Spacer Thickness and Temperature Dependences of the Interlayer Exchange Coupling in a Co/Pt/Co Three-Layer Structure

Round 1

Reviewer 1 Report

In this manuscript, the domain wall mobility in the Co/Pt/Co ultra-thin exchange coupled ferromagnetic layer is investigated as a function of the thickness and temperature between the non-magnetic layers. The results show that there is ferromagnetic interaction between the Co layers when the thickness of the Pt layer varies from 5 nm to 6 nm. The nonlinear relationship between the domain wall displacement and the applied electric field is measured. This is an interesting manuscript, but it has some shortcomings, as follows:

1. The authors has cited some relevant literatures in this research field, but in the introduction, it is suggested that the author add some recent literatures to support the research background.

2. This paper focuses on the description of experimental results, but lacks the discussion of relevant mechanisms. I suggest that the authors add some analysis and discussion of relevant mechanisms.

3. Fig.6 shows the relationship between effective field and interlayer distance, according to which the interlayer coupling mechanism can be deduced. Recently, there are literatures [Mater. Today comm. 34(2023) 105030; Frontiers of Physics 18(2023)43302] on the fitting of electrical coupling mechanism between layers, which can be used for reference by authors.

4. There are several minor deficiencies that need to be corrected by the authors.

1) There is no abscissa in Fig.8(a), so the bottom frame of Fig.8(a) needs to be added or merged with the top frame of Fig.8(b).

2) The two fitting formulas in Fig.8 and their correlation should be given.

5. "... both coercivity of the Co layer and critical thickness decrease at higher temperature, while the interlayer exchange constant J is changed weakly”. Can the authors give further analysis of this phenomenon?

Author Response

Refery1

Comments and Suggestions for Authors

In this manuscript, the domain wall mobility in the Co/Pt/Co ultra-thin exchange coupled ferromagnetic layer is investigated as a function of the thickness and temperature between the non-magnetic layers. The results show that there is ferromagnetic interaction between the Co layers when the thickness of the Pt layer varies from 5 nm to 6 nm. The nonlinear relationship between the domain wall displacement and the applied electric field is measured. This is an interesting manuscript, but it has some shortcomings, as follows:

1. The authors has cited some relevant literatures in this research field, but in the introduction, it is suggested that the author add some recent literatures to support the research background.

New references have been included into the Introduction with brief explanation, namely:

 

8. Omelchenko, P.; Montoya, E.; Girt, E.; Heinrich, B. Interlayer Exchange Coupling, Spin Pumping and Spin Transport in Metallic Magnetic Single and Bilayer Structures. J. Exp. Theor. Phys. 2020, 131, 113–129
9. Q. Liua, S. Jiang, and J. Tengc, Applied Surface Science 433, 556–559 (2018)
10. Szulc, K.; Mendisch, S.; Mruczkiewicz, M.; Casoli, F.; Becherer, M.; Gubbiotti, G. Nonreciprocal spin-wave dynamics in Pt/Co/W/Co/Pt multilayers. Phys. Rev. B 2021, 103, 134404.
11. Katagiri, M.; Cuya Huaman, J.L.; Matsumoto, T.; Suzuki, K.; Miyamura, H.; Balachandran, J. Magneto-Plasmonic Co@Pt@Au Nanocrystals for Biosensing and Therapeutics. ACS Appl. Nano Mater. 2020, 3, 418–427.
12. Morgunov, R.B.; Yurov, A.V.; Yurov, V.A.; Talantsev, A.D.; Bezverhnii, A.I.; Koplak, O.V. Oscillatory dynamics of the magnetic moment of a Pt/Co/Ir/Co/Pt synthetic antiferromagnet. Phys. Rev. B 2019, 100, 144407.
13. Morgunov, R.B.; Bezverkhnii, A.I.; Hehn, M.; Bello, J.L.; Fache, T.; Mangin, S. Dzyaloshinskii-Moriya interaction probed by magnetization reversal in bilayer Pt/Co/Ir/Co/Pt synthetic ferrimagnets. Phys. Rev. B 2021, 104, 134424.
14. Mazalski, P.; Anastaziak, B.; Ku´swik, P.; Kurant, Z.; Sveklo, I.; Maziewski, A. Demagnetization of an ultrathin Co/NiO bilayer with creation of submicrometer domains controlled by temperature-induced changes of magnetic anisotropy. J. Magn. Magn. Mat. 2020, 508, 166871.

 

2. This paper focuses on the description of experimental results, but lacks the discussion of relevant mechanisms. I suggest that the authors add some analysis and discussion of relevant mechanisms.

The text following below is added into the end of the Results and Discussion section.

Interlayer exchange between the ferromagnetic layers through the nonmagnetic layer depends on interlayer properties. It has the same origin as the RKKY interaction between magnetic impurities in the non-magnetic medium []. This interaction due to spin-polarized conductive electrons controls magnetic properties of such multilayers. The RKKY theory precicts []that for spacer-layer thicknesses, t, the coupling should be given by a sum of terms of the form

 J(t)= Σ(J^a/t²) sin(q^at + φ^a),                                                                   (4)

where sum is over all critical point, labeled by a, with critical spanning vector q^a, coupling strength, J^a and phase φ^a. This results in oscillatory behavior of the J(t) dependence taking both positive and negative values, that is, parallel or antiparallel spin orientation in the ferromagnetic layers. The oscillation period is known well, while the J(t) dependence itself is not studied in details in case of ferromagnetic interaction between the layers. Our work presents such information determined experimentally via direct measurement of the effective exchange field with its compensation by the external magnetic field as described above.

Further, The RKKY models predict a specific form of the temperature dependence [], including

an additional factor of the form

(2pk_BT t/ħv^a)/sinh(2pk_BT t/ħv^a)                                                           (5)

associated with each critical spanning vector. One can see that temperature appears here as a product by the interlayer thickness. We have studied dependence of the effective field on thickness, ΔH_J/Δt, at different temperatures (Fig..7). This dependence does not change much at different temperatures, as observed in our experiments.

 

3. Fig.6 shows the relationship between effective field and interlayer distance, according to which the interlayer coupling mechanism can be deduced. Recently, there are literatures [Mater. Today comm. 34(2023) 105030; Frontiers of Physics 18(2023)43302] on the fitting of electrical coupling mechanism between layers, which can be used for reference by authors.

The reference has been mentioned in Page 5 after the sentence «One can see that effective field H_J(t) grows with decrease of t, that is, increase of x»: Dependence of electric exchange on the distance between atomic layers has been discussed recently in [28].

 

4. There are several minor deficiencies that need to be corrected by the authors.

 

1) There is no abscissa in Fig.8(a) , so the bottom frame of Fig.8(a) needs to be added or merged with the top frame of Fig.8(b).

The field units are restored in Fig. 8(a).

 

2) The two fitting formulas in Fig.8 and their correlation should be given.

The fitting formulae and reliability R² have been added to Fig.8.

 

5. "... both coercivity of the Co layer and critical thickness decrease at higher temperature, while the interlayer exchange constant J is changed weakly”. Can the authors give further analysis of this phenomenon?

In the present paper we study dependence of the effective field on interlayer thickness ΔH_J/Δt at different temperatures (Fig.7). This dependence is found to be weak (page 5). Currently the existing theories of interlayer RKKY exchange interaction do not describe exactly its temperature dependence. Some of them predict that this interaction is proportional to the interface thickness multiplied by temperature. However the dependence H_J(t) itself varies weakly, as observed in our experiment.

Reviewer 2 Report

This manuscript presents an investigation of Co layer interaction in function of non-magnetic Pt layer thickness, external field and temperature, with a very nice technique. Despite of being a little confused and difficult to follow, some lack of information in the text could lead the findings for a non-interesting go. If the authors explain the criticisms below with this lack of information I would recommend the manuscript publication.   

-          It is well known that different Pt layers thickness utilized in bottom and top layer would bring DM interaction to the system. The authors should comment on that. In fact one would expect that skyrmions/bubbles would be formed in the process, is that not the case here?

-          The results were obtained in a large sample area of 30mm², but images just show a much zoomed part of it (around 150um length), is the result presented reproducible all over the sample along X₀?  The authors should let it clear.

-          An arrow from thick to thin region should be inserted in the figure 3 for reader’s better understanding.

-          Why is the behavior at 190K so different from the successive temperatures, I could not find enough discussions about that in the manuscript.

The most critical point is that the authors state, without describe how, that the Pt layer increases uniformly from 5 to 6nm. Was that achieved by angle deposition? If yes all the layers should have similar variation and successively varied coercivity, then the model for explanation in Fig 3. Could not be so simple and also relations using bottom layer uniform coercivity would be wrong.

Author Response

Refery2

Comments and Suggestions for Authors

This manuscript presents an investigation of Co layer interaction in function of non-magnetic Pt layer thickness, external field and temperature, with a very nice technique. Despite of being a little confused and difficult to follow, some lack of information in the text could lead the findings for a non-interesting go. If the authors explain the criticisms below with this lack of information I would recommend the manuscript publication.   

-          It is well known that different Pt layers thickness utilized in bottom and top layer would bring DM interaction to the system. The authors should comment on that. In fact one would expect that skyrmions/bubbles would be formed in the process, is that not the case here?

Indeed, interfaces between magnetic materials and materials with large spin-orbit interactions offer promise for giant interfacial DM interactions. However, for perpendicularly magnetized materials an interfacial DM interaction influences on the structure and dynamics of the domain wall [Thiaville, A., S. Rohart, É. Jué, V. Cros, and A. Fert, 2012, “Dynamics of Dzyaloshinskii domain walls in ultrathin magnetic films,” Europhys. Lett. 100, 57002]. In our experiment we consider quasi-static problem of domain wall displacement in the permanent magnetic field which is practically not dependent on the internal domain wall structure. Thus we do not consider any specific contribution of DMI. 

-          The results were obtained in a large sample area of 30mm², but images just show a much zoomed part of it (around 150um length), is the result presented reproducible all over the sample along X₀?  The authors should let it clear.

Figure 2 shows only small sample fragment ion the vicinity of the separation point between ferromagnetic and antiferromagnetic interlayer interaction. Displacement of the domain wall from х0 to х_CR has been measured, naturally, in the whole sample width along the y coordinate.

-          An arrow from thick to thin region should be inserted in the figure 3 for reader’s better understanding.

We believe that an additional arrow in Fig.3 would only complicate it because thickness t is not a vector and direction of thickness change is obvious from the sample sketch.

-          Why is the behavior at 190K so different from the successive temperatures, I could not find enough discussions about that in the manuscript.

There was a misprint in captions to Figs.5-6, the right value 293K is restored instead of 193K.

The most critical point is that the authors state, without describe how, that the Pt layer increases uniformly from 5 to 6nm. Was that achieved by angle deposition? If yes all the layers should have similar variation and successively varied coercivity, then the model for explanation in Fig 3. Could not be so simple and also relations using bottom layer uniform coercivity would be wrong.

All layers were deposited by usual direct sputtering as described in the experimental part of the paper. Gradual change of the Pt thickness is achieved with slow increase of the exposed surface. The own Co coercivity remain permanent in this process.

Reviewer 3 Report

Referee Report

on paper “Spacer thickness and temperature dependences of the interlayer exchange coupling in a Co/Pt/Co three-layer structure”

Submitted to Magnetochemistry

By V.S. Gornakov, I.V. Shashkov, O.A. Tikhomirov and Yu.P., Kabanov

 

The manuscript reported a domain wall mobility as a function of nonmagnetic interlayer thickness and temperature. Both motivation and method of the manuscript are inspiring for the development of ultrathin magnetic films and heterostructures possessing perpendicular magnetic anisotropy. It is recommended to make minor revisions. Here are some comments for the manuscript:

 

Comments

1. It would be helpful to provide a more detailed description in the introduction of the practical applications that may be associated with the results of this research. What problems or technical barriers may arise when implementing these findings in practice?

 

2.  The paper includes 21 references to the literature, but only one reference from 2022. All others are 10 or 20 years old. It would be beneficial to add references to articles in your field written in recent years. This will help readers verify the factual information and explore contemporary research in this area. Please consider the following articles related to research topics: 10.3390/nano10061077

 

3. In present study, you discuss the shape of hysteresis loops, but the actual loops were not included in the article. To enhance the understanding of the results, it would be beneficial to add an image showing the hysteresis loops to illustrate the observed phenomena and support your statements. Specifically, what parameters were measured, and what equipment was used?

 

4. Please provide a more detailed description of the methods and experimental conditions employed. For example, include a detailed description of the magnetron sputtering process and the parameters used in the experiment.

 

5. To improve the understanding of your work, it is advisable to provide a more detailed description of the obtained results and their significance. Explain the physical reasons underlying the observed effects. For instance, provide a more comprehensive explanation of the physical mechanisms that lead to the interaction between the two walls and their movement depending on the field amplitude.

 

6. The conclusion clearly and eloquently describes the obtained results. However, it would be interesting to learn about possible further research or practical applications of the obtained findings, as well as their contributions to the field.

 7. Please improve your English

My decision is minor revision

Author Response

Refery3

 

The manuscript reported a domain wall mobility as a function of nonmagnetic interlayer thickness and temperature. Both motivation and method of the manuscript are inspiring for the development of ultrathin magnetic films and heterostructures possessing perpendicular magnetic anisotropy. It is recommended to make minor revisions. Here are some comments for the manuscript:

 Comments

1. It would be helpful to provide a more detailed description in the introduction of the practical applications that may be associated with the results of this research. What problems or technical barriers may arise when implementing these findings in practice?

We have added to Introduction (Page 2) some references describing possible applications of thin magnetic films/heterostructures and discussing possible problems of their realization.

Intensive study of magnetic heterostructures properties [1-10] is pointed at mechanisms of their magnetization reversal and magnetic transport. The goal is to build adequate theoretical models necessary for design and optimization of the magnetic devices [11-14]. In the systems where two ferromagnetic (FM) layers are decoupled by a nonmagnetic (NM) layer, the significant problem is dependence of magnetization, coercivity, domain wall mobility and other properties on interlayer exchange interaction J = 2 H_J M b, where H_J is effective field of the interlayer exchange interaction between FM layers, M and b are magnetization and thickness of FM layers [6]. Further, J itself depends on both NM interlayer thickness t and temperature T. Change of these parameters can critically affect reliability and working characteristics of the magnetic devices.

2. The paper includes 21 references to the literature, but only one reference from 2022. All others are 10 or 20 years old. It would be beneficial to add references to articles in your field written in recent years. This will help readers verify the factual information and explore contemporary research in this area. Please consider the following articles related to research topics: 10.3390/nano10061077

New references have been included into the Introduction with brief explanation, namely:

 

8. Omelchenko, P.; Montoya, E.; Girt, E.; Heinrich, B. Interlayer Exchange Coupling, Spin Pumping and Spin Transport in Metallic Magnetic Single and Bilayer Structures. J. Exp. Theor. Phys. 2020, 131, 113–129
9. Q. Liua, S. Jiang, and J. Tengc, Applied Surface Science 433, 556–559 (2018)
10. Szulc, K.; Mendisch, S.; Mruczkiewicz, M.; Casoli, F.; Becherer, M.; Gubbiotti, G. Nonreciprocal spin-wave dynamics in Pt/Co/W/Co/Pt multilayers. Phys. Rev. B 2021, 103, 134404.
11. Katagiri, M.; Cuya Huaman, J.L.; Matsumoto, T.; Suzuki, K.; Miyamura, H.; Balachandran, J. Magneto-Plasmonic Co@Pt@Au Nanocrystals for Biosensing and Therapeutics. ACS Appl. Nano Mater. 2020, 3, 418–427.
12. Morgunov, R.B.; Yurov, A.V.; Yurov, V.A.; Talantsev, A.D.; Bezverhnii, A.I.; Koplak, O.V. Oscillatory dynamics of the magnetic moment of a Pt/Co/Ir/Co/Pt synthetic antiferromagnet. Phys. Rev. B 2019, 100, 144407.
13. Morgunov, R.B.; Bezverkhnii, A.I.; Hehn, M.; Bello, J.L.; Fache, T.; Mangin, S. Dzyaloshinskii-Moriya interaction probed by magnetization reversal in bilayer Pt/Co/Ir/Co/Pt synthetic ferrimagnets. Phys. Rev. B 2021, 104, 134424.
14. Mazalski, P.; Anastaziak, B.; Ku´swik, P.; Kurant, Z.; Sveklo, I.; Maziewski, A. Demagnetization of an ultrathin Co/NiO bilayer with creation of submicrometer domains controlled by temperature-induced changes of magnetic anisotropy. J. Magn. Magn. Mat. 2020, 508, 166871.

We believe that the another recommended paper «The Effect of Heat Treatment on the Microstructure and Mechanical Properties of 2D Nanostructured Au/NiFe System» by Tatiana Zubar, Valery Fedosyuk, Daria Tishkevich, et al, published in Nanomaterials 2020, 10(6), 1077; doi: 10.3390/nano10061077 is far of our research devoted to low temperatures, and our effects o are not related to annealing and change of the sample microstructure.

3. In present study, you discuss the shape of hysteresis loops, but the actual loops were not included in the article. To enhance the understanding of the results, it would be beneficial to add an image showing the hysteresis loops to illustrate the observed phenomena and support your statements. Specifically, what parameters were measured, and what equipment was used?

We have added Figure 4 showing the hysteresis loops obtained at 293K, 250K and 160K. The figures is introduced  in page 4 with following description:

Fig. 4 show local hysteresis loops obtained at different temperatures. It can be seen that coercivity of the sample increases at low temperatures. Steps in the loops at high temperature confirm difference in coercivity between the upper Co layer and the bottom one. At low temperature these steps are absent, this means that the walls in both layers move simultaneously. These loops can be used to obtain coercivity of both layers at different temperatures; however, more detailed information about the interlayer exchange interaction can be extracted from magnetooptic measurements of the wall motion in the external field as described in the paper.

Also added is caption to the new Fig.4:

Fig.4. Hysteresis loops of the sampel at (a) T=293K, (b) 250K and (c) 160K.

 

4. Please provide a more detailed description of the methods and experimental conditions employed. For example, include a detailed description of the magnetron sputtering process and the parameters used in the experiment.

The experimental part of the paper has been expanded to provide more detailed description of the sample preparation, measurements technique and the data processing.

5. To improve the understanding of your work, it is advisable to provide a more detailed description of the obtained results and their significance. Explain the physical reasons underlying the observed effects. For instance, provide a more comprehensive explanation of the physical mechanisms that lead to the interaction between the two walls and their movement depending on the field amplitude.

The text following below is added into the end of the Results and Discussion section.

 

Interlayer exchange between the ferromagnetic layers through the nonmagnetic layer depends on interlayer properties. It has the same origin as the RKKY interaction between magnetic impurities in the non-magnetic medium []. This interaction due to spin-polarized conductive electrons controls magnetic properties of such multilayers. The RKKY theory precicts []that for spacer-layer thicknesses, t, the coupling should be given by a sum of terms of the form

 J(t)= Σ(J^a/t²) sin(q^at + φ^a),                                                                   (4)

where sum is over all critical point, labeled by a, with critical spanning vector q^a, coupling strength, J^a and phase φ^a. This results in oscillatory behavior of the J(t) dependence taking both positive and negative values, that is, parallel or antiparallel spin orientation in the ferromagnetic layers. The oscillation period is known well, while the J(t) dependence itself is not studied in details in case of ferromagnetic interaction between the layers. Our work presents such information determined experimentally via direct measurement of the effective exchange field with its compensation by the external magnetic field as described above.

Further, The RKKY models predict a specific form of the temperature dependence [], including

an additional factor of the form

(2pk_BT t/ħv^a)/sinh(2pk_BT t/ħv^a)                                                           (5)

associated with each critical spanning vector. One can see that temperature appears here as a product by the interlayer thickness. We have studied dependence of the effective field on thickness, ΔH_J/Δt, at different temperatures (Fig..7). This dependence does not change much at different temperatures, as observed in our experiments.

As concerns to interaction between the two walls and their movement, we have especially chosen such experimental conditions where the domain walls in separate FM layers do not interact.

6. The conclusion clearly and eloquently describes the obtained results. However, it would be interesting to learn about possible further research or practical applications of the obtained findings, as well as their contributions to the field.
   
   We have added the following sentence to Conclusion:

As the results obtained using the wedge interlayer samples can be influenced by this shape, we are going to study temperature dependent domain wall mobility in the samples with fixed t in our following publications. The measured J(T) dependencies should help to deduce the adequate theory of interlayer exchange interaction in such trilayers.

Round 2

Reviewer 2 Report

The authors have not adressed my critiscisms properly. They have not explained correctly how they vary just the Pt thickness without vary other thicknesses and just ignore the fact that dzyaloshinskii-moriya interaction, which is dependent on multilayer thicknesses and temperature, would play a very important role in the results presented. They justify that by saying that DM would be just interfacial and important under dynamics, but that is totally wrong. Based on the lack of interest in discuss and improve the manuscript, or even make clear the not considered part, I think that the manuscript could show wrong conclusions and then I would not recomend its publication in the current form.   

Author Response

They have not explained correctly how they vary just the Pt thickness without vary other thicknesses… In order to form the wedge-shaped Pt spacer without varying thicknesses of other ferromagnetic layers it was grown by moving a knife-edge shutter during sputtering this Pt layer. So, the Co thickness and its own coercivity remain permanent in this process. Such formation of the interlayer wedge is widely used in different layered systems like: Fe/Cr/Fe (PRL 67, l40, 1991), Fe/Au/Fe (JAP 75, 6437–6439, 1994), Co/Pt/Co (JMMM 422 465–469, 2017 and JAP 113, 17C101, 2013), Pt/Co wedge/Pt (JMMM, 260 231–243, 2003 and PRL 94, 017203, 2005), and so on (see H. Zabel and S. D. Bader Eds., Magnetic Heterostructures, STMP 227 Springer, Berlin Heidelberg, 2008). The thickness of other FM layers remains permanent, their coercivity is also constant. To explain the growth process of the wedge Pt interlayer we add the following sentence into the Experiment section: «Wedge-shaped Pt spacer layers were grown by moving a knife-edge shutter in front of the Co bottom layer during Pt deposition.» --- … just ignore the fact that dzyaloshinskii-moriya interaction, which is dependent on multilayer thicknesses and temperature, would play a very important role in the results presented. They justify that by saying that DM would be just interfacial and important under dynamics, but that is totally wrong. In order to improve the manuscript and to make clear the considered part, we add into the Introduction section the new paragraph describing an important role in the influence of the Dzyaloshinskii-Moriya interaction on properties of the FM layers but not in the interlayer exchange coupling in the FM/NM/FM heterostructure. Dependences of this coupling on the spacer thickness and temperature are the main goal of our study. The co-called “proximity effect”, namely, induced magnetization in the thin Pt layer adjacent to Co, may influence on interlayer exchange coupling. However, this effect is very small at the used temperature and Pt thickness, thus we do not discuss it in our paper. “In many such heterostructures [1-6, 16, 17] the Pt layer thickness utilized in bottom and top layer would bring Dzyaloshinskii-Moriya interaction (DMI) to the system. The magnetic structures in FM layer coupled to the Pt layer can arise from interplay of spin stiffness, usual crystallographic anisotropy and DMI. Due to the Heisenberg-type exchange interaction the distinct change of magnetization should have comparatively long scale. As the film is ultrathin, only the in-plane degrees of freedom for such changes do exist. Namely, such long-ranged magnetic structures can be found on surfaces around domain walls of thin magnetic films. The theoretical [27, 28] and experimental [1-6, 29] papers show that DMI in ultrathin films acts only on its domain structure, while it has no influence on the exchange coupling between two FM layers through NM spacer when magnetization of the heterostructures is reversed.” 27. M. Heide, G. Bihlmayer, P. Mavropoulos, et al., Newslett. Psi-K Netw., 78, 1 (2006). 28. A. Thiaville, S. Rohart, ´E. Jue, et al., EPL, 100, 57002 (2012)

Author Response File: Author Response.docx

Round 3

Reviewer 2 Report

The authors have addressed all of my concerns and questions, so I recommend the manuscript publication in its present form.