Julien Lévêque

Elisa Rebolini

Marie-Bernadette Lepetit
email: bernadette.lepetit@neel.cnrs.fr

Andrés Saúl
email: andres.saul@cnrs.fr

Theoretical study of the magnetic properties of the CoCu 2 O 3 compound

In this work we present a theoretical study of the magnetic properties of the CoCu2O3 compound. The magnetic effective exchange interactions and zeroth-field splitting were computed using ab-initio methods, then the magnetic order and transition temperature were determined using classical Monte-Carlo simulations. We showed that, unlike other members of the ACu2O3 family, the presence of an additional magnetic atom, associated with a large folding of the puckered layers in the ( a, b) directions, induces a magnetic pattern based on coupled 3-leg ladders, quite different from the 2-leg structural ladders. The propagation vector has been found to be q = (0, 1 2 , 1 2 ). It is associated to a doubly-degenerated ground state suggesting a doubling of the unit cell. The large Co 2+ -ion anisotropy was shown to be of crucial importance in the high transition temperature observed in this compound.

I. INTRODUCTION

Following the discovery of high temperature superconductivity in Ba x La 5-x Cu 5 O 5 (3-y) by Müller and Bednorz [1], cuprates have attracted a lot of attention over the last decades. Apart from superconductivity, a large number of compounds of the cuprate family have been studied for their low-dimensional quantum magnetism. Indeed, the S = 1/2 character of the Cu 2+ ion, and the directionality of the associated 3d magnetic orbital, are responsible for a tendency to form one-or twodimensional magnetic systems with quantum character. For example, the A = Sr member of the ACu 2 O 3 family, a two-leg ladder compound has been extensively studied in the recent decades [2][3][4][5][6][7][8] for its one-dimensional properties.

Very few cuprates exhibit a three-dimensional magnetic ordering at a reasonable temperature (i.e. close to room temperature or higher). Among them, one can however cite the CuO oxide, that exhibits an antiferromagnetic long-range ordering below 220 K [9,10]. Another example is the A = Mg, Ca, and Co members of the ACu 2 O 3 family that exhibit a high temperature three-dimensional (3D) character, and that, in contrast to CuO, have been little studied. Interestingly, the MgCu 2 O 3 compound presents a 3D spin-ordering at 95 K [11], and the mixed Ca 1-x Co x Cu 2 O 3 compounds show ordering temperatures that range from 27 K for pure Ca (x = 0) [12] to 215 K for pure Co (x = 1) [13].

The room temperature crystal structure of this family is orthorhombic (P mmn or Cmmm). The copper atoms are located at the center of CuO 4 corner-sharing square-plaquettes, arranged in two-leg ladders along the b direction (see Fig. 1a). In each unit cell there are two symmetry-related ladders along the a direction (represented in blue and green). These two-leg copper ladders are zig-zag coupled, and form planar (Sr compound) or puckered (Mg, Ca, Co) layers in the ( a, b) directions (see Fig 1b). These layers are connected along the c direction, by AO 6 octahedra (A=Mg, Ca, Co), or AO 8 cubes (A=Sr), sharing corners with the CuO 4 plaquettes from adjacent copper-ladder layers (see Fig. 1b).

At this point one should note that the Sr compound also differs from the Mg, Ca, Co ones by its magnetic properties. Indeed, while the latter ones present a 3D magnetic order below its Néel temperature, the Sr compound remains essentially 1D [3]. It thus seems that the puckering of the ( a, b) layers plays a major role in the dimensionality of the magnetic ordering.

In this article we will study the magnetic properties of the CoCu 2 O 3 compound, the member of the ACu 2 O 3 family with the highest 3D ordering temperature. After the evaluation of the effective exchange interactions using ab-initio calculations, we will compute the associated magnetic order by classical Monte-Carlo methods.

This paper is organized as follows. Section II details the computational methods. Section III is devoted to the calculations of the exchange interactions and single ion anisotropy. In Section IV we discuss the magnetic order at zero and finite temperature. Finally, we conclude in Section V.

II. COMPUTATIONAL DETAILS

A. Ab-initio calculations

As the magnetic interactions are intrinsically exchange-correlation effects, we will use a multireference configuration interaction method to compute them, namely the Selected Active Space plus single excitation (SAS+S) method [15]. Indeed, this method insures that the following effects are treated explicitly i) the correlation effect within the 3d magnetic orbitals, ii) the ligand-to-metal charge transfers mediating the magnetic interactions, and iii) the screening effects on all the previous configurations (as configuration-dependent hole-particle excitations and their coupling).

As such configuration interaction methods require the diagonalization of large matrices, they can only be used on formally finite-size systems. We thus designed, for each magnetic integral, suitable fragments embedded in a set of renormalized charges [16] and Total Ions Pseudopotentials (TIPS) [17], in order to reproduce the effects of the rest of the crystal on the quantum fragment. The TIPS reproduce the exclusion effects due to the electrons of the first layers surrounding the fragment, and the set of charges is chosen in order to reproduce the Madelung potential seen by the fragment with an error smaller than 0.1 meV. The quantum fragments were chosen in order to include the magnetic atoms associated with the desired interaction, their first coordination shell, and any additional bridging ligands.

The fragment orbitals were optimized within a Complete Active Space Self Consistent Field [18] (CASSCF) calculation on the 3d electrons of the magnetic atoms, using the MOLCAS package [19]. We used a valence basis set of 3ζ + P quality, associated to relativistic core pseudopotentials of the Stuttgart group [20]. The SAS+S calculations were then done using the RelaxSE code [21]. The latter provides the fragment low-energy excitations, from which the effective exchange integrals can be deduced.

The anisotropy calculations were performed using the same method on a single ion embedded cluster, for the spin-orbit-free description, and the RASSI/ANISO [22] modules of MOLCAS for the spin-orbit part. More details are available in the supplementary material [23] The crystal structure used in all calculations is the room temperature X-Ray given in Ref. 24.

B. Monte-Carlo calculations

The Monte Carlo (MC) simulations were performed on the model magnetic Hamiltonian derived from our ab-initio effective exchange interactions and single ion anisotropies. We computed both the order parameters and the magnetic transition temperatures. For this purpose we used the standard Metropolis algorithm [25] on a classical approximation of the spin Hamiltonian. The calculations were performed using supercells up to 10×20×20 (24000 magnetic atoms). The thermodynamical averages were performed with 4000 Monte Carlo steps per atom. More details are available in the supplementary material [23]

III. RESULTS OF THE AB-INITIO CALCULATIONS A. Magnetic integrals

The formal charge analysis of CoCu 2 O 3 yields Cu 2+ and Co 2+ , corresponding respectively to 3d 9 and 3d 7 electronic configurations. The corresponding magnetic moments are S Cu = 1 2 and S Co = 3 2 , because the Co ion is in a high-spin configuration (as expected for such an ions and by continuity from the partially substituted compounds, Mg 1-x Co x Cu 2 O 3 for x =(0.05, 0.10, 0.15, 0.50) [26], and confirmed by our calculations).

The magnetic exchange interactions were obtained from the ab-initio calculations, by mapping the computed magnetic spectra onto the energy spectra of a Heisenberg Hamiltonian on the same fragments.

Ĥ = - <i,j> J ij Ŝi • Ŝj (1)
where Ŝi and Ŝj are the quantum spin operators associated to sites i and j respectively. The J ij are the effective exchange interactions, positive and negative values corresponds respectively to ferromagnetic (FM) and antiferromagnetic (AFM) interactions.

On Figure 1b one sees that the cobalt octahedra are located between two layers of copper ladders. However, magnetically they belong to only one of them. Indeed, the CuO 4 plaquettes define the orientation of the magnetic d x 2 -y 2 orbitals expected on the Cu 2+ ions. Looking at Fig. 1 one can see that the CuO 4 plaquettes of only one of the layers point toward the Co 2+ ion. As a result the Co 2+ ions should be considered as belonging to the connecting layer of copper ladders (see Fig. 1b).

There are seven independent Cu-Cu interactions in CoCu 2 O 3 , named J uuX (in orange on Fig. 2). Three of them are intra-ladder interactions : J uu2 is the ladderrung interaction, J uu5 the ladder-leg interaction and J uu7 the second neighbor intra-ladder interaction. J uu1 is the in-plane inter-ladder interaction. The last three are Cu-Cu interactions between the puckered planes, J uu3 , J uu4 and J uu6 .

There are five Co-Cu interactions, named J ouX (in magenta on Fig. 2). The intra-layer ones are J ou2 , where the Co atom is between two rungs of a ladder, and J ou4 , where the Co atom interacts with the next ladder nearest copper. The inter-layers interactions are denoted J ou1 , J ou3 and J ou5 (see Fig. Finally, there are two Co-Co interactions (in red in Fig. 2), J oo1 along the c axis and J oo2 along the b axis. The computed exchange interactions are presented in Table I. We can immediately see that the largest magnetic interaction is the AFM exchange along the ladders legs (J uu5 = -123.43 meV). When one looks at the ladder rungs (J uu2 ) however, the interaction does correspond neither to the largest J nor to the largest contributions to the classical magnetic energy, -J S i • S j . Indeed, the next largest magnetic energy contribution is due to the Cu-Co AFM interactions (J ou4 ) ; the interaction along the structural-ladder rungs being much smaller. The third energetic contribution comes from the Co-Co intra-layer interactions, namely J oo2 . As a result one should differentiate the magnetic ladders, based on J uu5 and J oo2 for the legs, J ou4 for the rungs, from the structural ones. Indeed, these interactions draw a magnetic-interaction pattern of three-leg Cu-Co-Cu ladders (see Fig. 3), obtained by the exchange of the legs of neighboring structural ladders (yellow on Fig. 2). Finally, the next contribution to the magnetic energy comes from the ferromagnetic (FM) Cu-Cu inter-ladder (structural or magnetic) zig-zag interactions (J uu1 ).

Comparing CoCu 2 O 3 to SrCu 2 O 3 and to the other members of the family, they all have in common large AFM ladder leg interactions. The main differences are related to the ladder rungs and more specifically to the bending of the Cu-O-Cu angle in the structural-ladder rungs. Indeed, this angle is close to 180 • in the SrCu 2 O 3 and results in an AFM interaction of -150 meV [27] (of the same order of magnitude as the ladder leg one) responsible for the one-dimensional character of the compound, and the correspondence between the structural and magnetic two-leg ladders. On the contrary the CaCu 2 O 3 system presents a large bending of the Cu-O-Cu angle, namely of 123 • [28] in the structural-ladder rungs. It results in a strongly reduced magnetic interaction (nevertheless still AFM (-11.5 meV) [27]) leading to a quasi-1D magnetic structure of coupled chains. In the present system the Cu-O-Cu angle is again reduced compared to the CaCu 2 O 3 (105 • [24]) and much closer to 90 • , yielding an enhanced reduction of the AFM term, and resulting in a FM interaction of J uu2 = 9.7 meV. This result is in agreement with the ferromagnetic ordering, experimentally observed (along the rungs) by neutron diffraction on the MgCu 2 O 3 compound [29], where the angle is also 105 • [30] To better understand the importance of the Cu-O-Cu angle bending, one should remember that the effective magnetic exchanges are the result of three terms [START_REF] Lepetit | Recent Research Developments in Quantum Chemistry[END_REF] :

• a direct exchange term between the magnetic atoms (J d ), this term is always FM and depends exponentially on the metal-metal distance,

• a through-space (also named kinetic or Anderson's superexchange) super-exchange term (J ss ), issued from electron transfers between the two magnetic atoms, this term is AFM and decreases exponentially with the metal-metal distance, it is thus very small in systems where the metal-metal bond is bridged by a ligand,

• finally the through-bridge super-exchange term (J sb ), issued from electron transfers between the bridging ligand and the magnetic atoms, this term is AFM and depends exponentially on the metal ligand distance and as the square of the cosine of the metal-ligand-metal angle (θ) ; it is the largest term in AFM bridged systems.

In a first approximation, the effective magnetic exchange can thus be assumed to be

J = J d (d Cu-Cu ) FM, scales as e -αd + J sb (R Cu-O , θ Cu-O-Cu )
AFM, scales as e -βR cos 2 θ

(2)

The bending of the Cu-O-Cu angle thus increases the FM term J d , as it is associated with a reduction of the Cu-Cu distance. Simultaneously it strongly reduces the AFM through-bridge super-exchange term when going from 180 • , where the latter is maximum, to 90 • where it cancels out. One thus sees that the Cu-O-Cu angle is a crucial parameter for the magnetic properties of the ACu 2 O 3 family.

Let us now focus on the magnetic character of the Asite in our compound. Structurally the CoCu 2 O 3 and MgCu 2 O 3 are very similar. However, the magnetic character of the Co 2+ ion transforms the coupled chain magnetic pattern found in the Mg compound, into a coupled three-leg ladder system in CoCu 2 O 3 (see Fig. 3). Let us remember that the second largest magnetic energy is brought by the copper-cobalt J ou4 interaction and the next one by the Co-Co ladder legs (J oo2 ).

Analyzing the interactions in the puckered layers a bit closer one sees that there are two frustrating magnetic interactions, namely the J uu1 FM interactions between the ladders, and the FM J ou1 interactions between the Co atoms and the Cu atoms of the neighboring magnetic ladders (see Fig. 3). Both interactions bring frustration with the AFM interaction along the ladder legs.

Finally, the interactions between the magnetic puckered layers are conveyed by the FM J ou3 and AFM J oo1 . As can be seen in Table I the remaining interactions can be considered negligible.

B. Anisotropy

As the Cu 2+ ion is in a S = 1/2 quantum spin state, the anisotropy of the compound is due to the Co 2+ ion. We thus computed the cobalt easy axes and zeroth-field splitting tensor on embedded CoO 6 fragments.

The zeroth-field splitting tensor is derived from the eigenstates and energies of the many-body, ab-initio, electronic plus spin-orbit Hamiltonian on the CoO 6 embedded fragment, using the pseudo-spin method of L. Ungur and L. F. Chiboratu [22].

We found that in our system the main anisotropy axes are along the crystallographic directions, b is the easy axis and c the hard one. They are associated with a strong anisotropy. Indeed, the zeroth-field splitting tensor can be written as

ĤZFS = D ˆ S • b b 2 - S(S + 1) 3 + E ˆ S • c c 2 - ˆ S • a a 2 (3)
with D = -10.60 meV and E = 2.10 meV. These values are comparable to some of the strongest magnetic exchange interactions. As a consequence one can expect the anisotropy to play a major role in the magnetic ordering.

IV. MAGNETIC PROPERTIES

A. Magnetic order at T = 0 K

As previously seen, the three exchange interactions with the strongest energy contributions, namely J uu5 , J ou4 and J oo2 , form 3-leg ladders along the b direction that do not correspond to the structural ones (see Fig. 3). These three AFM interactions, (J uu5 , J ou4 and J oo2 ) do not bring any frustration resulting in antiferromagnetically ordered three-leg ladders. Moreover, the large anisotropy of the Co ions aligns the spins along the b axis.

The next non-frustrated contribution to the magnetic energy comes from the FM interaction J uu2 , which connects second neighbor magnetic ladders, forming two independent magnetic puckered planes in the ( a-b) directions. These two independent subsystems are pictured in blue and green on Fig 3 . One should note that the two subsystems are related by the 2 y 1 or i symmetry operations. The different planes are then connected by the AFM J oo1 and FM J ou3 interactions, leading to two magnetically-independent, 3D, non-frustrated sub-systems. Both sub-systems are associated with a q = (0, 1 2 , 1 2 ) propagation vector. The two subsystems are coupled by the remaining non-negligible exchange interactions (see Table I), namely the FM J uu1 and J ou1 . These two interactions are frustrated and thus do not contribute to the magnetic energy in the proposed T = 0 magnetic order (see Fig. 4).

At this point the question is whether the above 2-fold degenerate magnetic ordering (pictured in Fig 4) is the ground state. It is easy to show that these two magnetic orders correspond to minima of the classical magnetic energy : nil gradient and positive Hessian.

Let us note, that both the CaCu 2 O 3 [12] and the MgCu 2 O 3 [29] compounds also exhibit degenerate ground states, however with different sub-systems and magnetic orders.

Doubly-degenerate ground states are very rare in real compounds, as any perturbation, coupling the two states, lifts the degeneracy. In CoCu 2 O 3 such a coupling does not exist in the present crystallographic space group and unit cell. One can however see that to couple the two ground states and reduce the magnetic frustration, one should double the crystallographic cell along the b direction. Indeed, such a symmetry reduction could allow lowering of the frustration brought by the inter magneticladders interactions, J uu1 and J ou1 . Let us remember that spin-1/2 chains could exhibit spin-Peierls transitions and that the dominant magnetic interaction in CoCu 2 O 3 is, by far, the AFM exchange along the Cu ladder leg. One can thus expect that such an effect is also at play in CoCu 2 O 3 producing the dimerization that doubles the unit cell and lowers the energy.

Comparing the magnetic orders of CoCu 2 O 3 with CaCu 2 O 3 and MgCu 2 O 3 , one sees that in addition to different magnetic ladders, as discussed in the previous section, these compounds also exhibit different propagation vectors. Indeed, the CaCu 2 O 3 is dominated by an incommensurate order q = (0.429, 1 2 , 1 2 ) [28] and MgCu 2 O 3 by the commensurate q = ( 1 2 , 1 2 , 0) [29] propagation vector. This is due to the non magnetic character of the Ca and Mg ions that probably induces a weakly AFM interaction between the ladders, mediated by these closed-shell ions.

B. Magnetic properties at finite temperature

To study the thermodynamic properties at finite temperature, we performed classical Monte-Carlo (MC) simulations. We computed both the specific heat, C p , and the long-range order parameter, LRO, characteristic of the q = (0, 1 2 , 1 2 ) magnetic order identified in the previous section. The calculation was done using the Heisenberg Hamiltonian defined from the exchange interactions given in Table I, complemented with the zeroth-field splitting tensor of the Co ions, as provided in Section III.

E cell = (2J oo2 + 2J oo1 ) S 2 Co + 2D S 2 Co - S Co (S Co + 1) 3 + (4J ou4 -4J ou3 + 4J ou5 ) S Cu S Co + (4J uu5 -2J uu2 + 4J uu6 + 4J uu3 + 4J uu7 ) S 2 Cu = -260.2 meV/cell (4)
As suggested in the previous section the frustrating interactions J uu1 , J ou1 , (as well as J ou2 and J uu4 ) do not contribute to the energy. The very small interactions, neglected in our previous analysis, namely J uu6 , J ou5 and J uu7 , have positive contributions to energy, i.e. these interactions are frustrated but their effect is negligible.

Let us note that, despite the quantum character of the spin-1/2 Cu ions, the obtained transition temperature is close enough to the T N = 215 K value observed in magnetic susceptibility and specific heat measurements [13]. In fact the Co anisotropy plays a major role, its inclusion in the model Hamiltonian breaks the rotational symmetry, transforming CoCu 2 O 3 in an Ising-like magnetic system. Indeed, in MC simulations where only the exchange interactions are taken into account (see blue curves in Figure 5), long range magnetic order is obtained by the 3D character of the Heisenberg Hamiltonian provided by the inter-plane interactions J uu3 , J ou3 and J oo1 . As the leading interactions of the system are quasi-2D, the symmetry breaking of the rotational invariant Hamiltonian is numerically more difficult to achieve, and the transition appears less clear in Fig. 5 but definitively takes place at lower temperature (T N ≈ 150 K). Nevertheless, the magnetic order remains identical, apart from the general spin orientation.

V. CONCLUSION

In this paper we theoretically determined the magnetic order and transition temperature of the CoCu 2 O 3 ladder compound. We first computed the effective magnetic interactions and anisotropy parameters using an abinitio multi-reference configuration interactions method (SAS+S [15,21]). With these parameters, we constructed a model Hamiltonian that has been used to determine the magnetic order at T = 0K and at finite temperature.

Compared to other members of the ACu 2 O 3 family the CoCu 2 O 3 compound is characterized by puckered layers with a large folding angle, and by a supplementary magnetic ion (Co 2+ ). These two aspects have strong consequences on the magnetic properties of the system. Indeed, our results allow us to predict that the magnetic ladders strongly differ from those of the other members of the family. First, not only they are not identical to the structural ladders, but they exhibit three and not two legs. Second, these magnetic ladders are strongly connected, both in the layers and between the layers, resulting in a two-fold degenerated ground state. Finally, there is the strong Co 2+ easy axis along the b direction, that not only reduces the otherwise infinite degeneracy, to a two-fold one, but also explains the strong increase (compared to the other members of the family) of the temperature at which the long-range magnetic order sets in. It would be nice if our predicted magnetic order could be experimentally verified, for instance by neutrons diffraction.

We would like to conclude on the magnetic frustration responsible for the degenerated ground state. This degeneracy is due to the existence of two 3D subsystems only coupled by frustrated interactions. One thus expects that a structural distortion should occur to lower this frustration and couple the two subsystems. Our analysis yields that the expected distortion should be a doubling of the unit cell along the b direction. Indeed, not only such a symmetry breaking would lower the magnetic frustration, but it would also allow the Cu chains (ladder legs) to display a spin-Peierls transition as expected in spin-1/2 chains. Such a transition is reasonably expected at, or close to, the magnetic ordering temperature, however no structural transition has been seen in X-Ray diffraction in the 115-300 K range, as stated in Ref. 13. One should however remember that the energy associated with the magnetic frustration (issued from J uu1 and J ou1 ) is small compared to the other energy scales in the system. As a result the atomic displacements associated with the symmetry breaking can be expected to remain weak, and thus difficult to see with diffraction techniques (as was learned over the last years by the study of multiferroic systems). Most probably only lattice dynamic studies will be able to clarify this point.

Figure 1 .

 1 Figure 1. Schematic representation of the crystal structure of CoCu2O3. a) along the c and b) b axes. The Cu atoms form two-leg ladders along the b direction and there are two symmetry-related ladders along the a direction. The Cu atoms were represented either in blue or in green to more easily visualize the two equivalent structural ladders. The Co atoms are in light gray, and the O in red. Atomic structures were drawn with VESTA [14].

  2.b).

Figure 2 .

 2 Figure 2. Definition of magnetic interactions in CoCu2O3, seen along the a) c and b) b directions. The Co atoms are in light gray, the Cu in blue and green and the O are masked. The Cu-Cu interactions are in orange, the Co-Cu in magenta, and the Co-Co interactions in red. Dash lines represent the puckered layers and yellow boxes are a guide to identify structural ladders. Atomic structures were drawn with VESTA [14].

Figure 3 .

 3 Figure 3. Schematic representation of the magnetic interaction pattern in CoCu2O3. This pattern is obtained from the structural pattern (Fig. 2a) by the exchange of the legs of neighboring ladders, as pictured by the red arrows. The main interactions are added for easy comparison. The dash black line represent the magnetic puckered layers including the Co atoms, the dash gray line show the rungs of the structural ladders and blue or green boxes show the magnetic ladders.

Figure 4 .

 4 Figure 4. Schematic representation of the magnetic structure of CoCu2O3. (a) Order on the puckered magnetic layers. (b) Order in the structural arrangement. The Co atoms are in light gray and the Cu in blue or green according to the magnetic sub-system they belong to. The latter are outlined by blue and green boxes. Atomic structures were drawn with VESTA [14].

Figure 5 .

 5 Figure 5. Results of Monte-Carlo simulations.with (a) LRO and (b) Specific heat versus temperature. The two curves represent our MC results with (orange) and without (blue) the Co 2+ zeroth-field splitting contribution to the model Hamiltonian.

Table I

 I

	d[Å]	Jij -Jij Si. Sj	Nature
			Cu-Cu intra layers
	Juu5 3.980 -123.43	-30.86 Leg structural ladders
	Juu1 2.829 27.85	6.96 Inter structural ladders
	Juu2 3.118	9.75	2.44 Rung structural ladders
	Juu7 5.056	0.09	0.02 Next-nearest-neighbor
				structural ladder
			Cu-Cu inter layers
	Juu3 3.198 -0.42	-0.10
	Juu4 3.213 -0.65	-0.16
	Juu6 4.466	1.94	0.49
			Cu-Co interactions
	Jou4 4.157 -26.97	-20.23	Intralayer
	Jou1 2.931	5.67	4.25	Intralayer
	Jou3 3.182	2.81	2.10	Interlayer
	Jou2 3.055	1.23	0.92	Interlayer
	Jou5 4.839	0.23	0.17	Interlayer
			Co-Co interactions
	Joo2 3.980 -4.22	-9.50	Leg-type
	Joo1 3.198 -1.05	-2.36	Interlayer type

. Effective exchange interactions (in meV) obtained from ab-initio calculations, associated Heisenberg energy and metal-metal distances (in Å). Negative values correspond to AFM interactions and positive to FM ones.

ACKNOWLEDGMENTS

We acknowledge financial support from the ANR HTHPCM. This work was performed using computer resources obtained from GENCI-IDRIS and CRIANN under projects N • 91842 and N • 2007013.


Gaëlle Saade

Sophie Chiavassa

Charbel Koumeir

Grégory Delpon

Manon Evin

Youssef Ghannam

Ferid Haddad

Noël Servagent

Stéphane Supiot

Vincent Potiron

Réduction de la radiotoxicité par hadronthérapie à ultra-haut débit de dose

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.

Méthodologie Introduction

Résultats Conclusion

•La radiothérapie à ultra-haut débit de dose (UHDR-RT) permet de réduire la toxicité sur les tissus sains (Effet Flash).

•Elle est effectuée en millisecondes vs quelques minutes pour le débit conventionnel (Conv-RT).

•La distribution spatiale de l'énergie des ions lourds (hadrons: protons, deutons…) est très localisée et la dose absorbée par les tissus sains est plus limitée que les photons.

 Est-ce que la balistique des protons à ultra-haut débit de dose permettra de réduire la toxicité chez l'embryon de poisson-zèbre ?

Effet de la protonthérapie UHDR sur les embryons de poisson-zèbre

Synopsis :

1-Etude de l'effet de l'irradiation en fonction de la dose avec des rayons X.

2-Validation du dispositif d'irradiation avec des protons accélérés.

3-Effet de la protonthérapie UHDR sur les embryons de poisson-zèbre (8-9 kGy/s) vs protonthérapie conventionnelle (12 Gy/min).

  sont les doses optimales créant des effets de longueur et de courbure avec un taux de survie élevé •La protonthérapie UHDR induit moins de toxicité par rapport à la conv-RT chez les embryons de poisson zèbre. •Ce modèle contribuera à l'étude des conditions d'irradiation à ultra-haut débit de dose, telles que la structure du faisceau, qui sont nécessaires à la protection contre la toxicité. •L'avantage balistique des protons et la radiothérapie UHDR pourraient faire dans l'avenir proche une bonne combinaison pour réduire les toxicités de l'irradiation en clinique. (de la tête à la queue) b: Longueur du corps b/a: courbure de la queue


Thomas Lacroix

CITY NETWORKS AND THE MULTI-LEVEL GOVERNANCE OF MIGRATION

Keywords: city networks, European Union, integration policies, migration governance, United States, welcoming policies

Hailed for their pragmatism, innovativeness and progressive views, cities and their networks seem to bring a fresh air in current migration debates. Our intent, in this special issue, is to address the scale and significance of this trend by contributing to a greater understanding of their networking activities. Revisiting the conceptual framework used in the literature to date, it addresses the diverse forms of networks, their drivers, internal operation and the functions they perform, at all levels of governance. This introductory paper starts with a review of the scholarship on migration-related city networks. Fromthere, we draw a more fine-grained sense of the ambivalent role of city networks in the design and implementation of migration governance. The final part of this introduction introduces the papers included in this issue, pointing to the ways in which each casts significant new light on these aspects which, in the current literature, remain unresolved.

of this role to convey a distinct voice in the global diplomacy of migration governance [START_REF] Thouez | Cities as emergent international actors in the field of migration: Evidence from the lead-up and adoption of the UN Global Compacts on Migration and Refugees[END_REF]. The recent creation of theMayoral mechanism, an institution bridging local authorities and the broader UN-driven global framework of migration governance, is a signal of their growing presence in international debates. Local authorities, it is argued, are carving a distinctive place in the concert of international stakeholders. Between the two ends of involvement, city networks are now instrumental in shaping an emerging voice and identity of cities as locally grounded international actors.

Our intent here is to address and question this trend by contributing to a greater understanding of city networking activities: the drivers, diverse forms of networks and the functions they perform, at all levels of governance, and their internal operation. The mushrooming of migration-related city networks is a worldwide phenomenon [START_REF] Lacroix | Migration-related city networks: A global overview[END_REF]. In Latin America, several organizations such as Sello migrante and Mercociudad were created to tackle the new migration realities the subcontinent is facing. In Africa (e.g. Africities, the coalition of African cities against racism) and in the Middle East (e.g. the Host Local Municipalities Network), local authorities organize to have their say in the management of refugee populations. And yet, over half of these networks are based in Europe and North America [START_REF] Caponio | Immigrant integration beyond national policies? Italian cities' participation in European city networks[END_REF][START_REF] Lacroix | Migration-related city networks: A global overview[END_REF][START_REF] Oomen | Decoupling and teaming up: The rise and proliferation of transnational municipal networks in the field of migration[END_REF]. The scholarship highlights the sheer diversity of existing configurations: some of them spontaneously created 'from below', partly in reaction to the authoritarian drift of migration management, and others driven by international organizations 'from above'-a distinction we shall explore. This body of work is part and parcel of a change of perspectives on migration and cities: from a mere background stage shaping immigrant settlement, cities are now increasingly regarded as policy agents embedded in multi-scalar dynamics. Hailed for their pragmatism, innovativeness and progressive views, cities and their networks seem to bring a fresh air in current migration debates; but are they genuinely the driver for change in migration governance that they are portrayed? This thematic issue steps back to explore some of the underlying issues, interrogating the drivers of diverse forms of city networks and their actual, if evolving, impacts at local, regional and international levels, concluding that their growing impact on migration governance is significant, but at an early stage. We revisit the functions city networks are said to perform, challenging the depiction in the literature of certain key functions as 'symbolic', providing a new typology of functions for future research. It addresses an imbalance in the literature by including a focus on the internal dynamics of networks and the socialization of their members that facilitates the accommodation of difference, before addressing a dimension not yet addressed by research, the role of universities in the facilitation of networks whose primary and apparent function is knowledge exchange. In sum, it considers what difference migration-related city networks actually make when it comes to influencing policy debates and advancing progressive policies. With a focus on developments in Europe and North America, it highlights the limitations and constraints weighing on city mobilizations, but also the potentialities of such collective involvement and their actual bearing on policymaking at the local, national and international levels.We learn more about the motivations and expectations of their members (is their interest in 'instrumental' or 'symbolic' outcomes?), their differing and evolving priorities (do they pursue a merely technical or a broader political agenda?), the implications for the operation of the network, and for migrants themselves. It explores the role of the meso-level of city networks in the circulation of more inclusive policy models, but also its potential capacity to unsettle the deadlock of global and regional migration governance. This introductory paper starts with a review of the extant international scholarship on migration-related city networks. Drawing on the state of our current knowledge, it gives, first, an overview of the nature of city networks in this field. This is not an easy task: confronted with the sheer diversity of collective groupings of cities, researchers usually prefer to use catch-all, vague definitions. From there, we strive to draw a more fine-grained sense of the ambivalent role of city networks in the design and implementation of migration governance: on the one hand, city networks have formed a milieu in which cities are increasingly being exposed and contribute to a city voice on migration issues; on the other hand, these networks remain selective groupings of potentially like-minded actors that allow the most active cities to have a platform for their leadership. The final part of this introduction introduces the series of papers included in this issue, pointing to the ways in which each casts significant new light on these questions which, in the current literature, remain unresolved.

CITIES AND MIGRANTS: FROM LOCAL SETTINGS TO GLOBAL ACTORS

The city appears as a focus of analysis in the academic literature on immigration as early as in theworks of the Chicago School. Robert Park et al., in particular, account for the division of urban spaces as the joint outcome of inter-individual competition and ethno-economic collaboration [START_REF] Park | The city: Suggestions for the study of human nature in the urban environment[END_REF]. This approach was imported in Europe from the late 60s onwards, at a time when immigration from former colonies was gaining momentum [START_REF] Miret | Migrations internationales et dynamiques des espaces métropolitains[END_REF][START_REF] Rex | Race, community and conflict: A study of Sparkbrook[END_REF]. Since the early 90s, scholarly attention centred on the neoliberal city and its embedding into globalized networks. Research on global cities [START_REF] Sassen | The global city[END_REF] addresses globalization as a canvas of interlinked metropolis hosting the headquarters of multinational companies. Their specific position in this geography of capital has made these cities a magnet for two opposite forms of migration: highly skilled labour working in the high tiers of the job market, and low-skilled, sometimes irregular (undocumented) immigrants working in service provision sector (such as cleaning, care and security) [START_REF] Yeoh | Globalising Singapore: Debating transnational flows in the city[END_REF]. Cities also are the matrix of super-diversity, that is contact zones where peoplewith different immigration backgrounds mingle (Cohen&Sheringham, 2017;[START_REF] Vertovec | Super-diversity and its implications[END_REF]. Cities are places of conflicts and competition, but also of artistic creativity, social adaptation and cultural innovation [START_REF] Bhabha | The location of culture[END_REF][START_REF] Holston | Cities and citizenship[END_REF][START_REF] Soja | Postmodern geographies: The reassertion of space in critical social theory[END_REF]. In parallel, research on the neoliberal city highlights the role of municipalities in the governance of immigrant populations and their settlement. Although local policies targeting immigrants are nothing new, the devolution of powers granted to local authorities all over the world in the last two decades and the introduction of public management techniques have given a new salience to the role of municipalities in this field. In addition to 'settings' of settlement, cities are now regarded as 'agents' of change in immigrant settlement and integration, as with housing and job markets, political and class tensions and cultural dynamics [START_REF] Caponio | The local dimension of migration policymaking[END_REF][START_REF] Varsanyi | Taking local control: Immigration policy activism in US cities and states[END_REF]. The growing presence of local authorities is, moreover, not limited to the local scene. The global consciousness of cities translates into the development of 'urban diplomacy': a growing number of cities nurture and implement an international agenda in domains as varied as the economy, culture and climate change [START_REF] Andonova | Transnational climate governance[END_REF][START_REF] Viltard | Conceptualiser la « diplomatie des villes[END_REF] and, most recently, immigration [START_REF] Thouez | Cities as emergent international actors in the field of migration: Evidence from the lead-up and adoption of the UN Global Compacts on Migration and Refugees[END_REF]. From settings to agents of change, local to global actors, these trends identified in the literature converge into the novel interest in migration-related city networks. Research on this issue is relatively small and recent. The scholarship on cities in international cooperation initially focused, from the early 90s onwards, on the place of local authorities in the building of a European political space [START_REF] Galès | Le retour des villes européennes: Sociétés urbaines, mondialisation, gouvernement et gouvernance[END_REF][START_REF] Van Der Knaap | The committee of the regions: The outset of a 'Europe of the regions[END_REF] and more recently on environmental governance [START_REF] Bulkeley | Environmental governance and transnational municipal networks in Europe[END_REF][START_REF] Kern | Cities, Europeanization and multi-level governance: Governing climate change through transnationalmunicipal networks[END_REF][START_REF] Fünfgeld | Facilitating local climate change adaptation through transnationalmunicipal networks[END_REF]. This surge of interest has paralleled the rise in the number of such city-led organizations at the national and international levels. Despite this trend being global (Lacroix, forthcoming), the literature almost exclusively focuses on North America andWestern Europe, and, to a lesser extent, on global-level networks1. As we will see below, the different contexts of emergence and evolution of migration-related city networks have driven both scholarships on different pathways.

North American networks

In North America, early works on migration-related networks focused on the Sanctuary cities in the United States. In the early 80s, the Reagan administration refused to acknowledge the refugee status of immigrants fleeing conflicts in Central America (Nicaragua, Guatemala and El Salvador). In reaction, church organizations called for 'civil disobedience', advocating for the reception and support of exiles in defiance of the national policy. San Francisco, in 1985, followed suit and became the first 'sanctuary city' by refusing to support immigration enforcement in its constituency2 [START_REF] Lippert | Sanctuary practices in international perspectives: Migration, citizenship and social movements[END_REF]. In the mid-90s, local authorities sawtheir powers and responsibilitieswidened with the Illegal Immigration Reform and Immigrant Responsibility Act and Welfare Reform Act [START_REF] Huang | Welcoming cities: Immigration policy at the local government level[END_REF]. In parallel, following the Clinton laws after theOklahoma City bombings and the Patriot Act after theWorld Trade Centre attack, the number of undocumented immigrants reached a staggering 13 million. In the mid-2000s, the failure of federal immigration reform triggered contradictory reactions among local authorities: while some of them supported the federal administration by enacting repressive legislation (e.g. barring landlords from renting accommodation or employers from recruiting undocumented people), others adopted pro-immigrant policies meant to protect this population from immigration enforcement [START_REF] Varsanyi | Taking local control: Immigration policy activism in US cities and states[END_REF]. Research shows that municipalities in the Southern United States experiencing a growth in the foreign population are more likely to endorse exclusionary policies. And conversely, coastal localities with better educated populations tend to be more inclusive [START_REF] Lacroix And Spencer Walker | The variegated landscape of local immigration policies in the United States[END_REF]. Therefore, it would be wrong to assume that local authorities have all endorsed a positive attitude towards migrants. Nevertheless, this context set the background for a revival of the Sanctuary city movement. It includes nearly 200 members in the United States (although not all cities adopting this approach adopt the 'sanctuary city' label). The sanctuary city movement is in itself a grouping of cities that rejects an anti-immigration enforcement rhetoric and agenda. Another instance is the so-called 'Welcoming cities ' movement. Launched in 2013' movement. Launched in , it embraces 93 cities (in 2020)). It is coordinated by a civil society organization, Welcoming America, which provides a platform for experience sharing and guidelines for welcoming policies [START_REF] Housel | Experiencing intentional recognition:Welcoming immigrants in Dayton, Ohio[END_REF]. Unlike sanctuary cities, which remains a relatively amorphous movement,Welcoming America provides an institutional backbone to the network ofWelcoming Cities. It puts a greater emphasis on the reception of immigrants and access to services than on anti-deportation activism.Other institutionalized migration-related city networks in the United States have also flourished, focusing not only on people with an irregular status, but also on racism, children of undocumented immigrants (the so-called dreamers) or unaccompanied minors. But these organizations have received less scrutiny3. Beyond their diversity, thesemovements appear as a host of relatively like-minded cities whose degree of engagement varies a great deal, from mayors merely displaying a symbolic support to a cause, to municipalities endorsing legislation in blunt contradiction with national orientations: such as creation of municipal ID cards [START_REF] De Graauw | Municipal ID cards for undocumented immigrants: Local bureaucratic membership in a federal system[END_REF], specific measures preventing the transfer of information to immigration enforcement administration (the 'don't ask, don't tell' policy) and policies meant to create a context of trust between the local administration and undocumented residents [START_REF] Mancina | Sanctuary cities and sanctuary power[END_REF]. The state/city conundrum over immigration has spurred a strand of research on the moral implications of local policies: should cities regulate immigration flows? Should they grant citizenship rights to their inhabitants? Authors respond positively arguing that cities are the authorities which ultimately cope with the bulk of immigration flows [START_REF] Shalit | Cities and immigration: Political andmoral dilemmas in the new era ofmigration[END_REF]. Others argue that cities are best equipped to copewith contemporary global challenges at large, and not migration only [START_REF] Barber | If mayors ruled the world: Dysfunctional nations, rising cities[END_REF]. And finally, residence, rather than belonging, should be an essential tenet of citizenship provision since it embeds citizenship in time and space [START_REF] Baubock | Cities vs states: Should urban citizenship be emancipated from nationality?[END_REF][START_REF] Lenard | Residence and the right to vote[END_REF]. Astrand ofwork studying the motives for these cities highlights two drivers: the presence of a large immigrant population and the liberal orientation of the local government. Drawing on a Baltimore case study, Felipe Filomeno argues that the existence of a committed civil society sector is also of crucial importance to bridge immigrants' needs (including those of the undocumented) and municipal political aims (Filomeno, 2017a; see also [START_REF] Majka | Becoming welcoming: Organizational collaboration and immigrant integration in Dayton,Ohio[END_REF]. Xi Huang and Cathy Yang Liu also found that higher levels of education and economic insecurity make cities more prone to be welcoming [START_REF] Huang | Welcoming cities: Immigration policy at the local government level[END_REF]. Fewer studies have paid attention to the actual effects of these municipal policies. Against the expectation of critiques of sanctuary policies, research has shown that these measures have either no or a positive effect on crime, and a positive effect on poverty rates [START_REF] O'brien | The politics of refuge: Sanctuary cities, crime, and undocumented immigration[END_REF][START_REF] Wong | The effects of sanctuary policies on crime and the economy[END_REF]. Susanne Schech argues that even the symbolic gesture of claiming the status of sanctuary/welcoming city affects the way in which immigration is presented in public debates. Cities and their mayors have built over time a narrative framed in terms of human rights or economic assets rather than of a burden for the welfare system [START_REF] Schech | Rescaling sovereignty?[END_REF].

While this above-mentioned research throws some light on the role played by networks, it has focused more on the cities within them than on the networks themselves. Others seek to move beyond methodological urbanism by showing that cities joining pro-immigration movements are embedded in a multi-scalar and multi-sectoral canvas of relations [START_REF] Filomeno | Theories of local immigration policy[END_REF][START_REF] Mcdaniel | Immigrant integration and receptivity policy formation in welcoming cities[END_REF]: hierarchical relations with national authorities and trans local connections with other cities and civil society networks. In this regard, several authors point out the international diffusion of the sanctuary movement, a movement in which cities are but one set of actors next to churches, universities or civil society organizations [START_REF] Lippert | Sanctuary practices in international perspectives: Migration, citizenship and social movements[END_REF][START_REF] Villazor | Sanctuary networks[END_REF]. Canada, as one of the countries where the sanctuary city movement is well embedded, illustrates this point [START_REF] Moffette | Sanctuary city organizing in Canada: From hospitality to solidarity[END_REF].Worthy of note has been Cities of Migration4, a web portal that offered information for and onwelcoming policies in the country and internationally. The drivers and modalities of this diffusion remain, however, understudied. Susanne Schech evokes the role of activists from Toronto touring in Switzerland or Germany to present the sanctuary policy of the city [START_REF] Schech | Rescaling sovereignty?[END_REF]. Zurich, following the New York model, is in the process of planning a municipal IDcard, subject to the final approval of the not insignificant cost by the city parliament. And one observes the multiplication, since 2006, of cities of sanctuary in the United Kingdom. But, beyond these apparent similarities, the situations in North American and Europe are extremely different [START_REF] Bauder | Sanctuary cities: Policies and practices in international perspective[END_REF]: while in the first case, the focus of sanctuary policies is undocumentedworkers to be protected from immigrant enforcement, European 'welcoming cities' target asylum seekers and other newly arrived and vulnerable immigrants. Those that are inclusive of migrantswith an irregular status do not adopt the city of sanctuary label, nor overt measures to oppose enforcement measures. While in North America, cities represent a dissenting voice in the federal state architecture, in Europe, their networks are part and parcel of the European political space and, more often than not, thosewithin the EU operatewithin its institutional framework. Against this background, the divergent pathways taken by the European scholarship on migration-related city networks comes with no surprise.

European networks

In the European Union, it was not until 1992 and the Maastricht treaty that a political space for local authorities took shape at EU level. During this period, a number of representative institutions and networks came to fruition: the Assembly of Regions (AoR), the Committee for European Municipalities and Regions and, not long before, Eurocities, a grassroots network of Europe's largest cities created to voice their needs and concerns. Through the URBAN programme, the Commission supported city-level poverty-reduction programmes [START_REF] Russeil | Quelles expertises urbaines pour une 'Europe des villes' ? Le réseau « Eurocities » et ses experts[END_REF] and consolidated the role of AoR, CEMR and Eurocities as policy partners. Immigrant integration became part of the urban agenda of the European Union in the mid-2000s only. The active lobbying of Eurocities (now with a group of members focused on that issue, in itsWorking Group on Migration and Integration [WGIM]), coupled with a relative disengagement ofMember States, has driven this shift. The adoption of the 2000 Lisbon strategywhich identifies immigration as a key economic asset and the ensuing implementation of the Framework Programmeon Solidarity and Management of Migration Flows in 2007 were a catalyst for the so-called 'local turn' of integration policies [START_REF] Caponio | The local dimension of migration policymaking[END_REF]. Interestingly, this 'turn' took place at a time when European institutions were, under pressure from Member states, curtailing their support to local authorities. TheURBAN programmewas replaced byURBACT in 2006, which puts the emphasis on benchmarking and experience sharing instead of financial support [START_REF] Russeil | Quelles expertises urbaines pour une 'Europe des villes' ? Le réseau « Eurocities » et ses experts[END_REF]. That context favoured the setting up of a multiplication of city networks across Europe: Long-standing European networks such as Eurocities' WGIM; the Euro-Mediterranean Regional and Local Assembly (ARLEM-) (2010), Solidarity cities (2016) and time limited networks such as Cities for Local Integration Policies (CLIP) in 2006 and the City-to-City project (MC2CM) (2015), to name but a few. These networks have contributed to informing and disseminating some of the policy models that have fed into the local turn of integration policies. However, the gist of the research to date focuses on cities and their local policies, either as stand-alone case studies or in a comparative perspective [START_REF] Caponio | The local dimension of migration policymaking[END_REF][START_REF] Hoekstra | Migration governance in three European cities: New local paradigms?[END_REF]. We learn little of the contribution of the different functions the networks perform, or the implications of the differing forms these networks take or their evolving internal dynamics. City networks have thus, in comparison, received scant attention. Barbara Oomen is an exception in offering an overview of this European dynamic [START_REF] Oomen | Decoupling and teaming up: The rise and proliferation of transnational municipal networks in the field of migration[END_REF]. The author argues that the multiplication of migration-related city networks signals a decoupling between urban-level progressive policies and national-level restrictive migration policies. This 'decoupling' thrust does not, for themost part, compare with the overtly confrontational situation observed in the United States between local and national administrations but it points to the difficult coordination between local and national policymaking where responsibilities for migrants overlap. A strand of research has addressed this issue under the lens of multi-level governance (MLG), exploring vertical relationships with higher tiers and horizontal relationships between cities and with non-state actors in civil society [START_REF] Caponio | Theorising migration policy inmultilevel states: Themultilevel governance perspective[END_REF]. Research has explored the conditions which lead to different modes of vertical relationship, consensual and conflictual [START_REF] Poppelaars | Two worlds apart: The divergence of national and local immigrant integration policies in the Netherlands[END_REF], including 'de-coupling' found most clearly in the governance relationship on irregular migrants [START_REF] Spencer | Multi-level governance of an intractable policy problem: Migrants with irregular status in Europe[END_REF]. Although there are also local authoritieswhich support the restrictive and 'hostile' approaches of their national governments [START_REF] Lacroix And Spencer Walker | The variegated landscape of local immigration policies in the United States[END_REF] on the United States, [START_REF] Marchetti | Cities of exclusion: Are local authorities refusing asylum seekers[END_REF] on Italian cities for instance), most research is undertaken on inclusive policies and on the networks within that frame5 [START_REF] Marchetti | Cities of exclusion: Are local authorities refusing asylum seekers[END_REF].

Multi-scalar policy frameworks and the rise of assertive city networks

The MLG approach focuses on the local level within a broader multi-scalar policy framework. By contradistinction, another body of works focuses on the interplay of multi-scalar actors, legal and policy regimes at the local level. This approach raises the question of scaling. What makes a policy or a process 'local' when its actors are not necessarily local actors? The transnational scholarship had pointed out the intertwined scalar nature of the migration process in the neoliberal city [START_REF] Schiller | Locatingmigration: Rescaling cities and migrants[END_REF]. Likewise, civic mobilizations and immigrant associationism are fashioned locally by a range of legal strata, from global human right regimes to national legal frameworks and local political contexts [START_REF] Soysal | Limits of citizenship: Migrants and postnational membership in Europe[END_REF]. Another strand of work points to the complex scalar dimension of local policies. The body of research on 'street-level bureaucrats', in particular, shows how local agents interpret and combine various and at times conflicting national, local and supranational sets of rules in their daily activities; as shown, for example, by studies of civil servants assessing the credibility of asylum seekers' narratives [START_REF] Tangen | The role of credibility in constructing the victim of trafficking status[END_REF] or visa applications [START_REF] Alpes | Dealing with law in migration control: The powers of Street-level Bureaucrats at French Consulates[END_REF]. Likewise, different local-level administrations can follow conflicting guidelines. This has been shown in Toronto where the actual implementation of the sanctuary policy is constrained by the local police' ingrained adherence to the national-level security institutional framework [START_REF] Hudson | City of hope, city of fear: Sanctuary and security in Toronto, Canada[END_REF]. Over the last decade, another networking dynamic, akin to the one observed in the United States, gained momentum: the emergence of more grassroots and assertive city networks, related to the dispersal policy of asylum seekers in different European countries. This strategy raised the issue of responding to their local presence, including in smaller cities and rural areas in which this question had been virtually unknown [START_REF] Tazzioli | The politics of migrant dispersal. Dividing and policing migrant multiplicities[END_REF]. The 'migration crisis' of 2015-2016 amplified this trend, while mayors were confronted by the pressing needs of newly arrived and vulnerable populations. In countries such as Italy, Spain and France, the security-oriented response of state authorities towards asylum seekers triggered resentment and calls for more humane approaches. This context favoured the development of militant forms of mobilizations, decoupled from and, at times, in opposition to national policies. The ICORN (International Cities of Refuge Network) initiated by the parliament of writers in 1996 and the cities of sanctuary movement in the United Kingdom (the latter launched in 2006 in Sheffield) can be regarded as two forerunners [START_REF] Bagelman | Sanctuary city: A suspended state[END_REF][START_REF] Ridgley | Cities of refuge: Immigration enforcement, police, and the insurgent genealogies of citizenship in U.S. Sanctuary Cities[END_REF]. The countries bordering the Mediterranean became a crucible of such mobilization after 2015 [START_REF] Lacroix | Migration and municipal militancy in the Mediterranean (No. 4; EuroMedMig Working Paper Series[END_REF]. They can take diverse forms: refusal to implement liberty-threatening legislation (cf. the anti-Salvini decree movement in 2018); promotion of alternative migration governance (unconditional welcoming in France, migration as a human right in Italy); programmes of reception and settlement of asylum seekers in Southern Italy or Catalonia; lobbying for the closure of detention centres in Barcelona; and so forth. Their field of involvement moves beyond the realm of integration policies to claim alternative migration policies, the prerogative of the national state. An instance is the claim by the Sea to City movement for the opening of legal corridors allowing the circulation of asylum seekerswithin Europe from port to host cities. Another contrast with prior engagements is the emphasis put on the 'right to have rights' of those with irregular, or undocumented, status, excluded by national laws from the right to work and to access most welfare support (see Sarah Spencer in this volume). These challenging demands resonate with the sanctuary movement in North America. Another similarity is the presence and influence of civil society actors who are, in many cases, the actual spur of city mobilizations (Tiziana Caponio in this volume). It has been the case for the city of sanctuary movement in the United Kingdom, 'safe port' (Seebrücke) in Germany and Communes hospitalières in Belgium. The parallel stops there, though. On both sides on the Atlantic, municipalmilitancy dwells on a distinct intellectual framework: from the libertarian municipalism ofMurray Bookchin to the Derridian notion of hospitalité, Europe-based city involvement differs from the religion-touched notion of sanctuary [START_REF] Bauder | Sanctuary cities: Policies and practices in international perspective[END_REF]. Likewise, the general terminology used to name their commitment refers to the welcoming of newcomers rather than to the protection of settled populations :welcome, hospitalité, refuge, safe ports and solidarity [START_REF] Boudou | De la ville-refuge aux sanctuary cities : L'idéal de la ville comme territoire d'hospitalité[END_REF][START_REF] Furri | Villes-refuge, villes rebelles et néo-municipalisme[END_REF]. This new lexicon marks an expansion of focus, from integration to welcoming, from long-term settlement to short-term needs (Anouk Flamant in this volume). In practice, this distinction should not be overstated: integration is also on the agenda of grassroots activist organizations geared towards vulnerable immigrants (e.g. Welcoming America), whereas hospitality has equally become an issue of concern of more established institutions: Eurocities has supported the solidarity cities network since 2016 andUrbact the arrival cities programme since 2015.

Going global?

Finally, the last strand of work we want to highlight here asks whether city networks, on migration but also beyond, are going global. Indeed, the development of city networking is generally presented as inherent to globalization and the emergence of global cities [START_REF] Curtis | Cities and global governance: State failure or a new global order?[END_REF][START_REF] Oosterlynck | The city as a global political actor[END_REF]. The research on networks per se has highlighted how these networks have been instrumental in the development of international economic strategies, urban marketing, policy tourism and urban diplomacy [START_REF] Jacobs | Urban geographies I: Still thinking cities relationally[END_REF]. And the resources drawn from their embedding in cities' modes of operation does not only affect their capacity to upscale their agenda at the global level, it is also a tool for adjusting intercity relations at the national level [START_REF] Peyroux | Circulation des politiques urbaines et internationalisation des villes: La stratégie des relations internationales de Johannesburg[END_REF]. Their role has primarily been pointed out in the governance of climate change [START_REF] Bulkeley | Environmental governance and transnational municipal networks in Europe[END_REF][START_REF] Andonova | Transnational climate governance[END_REF][START_REF] Kern | Cities, Europeanization and multi-level governance: Governing climate change through transnationalmunicipal networks[END_REF] [START_REF] White | Intercultural cities: Policy and practice for a new era[END_REF], and various initiatives are led by United Cities and Local Governments, a UN body representing local authorities. In 2015, the International Organization for Migration organized its annual conference on the theme of cities and migration [START_REF] Ahouga | The local turn in migration management: The IOM and the engagement of local authorities[END_REF]. This paved the way for the inclusion of local authorities in the preparation of the Global Compact on Migration, an international framework of collaboration for migration governance. This process resulted in the creation of theMayoral Forum for Migration andDevelopment andMayoral Migration mechanism, two bodies formalizing the presence of local authorities in the broader migration governance framework, along with states and civil society organizations [START_REF] Oomen | Decoupling and teaming up: The rise and proliferation of transnational municipal networks in the field of migration[END_REF]). Yet it is not clear that on all issues there is drive by international and regional organizations for a stronger municipal voice: while evident in some instances, the limits of this symbiotic relationship remain to be explored.

. Immigration is another domain of engagement: the Global Parliament ofMayors, the Council of Europe's Intercultural Cities and the global network of municipalities, Metropolis, are three examples of global city networkswhose ambition is to advance an urban agenda in global discussions, including migration. This commitment to develop global networks has, significantly, been fuelled by the support of international organizations. Since the beginning of the 2000s, the growing engagement of international organizations with local authorities is underpinned by their search for partners beyond national governments. International institutions have supported the creation and activities of cities in the domain of immigration, including the UNESCO-led ICCARnetwork (International Coalition of Cities Against Racism). Intercultural Cities is supported by the Council of Europe

MOVING BEYOND THE STATE OF THE ART: WHAT KIND OF 'NETWORK' FOR WHAT IMPACT?

The multiplication of migration-related city networks results from parallel and interrelated local, regional and global dynamics: the growing gap between evolving local integration strategies and the national migration policies, the place of municipalities on the agenda of international organizations and, in Europe, the building of a multi-scalar political space. These intertwined trends have led to a flurry of different forms of mobilizations and institutions, often termed as 'networks' by the researchers, but covering very different realities. It is worth noting that the definitions found in the literature remain elusive (and this imprecision is also found in the other strands of literature): they are commonly defined as groups of cities endowed with some form of organizational structure and pursuing a common agenda.

These grassroots mobilizations tend to be loosely coordinated networks of permanent members adhering to a common political agenda: sanctuary, unconditional welcoming (ANVITA in France) or, for instance, circulation as a human right. Some of them are spontaneous and others result from civil society movements (Seebrücke in Germany, Sanctuary cities in the United States and the United Kingdom, Communes hospitalières in Belgium) but the vast majority of them are national networks. By contrast, networks sponsored by one or several state and/or international organizations tend to be international in scope. They tend to enjoy greater financial resources, and stronger capacities of coordination.

Differing functions still little understood

The scholarship on migration-related city networks on both sides of the Atlantic has, as we saw, followed relatively distinct pathways, accounted for by the divergent histories of their institutionalization. This thematic issue seeks to bridge both strands of work by investigating, first, the bearing of city networks on the formulation and implementation of migration and integration policies. Said differently, what difference does networking make for cities, for migrants and for migration governance? Barbara Oomen identified three functions of these organizations: practical, symbolic and juris-generative. The exchange of practical experiences (practical) and the showcasing of practices (symbolic) are central: city networks enable the adjustment and circulation of policy models that may have a direct impact on migrants' integration, in particular. The symbolic statement of pro-immigrant narratives, in turn, fosters a re-branding of cities as cosmopolitan and welcoming, but may also have an indirect impact on migrants through their bearing on the perception of immigration and on electoral behaviours. Finally, the legislative changes for which some city networks advocatemay have long-term impacts on national and international policy orientations. But what is the actual added value of networks in relation to these three goals? Are they more than a sum of cities engaged in similar activities? The literature tends to showcase committed cities with charismatic mayors and a global outreach such as Michael Bloomberg in New York, Valerie Plante in Montreal, Ada Colau in Barcelona and Domenico Lucano in Riace (De Graauw, 2014;[START_REF] Driel | Local identity and the reception of refugees: The example of Riace[END_REF][START_REF] Russell | Beyond the local trap: New municipalism and the rise of the fearless cities[END_REF]. Is the embedding of the latter intomunicipal networks of any use to them? Do they represent more than a stage on which these leaders can voice their engagement? And what of their actual role for 'ordinary cities' [START_REF] Robinson | Ordinary cities: Between modernity and development[END_REF]. Does the participation of these low-profile cities induce more than some cosmetic changes in their approach to immigrant integration? Are they, as members of the network, in a stronger position to overcome the legal and political constraints that they face [START_REF] Wilcock | Hostile immigration policy and the limits of sanctuary as resistance[END_REF]?

PAPERS IN THIS THEMATIC ISSUE

These aspects are revisited by the papers in this thematic issue, as are questions that are even less well explored, such as the differing aspirations and priorities of city participants within a network, the tensions to which that can give rise and their implications. Providing fresh empirical material, the papers throw light on questions essential to understanding the unfolding phenomenon of city networks, the long-term impact of which on migration governance could be profound. Taking up our core question, Colleen Thouez explores the implications of cities becoming international, theways in which they are mobilizing in national and international contexts, and the emerging outcomes. While not over-stating the significance of this development, at this early stage, she nevertheless argues that we have in the past decade seen new configurations of power emerging, the political leadership of cities seeking to use their collective influence to shift debates on migration, as on climate change. Going beyond the standard, instrumental, function of sharing best practices, she illustrates her argument on these 'symbolic' roles with two networks she foresees likely to have a growing influence: one in the United States, addressing the Federal Government's response to the needs of undocumented migrants during the Covid-19 pandemic, and, in contrast, a network of cities that are 'cross-border problem solvers', connecting cities across the major migration corridors between Africa and Europe to shape new approaches to inter-state cooperation. Thouez argues that these developments point to a redesign of governance in which local knowledge informs national policy, local action drives national responses and local needs trigger global cooperation. In contrast to Oomen's work, in which city networks are part of a strategy to resist national policies, Thouez finds some city diplomacy on the international stage is fostered by national governments, here contributing to, not thwarting, their objectives. She concludes that 'cooperative localism', led by principled and pragmatic mayors, could lead to cities becoming significant players in migration policy debates at the international level. For that to happen, unity will need to triumph over division at the local level. Cities' visible contribution in leading the response to Covid-19 will serve to strengthen their authority to play that role. Anouk Flamant takes that analysis of city engagement in networks forward through her focus on three large French cities: Nantes, Lyon and Strasbourg. The 2015 'refugee crisis' represented a turning point for each city but also, for some, an opportunity to claim increased reach on migration matters, and served as a spur to developing new relationships with cities and with civil society. She finds that engagement in national networks, albeit not always signifying a high level of actual involvement, was a factor in those cities' capacity to adopt a pro-active and assertive approach to the reception of migrants. That contributed to a trend from weak integration policies to a surge of welcoming measures-the making of those cities as 'welcoming communities'-with implications for relations between cities, their regional embedding and the national authorities. Like Oomen, Flamant does find that networking between cities was a resource for those activist cities to reinforce decoupling from national policies. Where relations with national authorities were cooperative, however, cities favour the networks' instrumental functions. The role of city networks is thus not only understood under a geopolitical lens.Opening the box of migration-related networks uncovers the complexity of interrelations between actors. The exchange of experiences, the production and learning of expertise, the building of common narratives, the experimentations of policy models or the acculturation to the codes of conducts with state bureaucrats, international organizations and civil society actors creates a sense of groupness and an identity of national or international players. City networks are, in that regards, agents of socialization. But cities and mayors never act in isolation. They are always already embedded into a range of relations with civil society organizations and other public actors. Tiziana Caponio argues that this focus on the 'vertical' dimension of city networking (i.e. the relation cities maintain with the higher tiers of government) can overlook the significance of horizontal networks, here addressing not only city-to-city engagement but city networks that also embrace civil society. She finds horizontal state-society relations poorly conceptualized and mistakenly treated as subordinate in importance to vertical multi-level governance arrangements. Taking as her case studies the Eurocities' Working Group on Migration and Integration, the Council of Europe's Intercultural Cities and, like Thouez, the U.S. network, Welcoming America, she finds they differ in the extent to which they have vertical or horizontal agendas. While Eurocities maintains a strong vertical agenda focused on influencing the polices of higher tiers, with a marginal civil society role, Welcoming America displays a more horizontal agenda,more likely to be shaped by a policy vision (such as welcoming or interculturalism), and focuses on mutual learning. In between, Intercultural Cities maintains balanced relations with the Council of Europe member states on the one hand, and local NGOs involved in intercultural policies on the other. Civil society can play a key role, so that inter-governmental relations are less the driver than a means for the network to deliver its world view. Alternatively, in a top-down network, the parent body can be the driver, with inter-governmental relations to the fore and civil society, once again, marginalized to the implementation stage. Caponion's study found, nevertheless, that the balance in these relationships can evolve over time. Here, institutional contexts provide only a partial explanation. Rather, the agendas of the cities' political leaders, and of the leaders of city networks, play a crucial role. She urges caution in claiming that city networks promote new alliances in migration policymaking or represent an effective challenge to national restrictive approaches: rather, the extent to which they do in each case must be a matter of empirical analysis. Comparing top-down networks with those which are city led, she concludes that collaborative relations on the horizontal and vertical dimension are more likely to be achieved in a top-down programme: coordination between actors and organizations with different interests and levels of power will not emerge spontaneously. The role of researchers as facilitators of city networks, raised by Spencer and explored in depth by Broadhead and Allen, provides an interesting, contrasting model for achieving that goal (see below). Sarah Spencer picks up that analysis in her scrutiny of a network established to address one particular and sensitive multi-level governance issue, city responses to migrants with irregular status. Unusual in exploring the evolving, internal dynamic of a network and uncovering the reasons for participants' differing aspirations, she demonstrates how tensions were resolved through exposure to each other's reasoning, in the context of relationships of trust fostered before and during the network's operation. Facilitating accommodation of differences, socialization contributed to achievement of the network's goals. Challenging the widely used depiction of the key functions of networks in the literature as 'symbolic', Spencer identifies instead its constituent parts, legitimation, substantiation, framing and advocacy, finding numerous examples to illustrate her case. An expanded typology of functions of city networks is provided to guide future researchers in the field. In contrast to Thouez's finding of an appetite among international institutions for city voices to counter less constructive national approaches, Spencer finds at EU level, on the issue of irregular migrants, only a tentative willingness to respond to first overtures from those cities eager to engage. There is scant research on the role of experts in city networks [START_REF] Russeil | Quelles expertises urbaines pour une 'Europe des villes' ? Le réseau « Eurocities » et ses experts[END_REF]. As demands for research impact grow, universities increasingly facilitate as well as study social change in concert with decision-makers and users, a development under-examined and under-theorized. Another impetus for the growing presence of academics is the role of scholarly oriented think tanks such as the Migration Policy Institute or International Committee for Migration Policy Development (ICMPD) providing guidance to cities on migration issues. This gap is addressed by Jacqueline Broadhead andWilliam Allen in their focus on the role of academic researchers not simply as participants but as facilitators of networks. Those networks are also, in turn, their object of study. Drawing upon analysis of two university-initiated networks, engaging 28 European cities, the authors cast light on the particular role that universities are here playing as facilitators of change. They argue that the knowledge exchangewhich the researchers facilitate is a vector through which cities are socialized into a more cohesive group with shared goals and agendas for change: thus, the instrumental function of shared learning contributes to the 'symbolic' functions of framing and developing common goals. Those goals are taken forward by each city, reflecting its own context, and collectively, to an extent, in a nascent advocacy agenda. Broadhead and Allen suggest that the boundary between facilitating the instrumental function of knowledge exchange and engagement in symbolic functions, not least advocacy, could raise ethical issues for researchers, as Spencer also found for city policymakers where the network's role threatened to extend beyond the instrumentalmandate they had been given. We began this introduction by noting that cities have been celebrated as the crucible for innovative experimentations and asking whether that is also true in relation to migration. The answer, on innovation, we can see is most certainly yes. On the necessary next question, whether this will lead to a step-change in their influence on national, regional and international policy agendas-to Barber's 'cities ruling the world' ( 2013)-an answer could only as yet be tentative. That leaves a rich agenda for future research to which each of the articles in this themed issue individually attests.

An exception is Tarumoto (2018) on city networks in Japan

This claim is embedded in a century-long dispute between local and federal governments on migration issues: it is not until the early 20th century, with a Supreme Court decision in 1882 and the creation of the Bureau ofImmigration and Naturalisation in 1906, that the federal state gained the exclusive power to regulate migration management over municipalities.

Instances include City for Action, the National League for Cities and the Coalition of Cities against Racism and Discrimination Studies.

http://citiesofmigration.ca/

In France, examples are manifold. Following the dismantling of the Calais Jungle in 2016, a group of far-right cities created the 'ma commune sans migrant' network. In 2013, the city of Calais launched a call to its inhabitants to report any informal squat.

City networks: Towards a typology

The elements of this definition are to be clarified. Some organizations specialize on migration-related issues (to develop an integration policy for instance); others are generalist institutions for which immigration is but a theme among others. This is particularly so for national or international associations of cities (e.g. the U. K.-based Local Government Association and Eurocities). Said differently, some networks are formed ex-ante to identify and address common areas of interest, including with regard to immigration. Other are formed ex-post, around a common issue or project. The membership can also vary. Members can be exclusively composed of municipalities (whether elected officials, administrative or technical staff), or be composite groups also including NGOs, ministerial representatives or international organizations. They can be formed of permanent members, or made up of rotating groups whose composition fluctuates. This is particularly true for forums representing local authorities in international organizations: such as the Congress of Local and Regional Authorities of the Council of Europe; the Mayoral Forum for mobility, migration and development, which embodies the 'migration' voice of municipalities at the United Nations; or the International Organization for Migration. And finally, they can display a temporary membership, when a network is formed around a particular, often time-limited initiative, with one or more functions: an example is that of City-2-City, a project meant to foster experience exchanges between cities on both sides of the Mediterranean, piloted by the International Centre for Migration PolicyDevelopment (ICMPD). Another instance is the City Initiative on Irregular Migrants in Europe (C-MISE), the focus of Spencer's paper in this volume, and the Communes hospitalières in Belgium, resulting from a campaign of mobilization around the reception and the perception of migration launched by theNGOCNCD11.11.11. The institutional structure of a network can be centralized with a dedicated administrative and decision-making body, or decentralized, each municipality managing its own involvement, with no more in common than adherence to a common framework or charter: Sello Migrante, in Latin America, brings together Chilean municipalities around a charter for the reception of Haitian refugees. This sheer diversity of networks is also a result of the variety of their aims and modes of creation.We have distinguished between networks formed out of grassroots mobilizations in confrontation with existing immigration policies (mostly in the United States and more recently in Europe) while others have been initiated and supported by state or international organizations (mostly at the European and global levels).Both categories present very different features.