoto, H. Ohsumi, M. Takata, Phys. Rev. B 86 (2012) 125142. [3] Y. Ishitsuka, T. Ishikawa, R. Koborinai, T. Omura, T. Katsufuji, Phys. Rev. B 90 (2014) 224411. [4] G.J. MacDougall, V.O. Garlea, A.A. Aczel, H.D. Zhou, S.E. Nagler, Phys. Rev. B 86 (2012) 060414. [5] H. Takei, T. Suzuki, T. Katsufuji, Appl. Phys. Lett. 91 (2007) 072506. [6] M. Tanaka, T. Tokoro, Y. Aiyama, J. Phys. Soc. Jpn. 21 (1966) 262. [7] F. Hartmann-Boutron, P. Imbert, J. Appl. Phys. 39 (1968) 775. [8] M. Abe, M. Kawachi, S. Nomura, J. Solid State Chem. 10 (1974) 351. [9] M.P. Gupta, H.B. Mathurt, J. Phys. C: Solid State Phys. 8 (1975) 370. [10] C.D. Spencer, P.A. Smith, R.P. Stillwell, J. Phys. Chem. Solids 39 (1978) 103. [11] S. Nakamura, A. Fuwa, J. Phys. Soc. Jpn. 85 (2016) 014702. [12] S. Nakamura, A. Fuwa, Phys. Procedia 75 (2015) 747. [13] I. Kagomiya, S. Nakamura, S. Matsumoto, M. Tanaka, K. Kohn, J. Phys. Soc. Jpn. 74 (2005) 450. [14] S. Nakamura, M. Sato, S. Morimoto, S. Nasu, Y. Tsunoda, Hyperfine Interact. 169 (2006) 1235. [15] Shin Nakamura, Akio Fuwa, Yorihiko Tsunoda, Hyperfine Interact. 208 (2012) 29.
Fig. 7. Spin order of FeV2O4 in (a) the orthorhombic and (b) the LT tetragonal phases.
4. Conclusion We have conducted 57Fe Mössbauer spectroscopy of the single crystal of FeV2O4 in order to clarify the spin order. A measurement in applied magnetic field has been also conducted. By applying a slight compression in the sample plane, almost single domain state was achieved in the low temperature phases. The spectra consist of major Fe2+ spectra corresponding to the A-site Fe ion and minor Fe2.5+ spectra originating from Fe ion substituted on the B-site. The B-site spectrum well represents the local structure and the magnetic structure of V3+ ion on the B-site. The Mössbauer parameters change according to the structural and magnetic transition. Especially, the changes of the A-site parameters at the orbital order (65 K) are notable. In the orthorhombic phase below 110 K, Fe2+ and V3+ spins form a collinear ferrimagnetic order along the a-axis. Below 65 K in the LT tetragonal phase, however, both spins incline from the c-axis to form a canted
5