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Magnetocaloric effect in Tb(Co0.94Fe0.06)2 alloy with negligible thermal hysteresis and wide working temperature range
Journal Pre-proofs Magnetocaloric effect in Tb(Co0.94Fe0.06)2 alloy with negligible thermal hysteresis and wide working temperature range Adil Murtaza, Jingwen Mi, Yebei Li, Chunxi Hao, Muhammad Yaseen, Awais Ghani, Azhar Saeed, Wenliang Zuo, Yin Zhang, Chao Zhou, Sen Yang, Xiaoping Song PII: DOI: Reference:
S0304-8853(19)33061-6 https://doi.org/10.1016/j.jmmm.2020.166521 MAGMA 166521
To appear in:
Journal of Magnetism and Magnetic Materials
Received Date: Revised Date: Accepted Date:
1 September 2019 23 December 2019 27 January 2020
Please cite this article as: A. Murtaza, J. Mi, Y. Li, C. Hao, M. Yaseen, A. Ghani, A. Saeed, W. Zuo, Y. Zhang, C. Zhou, S. Yang, X. Song, Magnetocaloric effect in Tb(Co0.94Fe0.06)2 alloy with negligible thermal hysteresis and wide working temperature range, Journal of Magnetism and Magnetic Materials (2020), doi: https://doi.org/10.1016/ j.jmmm.2020.166521
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1 1 2
Magnetocaloric effect in Tb(Co0.94Fe0.06)2 alloy with negligible thermal hysteresis and wide working temperature range
3 4 5 6 7 8 9 10 11
Adil Murtazaa, Jingwen Mia, Yebei Lia, Chunxi Haoa, Muhammad Yaseenb, Awais Ghania, Azhar Saeeda, Wenliang Zuoa, Yin Zhanga, Chao Zhoua, Sen Yang a,* and Xiaoping Songa
12
Abstract
13
In the present work, the magnetocaloric effect (MCE) and magnetic properties of
14
Tb(Co0.94Fe0.06)2 alloy were studied. X-ray diffraction pattern taken at room temperature
15
confirms that the sample crystallizes in single phase with rhombohedral structure. The
16
paramagnetic to ferromagnetic phase transition was observed at 304 K near the room
17
temperature. Banerjee criterion and universal scaling of the MCE was employed to confirm
18
the second-order nature of the magnetic transition. Differential scanning calorimetry and
19
magnetic characterizations have shown the absence of thermal and magnetic hysteresis in the
20
paramagnetic-ferromagnetic
21
Tb(Co0.94Fe0.06)2 associated with the ferromagnetic transition has been observed over a wide
22
working temperature range (93K) leading to large refrigerant capacity. The maximum value
23
of magnetic entropy change (-ΔSM) under 5T magnetic field is 4.3 J/kgK and the
24
corresponding value of refrigerant capacity is 368.7 J/kg. Interestingly, the magnetocaloric
25
performance of Tb(Co0.94Fe0.06)2 alloy is comparable with some rare-earth-based
26
magnetocaloric materials. These remarkable features make this alloy a suitable candidate for
27
magnetic refrigeration at room temperature.
a
School of Science, MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, China bDepartment of Physics, University of Agriculture, Faisalabad 38040, Pakistan
transition
region.
The
magnetic
entropy
change
for
28 29 30
Keywords: Magnetocaloric effect; Thermal hysteresis; Magnetic properties; Second-order
31
phase transition; Refrigerant capacity; Universal Scaling
32 33 34
____________________________
35
* Electronic email: [email protected]
36 1
2 1
1. Introduction
2
The magnetocaloric effect (MCE) being a magneto-thermodynamic phenomenon has
3
drawn a constant interest for its potential applications in refrigeration technology due to its
4
high thermodynamic efficiency, ecological concerns and a large probability of applications in
5
a wide temperature span [1-4]. The magnetic materials exhibiting large magnetic entropy
6
change over wide working temperature with narrow thermal hysteresis are promising
7
candidates [5,6]. For this propose, MCE has been studied in different types of materials e.g.,
8
rare-earth (RE) containing and RE-free crystalline materials, Gd-based compounds, Heusler
9
alloys, MnAs-based alloys, multiphase materials and composites and nanostructured
10
materials [7]. Of course, different materials have shown different magnetocaloric
11
performance i.e., working temperature range, magnetic entropy change, and refrigerant
12
capacity and so on; the detailed information can be obtained in reference 7. Among those, a
13
large MCE can be expected in RECo2 Laves phase compounds owing to the fact that the RE-
14
Co sublattices moments couples antiferromagnetically and the observed RE magnetic
15
moments are close to their free ionic values [8]. The RECo2 with the first-order magnetic
16
transition (FOMT) e.g., DyCo2, HoCo2, ErCo2 are of particular importance for MCE owing to
17
their large magnetic entropy change (∆SM) around their phase transition temperature (TC) [9].
18
However, they possess narrow working temperature ranges and exhibit thermal hysteresis
19
with change in magnetization with temperature and magnetic field; which causes an obvious
20
decrease of the refrigerant capacity (RC); an essential parameter to evaluate the MCE [10].
21
To overcome these problems, materials undergoing a second-order magnetic transition
22
(SOMT) for example TbCo2, PrCo2, and NdCo2 may be used [11]. Although these materials
23
generally show smaller ∆SM than giant MCE materials, however, they possess narrow
24
thermal hysteresis yielding high RC. Besides, their -∆SM can be extended through a wide
25
temperature range [12]. On the basis of the lack of thermal hysteresis and the possibility of
2
3 1
high RC, materials with SOMT can be used as an alternative for designing magnetic
2
refrigerator prototypes. The low magnetic phase transition temperature (TC) of those materials
3
may limit their room temperature (RT) applications [13]. Earlier studies indicate that the
4
magnetic phase transition temperature (TC) of the RECo2 family can be tuned even up to RT
5
by substitution of a sufficient amount of 3d-elements (Fe) for Co [14, 15]. In the present work,
6
we selected the TbCo2 compound, which shows the paramagnetic (PM) to ferromagnetic (FM)
7
phase transition of second-order at TC≈234K; well below the RT [16]. By substituting a small
8
amount of Fe (6%) for Co in the TbCo2 compound, we obtained an interesting composition of
9
Tb(Co0.94Fe0.06)2 which shows the phase transition temperature at ≈304 K without any change
10
in SOMT character. Contrary to the earlier studies, those carried out magnetocaloric
11
measurements under single thermal process (cooling or heating) and were unable to find the
12
size of thermal hysteresis, in the present work; we studied the magnetocaloric performance
13
under both heating and cooling process in order to reveal the effect of thermal hysteresis on
14
the RC. The wide operating temperature range, small thermal hysteresis, and large RC value
15
were simultaneously realized in this alloy, which makes Tb(Co0.94Fe0.06)2 alloy a promising
16
candidate for magnetic refrigeration applications. Interestingly, the magnetocaloric
17
performance of Tb(Co0.94Fe0.06)2 alloy is comparable with commonly used some RE-based
18
(RE=Tb, Gd, Er, Ho, Nd) magnetocaloric materials. Our results may open new opportunities
19
to search novel functional materials for magnetic refrigeration.
20 21
2. Experimental details
22
The ingot of Tb(Co0.94Fe0.06)2 alloy was melted in an electric arc-melting furnace in a
23
pure argon atmosphere. The sample was melted five times to ensure better homogeneity and
24
then annealed in a vacuum-sealed quartz tube at 850 K for 24 hours. Crystal structural
25
analysis was carried out by X-ray diffraction (XRD) using Rigaku D-MAX 2500 V
3
4 1
diffractometer with Cu Kα radiation in an angular range of 20o≤2θ≤80o with a 0.05o step size.
2
A high precision step scanning XRD with step size of 0.001° was also employed to observe
3
the splitting of (222) and (440) reflections. The XRD data was analyzed by using Materials
4
Data Inc. Software Jade 6.0. Phase homogeneity and elemental composition of
5
Tb(Co0.94Fe0.06)2 alloy was checked by using scanning electron microscopy (SEM) and
6
energy dispersive X-ray (EDX) spectroscopy, respectively. The phase transition temperature
7
(TC) was determined from the temperature dependences of magnetization (M-T) and AC
8
susceptibility (χ). To check the thermal hysteresis, M-T curves were measured in cooling and
9
heating modes under applying magnetic field of 0.05 T. Phase transition behavior of the
10
sample was characterized by differential scanning calorimeter (DSC, Q2000 from TA
11
Instruments) at a cooling/heating rate of 5 K/min. Field-dependent magnetization (M-H)
12
curves at different temperatures between 280-320 K under magnetic field of 6T were
13
measured by using Quantum design SQUID. The magnetic entropy change (∆S) was
14
calculated from M-H isotherms by using the Maxwell equation.
15 16
3. Results and Discussion
17
In order to reveal the crystal structure and phase analysis, room-temperature XRD of
18
Tb(Co0.94Fe0.06)2 alloy was carried out as shown in Fig.1(a). According to analysis, several
19
well-defined reflections appearing at 2θ= 20.91°, 34.44°, 40.64°, 42.44°, 56.11°, 61.34°,
20
65.47°, and 72.24° can be assigned to (111), (220), (311), (222), (331), (422), (511) and
21
(440), respectively. The peaks position and relative intensity of all Bragg diffraction
22
reflections correspond to those expected for the MgCu2-type Laves phase structure. No extra
23
peaks corresponding to either impurities or secondary phases were observed in the
24
diffraction pattern indicates that the homogenized alloy contains mainly Tb(Co, Fe) single-
25
phase having the 1:2 stoichiometry. The sharp diffraction peaks illustrate a good crystallinity
4
5 1
of this alloy. Based on the knowledge that ferromagnetic transition involves structural
2
change, the paramagnetic cubic Laves phase will be distorted into a rhombohedral (R) or
3
tetragonal (T) phase having an easy magnetization direction (EMD) lies along the [111] or
4
[100] respectively [17]. As is known, the in Laves phase MgCu2-type compounds EMD can
5
be inferred from the profile of (222) and (440) reflections in the XRD pattern [18]. Therefore,
6
in order to determine the EMD of Tb(Co0.94Fe0.06)2 alloy, the (222) and (440) reflections
7
were step scanned in the angular range of 41°-43° and 72°-74° respectively with a step size
8
of 0.001°. It is evident that the characteristic reflections of (222) and (440) split into two
9
peaks as shown in the insets of Fig. 1(a). These results are in agreement with the synchrotron
10
XRD and neutron powder diffraction (NPD) data shown in previous studies revealing that
11
the characteristic reflections of (222), (440) split into two peaks but (800) reflections have no
12
splitting [19]. These features show that Tb(Co0.94Fe0.06)2 alloy has a lower cubic symmetry
13
and exhibits characteristics of a rhombohedral (R) phase with EMD along [111]. Such a
14
crystal lattice belongs to the space group R-3m with Tb atoms on the 2c sites, Co/Fe atoms
15
on the 1b and 3e sites [20]. The calculated lattice parameters are αR=89.95o and aR=0.738 nm.
16
The SEM image as shown in Fig. 1(b), illustrates the dark grey phase corresponding to
17
the main Tb(Co, Fe) single phase. The elemental compositions were checked by EDX
18
analysis of the marked area in the SEM image. The observed EDX results show the presence
19
of several well-defined peaks related to Tb, Co, and Fe, which reveal that the prepared
20
sample is composed of Tb, Co, and Fe only. Further, it is observed that no other peak related
21
to impurities is present in the EDX spectra, which confirms the formation and purity of
22
Tb(Co0.94Fe0.06)2 alloy.
5
6
1 2 3 4 5 6 7
Fig. 1 (a) X-ray diffraction pattern of Tb(Co0.94Fe0.06)2 with rhombohedral structure. The splitting in (222) and (440) peaks are shown in the insets. The bold blue line is experimental data, while thin red and green lines are fitted one. (b) Scanning electron microscopy (SEM) and energy-dispersive X-ray (EDX) analysis of the marked area in SEM image.
8
heating and cooling processes under an applied field of 0.05 T are shown in Fig. 2(a). It can
The temperature versus magnetization (M-T) curves measured from 90 K to 400 K in the
6
7 1
be seen that this Tb(Co0.94Fe0.06)2 alloy undergoes magnetic transition during cooling and
2
heating modes. Both curves converge with each other in the phase transition region,
3
indicating an absence of thermal hysteresis due to the SOMT. The derivative of M-T curve
4
(inset of Fig. 2(a)) indicates that paramagnetic (PM) to ferromagnetic (FM) transition occurs
5
at TC≈304 K; which is higher than 230 K (for TbCo2) and thus make Tb(Co0.94Fe0.06)2 alloy
6
suitable candidate for RT magnetic refrigeration. As is known in RECo2 compounds, the TC is
7
determined by 3d-3d exchange interactions between the Co-Co sublattice magnetic moments
8
and the 3d-4f hybridization between Co-RE inter-sublattice moments [21]. The 3d-3d
9
interactions are direct and stronger. The 3d-4f hybridization indirect and of intermediate
10
strength depending on the nature of the 3d sublattice moments. The nature of 3d sublattice
11
magnetic moments of REFe2 and RECo2 is also very different. The magnetic moments of Fe
12
are intrinsic moments (localized 3d), while the magnetic moments of Co ion are induced
13
moments (itinerant 3d) by the RE-Co interaction. With the substitution of Fe for Co, the
14
itinerant character of Co-3d moments is replaced by a more localized character of Fe-3d
15
moments. This localization leads to an increase in 4f-3d hybridization. According to Brooks
16
et al. [22], the 3d–3d interactions depend critically on the 4f–3d hybridization. Therefore, the
17
increase in 4f-3d hybridization would strengthen the 3d–3d exchange interactions [23]. Thus,
18
with the partial replacement of Fe by Co in TbCo2, the 3d exchange interactions increase,
19
which results in the increase of TC. Similar results have been observed in Ho(Co1-xFex)2 [24],
20
and Dy(Co1-xFex)2 [25]. The nature of the magnetic transition was confirmed by DSC
21
measurements as shown in Fig. 2(b). DSC curves during the cooling and heating process
22
show exothermic and endothermic peaks respectively at T≈303 K; which is very close to its
23
TC. Negligible thermal hysteresis between the cooling and heating in DSC measurements as
24
strong evidence of SOMT, consistent with the negligible hysteresis in M-T curves. The
25
inverse magnetic susceptibility (𝜒 ―1) measured under an applied field of 0.02 T in the
7
8 1
temperature range of 300-400 K obeys Curie-Weiss law 𝜒 ―1 = (𝑇 + 𝜃𝑃) 𝐶 as shown on the
2
right-hand scale in Fig. 2(a). Here, θp is the paramagnetic Curie temperature and C is the
3
Curie constant related to the effective magnetic moment (μeff) of Tb ions in the paramagnetic
4
state [26]. The linear fitting of susceptibility curve yields θp ≈302 K and the μeff ≈9.4 μB/f.u;
5
close to the free Tb ion (gJ=9.72 μB) [27]. The positive value of θp and the nature of inverse
6
susceptibility in the magnetically ordered state indicate the presence of dominant
7
ferromagnetic interactions in this alloy. The substitution of a small amount of Fe by Co leads
8
to an increase in TC and broadens the magnetic transition in Tb(Co0.94Fe0.06)2, as compared to
9
TbCo2.
10
11 12 13 14 15 16 17
Fig. 2 (a) Temperature-dependent magnetization (M-T) curves measured in cooling and heating modes under a magnetic field of 0.05 T. Inset: the derivative of the M-T curve. Curie-Weiss fit to the paramagnetic susceptibility (right-hand scale). (b) DSC curves in the heating and cooling cycles of at the rate of 5 K/min.
8
9 1
In order to analyze the effect of thermal hysteresis on the MCE and well calculate the
2
RC, the isothermal M-H curves were measured under the field of 6 T at different
3
temperatures below and above TC under field decreasing and increasing modes (Fig.3 (a)).
4
Before starting the measurement, initially, the sample was cooled down to the desired
5
temperature in zero applied field, and the M–H curves were measured by increasing magnetic
6
field from 0 T to a predetermined maximum 6 T and then decreasing magnetic field from 6 T
7
back to 0 T. After one isothermal curve was measured, the temperature was increased slowly
8
with step scan of 4 K to measure another curve under increasing and decreasing field
9
processes. For clarity, we have shown the M-H curves at selected temperatures between 280-
10
324 K. The open circles denote a representative field decreasing process, while the solid lines
11
correspond to field increasing process. The magnetization decreases with increasing
12
temperature; signifying the magnetic transition from low-temperature FM to high-
13
temperature PM phase. The M-H curves in both processes are very symmetrical and coincide
14
well with each other specifying that both processes are similar and there is negligible (near-
15
zero) hysteresis; which is an important factor for reversibility of the MCE of refrigerant
16
materials. The magnetization curves in the regions below TC increase sharply with the applied
17
magnetic field up to 0.5 T confirming the FM. At the higher field, the increasing trend of
18
magnetization is getting smaller. Additionally, it should be noticed that the M-H curves show
19
unsaturation even under high magnetic field of 6 T. It may be due to high magnetic
20
anisotropy in Tb-based alloys [28]. The other possible reason for this unsaturation might be a
21
non-collinear magnetic structure that needs a strong enough applied field to align the
22
magnetic domains in this alloy [29]. To further understand this behavior, the temperature
23
dependence magnetization under field-cooled (FC) and zero-field-cooled (ZFC) modes were
24
measured as shown in Fig. 3(b). In ZFC mode, the sample was first cooled down from 400 K
25
(PM state) to 90 K in the absence of an applied magnetic field (0.05 T). Later on,
9
10 1
magnetization (MZFC) was recorded during the warming of the sample from 90 K to 400 K in
2
the presence of an applied magnetic field. Whereas for FC mode, the sample was cooled
3
down in the presence of applied magnetic field and temperature dependence magnetization
4
(MFC) was measured during the warming cycle from 90 K to 400 K. Both the FC and ZFC
5
curves show a sharp magnetic transition from a high temperatures PM phase to a
6
ferromagnetic FM phase at TC. Under the applied field of 500Oe, the FC magnetization curve
7
shows the irreversible behavior before the maxima showing large magnetization than ZFC.
8
Both the FC and ZFC curves are overlapped with each other around and above TC, which
9
indicates no thermal hysteresis, making it potentially interesting for MCE application.
10
However, at low temperatures (T
11
observed. This difference is known as the thermomagnetic irreversibility; which is caused by
12
the domain wall (DW) pinning effect in high arises magnetic materials or may be related to
13
the non-collinear magnetic structure below TC [30]. During the FC process, when a sample is
14
cooled in a magnetic field, the thermal energy of domains is sufficient to orient them along
15
the field; in this case, the irreversibility is observed. While, during the ZFC process at low
16
temperatures, the DWs are pinned so the MZFC remains low (close to zero) and as the
17
temperature increases, the magnetization starts to increase and reaches a maximum value near
18
TC. In the case of FC, the magnetic field applied during cooling prevents the pinning of DW
19
and therefore, the MFC increases with decreasing temperature.
20
According to the global rule of magnetic coupling, in light RE-3d based compounds, the
21
RE magnetic moment (μRE) couples antiparallel to 3d element magnetic moment (μ3d) [31].
22
Following this rule, the total magnetic moment per formula unit of the Tb(Co0.94Fe0.06)2 can
23
be written as
24
μtot = μTb - 1.88μCo - 0.12μFe
(1)
10
11 1
The total moment μtot is calculated to be 5.93 μB/f.u. By taking μCo= 1.19 μB/ion and μFe=1.9 μB/
2
ion,
3
pure TbCo2, the total moment (μtot) decreases from 6.34 μB/f.u to 5.93 μB/f.u for TbCo2 and
4
Tb(Co0.94Fe0.06)2 respectively. The decrease in the total moment (μtot) implies the increase in
5
Co(Fe) moment due to the antiferromagnetic coupling between Tb and Co(Fe). Effectively,
6
the moment of the Co(Fe) 3d sublattice increases with increasing Fe concentration, however,
7
the magnetic moment of Tb remains almost unchanged in the Co-rich Tb(Co1−xFex)2
8
compounds. This decrease in the total moment and increase in the 3d sublattice magnetic
9
moment suggest that the substitution of a small amount of Fe by Co substantially changes the
10
band structure and the magnetic states in the 3d subsystem of such alloys. These results are
11
similar to those noticed for the series of RE(Co1-xFex)2 (RE=Dy, Ho, Er) alloys [32].
the observed value of μTb=8.40μB, which is close to its free ion value. Comparing with
12
Since the MCE have a strong correlation with the nature of the corresponding magnetic
13
phase transition, it is essential to study the nature of the phase transition in Tb(Co0.94Fe0.06)2
14
alloy. For this purpose, the Banerjee criterion and universal scaling of MCE were carried out.
15
According to the Banerjee criterion, the nature of transition can be estimated by Arrott plots
16
(M2-H/M) around TC [33]. Arrott plots exhibit linear curves in all M2 ranges near TC (Fig.
17
3(c)), indicating that the nature of magnetic transition from PM to FM phase is of second
18
order. Another criterion to explore the nature of the phase transition is the Landau free energy
19
[34]. Following this approach, the magnetic free energy (F) can be written as a function of
20
magnetization (M) as
F (M,T) =
21
22
At equilibrium
23
(EOS)
24
∂𝐹
A(T) 2 B(T) 4 C(T) 6 M + M + M - MH 2 4 6
(2)
∂𝑀 the magnetization and field can be related to the equation of state
A(T)M + B(T)M 3 + C(T)M 5 = H
(3) 11
12 1
The coefficients A, B are temperature-dependent and can be determined by fitting of M-H
2
curve by a polynomial function. According to the thermodynamic Landau theory, if the
3
coefficients B(T) is positive, then it implies a SOMT, otherwise, the transition is of the first
4
order. As expected, the coefficient B(T) is positive near TC as shown in Fig. 3(d), where the
5
coefficient A(T) is also positive and shows a minimum at TC indicating a SOMT in
6
Tb(Co0.94Fe0.06)2 system. The derived TC≈304 K is in good agreement with that obtained by
7
M-T and DSC results.
8 12
13 1 2 3 4 5
Fig. 3 (a) Isothermal magnetization (M-H) curves during decreasing field (circles) and increasing field (solid lines) processes at different temperatures near TC. (b) Temperature dependence of ZFC and FC magnetization curves under 0.05 T magnetic field (c) Arrott plots M2 vs H/M curves. (d) Landau coefficients (A, B) as a function of temperature.
6
The magnetic entropy change (ΔSM) of the Tb(Co0.94Fe0.06)2 in the cooling and heating
7
process was calculated from the magnetization data (Fig. 3(a)) by using the Maxwell equation
8
[35]. H
M(H,T) ΔS M (T, ΔH) = dH T 0
9
(4)
10
The calculated results of ∆SM as functions of temperature are shown in Fig. 4(a). The ∆SM
11
curves of both processes are almost overlapping, indicating a very small (near-zero) thermal
12
hysteresis. Such a negligible thermal hysteresis will remarkably increase the refrigeration
13
efficiency and thus endorsing their applications in magnetic refrigeration. Moreover,
14
magnetic entropy curves show peak value around the TC and decrease gradually below TC,
15
indicating a spreading distribution of magnetic entropy (Fig. 4(a)). Besides, ΔSM value
16
increases obviously with the increase in the applied field and the maximum value of ΔSM
17
under the field of 5 T is about 4.3 J/kgK, which is a little bit higher than ΔSM=3.7 J/kgK for
18
TbCo1.9Fe0.1 [36]. Besides entropy, another crucial factor which determines the efficiency of
19
a magnetocaloric material is the refrigerant capacity (RC) and usually define as the amount of
20
heat transferred between the cold and hot reservoirs [10] and calculated as area under the
21
∆SM(T) curve using the temperatures of the full width at half maximum (FWHM) as the limits
22
of integration i.e. 𝑅𝐶 = ∫𝑇ℎ𝑜𝑡 ∆𝑆𝑀(𝑇,𝐻)𝑑𝑡. Here, Tcold and Thot are taken as those temperatures
23
where ∆SMax equals ∆SMax/2. Using these expressions, the RC value of Tb(Co0.94Fe0.06)2 alloy
24
is calculated from the ∆SM-T curve and the results are displayed in the inset of Fig. 4(a). The
25
obtained RC value approximately equals to 368.7 J/kg, which is higher than RC=357 J/kg for
26
TbCo2, RC=271 J/kg for TbCo1.9Fe0.1 and RC=299 J/kg for TbCo1.94Fe0.06. The width of the
𝑇
𝑐𝑜𝑙𝑑
13
14 1
∆SM-T curve in Tb(Co0.94Fe0.06)2 alloy is also wider than TbCo2. This is because the
2
substitution of Fe by Co broadens the magnetic transition over a wide temperature range.
3
Such kind of broadening was observed in many other systems and attributed to the magnetic
4
randomness disorder at low temperatures in the RE sublattice on substituting Fe at the Co site
5
[25]. The working temperature range defined as FWHM of ΔSM vs T peak, i.e. THot-TCold. It is
6
obvious that the working temperature span observed in Tb(Co0.94Fe0.06)2 is 93 K, which is
7
obviously higher than that of pure TbCo2 (50 K). This wide working temperature span gives
8
rise to a relatively large RC value of 368.7 J/kg than other compositions under the same field
9
change (H=5T). Therefore, the substitution of Fe for Co in TbCo2 not only increased the
10
phase transition temperature but also increased the working temperature range for the MCE
11
and refrigerant capacity (RC) as well. The operating temperature and RC of these alloys can
12
be further increased with different Fe concentrations.
13
Recently, Franco et.al., constructed a phenomenological universal curve to study the
14
nature of phase transition in SOMT [37]. The basis of the procedure is that the magnetic
15
entropy change ΔSM (T) under different magnetic fields for a SOMT collapses onto a single
16
curve near transition region when the temperature is rescaled and this scaling of MCE holds
17
over a wide temperature range [38]. In the present study, we designed a universal master
18
curve by using experimental results to study the nature of the magnetic transition of
19
Tb(Co0.94Fe0.06)2 alloy. In this method, we normalized each magnetic entropy change (ΔSM(T))
20
curve with respect to their own peaks (ΔSMMax(T)) and the temperature axis is rescaled to a
21
new variable θ which is determined from two temperatures T1 and T2 using the following
22
expressions
23
(T - TC ) - (T - T ) T ≤ TC 1 C θ= (T T C ) T＞TC (T2 - TC )
(5) 14
15 1
T1 and T2 are selected in such a way where ΔSM(T1)/ΔSMMax=ΔSM(T2)/ΔSMMax=h. Here h
2
(0﹤h﹤1) is the height of normalized entropy change. As the large h value gives numerical
3
errors. Thus, we used h=0.5 and TC as the temperature of the ΔSMMax. It is evident from the
4
graph between ΔSM/ΔSMMax versus temperature θ in (Fig. 4(b)) that normalized isothermal
5
magnetic entropy change curves under various fields collapse on a single curve in the
6
temperature range of 240–350 K for θ<0 (FM state) as well as θ>0 (PM). For θ<0 (FM state);
7
the magnetic entropy curves under various field falls on a single curve as magnetization
8
follows EOS and it depends on the critical exponents associated with the order of the phase
9
transition. While for θ>0 (PM state), the magnetization is proportional to the magnetic field
10
and change in magnetic moment with the field will be the same at a particular temperature
11
and hence ΔSM will also collapse in this region. Therefore, the universal curve confirms that
12
the nature of the magnetic transition in Tb(Co0.94Fe0.06)2 alloy is second order.
15
16
1 2 3 4 5
Fig. 4 (a) Temperature dependent magnetic entropy change under different applied magnetic fields. The shaded area in the inset indicates the RC. (b) Normalized ΔSM vs rescaled temperature (θ) under different applied fields.
6
The working temperature range and RC values of Tb(Co0.94Fe0.06)2 alloy are compared with
7
those of commonly used RE-based magnetocaloric materials [7, 9, 11, 14, 15, 39] under the
8
same magnetic field change as shown in Fig. 5. It can be seen that the working temperature
9
range of (Co0.94Fe0.06)2 alloy is much broader than that for other reported materials with 16
17 1
FOMT or SOMT (Fig. 5(a)). Such a wide working temperature range is important for
2
practical applications. Although the RC value of 368.7 J/kg of Tb(Co0.94Fe0.06)2 alloys is
3
lower than some of those materials with much lower phase transition TC but larger than some
4
materials near the room temperature (Fig. 5(b)). Negligible (near-zero) thermal hysteresis,
5
wide operating temperature, and large RC were simultaneously realized in Tb(Co0.94Fe0.06)2
6
alloy makes this a suitable candidate for magnetic refrigeration at ambient temperature.
7 8 9 10
Fig. 5. A comparison of magnetocaloric performance (a) working temperature (b) refrigerant capacity (RC) of Tb(Co0.94Fe0.06)2 with other RE-based magnetocaloric materials [7, 9, 11, 14, 15, 39].
11
4. Conclusions 17
18 1
In conclusion, we have studied the MCE and magnetic properties of room temperature
2
magnetocaloric material Tb(Co0.94Fe0.06)2 alloy. The structural analysis confirms that
3
Tb(Co0.94Fe0.06)2 compound has a single phase with the rhombohedral structure. The second-
4
order magnetic transition from PM to FM with a Curie temperature (TC≈304 K) was
5
confirmed by the Banerjee criterion and universal scaling. The maximum magnetic entropy
6
change (-∆SM=4.3 J/kg K) over wide operating temperature (93 K) and large RC (368.7 J/kg)
7
at field change of 5 T were realized. Negligible (near-zero) thermal and magnetic hysteresis
8
was also observed. Moreover, the Tb(Co0.94Fe0.06)2 alloys show a wide working temperature
9
and large refrigerant capacity (RC) near ambient temperature as compared to some other
10
magnetocaloric materials with FOMT or SOMT under the same field. These superior
11
properties make Tb(Co0.94Fe0.06)2 alloy an appropriate material for RT magnetic refrigeration.
12
The present study may provide an effective way to search MCE materials displaying wide
13
working temperature range and narrow hysteresis and thus endorse their applications in
14
magnetic refrigeration technology.
15 16
Acknowledgments
17
This paper was supported by the National Science Foundation of China (No. 51850410517,
18
51701149, 51601140 and 51801145); China Postdoctoral Science Foundation (Grants No.
19
2018M643612); National Science Basic Research Plan in Shaanxi Province of China
20
(Program 2018JM5168); the Fundamental Research Funds for the Central Universities; the
21
World-Class Universities (Disciplines) and the Characteristic Development Guidance Funds
22
for the Central Universities.
23 24
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1 2
Magnetocaloric effect (MCE) was studied in Tb(Co0.94Fe0.06)2 alloy.
3
PM to FM transition with negligible thermal hysteresis occurs at RT.
4
The maximum magnetic entropy change is 4.3 J/kgK under ΔH = 5 T.
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Wide working temperature window of 93 K and large RC= 368.7 J/kg was also realized.
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Universal scaling of magnetic entropy change was constructed to confirm the SOMT.
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27 1 2
Dear Editor,
3
We would like to submit our revised manuscript entitled “Magnetocaloric effect in
4
Tb(Co0.94Fe0.06)2 alloy with negligible thermal hysteresis and wide working temperature
5
window” for publication in the Journal of Magnetism and Magnetic Materials.
6
We confirm that this manuscript has not been published elsewhere and is not under consideration
7
by any other journal. All authors have approved the manuscript and agree with submission to
8
“Journal of Magnetism and Magnetic Materials”.
9 10
We would like to publish our manuscript in your esteemed journal. We are looking forward to your quick review and publication under your supervision.
11 12
Sincerely yours,
13 14 15 16
Dr. Sen Yang (Mr.) Professor,
17
School of Science
18 19 20 21 22
Address: Xingqing Campus, Xi’an Jiaotong University, Xianning West Road 28#, Beilin District, Xi’an City, Shaanxi Province, China, P.R., 710049. Phone: +86-18629007677 E-mail: [email protected]
27
S0304-8853(19)33061-6 https://doi.org/10.1016/j.jmmm.2020.166521 MAGMA 166521
To appear in:
Journal of Magnetism and Magnetic Materials
Received Date: Revised Date: Accepted Date:
1 September 2019 23 December 2019 27 January 2020
Please cite this article as: A. Murtaza, J. Mi, Y. Li, C. Hao, M. Yaseen, A. Ghani, A. Saeed, W. Zuo, Y. Zhang, C. Zhou, S. Yang, X. Song, Magnetocaloric effect in Tb(Co0.94Fe0.06)2 alloy with negligible thermal hysteresis and wide working temperature range, Journal of Magnetism and Magnetic Materials (2020), doi: https://doi.org/10.1016/ j.jmmm.2020.166521
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1 1 2
Magnetocaloric effect in Tb(Co0.94Fe0.06)2 alloy with negligible thermal hysteresis and wide working temperature range
3 4 5 6 7 8 9 10 11
Adil Murtazaa, Jingwen Mia, Yebei Lia, Chunxi Haoa, Muhammad Yaseenb, Awais Ghania, Azhar Saeeda, Wenliang Zuoa, Yin Zhanga, Chao Zhoua, Sen Yang a,* and Xiaoping Songa
12
Abstract
13
In the present work, the magnetocaloric effect (MCE) and magnetic properties of
14
Tb(Co0.94Fe0.06)2 alloy were studied. X-ray diffraction pattern taken at room temperature
15
confirms that the sample crystallizes in single phase with rhombohedral structure. The
16
paramagnetic to ferromagnetic phase transition was observed at 304 K near the room
17
temperature. Banerjee criterion and universal scaling of the MCE was employed to confirm
18
the second-order nature of the magnetic transition. Differential scanning calorimetry and
19
magnetic characterizations have shown the absence of thermal and magnetic hysteresis in the
20
paramagnetic-ferromagnetic
21
Tb(Co0.94Fe0.06)2 associated with the ferromagnetic transition has been observed over a wide
22
working temperature range (93K) leading to large refrigerant capacity. The maximum value
23
of magnetic entropy change (-ΔSM) under 5T magnetic field is 4.3 J/kgK and the
24
corresponding value of refrigerant capacity is 368.7 J/kg. Interestingly, the magnetocaloric
25
performance of Tb(Co0.94Fe0.06)2 alloy is comparable with some rare-earth-based
26
magnetocaloric materials. These remarkable features make this alloy a suitable candidate for
27
magnetic refrigeration at room temperature.
a
School of Science, MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, China bDepartment of Physics, University of Agriculture, Faisalabad 38040, Pakistan
transition
region.
The
magnetic
entropy
change
for
28 29 30
Keywords: Magnetocaloric effect; Thermal hysteresis; Magnetic properties; Second-order
31
phase transition; Refrigerant capacity; Universal Scaling
32 33 34
____________________________
35
* Electronic email: [email protected]
36 1
2 1
1. Introduction
2
The magnetocaloric effect (MCE) being a magneto-thermodynamic phenomenon has
3
drawn a constant interest for its potential applications in refrigeration technology due to its
4
high thermodynamic efficiency, ecological concerns and a large probability of applications in
5
a wide temperature span [1-4]. The magnetic materials exhibiting large magnetic entropy
6
change over wide working temperature with narrow thermal hysteresis are promising
7
candidates [5,6]. For this propose, MCE has been studied in different types of materials e.g.,
8
rare-earth (RE) containing and RE-free crystalline materials, Gd-based compounds, Heusler
9
alloys, MnAs-based alloys, multiphase materials and composites and nanostructured
10
materials [7]. Of course, different materials have shown different magnetocaloric
11
performance i.e., working temperature range, magnetic entropy change, and refrigerant
12
capacity and so on; the detailed information can be obtained in reference 7. Among those, a
13
large MCE can be expected in RECo2 Laves phase compounds owing to the fact that the RE-
14
Co sublattices moments couples antiferromagnetically and the observed RE magnetic
15
moments are close to their free ionic values [8]. The RECo2 with the first-order magnetic
16
transition (FOMT) e.g., DyCo2, HoCo2, ErCo2 are of particular importance for MCE owing to
17
their large magnetic entropy change (∆SM) around their phase transition temperature (TC) [9].
18
However, they possess narrow working temperature ranges and exhibit thermal hysteresis
19
with change in magnetization with temperature and magnetic field; which causes an obvious
20
decrease of the refrigerant capacity (RC); an essential parameter to evaluate the MCE [10].
21
To overcome these problems, materials undergoing a second-order magnetic transition
22
(SOMT) for example TbCo2, PrCo2, and NdCo2 may be used [11]. Although these materials
23
generally show smaller ∆SM than giant MCE materials, however, they possess narrow
24
thermal hysteresis yielding high RC. Besides, their -∆SM can be extended through a wide
25
temperature range [12]. On the basis of the lack of thermal hysteresis and the possibility of
2
3 1
high RC, materials with SOMT can be used as an alternative for designing magnetic
2
refrigerator prototypes. The low magnetic phase transition temperature (TC) of those materials
3
may limit their room temperature (RT) applications [13]. Earlier studies indicate that the
4
magnetic phase transition temperature (TC) of the RECo2 family can be tuned even up to RT
5
by substitution of a sufficient amount of 3d-elements (Fe) for Co [14, 15]. In the present work,
6
we selected the TbCo2 compound, which shows the paramagnetic (PM) to ferromagnetic (FM)
7
phase transition of second-order at TC≈234K; well below the RT [16]. By substituting a small
8
amount of Fe (6%) for Co in the TbCo2 compound, we obtained an interesting composition of
9
Tb(Co0.94Fe0.06)2 which shows the phase transition temperature at ≈304 K without any change
10
in SOMT character. Contrary to the earlier studies, those carried out magnetocaloric
11
measurements under single thermal process (cooling or heating) and were unable to find the
12
size of thermal hysteresis, in the present work; we studied the magnetocaloric performance
13
under both heating and cooling process in order to reveal the effect of thermal hysteresis on
14
the RC. The wide operating temperature range, small thermal hysteresis, and large RC value
15
were simultaneously realized in this alloy, which makes Tb(Co0.94Fe0.06)2 alloy a promising
16
candidate for magnetic refrigeration applications. Interestingly, the magnetocaloric
17
performance of Tb(Co0.94Fe0.06)2 alloy is comparable with commonly used some RE-based
18
(RE=Tb, Gd, Er, Ho, Nd) magnetocaloric materials. Our results may open new opportunities
19
to search novel functional materials for magnetic refrigeration.
20 21
2. Experimental details
22
The ingot of Tb(Co0.94Fe0.06)2 alloy was melted in an electric arc-melting furnace in a
23
pure argon atmosphere. The sample was melted five times to ensure better homogeneity and
24
then annealed in a vacuum-sealed quartz tube at 850 K for 24 hours. Crystal structural
25
analysis was carried out by X-ray diffraction (XRD) using Rigaku D-MAX 2500 V
3
4 1
diffractometer with Cu Kα radiation in an angular range of 20o≤2θ≤80o with a 0.05o step size.
2
A high precision step scanning XRD with step size of 0.001° was also employed to observe
3
the splitting of (222) and (440) reflections. The XRD data was analyzed by using Materials
4
Data Inc. Software Jade 6.0. Phase homogeneity and elemental composition of
5
Tb(Co0.94Fe0.06)2 alloy was checked by using scanning electron microscopy (SEM) and
6
energy dispersive X-ray (EDX) spectroscopy, respectively. The phase transition temperature
7
(TC) was determined from the temperature dependences of magnetization (M-T) and AC
8
susceptibility (χ). To check the thermal hysteresis, M-T curves were measured in cooling and
9
heating modes under applying magnetic field of 0.05 T. Phase transition behavior of the
10
sample was characterized by differential scanning calorimeter (DSC, Q2000 from TA
11
Instruments) at a cooling/heating rate of 5 K/min. Field-dependent magnetization (M-H)
12
curves at different temperatures between 280-320 K under magnetic field of 6T were
13
measured by using Quantum design SQUID. The magnetic entropy change (∆S) was
14
calculated from M-H isotherms by using the Maxwell equation.
15 16
3. Results and Discussion
17
In order to reveal the crystal structure and phase analysis, room-temperature XRD of
18
Tb(Co0.94Fe0.06)2 alloy was carried out as shown in Fig.1(a). According to analysis, several
19
well-defined reflections appearing at 2θ= 20.91°, 34.44°, 40.64°, 42.44°, 56.11°, 61.34°,
20
65.47°, and 72.24° can be assigned to (111), (220), (311), (222), (331), (422), (511) and
21
(440), respectively. The peaks position and relative intensity of all Bragg diffraction
22
reflections correspond to those expected for the MgCu2-type Laves phase structure. No extra
23
peaks corresponding to either impurities or secondary phases were observed in the
24
diffraction pattern indicates that the homogenized alloy contains mainly Tb(Co, Fe) single-
25
phase having the 1:2 stoichiometry. The sharp diffraction peaks illustrate a good crystallinity
4
5 1
of this alloy. Based on the knowledge that ferromagnetic transition involves structural
2
change, the paramagnetic cubic Laves phase will be distorted into a rhombohedral (R) or
3
tetragonal (T) phase having an easy magnetization direction (EMD) lies along the [111] or
4
[100] respectively [17]. As is known, the in Laves phase MgCu2-type compounds EMD can
5
be inferred from the profile of (222) and (440) reflections in the XRD pattern [18]. Therefore,
6
in order to determine the EMD of Tb(Co0.94Fe0.06)2 alloy, the (222) and (440) reflections
7
were step scanned in the angular range of 41°-43° and 72°-74° respectively with a step size
8
of 0.001°. It is evident that the characteristic reflections of (222) and (440) split into two
9
peaks as shown in the insets of Fig. 1(a). These results are in agreement with the synchrotron
10
XRD and neutron powder diffraction (NPD) data shown in previous studies revealing that
11
the characteristic reflections of (222), (440) split into two peaks but (800) reflections have no
12
splitting [19]. These features show that Tb(Co0.94Fe0.06)2 alloy has a lower cubic symmetry
13
and exhibits characteristics of a rhombohedral (R) phase with EMD along [111]. Such a
14
crystal lattice belongs to the space group R-3m with Tb atoms on the 2c sites, Co/Fe atoms
15
on the 1b and 3e sites [20]. The calculated lattice parameters are αR=89.95o and aR=0.738 nm.
16
The SEM image as shown in Fig. 1(b), illustrates the dark grey phase corresponding to
17
the main Tb(Co, Fe) single phase. The elemental compositions were checked by EDX
18
analysis of the marked area in the SEM image. The observed EDX results show the presence
19
of several well-defined peaks related to Tb, Co, and Fe, which reveal that the prepared
20
sample is composed of Tb, Co, and Fe only. Further, it is observed that no other peak related
21
to impurities is present in the EDX spectra, which confirms the formation and purity of
22
Tb(Co0.94Fe0.06)2 alloy.
5
6
1 2 3 4 5 6 7
Fig. 1 (a) X-ray diffraction pattern of Tb(Co0.94Fe0.06)2 with rhombohedral structure. The splitting in (222) and (440) peaks are shown in the insets. The bold blue line is experimental data, while thin red and green lines are fitted one. (b) Scanning electron microscopy (SEM) and energy-dispersive X-ray (EDX) analysis of the marked area in SEM image.
8
heating and cooling processes under an applied field of 0.05 T are shown in Fig. 2(a). It can
The temperature versus magnetization (M-T) curves measured from 90 K to 400 K in the
6
7 1
be seen that this Tb(Co0.94Fe0.06)2 alloy undergoes magnetic transition during cooling and
2
heating modes. Both curves converge with each other in the phase transition region,
3
indicating an absence of thermal hysteresis due to the SOMT. The derivative of M-T curve
4
(inset of Fig. 2(a)) indicates that paramagnetic (PM) to ferromagnetic (FM) transition occurs
5
at TC≈304 K; which is higher than 230 K (for TbCo2) and thus make Tb(Co0.94Fe0.06)2 alloy
6
suitable candidate for RT magnetic refrigeration. As is known in RECo2 compounds, the TC is
7
determined by 3d-3d exchange interactions between the Co-Co sublattice magnetic moments
8
and the 3d-4f hybridization between Co-RE inter-sublattice moments [21]. The 3d-3d
9
interactions are direct and stronger. The 3d-4f hybridization indirect and of intermediate
10
strength depending on the nature of the 3d sublattice moments. The nature of 3d sublattice
11
magnetic moments of REFe2 and RECo2 is also very different. The magnetic moments of Fe
12
are intrinsic moments (localized 3d), while the magnetic moments of Co ion are induced
13
moments (itinerant 3d) by the RE-Co interaction. With the substitution of Fe for Co, the
14
itinerant character of Co-3d moments is replaced by a more localized character of Fe-3d
15
moments. This localization leads to an increase in 4f-3d hybridization. According to Brooks
16
et al. [22], the 3d–3d interactions depend critically on the 4f–3d hybridization. Therefore, the
17
increase in 4f-3d hybridization would strengthen the 3d–3d exchange interactions [23]. Thus,
18
with the partial replacement of Fe by Co in TbCo2, the 3d exchange interactions increase,
19
which results in the increase of TC. Similar results have been observed in Ho(Co1-xFex)2 [24],
20
and Dy(Co1-xFex)2 [25]. The nature of the magnetic transition was confirmed by DSC
21
measurements as shown in Fig. 2(b). DSC curves during the cooling and heating process
22
show exothermic and endothermic peaks respectively at T≈303 K; which is very close to its
23
TC. Negligible thermal hysteresis between the cooling and heating in DSC measurements as
24
strong evidence of SOMT, consistent with the negligible hysteresis in M-T curves. The
25
inverse magnetic susceptibility (𝜒 ―1) measured under an applied field of 0.02 T in the
7
8 1
temperature range of 300-400 K obeys Curie-Weiss law 𝜒 ―1 = (𝑇 + 𝜃𝑃) 𝐶 as shown on the
2
right-hand scale in Fig. 2(a). Here, θp is the paramagnetic Curie temperature and C is the
3
Curie constant related to the effective magnetic moment (μeff) of Tb ions in the paramagnetic
4
state [26]. The linear fitting of susceptibility curve yields θp ≈302 K and the μeff ≈9.4 μB/f.u;
5
close to the free Tb ion (gJ=9.72 μB) [27]. The positive value of θp and the nature of inverse
6
susceptibility in the magnetically ordered state indicate the presence of dominant
7
ferromagnetic interactions in this alloy. The substitution of a small amount of Fe by Co leads
8
to an increase in TC and broadens the magnetic transition in Tb(Co0.94Fe0.06)2, as compared to
9
TbCo2.
10
11 12 13 14 15 16 17
Fig. 2 (a) Temperature-dependent magnetization (M-T) curves measured in cooling and heating modes under a magnetic field of 0.05 T. Inset: the derivative of the M-T curve. Curie-Weiss fit to the paramagnetic susceptibility (right-hand scale). (b) DSC curves in the heating and cooling cycles of at the rate of 5 K/min.
8
9 1
In order to analyze the effect of thermal hysteresis on the MCE and well calculate the
2
RC, the isothermal M-H curves were measured under the field of 6 T at different
3
temperatures below and above TC under field decreasing and increasing modes (Fig.3 (a)).
4
Before starting the measurement, initially, the sample was cooled down to the desired
5
temperature in zero applied field, and the M–H curves were measured by increasing magnetic
6
field from 0 T to a predetermined maximum 6 T and then decreasing magnetic field from 6 T
7
back to 0 T. After one isothermal curve was measured, the temperature was increased slowly
8
with step scan of 4 K to measure another curve under increasing and decreasing field
9
processes. For clarity, we have shown the M-H curves at selected temperatures between 280-
10
324 K. The open circles denote a representative field decreasing process, while the solid lines
11
correspond to field increasing process. The magnetization decreases with increasing
12
temperature; signifying the magnetic transition from low-temperature FM to high-
13
temperature PM phase. The M-H curves in both processes are very symmetrical and coincide
14
well with each other specifying that both processes are similar and there is negligible (near-
15
zero) hysteresis; which is an important factor for reversibility of the MCE of refrigerant
16
materials. The magnetization curves in the regions below TC increase sharply with the applied
17
magnetic field up to 0.5 T confirming the FM. At the higher field, the increasing trend of
18
magnetization is getting smaller. Additionally, it should be noticed that the M-H curves show
19
unsaturation even under high magnetic field of 6 T. It may be due to high magnetic
20
anisotropy in Tb-based alloys [28]. The other possible reason for this unsaturation might be a
21
non-collinear magnetic structure that needs a strong enough applied field to align the
22
magnetic domains in this alloy [29]. To further understand this behavior, the temperature
23
dependence magnetization under field-cooled (FC) and zero-field-cooled (ZFC) modes were
24
measured as shown in Fig. 3(b). In ZFC mode, the sample was first cooled down from 400 K
25
(PM state) to 90 K in the absence of an applied magnetic field (0.05 T). Later on,
9
10 1
magnetization (MZFC) was recorded during the warming of the sample from 90 K to 400 K in
2
the presence of an applied magnetic field. Whereas for FC mode, the sample was cooled
3
down in the presence of applied magnetic field and temperature dependence magnetization
4
(MFC) was measured during the warming cycle from 90 K to 400 K. Both the FC and ZFC
5
curves show a sharp magnetic transition from a high temperatures PM phase to a
6
ferromagnetic FM phase at TC. Under the applied field of 500Oe, the FC magnetization curve
7
shows the irreversible behavior before the maxima showing large magnetization than ZFC.
8
Both the FC and ZFC curves are overlapped with each other around and above TC, which
9
indicates no thermal hysteresis, making it potentially interesting for MCE application.
10
However, at low temperatures (T
11
observed. This difference is known as the thermomagnetic irreversibility; which is caused by
12
the domain wall (DW) pinning effect in high arises magnetic materials or may be related to
13
the non-collinear magnetic structure below TC [30]. During the FC process, when a sample is
14
cooled in a magnetic field, the thermal energy of domains is sufficient to orient them along
15
the field; in this case, the irreversibility is observed. While, during the ZFC process at low
16
temperatures, the DWs are pinned so the MZFC remains low (close to zero) and as the
17
temperature increases, the magnetization starts to increase and reaches a maximum value near
18
TC. In the case of FC, the magnetic field applied during cooling prevents the pinning of DW
19
and therefore, the MFC increases with decreasing temperature.
20
According to the global rule of magnetic coupling, in light RE-3d based compounds, the
21
RE magnetic moment (μRE) couples antiparallel to 3d element magnetic moment (μ3d) [31].
22
Following this rule, the total magnetic moment per formula unit of the Tb(Co0.94Fe0.06)2 can
23
be written as
24
μtot = μTb - 1.88μCo - 0.12μFe
(1)
10
11 1
The total moment μtot is calculated to be 5.93 μB/f.u. By taking μCo= 1.19 μB/ion and μFe=1.9 μB/
2
ion,
3
pure TbCo2, the total moment (μtot) decreases from 6.34 μB/f.u to 5.93 μB/f.u for TbCo2 and
4
Tb(Co0.94Fe0.06)2 respectively. The decrease in the total moment (μtot) implies the increase in
5
Co(Fe) moment due to the antiferromagnetic coupling between Tb and Co(Fe). Effectively,
6
the moment of the Co(Fe) 3d sublattice increases with increasing Fe concentration, however,
7
the magnetic moment of Tb remains almost unchanged in the Co-rich Tb(Co1−xFex)2
8
compounds. This decrease in the total moment and increase in the 3d sublattice magnetic
9
moment suggest that the substitution of a small amount of Fe by Co substantially changes the
10
band structure and the magnetic states in the 3d subsystem of such alloys. These results are
11
similar to those noticed for the series of RE(Co1-xFex)2 (RE=Dy, Ho, Er) alloys [32].
the observed value of μTb=8.40μB, which is close to its free ion value. Comparing with
12
Since the MCE have a strong correlation with the nature of the corresponding magnetic
13
phase transition, it is essential to study the nature of the phase transition in Tb(Co0.94Fe0.06)2
14
alloy. For this purpose, the Banerjee criterion and universal scaling of MCE were carried out.
15
According to the Banerjee criterion, the nature of transition can be estimated by Arrott plots
16
(M2-H/M) around TC [33]. Arrott plots exhibit linear curves in all M2 ranges near TC (Fig.
17
3(c)), indicating that the nature of magnetic transition from PM to FM phase is of second
18
order. Another criterion to explore the nature of the phase transition is the Landau free energy
19
[34]. Following this approach, the magnetic free energy (F) can be written as a function of
20
magnetization (M) as
F (M,T) =
21
22
At equilibrium
23
(EOS)
24
∂𝐹
A(T) 2 B(T) 4 C(T) 6 M + M + M - MH 2 4 6
(2)
∂𝑀 the magnetization and field can be related to the equation of state
A(T)M + B(T)M 3 + C(T)M 5 = H
(3) 11
12 1
The coefficients A, B are temperature-dependent and can be determined by fitting of M-H
2
curve by a polynomial function. According to the thermodynamic Landau theory, if the
3
coefficients B(T) is positive, then it implies a SOMT, otherwise, the transition is of the first
4
order. As expected, the coefficient B(T) is positive near TC as shown in Fig. 3(d), where the
5
coefficient A(T) is also positive and shows a minimum at TC indicating a SOMT in
6
Tb(Co0.94Fe0.06)2 system. The derived TC≈304 K is in good agreement with that obtained by
7
M-T and DSC results.
8 12
13 1 2 3 4 5
Fig. 3 (a) Isothermal magnetization (M-H) curves during decreasing field (circles) and increasing field (solid lines) processes at different temperatures near TC. (b) Temperature dependence of ZFC and FC magnetization curves under 0.05 T magnetic field (c) Arrott plots M2 vs H/M curves. (d) Landau coefficients (A, B) as a function of temperature.
6
The magnetic entropy change (ΔSM) of the Tb(Co0.94Fe0.06)2 in the cooling and heating
7
process was calculated from the magnetization data (Fig. 3(a)) by using the Maxwell equation
8
[35]. H
M(H,T) ΔS M (T, ΔH) = dH T 0
9
(4)
10
The calculated results of ∆SM as functions of temperature are shown in Fig. 4(a). The ∆SM
11
curves of both processes are almost overlapping, indicating a very small (near-zero) thermal
12
hysteresis. Such a negligible thermal hysteresis will remarkably increase the refrigeration
13
efficiency and thus endorsing their applications in magnetic refrigeration. Moreover,
14
magnetic entropy curves show peak value around the TC and decrease gradually below TC,
15
indicating a spreading distribution of magnetic entropy (Fig. 4(a)). Besides, ΔSM value
16
increases obviously with the increase in the applied field and the maximum value of ΔSM
17
under the field of 5 T is about 4.3 J/kgK, which is a little bit higher than ΔSM=3.7 J/kgK for
18
TbCo1.9Fe0.1 [36]. Besides entropy, another crucial factor which determines the efficiency of
19
a magnetocaloric material is the refrigerant capacity (RC) and usually define as the amount of
20
heat transferred between the cold and hot reservoirs [10] and calculated as area under the
21
∆SM(T) curve using the temperatures of the full width at half maximum (FWHM) as the limits
22
of integration i.e. 𝑅𝐶 = ∫𝑇ℎ𝑜𝑡 ∆𝑆𝑀(𝑇,𝐻)𝑑𝑡. Here, Tcold and Thot are taken as those temperatures
23
where ∆SMax equals ∆SMax/2. Using these expressions, the RC value of Tb(Co0.94Fe0.06)2 alloy
24
is calculated from the ∆SM-T curve and the results are displayed in the inset of Fig. 4(a). The
25
obtained RC value approximately equals to 368.7 J/kg, which is higher than RC=357 J/kg for
26
TbCo2, RC=271 J/kg for TbCo1.9Fe0.1 and RC=299 J/kg for TbCo1.94Fe0.06. The width of the
𝑇
𝑐𝑜𝑙𝑑
13
14 1
∆SM-T curve in Tb(Co0.94Fe0.06)2 alloy is also wider than TbCo2. This is because the
2
substitution of Fe by Co broadens the magnetic transition over a wide temperature range.
3
Such kind of broadening was observed in many other systems and attributed to the magnetic
4
randomness disorder at low temperatures in the RE sublattice on substituting Fe at the Co site
5
[25]. The working temperature range defined as FWHM of ΔSM vs T peak, i.e. THot-TCold. It is
6
obvious that the working temperature span observed in Tb(Co0.94Fe0.06)2 is 93 K, which is
7
obviously higher than that of pure TbCo2 (50 K). This wide working temperature span gives
8
rise to a relatively large RC value of 368.7 J/kg than other compositions under the same field
9
change (H=5T). Therefore, the substitution of Fe for Co in TbCo2 not only increased the
10
phase transition temperature but also increased the working temperature range for the MCE
11
and refrigerant capacity (RC) as well. The operating temperature and RC of these alloys can
12
be further increased with different Fe concentrations.
13
Recently, Franco et.al., constructed a phenomenological universal curve to study the
14
nature of phase transition in SOMT [37]. The basis of the procedure is that the magnetic
15
entropy change ΔSM (T) under different magnetic fields for a SOMT collapses onto a single
16
curve near transition region when the temperature is rescaled and this scaling of MCE holds
17
over a wide temperature range [38]. In the present study, we designed a universal master
18
curve by using experimental results to study the nature of the magnetic transition of
19
Tb(Co0.94Fe0.06)2 alloy. In this method, we normalized each magnetic entropy change (ΔSM(T))
20
curve with respect to their own peaks (ΔSMMax(T)) and the temperature axis is rescaled to a
21
new variable θ which is determined from two temperatures T1 and T2 using the following
22
expressions
23
(T - TC ) - (T - T ) T ≤ TC 1 C θ= (T T C ) T＞TC (T2 - TC )
(5) 14
15 1
T1 and T2 are selected in such a way where ΔSM(T1)/ΔSMMax=ΔSM(T2)/ΔSMMax=h. Here h
2
(0﹤h﹤1) is the height of normalized entropy change. As the large h value gives numerical
3
errors. Thus, we used h=0.5 and TC as the temperature of the ΔSMMax. It is evident from the
4
graph between ΔSM/ΔSMMax versus temperature θ in (Fig. 4(b)) that normalized isothermal
5
magnetic entropy change curves under various fields collapse on a single curve in the
6
temperature range of 240–350 K for θ<0 (FM state) as well as θ>0 (PM). For θ<0 (FM state);
7
the magnetic entropy curves under various field falls on a single curve as magnetization
8
follows EOS and it depends on the critical exponents associated with the order of the phase
9
transition. While for θ>0 (PM state), the magnetization is proportional to the magnetic field
10
and change in magnetic moment with the field will be the same at a particular temperature
11
and hence ΔSM will also collapse in this region. Therefore, the universal curve confirms that
12
the nature of the magnetic transition in Tb(Co0.94Fe0.06)2 alloy is second order.
15
16
1 2 3 4 5
Fig. 4 (a) Temperature dependent magnetic entropy change under different applied magnetic fields. The shaded area in the inset indicates the RC. (b) Normalized ΔSM vs rescaled temperature (θ) under different applied fields.
6
The working temperature range and RC values of Tb(Co0.94Fe0.06)2 alloy are compared with
7
those of commonly used RE-based magnetocaloric materials [7, 9, 11, 14, 15, 39] under the
8
same magnetic field change as shown in Fig. 5. It can be seen that the working temperature
9
range of (Co0.94Fe0.06)2 alloy is much broader than that for other reported materials with 16
17 1
FOMT or SOMT (Fig. 5(a)). Such a wide working temperature range is important for
2
practical applications. Although the RC value of 368.7 J/kg of Tb(Co0.94Fe0.06)2 alloys is
3
lower than some of those materials with much lower phase transition TC but larger than some
4
materials near the room temperature (Fig. 5(b)). Negligible (near-zero) thermal hysteresis,
5
wide operating temperature, and large RC were simultaneously realized in Tb(Co0.94Fe0.06)2
6
alloy makes this a suitable candidate for magnetic refrigeration at ambient temperature.
7 8 9 10
Fig. 5. A comparison of magnetocaloric performance (a) working temperature (b) refrigerant capacity (RC) of Tb(Co0.94Fe0.06)2 with other RE-based magnetocaloric materials [7, 9, 11, 14, 15, 39].
11
4. Conclusions 17
18 1
In conclusion, we have studied the MCE and magnetic properties of room temperature
2
magnetocaloric material Tb(Co0.94Fe0.06)2 alloy. The structural analysis confirms that
3
Tb(Co0.94Fe0.06)2 compound has a single phase with the rhombohedral structure. The second-
4
order magnetic transition from PM to FM with a Curie temperature (TC≈304 K) was
5
confirmed by the Banerjee criterion and universal scaling. The maximum magnetic entropy
6
change (-∆SM=4.3 J/kg K) over wide operating temperature (93 K) and large RC (368.7 J/kg)
7
at field change of 5 T were realized. Negligible (near-zero) thermal and magnetic hysteresis
8
was also observed. Moreover, the Tb(Co0.94Fe0.06)2 alloys show a wide working temperature
9
and large refrigerant capacity (RC) near ambient temperature as compared to some other
10
magnetocaloric materials with FOMT or SOMT under the same field. These superior
11
properties make Tb(Co0.94Fe0.06)2 alloy an appropriate material for RT magnetic refrigeration.
12
The present study may provide an effective way to search MCE materials displaying wide
13
working temperature range and narrow hysteresis and thus endorse their applications in
14
magnetic refrigeration technology.
15 16
Acknowledgments
17
This paper was supported by the National Science Foundation of China (No. 51850410517,
18
51701149, 51601140 and 51801145); China Postdoctoral Science Foundation (Grants No.
19
2018M643612); National Science Basic Research Plan in Shaanxi Province of China
20
(Program 2018JM5168); the Fundamental Research Funds for the Central Universities; the
21
World-Class Universities (Disciplines) and the Characteristic Development Guidance Funds
22
for the Central Universities.
23 24
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1 2
Magnetocaloric effect (MCE) was studied in Tb(Co0.94Fe0.06)2 alloy.
3
PM to FM transition with negligible thermal hysteresis occurs at RT.
4
The maximum magnetic entropy change is 4.3 J/kgK under ΔH = 5 T.
5
Wide working temperature window of 93 K and large RC= 368.7 J/kg was also realized.
6
Universal scaling of magnetic entropy change was constructed to confirm the SOMT.
7 8 9 26
27 1 2
Dear Editor,
3
We would like to submit our revised manuscript entitled “Magnetocaloric effect in
4
Tb(Co0.94Fe0.06)2 alloy with negligible thermal hysteresis and wide working temperature
5
window” for publication in the Journal of Magnetism and Magnetic Materials.
6
We confirm that this manuscript has not been published elsewhere and is not under consideration
7
by any other journal. All authors have approved the manuscript and agree with submission to
8
“Journal of Magnetism and Magnetic Materials”.
9 10
We would like to publish our manuscript in your esteemed journal. We are looking forward to your quick review and publication under your supervision.
11 12
Sincerely yours,
13 14 15 16
Dr. Sen Yang (Mr.) Professor,
17
School of Science
18 19 20 21 22
Address: Xingqing Campus, Xi’an Jiaotong University, Xianning West Road 28#, Beilin District, Xi’an City, Shaanxi Province, China, P.R., 710049. Phone: +86-18629007677 E-mail: [email protected]
27