# Exchange bias effect in CaMn1-xRexO3

V. Markovich, I. Fita, A. Wisniewski, R. Puzniak, Christine Martin, G. Jung, G. Gorodetsky

<figure><img src="image_1.png" /></figure>

## To cite this version:

V. Markovich, I. Fita, A. Wisniewski, R. Puzniak, Christine Martin, et al., Exchange bias effect in CaMn1-xRexO3. AIP Advances, 2017, 7 (5), pp.055801. 10.1063/1.4972798. [https://doi.org/10.1063/1.4972798](https://doi.org/10.1063/1.4972798)

HAL Id: hal-02175451

https://normandie-univ.hal.science/hal-02175451

Submitted on 1 Jun 2022

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Exchange bias effect in CaMn₁-xRe###O₃

Cite as: AIP Advances **7**, 055801 (2017); https://doi.org/10.1063/1.4972798

Submitted: 31 August 2016 • Accepted: 22 September 2016 • Published Online: 20 December 2016

V. Markovich, I. Fita, A. Wisniewski, et al.

<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /></figure>

View Online

<figure><img src="image_5.png" /></figure>

Export Citation

<figure><img src="image_6.png" /></figure>

CrossMark

ARTICLES YOU MAY BE INTERESTED IN

Doping dependent magnetism and exchange bias in CaMn₁-xWxO₃ manganites

Journal of Applied Physics **116**, 093903 (2014); https://doi.org/10.1063/1.4894280

Giant zero field cooled spontaneous exchange bias effect in phase separated La₁.₅Sr₀.₅CoMnO₆

Applied Physics Letters **103**, 252410 (2013); https://doi.org/10.1063/1.4855135

Exchange bias and memory effect in double perovskite Sr₂FeCoO₆

Applied Physics Letters **101**, 142401 (2012); https://doi.org/10.1063/1.4756792

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>
Exchange bias effect in CaMn<sub>1-x</sub>Re<sub>x</sub>O<sub>3</sub>

V. Markovich,<fnref n="1" />,ª I. Fita,<fnref n="2" /> A. Wisniewski,<fnref n="2" /> R. Puzniak,<fnref n="2" /> C. Martin,<fnref n="3" /> G. Jung,<fnref n="1" />,<fnref n="2" /> and G. Gorodetsky<fnref n="1" />

(Presented 2 November 2016; received 31 August 2016; accepted 22 September 2016; published online 20 December 2016)

Exchange bias effect in CaMn<sub>1-x</sub>Re<sub>x</sub>O<sub>3</sub> (x ≤ 0.1) has been investigated. The effect is very small in the samples doped at x = 0.02 and 0.04, but increases monotonously with further increase in Re doping. For x = 0.1, both vertical and horizontal shifts in hysteresis loop of field cooled sample decrease monotonously with increasing temperature and vanish above 70 K, while coercivity disappears only above 90 K upon approaching the Néel temperature. Exchange bias field, coercivity, and remanence asymmetry depend sensitively on temperature and maximal measuring field. Magnetic training effect has been studied for x = 0.06, 0.08, 0.1 samples and analyzed using a spin relaxation model. The observed exchange bias is attributed to the low-temperature phase separation into ferromagnetic clusters and the G-type and/or C-type antiferromagnetic matrix. © 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). [http://dx.doi.org/10.1063/1.4972798]

The exchange bias (EB) phenomenon, discovered by Meiklejohn and Bean,<fnref n="1" /> has been intensively studied because of its importance for the magnetic information storage technologies.<fnref n="2" />⁻⁵ Usually, the EB effect manifests itself by shifts in the isothermal magnetization vs applied field curves along the field direction and sometimes along the magnetization axis, as well as by an enhancement of the coercive field H<sub>C</sub> in the field cooled (FC) process. In general, the EB results from coupling between ferromagnetic (FM) spins and interfacial, uncompensated antiferromagnetic (AFM) spins, occurring during cooling of a FM-AFM system through the Néel temperature in applied magnetic field. After the first observation of the EB effect in Pr<sub>1/3</sub>Ca<sub>2/3</sub>MnO<sub>3</sub> manganite by Niebieskikwiat and Salamon,⁶ it has been reported for various phase-separated manganites and cobaltites.⁵,⁷⁻⁹

The parent CaMnO<sub>3</sub> manganite is the G-type antiferromagnet in which the spin of Mn<sup>4+</sup> ion is antiparallel to the spins of the six nearest neighbor Mn<sup>4+</sup> ions. The Néel temperature T<sub>N</sub> of CaMnO<sub>3</sub> may vary in the range 110–130 K, depending on the concentration of oxygen vacancies.<sup>10,11</sup> Doping of Mn sites with metal atoms with valence > 4+ creates Mn<sup>3+</sup> ions and induces FM clusters in the AFM matrix.<sup>12</sup> It was found that the occurrence of EB depends strongly on relative ratio of volumes of FM clusters and AFM matrix. Noticeable EB appears in the systems with small volume of FM clusters.<sup>8</sup> Our recent study<sup>13</sup> on magnetic properties of Re-doped CaMn<sub>1-x</sub>Re<sub>x</sub>O<sub>3</sub> (CMRO) (0 ≤ x ≤ 0.1) suggested that the ground state evolves with increasing x, from the G-type AFM state with weak FM component (for x up to 0.06) to mostly C-type AFM state with charge ordering for x = 0.08 and 0.1.

In this paper, we report on EB effect in CMRO system. In particular we report on the temperature dependence of hysteresis loops in various maximal magnetic fields H<sub>MAX</sub>, up to 50 kOe and on training effect (TE) for x = 0.06, 0.08 and 0.1 samples.

In our studies, we have employed polycrystalline samples prepared by a standard ceramic route in air, with intermediate crushing and heating.<sup>12</sup> The magnetic measurements and X-rays diffraction data have shown that CMRO samples are paramagnetic (PM) with *Pnma* crystallographic symmetry

<footnote n="1">¹Department of Physics, Ben-Gurion University of the Negev, 84105 Beer-Sheva, Israel</footnote>

<footnote n="2">²Institute of Physics, Polish Academy of Sciences, PL-02668 Warsaw, Poland</footnote>

<footnote n="3">³Laboratoire CRISMAT, UMR 6508, ISMRA, 14050 Caen Cedex, France</footnote>

<footnote><sup>a</sup>Corresponding Author Vladimir Markovich: markoviv@bgu.ac.il</footnote>
at room temperature.¹³ Magnetic measurements were performed using PAR 4500 vibrating sample magnetometer in magnetic field ≤ 15 kOe, while dc magnetization measurements at higher magnetic field were carried out using the vibrating sample magnetometer (VSM) option of Quantum Design Physical Property Measurement System.

Temperature dependences of the field cooled and zero field cooled magnetization, $M_{FC}$ and $M_{ZFC}$, of CaMn₁-xRexO₃ (0.04 ≤ x ≤ 0.1), recorded at applied field of 100 Oe, are shown in Fig. 1(a), while those for x = 0.02 sample are shown in the inset to Fig. 1(a). Magnetization at temperatures above 110 K is very small for all studied samples. Low temperature magnetization for the sample with x = 0.1 remains very low while that for the sample with x up to 0.08 varies non-monotonously with x. The temperature evolution of $M_{FC}$ and $M_{ZFC}$ demonstrates that: (i) $T_N$, associated with increase of $M_{FC}$, decreases with increasing x from ~ 110 K at x = 0.04 to ~ 95 K at x = 0.1. (ii) $M_{FC}$ and $M_{ZFC}$ of all studied samples considerably split below $T_N$, indicating the presence of frustrated magnetic states. (iii) $M_{FC}$ and $M_{ZFC}$ for the sample with x = 0.02 exhibit a maximum below $T_N$ and then change the sign and become negative at $T < 40$ K.

Low temperature $M_{FC}$ recorded at H = 15 kOe (Fig. 1(b)) increases with increasing x up to x = 0.04 and decreases with further increase in x. In the PM range, $150 < T < 250$ K, $M_{FC}$ increases with increasing doping for 0.02 ≤ x ≤ 0.08, while $M_{FC}$ at x = 0.1 almost coincides with that at x = 0.08. Field cooled magnetization of the latter samples exhibits wide maximum related to the charge/orbital ordering (CO/OO) at $T_{CO} \approx 121$ K for the sample with x = 0.08 and $T_{CO} \approx 139$ K for that with x = 0.1. Inset to Fig. 1(b) shows magnetic hysteresis loops measured at T = 10 K after ZFC. The spontaneous magnetization $M_0$, evaluated by linear extrapolation of the high field magnetization

<figure><img src="image_9.png" /><figcaption>FIG. 1. (a) and inset in (a) $M_{ZFC}(T)$ (open symbols) and $M_{FC}(T)$ (solid symbols) recorded in H = 100 Oe for CaMn₁-xRexO₃ samples with x = 0.02 (triangles), x = 0.04 (stars), x = 0.06 (circles), x = 0.08 (squares), x = 0.1 (diamonds). (b) $M_{FC}(T)$ recorded in magnetic field of H = 15 kOe. Inset shows hysteresis loops for CaMn₁-xRexO₃ samples recorded at T = 10 K after ZFC. (c) Hysteresis loops of CMRO at various T, as measured after FC in $H_{cool}$ = 15 kOe.</figcaption></figure>
to $H = 0$, is very small (0.79 emu/g) for $x = 0.02$, increases quickly with increasing $x$, peaks at $x = 0.04$ ($M_0 \approx 3.53$ emu/g), and then drops to 0.24 emu/g for $x = 0.1$. Small values of $M_0(x)$ indicate that at low temperatures, the major part of the magnetic volume of CMRO samples is occupied by AFM matrix.

Figure 2(a) shows hysteresis loops measured at various temperatures for the sample with $x = 0.1$ after FC in $H_{\text{cool}} = 15$ kOe. There is no magnetic hysteresis above 100 K. Loops recorded at $T < 80$ K show shifts along magnetic field axis which is absent in the ZFC loops, as expected for the EB effect. This shift of the hysteresis loop is usually quantified as $H_{\text{EB}} = -(H_1+H_2)/2$, where $H_1$ and $H_2$ are the fields at which the magnetization equals zero for decreasing and increasing branch of the loop, respectively.¹⁻⁵ The shift along the magnetization axis is quantified as $M_{\text{EB}} = (M_1+M_2)/2$, where $M_1$ and $M_2$ are the magnetizations at $H = 0$ for decreasing and increasing branches of the hysteresis loop, respectively. The presence of a vertical shift can be linked to the remanent state, arising from the presence of a FM-like phase distributed in the AFM matrix. It appears that $H_{\text{EB}}$ is very small for the sample with $x = 0.02$ and 0.04, and increases with increasing doping at $x > 0.04$, as the volume of FM phase decreases. Therefore, we have studied in details the EB effect only for higher doping levels, $x = 0.06, 0.08$, and 0.1.

For maximal applied magnetic field $H_{\text{MAX}} = 15$ kOe, the magnetization is far from being saturated. The ascending and descending branches of hysteresis loops coincide only at fields close to the $H_{\text{MAX}}$. Thus, the observed $H_{\text{EB}}$ and $M_{\text{EB}}$ may represent somewhat the effect of minor loops.¹⁴⁻¹⁶ It was suggested that the presence of the “true” EB may be derived only from effectively saturated hysteresis loops recorded in high enough $H_{\text{MAX}}$.¹⁴⁻¹⁶ A system will be considered effectively saturated if the ascending and descending branches of its hysteresis loop coincide at fields higher than the anisotropy field.

<figure><img src="image_10.png" /><figcaption>FIG. 2. (a) Hysteresis loops of $x = 0.1$ sample, at various $T$, as measured after FC in $H_{\text{cool}} = 15$ kOe. (b) Hysteresis loops of $x = 0.1$ sample as measured at $T = 10$ K after FC in $H_{\text{cool}} = 15$ kOe with different $H_{\text{MAX}}$. (c,d) $H_{\text{EB}}$, $M_{\text{EB}}$, $H_{\text{C}}$, and $M_{\text{C}}$ as a function of $H_{\text{MAX}}$.</figcaption></figure>
To verify if the EB in CMRO is an intrinsic one, we have investigated the dependence of $H_{EB}$ and $M_{EB}$ on $H_{MAX}$ for the sample doped at $x = 0.1$. It can be seen in Fig. 2(b) that for low $H_{MAX}$, loops exhibit large horizontal and vertical shifts. However, for the same cooling field $H_{cool}$ and large enough $H_{MAX}$, $H_{EB}$ and $M_{EB}$ stabilize, see Fig. 2(c). It appears that $H_{EB}$ and $M_{EB}$ decrease with increasing measuring field $H_{MAX}$ in very similar manner, while $H_{C}$ and $M_{C}$ increase with increasing field, see Fig. 2(d). Here, the coercivity $H_{C}$ is defined as the half-width of the loop $H_{C} = (H_{2} - H_{1})/2$, while the magnetic coercivity $M_{C} = (M_{1} - M_{2})/2$ is the “vertical axis” equivalent of $H_{C}$.

The essential property of any exchange biased system is so-called training effect, which manifests itself in the reduction of $H_{EB}$ with increasing number of consecutively recorded loops at a fixed temperature.3,5,9 We have measured 10 hysteresis loops for $x = 0.06, 0.08$, and $0.1$ samples at $T = 10$ K after FC at $H_{cool} = 20$ kOe with $H_{MAX} = 50$ kOe. It is well known that $H_{EB}$ change is the most significant between the first and the second loop.3,5,9 Moreover, the change is the most pronounced at the left branch of the loop, while the right branch evolves only slightly. Figure 3(a) shows the recording of 10 hysteresis loops for $x = 0.1$ sample, while Fig. 3(b) presents an enlarged view of the shift in the left branch of $M(H)$. The loops shift toward lower fields upon increasing number of field cycles $n$. Figure 3(c) shows the dependence of both $H_{1}$ and $H_{2}$ on the number $n$ of field cycles, while the evolution of $H_{EB}$ with $n$ is presented in Fig. 3(d). The dependence of $H_{EB}$ on the number of cycles $n$ can be well fitted by a simple power law expression,3,5,9

$$H_{EB}(n) - H_{EB\infty} \propto A/\sqrt{n}, \quad (1)$$

<figure><img src="image_11.png" /><figcaption>FIG. 3. (a) Consecutively measured ten hysteresis loops of the sample with $x = 0.1$ at $T = 10$ K cooled under $H_{cool} = 20$ kOe with $H_{MAX} = \pm 50$ kOe. (b) The enlarged view of these loops to reveal the shift of the loops with increasing loop number. (c) Variation of the coercive fields $H_{1}$ and $H_{2}$ with number of recurrent hysteresis loops $n$. (d) The symbols represent the experimental data for $H_{EB}$ versus loop index number. Dashed line corresponds to a fit with a power law (Eq. (1)) for $n \ge 2$, while solid line illustrates the best fit with the Eq. (2).</figcaption></figure>
<table><caption>TABLE I. Values of expressions 1 and 2 fitting parameters approximating experimental data for TE.</caption><thead><tr><th></th><th colspan="6">H<sub>EB</sub>(n) = H<sub>EB∞</sub> + A<sub>f</sub> exp(-n/P<sub>f</sub>) + A<sub>i</sub> exp(-n/P<sub>i</sub>)</th></tr><tr><th>sample</th><th>H<sub>EB∞</sub> (Oe)</th><th>A<sub>f</sub> (Oe)</th><th>P<sub>f</sub></th><th>A<sub>i</sub> (Oe)</th><th>P<sub>i</sub></th><th>R<sup>2</sup></th></tr></thead><tbody><tr><td>x=0.06</td><td>39±4</td><td>110±20</td><td>0.4±0.1</td><td>9±2</td><td>6±3</td><td>0.983</td></tr><tr><td>x=0.08</td><td>78±3</td><td>56000±8000</td><td>0.1±0.1</td><td>12±2</td><td>6±2</td><td>0.987</td></tr><tr><td>x=0.1</td><td>199±5</td><td>2000±1000</td><td>0.2±0.1</td><td>29±2</td><td>7±3</td><td>0.998</td></tr></tbody></table><table><thead><tr><th></th><th colspan="3">H<sub>EB</sub>(n) - H<sub>EB∞</sub> ∝ A/√n</th></tr><tr><th>sample</th><th>H<sub>EB∞</sub> (Oe)</th><th>A (Oe)</th><th>R<sup>2</sup></th></tr></thead><tbody><tr><td>x=0.06</td><td>36.7±0.6</td><td>14±2</td><td>0.936</td></tr><tr><td>x=0.08</td><td>70.1±0.8</td><td>17±2</td><td>0.954</td></tr><tr><td>x=0.1</td><td>194±2</td><td>40±3</td><td>0.963</td></tr></tbody></table>

where $H_{EB\infty}$ is the value of the EB field recorded at $n \to \infty$. The dashed line in Fig. 3(d) shows the best fitted curve for $n \ge 2$ with $H_{EB\infty} = 194 \pm 2$ Oe. Fitting parameters for all doping levels are presented in Table I. It should be underlined that the relation (1) holds only for $n \ge 2$ and cannot explain steep relaxations between the first and the second loop.

Recently, the TE has been alternatively described using two different relaxation rates for frozen and rotatable uncompensated spin components at the interface.¹⁷ In this approach

$$H_{EB}(n) = H_{EB\infty} + A_{f} \exp(-n/P_{f}) + A_{i} \exp(-n/P_{i}), \quad (2)$$

where $A_f$ and $P_f$ are related to changes in the frozen spins configuration, and $A_i$ and $P_i$ are evolving parameters linked to the rotatable spin component at the FM/AFM interface. The magnetic field dimension is dimension of parameters $A$, while parameters $P$ are dimensionless and in some sense act as a relaxation time, although the continuous time variable is replaced by a discrete loop number. Equation (2) fits to the data much better than the simple power law, including the first two points, as proved by the fitting quality parameter $R^2$. The relevant fitting parameters are shown in Table I. It appears that for all studied samples the contributions of rotatable uncompensated AFM spins and frozen AFM components at the interface are comparable at the initial stage of the training but the frozen AFM component relaxes much slower with respect to the rotatable one. Indeed, the rotatable uncompensated AFM spins relax much quicker for higher doped samples ($x = 0.08$ and $0.1$) and their contribution becomes vanishingly small already at $n = 2$, while for $x = 0.06$ the rotatable contribution remains still essential for $n = 2$. The difference in the relaxation of both components may be measured by the relative rate of relaxation of frozen and rotatable spins $P_f / P_i$ which for the sample with $x = 0.06$ is significantly larger than that for the samples with higher doping levels. In principle, that difference may be a consequence of differences in phase separation in different samples. We have recently proposed that small FM clusters are distributed in the G-type AFM matrix for $x = 0.06$ case, while and in samples with $x = 0.08$ and $0.1$, the matrix is more anisotropic C-type CO AFM.¹³ Unfortunately, significant errors in the fitting parameters do not enable us to confirm such a claim in this case. We may only conclude that Eq. (2) describes well the TE effect in studied samples.

This work was supported by the Polish NCN grants 2014/15/B/ST3/03898 and 2012/05/B/ST3/03157.

<footnote n="1">¹ W. H. Meiklejohn and C. P. Bean, *Phys. Rev.* **102**, 1413 (1956); **105**, 904 (1957); W. H. Meiklejohn, *J. Appl. Phys.* **33**, 1328 (1962).</footnote>

<footnote n="2">² J. Nogués and I. K. Schuller, *J. Magn. Magn. Mater.* **192**, 203 (1999).</footnote>

<footnote n="3">³ J. Nogués, J. Sort, V. Langlais, V. Skumryev, S. Suriñach, J. S. Muñoz, and M. D. Baró, *Phys. Rep.* **422**, 65 (2005).</footnote>

<footnote n="4">⁴ F. Radu and H. Zabel, in *Magnetic Heterostructures: Advances and Perspectives in Spin structures and Spin transport*, Ed. H. Zabel and S. D. Bader, Springer Tracts in Modern Physics (Springer-Verlag, Berlin, 2008), vol. 227, pp. 97–184.</footnote>

<footnote n="5">⁵ S. Giri, M. Patra, and S. Majumdar, *J. Phys.: Condens. Matter.* **23**, 073201 (2011).</footnote>

<footnote n="6">⁶ D. Niebieskikwiat and M. B. Salamon, *Phys. Rev. B* **72**, 174422 (2005).</footnote>

<footnote n="7">⁷ T. Qian, G. Li, T. F. Zhou, X. Q. Xiang, X. W. Kang, and X. G. Li, *Appl. Phys. Lett.* **90**, 012503 (2007).</footnote>
<footnote n="8"><sup>8</sup> I. Fita, V. Markovich, A. Wisniewski, R. Puzniak, C. Martin, V. N. Varyukhin, and G. Gorodetsky, Phys. Rev. B **88**, 064424 (2013).</footnote>

<footnote n="9"><sup>9</sup> S. Karmakar, S. Taran, E. Bose, B. K. Chaudhuri, C. P. Sun, C. L. Huang, and H. D. Yang, Phys. Rev. B **77**, 144409 (2008).</footnote>

<footnote n="10"><sup>10</sup> J. B. MacChesney, H. J. Williams, J. F. Potter, and R. C. Sherwood, Phys. Rev. **164**, 779 (1967).</footnote>

<footnote n="11"><sup>11</sup> E. O. Wollan and W. C. Koehler, Phys. Rev. **100**, 545 (1955).</footnote>

<footnote n="12"><sup>12</sup> B. Raveau, A. Maignan, C. Martin, and M. Hervieu, Mater. Res. Bull. **35**, 1579 (2000).</footnote>

<footnote n="13"><sup>13</sup> V. Markovich, I. Fita, A. Wisniewski, R. Puzniak, C. Martin, D. Mogilyansky, G. Jung, and G. Gorodetsky, to be published.</footnote>

<footnote n="14"><sup>14</sup> G. Salazar-Alvarez, J. Sort, S. Suriñach, M. D. Baró, and J. Nogués, J. Am. Chem. Soc. **129**, 9102 (2007).</footnote>

<footnote n="15"><sup>15</sup> J. Geshev, J. Magn. Magn. Mater. **320**, 600 (2008); J. Phys.: Condens. Matter **21**, 078001 (2009); J. Appl. Phys. **105**, 066108 (2009).</footnote>

<footnote n="16"><sup>16</sup> A. Harres, M. Mikhov, V. Skumryev, A. M. H. de Andrade, J. E. Schmidt, and J. Geshev, J. Magn. Magn. Mater **402**, 76 (2016).</footnote>

<footnote n="17"><sup>17</sup> S. K. Mishra, F. Radu, H. A. Dürr, and W. Eberhardt, Phys. Rev. Lett. **102**, 177208 (2009).</footnote>