Udishnu Sanyal

Semih Ener

Evangelia Anagnostopoulou

Marc Pousthomis

Pier- Francesco Fazzini

Lise-Marie Lacroix

Konstantin P Skokov

Oliver Gutfleisch

Guillaume Viau

Co@CoSb core-shell nanorods: from chemical coating at the nanoscale to macroscopic consolidation

Core-shell magnetic anisotropic particles were prepared by reduction of Sb acetate at the surface of cobalt nanorods dispersed in a solution consisting of 1,2 tetradecanediol in oleylamine. X-ray diffraction and local EDS analyses revealed a thin β-CoSb shell with a controlled thickness ranging from 5 to 15 nm that depended on the Sb/Co molar ratio and the reduction temperature. The shell completely coats the rod surface but does not alter the shape anisotropy or the hcp structure of the cobalt cores, and the hard magnetic properties are preserved after coating with a coercivity higher than 3 kOe. Consolidated nanostructured materials that exhibit properties of permanent magnets were prepared by compaction of the core-shell Co@CoSb nanorods. The thin CoSb shell was very efficient for preventing the cobalt anisotropic core from sintering at high temperatures (up to 300°C) and high pressures (up to 1.5 GPa). These results indicate that the bottom-up approach is very promising for preparation of nanostructured hard magnetic materials.

TABLE OF CONTENT GRAPHIC INTRODUCTION

The tremendous progress in liquid-phase synthesis has yielded metallic nanoparticles with controlled sizes and shapes, including nanoparticles prepared from iron-group transition metals, such as Fe, Co or Ni that exhibit unique magnetic properties due to their size reduction compared to the bulk materials. These promising materials could be used in data recording, [START_REF] Liakakos | Solution Epitaxial Growth of Cobalt Nanowires on Crystalline Substrates for Data Storage Densities beyond 1 Tbit/in2[END_REF] sensing or biomedical applications. [START_REF] Lu | Magnetic nanoparticles: synthesis, protection, functionalization, and application[END_REF] The synthesis of monometallic, alloy and oxide, magnetic nanoparticles being now well mastered, the focus has shifted to increasing the complexity by combining other properties, such as luminescence, plasmonic, catalytic activity, thermal stability or resistance, to oxidation within a single magnetic particle. [START_REF] Salgueiriño-Maceira | Increasing the Complexity of Magnetic Core/Shell Structured Nanocomposites for Biological Applications[END_REF] The synthesis of hybrid particles composed of different materials has been recently reviewed. [START_REF] Chaudhuri | Core/shell nanoparticles: classes, properties, synthesis mechanisms, characterization, and applications[END_REF][START_REF] Hao | functionalization, and biomedical applications of multifunctional magnetic nanoparticles[END_REF] The overgrowth of a second material onto a predefined object is rather complex and leads to core-shell, [START_REF] Wei | Multifunctional composite coreshell nanoparticles[END_REF] heterodimer 7 or dumbbell-like particles. [START_REF] Wang | Recent Progress in Syntheses and Applications of Dumbbell-like Nanoparticles[END_REF] Currently, most of the studies have focused on isotropic particles, and only a few studies have mention complex anisotropic objects. However, shape anisotropy is mandatory for several applications, such as plasmonic-based biodetection, [START_REF] Schrittwieser | Modeling and Development of a Biosensor Based on Optical Relaxation Measurements of Hybrid Nanoparticles[END_REF] surface-specific catalytic reactions [START_REF] Liu | Synthesis of shapecontrollable cobalt nanoparticles and their shape-dependent performance in glycerol hydrogenolysis[END_REF] or hard magnetic materials. [START_REF] Maurer | Magnetic nanowires as permanent magnet materials[END_REF] Recently, several groups have worked on the bottom-up approach of permanent magnets prepared with magnetic nanorods and nanowires. [START_REF] Gandha | High Energy Product Developed from Cobalt Nanowires[END_REF][START_REF] Anagnostopoulou | Dense arrays of cobalt nanorods as rare-earth free permanent magnets[END_REF][START_REF] Liébana-Viñas | Structure-Correlated Exchange Anisotropy in Oxidized Co80Ni20 Nanorods[END_REF][START_REF] Ouar | Spark Plasma Sintering of Co80Ni20 nanopowders synthesized by polyol process and their magnetic and mechanical properties[END_REF] Permanent magnets are a special class of magnetic material that exhibits both high coercivity and high magnetization. [START_REF] Gutfleisch | Magnetic Materials and Devices for the 21st Century: Stronger, Lighter, and More Energy Efficient[END_REF][START_REF] Gutfleisch | Controlling the properties of high density permanent magnetic materials[END_REF] In particular, cobalt nanorods (Co NRs) with a hcp structure are interesting for this application because when their long axis is parallel to the hcp c axis, they exhibit both shape and magnetocrystalline anisotropies. In this case, their magnetization loop exhibits a very high coercivity. [START_REF] Gandha | High Energy Product Developed from Cobalt Nanowires[END_REF] Different models have predicted that magnets consisting of Co NR assemblies that are sufficiently dense (magnetic volume fraction of c.a. 50%) to exhibit a high magnetization can achieve a high energy product, which is the figure of merit of a permanent magnet. [START_REF] Toson | Nanostructured Hard Magnets: A Micromagnetic Study[END_REF][START_REF] Panagiotopoulos | Packing fraction dependence of the coercivity and the energy product in nanowire based permanent magnets[END_REF] The interest in this new class of materials is their potential to fill the gap between hexaferrite-and rare earth-based permanent magnets. [START_REF] Anagnostopoulou | Dense arrays of cobalt nanorods as rare-earth free permanent magnets[END_REF] Fabrication of Co NR-based magnets requires a compaction step to endow the rod assembly with mechanical strength. High coercivity in these materials could be obtained only when the magnetization reversal proceeds via individual reversal in each nanorods. Indeed, the small rod diameter makes difficult the nucleation of the magnetization reversal. [START_REF] Pousthomis | Localized Magnetization Reversal Processes in Cobalt Nanorods with Different Aspect Ratios[END_REF][START_REF] Bran | Tuning the magnetization reversal process of FeCoCu nanowire arrays by thermal annealing[END_REF] Therefore, two contradictory issues must be addressed by the compaction, a high cobalt NR volume fraction must be attained but at the same time the NR morphology must not be altered. For an increase in the particle mean size and/or loss of shape anisotropy, the coercivity decreases substantially, preventing permanent magnet applications. [START_REF] Ouar | Spark Plasma Sintering of Co80Ni20 nanopowders synthesized by polyol process and their magnetic and mechanical properties[END_REF] Based on the results of previous studies, it is established that raw Co NRs undergo sintering and oxidation when they are heated at a temperature higher than 200°C. [START_REF] Ait Atmane | High temperature structural and magnetic properties of cobalt nanorods[END_REF] Consolidation at the high pressures involved in the cold and hot compaction processes can produce the same effect. The growth of a thin layer at the Co NR surface could improve their stability. For example, encapsulation of the Co NRs in a thin carbon layer via treatment in organic solvents at a high temperature enhanced their thermal stability. [START_REF] Ibrahim | Carbon Coating, Carburization and High Temperature Stability Improvement of Cobalt Nanorods[END_REF] For the compaction process, an inorganic material is more favorable than a carbon shell but the growth of a continuous shell surrounding the Co NRs is not straightforward. Soulantica et al. studied the overgrowth of various metals on the Co NRs surface. Fe-Co dumbbells were formed by the growth of iron cubes at the cobalt NRs tips. [START_REF] Liakakos | Co-Fe Nanodumbbells : Synthesis, Structure and Magnetic Properties[END_REF] Co NRs decorated with gold nanoparticles were obtained by the overgrowth of gold, [START_REF] Wetz | Hybrid Co-Au nanorods : Controlling Au nucleation and location[END_REF] but when the surface wettability was changed by adding trace amounts of Sn and Pt a continuous gold shell around the Co NRs was formed. [START_REF] Lentijo-Mozo | Air-and Water-Resistant Noble Metal Coated Ferromagnetic Cobalt Nanorods[END_REF] In this study, we report the synthesis of original anisotropic core-shell Co@CoSb nanorods by growing a polycrystalline CoSb shell on the surface of pre-formed Co nanorods.

Transition metal antimonides are intermetallic compounds that have attracted much interest due to their electric and thermoelectric [START_REF] Mcguire | Crystal structure, electronic structure, and thermoelectric properties of AuTlSb: A new pyrite superstructure[END_REF][START_REF] Meng | Pressure Tuning in the Chemical Search for Improved Thermoelectric Materials: NdxCe3-xPt3Sb4[END_REF][START_REF] Brown | Yb14MnSb11: New High Efficiency Thermoelectric Material for Power Generation[END_REF] properties . Some antimonides have also been identified as interesting materials for use as anodes in lithium ion batteries. [START_REF] Xie | Low temperature solvothermal synthesis of nanosized NiSb as a Li-ion battery anode material[END_REF][START_REF] Wang | Preparation and electrochemical performance of CoSb alloy anode material for Li-ion batteries[END_REF][START_REF] Yang | Electrochemical performance of template-synthesized CoSb nanowires array as an anode material for lithium ion batteries[END_REF] However, the synthesis of metal antimonide nanoparticles has been rarely reported. Recently, Tremel et al. synthesized a series of nanocrystalline metal antimonides (M-Sb, M = Co, Ni, Fe, Cu2, Zn) using metal complexes and Sb nanoparticles. [START_REF] Kieslich | Solution Synthesis of Nanoparticular Binary Transition Metal Antimonides[END_REF][START_REF] Birkel | Wet Chemical synthesis and a combined X-ray and Mössbauer study of the formation of FeSb2 nanoparticles[END_REF] In addition, Schaak and co-workers described the formation of intermetallic compound using the polyol process, [START_REF] Leonard | Low-Temperature Polyol Synthesis of AuCuSn2 and AuNiSn2: Using Solution Chemistry to Access Ternary Intermetallic Compounds as Nanocrystals[END_REF] and in particular, cobalt antimonide CoSbx (x=1, 3) nanocrystals were synthesized. [START_REF] Cable | Low-Temperature Solution Synthesis of Nanocrystalline Binary Intermetallic Compounds Using the Polyol Process[END_REF] Herein, the reduction conditions to form CoSb nanoparticles from a mixture of cobalt and antimony precursors in oleylamine are reported, and we describe the structural and chemical characterization of the Co@CoSb nanorods obtained by reduction of antimony acetate at the surface of Co NRs prepared by the polyol process. A significant improvement in the high temperature stability of these materials was obtained compared to the raw cobalt rods. In addition, we report examples of consolidation on the core-shell Co@CoSb nanorods, demonstrating that dense materials can be obtained without altering the coercivity.

EXPERIMENTAL SECTION

Cobalt(II) acetate and antimony(III) acetate were purchased from Alfa Aesar, sodium hydroxide, lauric acid, 1,2-butanediol and oleylamine were obtained from Acros, and 1,2 tetradecanediol and hydrated ruthenium chloride were obtained from Sigma-Aldrich (ref.

Sigma Aldrich 84050). All the raw chemicals were used without additional purification.

Preparation of Co nanorods:

Cobalt nanowires were produced by the polyol process according to a previously reported procedure. [START_REF] Soumare | Kinetically controlled synthesis of cobalt nanorods with high magnetic coercivity[END_REF] Cobalt laurate was prepared by mixing equimolar aqueous solutions of cobalt acetate and sodium laurate. The pink precipitate was washed with deionized water and dried overnight at 50°C to remove the excess water. The cobalt nanorods were prepared by reduction of cobalt laurate in a basic solution of 1,2butanediol. A suspension of cobalt(II) laurate (8×10 -2 mol.L -1 ) was dispersed in a solution containing sodium hydroxide (7.5×10 -2 mol.L -1 ) in 1,2-butanediol. Ruthenium chloride was added to the medium to control the nucleation step ([Ru]/[Co] = 2.5%). The suspension was heated to 175°C for 30 min under mechanical stirring (speed 80 rpm). The solution turned black, indicating cobalt reduction. Then, the cobalt suspension was cooled to room temperature.

Preparation of Co@CoSb nanorods: 10 mL of a suspension of Co nanorods in 1,2butanediol (0.08 mol.L -1 ) were taken, and the Co powder was isolated after washing several times with chloroform and absolute ethanol. Then, the resulting Co powder was transferred into a three-neck round-bottom flask containing 20 mL of oleylamine with the appropriate amounts of antimony acetate, Sb(CH3CO2)3, and 1,2 tetradecanediol (TDD). The reaction mixture was heated to 250°C for 30 min. Next, the black-brown mixture was cooled to room temperature. Absolute ethanol was added at room temperature, and a black material was precipitated and isolated by centrifugation (10000 rpm). Then, the black powder was isolated after several washing with absolute ethanol.

In all experiments, the Co amount remained constant (0.8 mmol), and the Sb:TDD molar ratio was 3. Three Sb:Co compositions were targeted by varying the Sb amount. Sample CoSb_8 (Sb:Co = 0.125): 29.9 mg (0.1 mmol) of antimony acetate, Sb(CH3CO2)3 and 69.1 mg (0.3 mmol) of 1,2 tetradecanediol were added to 0.8 mmol of Co nanorods dispersed in oleylamine.

Sample CoSb_4 (Sb:Co = 0.25): 59.8 mg (0.2 mmol) of Sb(CH3CO2)2 and 138.2 mg (0.6 mmol) of 1,2 tetradecanediol were introduced for the reaction. Sample CoSb_2 (Sb:Co = 0.5): 119.6 mg (0.4 mmol) of Sb(CH3CO2)2 and 276.4 mg (1.2 mmol) of 1,2 tetradecanediol were introduced for the reaction.

Preparation CoSb nanoparticles:

In a typical experiment, 35.7 mg (0.1 mmol) of Co(acac)3 and 28.9 mg (0.1 mmol) of Sb(CH3CO2)3 were added to 20 mL of oleylamine and stirred vigorously until all the reagents were completely dissolved. The color of the solution became dark green. Then, the reaction was heated at 250°C for 30 min, which resulted a black colloid. The reaction mixture was allowed to cool at room temperature, and ethanol was added to this mixture. The black powder was precipitated, washed several times with absolute ethanol, collected by centrifugation and dried under air prior to characterization. In a second synthesis, 69.1 mg (0.3 mmol) of 1,2 tetradecanediol was added to the starting mixture.

Annealing experiments: To carry out the annealing experiment, the Co@CoSb powders were placed in a ceramic boat and transferred into a furnace. The annealing experiment was carried out under forming gas (i.e., Ar + H2 (7%)) for 1 h at various temperatures (i.e., 250°C, 300°C and 400°C). Then, the powders were allowed to cool to room temperature under Ar gas and used for further characterization.

Consolidation:

The Co@CoSb nanorods were consolidated into bulk materials to investigate the possibility of preparing bulk permanent magnets. The consolidation studies were carried out in two different ways involving cold compaction and hot pressing. For cold compaction, a uniaxial hydraulic press that was equipped with a 1.7 T electromagnet was used. The direction of the magnetic field was perpendicular to the pressing direction. In addition, an electromagnet was used to create "green bodies (pre-aligned nanorods)", which were used for hot compaction. The measured densities of the consolidated materials were calculated from their weight and volume. The theoretical densities were calculated according to the Co@CoSb chemical compositions, and possible organic compounds were neglected. The packing densities were calculated from the ratios of the measured and theoretical densities of the samples. Hot compaction of the green bodies was performed at 180°C under a pressure of 150 MPa for 2 min.

Characterization:

The transmission electron microscopy (TEM) characterizations were performed using a JEOL 1400 microscope operating at 120 kV. High-resolution transmission electron microscopy (HRTEM) images and scanning transmission electron microscopy (STEM) -energy dispersive X-ray (EDX) mapping were acquired on a JEOL 2100F field emission transmission electron microscope that operated at 200 kV. To prepare the TEM samples, the metal nanopowder was redispersed in chloroform by sonication for approximately, 15 min and then, 2 μL of this suspension was placed on a carbon-coated copper grid and dried under vacuum. The X-ray diffraction measurements were carried out using a PANalytical X'Pert Pro diffractometer that was equipped with an X'celerator detector using Co Kα radiation (λ = 1.7889 Å). All the measurements were carried out in a 2θ range of 25-85 o with a 0.067 o step size and 300 s per step. The magnetic properties of the powders of randomly oriented core-shell Co@CoSb nanorods were investigated up to 3T using a Quantum Design Physical Property Measurement System (PPMS) with a vibrating sample magnetometer (VSM) configuration. The magnetic characterizations of the compacted samples were performed with a Metis pulse magnetometer. The demagnetization corrections were performed using the shape and dimensions of the consolidated products. Full hysteresis measurements were performed in an external field interval of -3.6 to -3.6 T. The magnetic measurements of the bulk magnets were performed with the applied field parallel to the direction of the magnetic field used for rod alignment during (CP) or before (HP) consolidation.

RESULTS AND DISCUSSION

Formation of CoSb alloy nanostructures. The powders prepared by the reaction of 5 mM of Co(acac)3 and 5 mM of Sb(CH3CO2)3 in hot oleylamine were analyzed by TEM and X-ray diffraction (XRD). When the reaction mixture was heated to 250°C for 30 min, the XRD pattern of the final powder exhibited peaks corresponding to the β-CoSb alloy [START_REF] Ishida | The Co-Sb (Cobalt-Antimony System)[END_REF] with a NiAs structure (jcpds file n° 33-0097) along with peaks that were assigned to antimony oxide (Sb2O3, jcpds file n° 05-0534) (Fig. 1). When the same reaction was carried out in the presence of 1,2 tetradecanediol (15 mM), the powder XRD pattern exhibited only reflections corresponding to CoSb, demonstrating that the formation of antimony oxide was completely inhibited (Fig. 1). The TEM images showed agglomerated nanoplatelets (supplementary information, Fig. S1). Reduction of Co(acac)3 in oleylamine has been previously employed to produced small Co nanoparticles. [START_REF] Dugay | Charge transport and interdot coupling tuned by the tunnel barrier length in assemblies of nanoparticles surrounded by organic ligands[END_REF] Here, we demonstrated that hot oleylamine can also reduce antimony acetate. However, to avoid antimony oxide formation, the addition of tetradecanediol was required. The effect of tetradecanediol can be interpreted in two ways.

First, TDD may be a stronger reducing agent than oleylamine, and second, as an α-diol, TDD may form an alkoxide at high temperatures with the Sb 3+ cations, preventing the formation of Sb oxide. Interestingly, phase separation leading to pure Sb and Co NPs did not occur, and the binary CoSb alloy was easily obtained. Kieslich et al. previously demonstrated that the thermodecomposition of Co2(CO)8 at 280°C in the presence of Sb nanoparticles leads to binary CoSb particles. [START_REF] Kieslich | Solution Synthesis of Nanoparticular Binary Transition Metal Antimonides[END_REF] We confirmed that Co and Sb easily form alloys using a hightemperature liquid-phase process.

Co@CoSb nanorod synthesis via reaction of antimony acetate with Co NRs

Effect of the reaction temperature Based on our results obtained for the synthesis of CoSb nanoparticles, we investigated coating anisotropic Co nanorods with a CoSb shell using TDD as a reducing agent. To favor the heterogeneous growth of Sb at the surface of the Co NRs and prevent self-nucleation, we lowered the reaction temperature and used a Sb/Co ratio of 1/4 and a reaction time of 30 min. At 150°C, Sb2O3 nanoparticles precipitated next to the hcp Co nanorods, as shown by the TEM image and XRD pattern (Fig. 2a,d). This result suggests that this temperature allows for nucleation of Sb2O3 nanoparticles but is not sufficient to reduce the Sb(III) species. At 200°C, the Co nanorods appeared to evolve, and darker contrast and cubic facets were observed in the TEM image (Fig. 2b). Small particles were still observed. The formation of

Effect of the Sb/Co ratio

To increase the rate of the reaction and ensure total reduction of the Sb(III) species, the reaction conditions were chosen to be 250°C for 30 min. The TEM images and XRD patterns of the powders synthesized with Sb/Co molar ratios varying between 1/8 and 1/2 are shown in figure 3. Under these conditions, the precipitation of Sb2O3 particles was not observed, which was confirmed by XRD and TEM analyses. The TEM images indicated the preservation of the anisotropic morphology of the nanoparticles regardless of the Sb amount added to the reaction. For low Sb/Co ratios (≤ 1/4), the coating is fairly inhomogeneous, and completely covered rods as well as naked rods can be observed. In addition, intermediate states consisting of small islands were observed at the Co NR surface (Fig. 3a-b). An Sb/Co ratio of 1/2 was required to obtain completely covered rods embedded in a continuous CoSb shell. The XRD patterns were indexed as a mixture of hcp Co and CoSb, and the relative intensity of the CoSb peaks increased with the initial Sb/Co ratio (Fig. 3d). For a coating with a Sb/Co ratio of 1/4, comparison of figures 2c and 3b indicates that a more homogeneous coating was achieved when the reaction was carried out at a lower temperature.

Chemical analysis

The Sb and Co contents in the final powder were determined based on energy dispersive Xray analysis on large areas that was measured with scanning electron microscopy. The Sb/Co ratio in the final powder was always 1.5 times higher than that in the starting mixture (Tab.

(l)

Microstructure XRD line broadening can provide microstructural information that is averaged over billions of particles. For the Co NRs prepared by the polyol process, the XRD line broadening is strongly dependent on the (hkil) indexes. The (0002) line is always much narrower than the (10-10) line, which demonstrates a crystallographic coherence that is higher along the c axis than perpendicular to the c axis. This characteristic indicates that the rod growth axis is parallel to the crystallographic c axis. [START_REF] Soumare | Kinetically controlled synthesis of cobalt nanorods with high magnetic coercivity[END_REF][START_REF] Viau | Highly crystalline cobalt nanowires with high coercivity prepared by soft chemistry[END_REF] To follow the variation in the mean crystallite size of the hcp-Co core and the ß-CoSb shell, the XRD patterns of the Co@CoSb rods were fitted using pseudo-Voight profiles (Fig. 4a). The crystallite sizes for different lines of the hcp-Co and ß-CoSb phases of the Co@CoSb pattern as a function of increasing Sb content are plotted in figure 4b. The mean crystallite size (L(0002)) calculated from the (0002) line broadening was higher than the crystallite size (L(10-10)) calculated from the (10-10) line broadening.

This observation confirms that the shape anisotropy of the parent Co NRs was preserved after CoSb coating. For the CoSb shell, no clear anisotropy of the crystallites was detected. The mean crystallite sizes calculated for the first three more intense reflections (i.e., (10-11), (10-12) and (11-20)) of the ß-CoSb phase were very close (i.e., in the range 13-20 nm).

Therefore, the CoSb shell was polycrystalline, and an epitaxial relationship between CoSb and the parent Co rod was not observed. Thermal stability and magnetic properties of the Co@CoSb nanorods. To investigate the high-temperature stability of the Co@CoSb nanorods, annealing from 250°C to 400°C under forming gas was carried out for 1 h. Figure S4 in the supplementary information shows the room temperature XRD patterns of the Co50@(Co0.5Sb0.5)50 powders that were obtained after annealing at various temperatures. No apparent change was observed, and the reflections due to both hcp Co and CoSb were observed without any variation in the relative intensities. No additional phase appeared even after annealing at 400°C. The same observation was performed for the other Co@CoSb compositions. The effect of annealing on the morphology of the Co@CoSb nanorods was studied by TEM (Fig. S5 of supplementary information).

Although no significant difference was observed between the raw Co@CoSb particles and those annealed at 300°C, the particles appeared to be more agglomerated after annealing at 400°C. However, their anisotropic morphology appears to be preserved. Therefore, 400°C is The texture of the Co hcp phase was examined in more detail to follow any variation in the anisotropy of the Co cores. The crystallite sizes calculated from the (10-10), ( 0002) and (10-11) line broadening in the Co50@(Co0.5Sb0.5)50 sample that was annealed at different temperatures are shown in figure 7. The corresponding XRD patterns are provided in the supplementary information (Fig. S7). The crystallite sizes of the Co hcp phase were nearly constant (Fig. 7), confirming that the anisotropy of the Co cores was preserved during annealing even up to 400°C. The crystallite size of the β-CoSb phase increased only slightly due to annealing at 300°C (Fig. 7). After annealing at 400°C, the crystallite sizes doubled (Fig. 7), indicating strong modification of the shell texture that is in agreement with the coalescence observed in the TEM images (Fig. S5). The same trends were observed for the Co70@(Co0.5Sb0.5)30 powders (see supplementary information Fig. S7 andS8).

L (nm)

T (°C)

L(10-10) L(0002) Co-hcp β-CoSb
The room temperature magnetization loops M(H) for different Co@CoSb powders that were annealed under forming gas are shown in figure 8. In each case, the remanence to saturation ratio was 0.5, which is the value expected for a randomly oriented anisotropic particle assembly. The coercivity of the Co NRs depends on their aspect ratio and crystallinity. [START_REF] Pousthomis | Localized Magnetization Reversal Processes in Cobalt Nanorods with Different Aspect Ratios[END_REF] The coercivities of the parent Co NRs and the Co@CoSb powders were 3.1 kOe and 3.1 -3.4 kOe, respectively (Table 2). Therefore, the Co NR coating with CoSb did not alter the coercivity. The magnetic measurement confirmed that the anisotropy of the hcp Co core was preserved during the coating and annealing processes. Therefore, surface modification of the Co nanorods with CoSb enhanced their thermal stability. A similar annealing experiment was performed on the uncoated Co nanorods and indicated that they were stable only up to 200°C (the anisotropic structure is lost above this temperature). [START_REF] Ait Atmane | High temperature structural and magnetic properties of cobalt nanorods[END_REF] The spontaneous magnetization per gram of sample (Ms) decreased as the CoSb content in the Co@CoSb composition increased (Table 2). CoSb is a paramagnetic compound, [START_REF] Amornpitoksuk | Structural and magnetic properties of the ternary solid solution between CoSb and Fe1+δSb[END_REF] and only the ferromagnetic Co cores contribute to the magnetization at room temperature. The theoretical Ms of the Co@CoSb powders, which is expressed in emu.g -1 , was calculated as the product of the hcp Co weight percent and the bulk Co spontaneous magnetization (Ms(Co) = 160 emu.g -1 ). The experimental values for the Co70@(CoSb)30 and Co50@(CoSb)50 samples were slightly lower than the expected values (78% and 84%, respectively). This result may be due to the presence of carbon at the surface of the particles due to a low annealing temperature, by minor diffusion of Co into the CoSb phase during the annealing process that could lower the magnetization, or by magnetic disorder at the Co/CoSb interface (spin canting). Consolidation of the Co@CoSb nanorods. Bulk magnets were obtained by cold and hot consolidation of the Co70@(CoSb)30 nanorods (Fig. 9). Their properties are summarized in table 3. The cold-pressed sample exhibited the highest packing density (56%), which was induced by an applied pressure of 1.5 GPa. A lower pressure of 150 MPa was applied during the hot compaction, which results in a lower density (46%). The Co@CoSb nanorods tend to create agglomerates, and an applied external magnetic field of 1.7 T was not sufficiently strong to disentangle these agglomerates and create a perfect alignment. The Mr/Ms ratio was higher in the hot-compacted sample (60%). The high pressure used for the cold-pressed sample disturbed the alignment of the nanorods and decreased the Mr/Ms ratio (46%). The coercivity of the two consolidated samples was equal to 3.1 kOe, which is the same as that measured for the Co70@(CoSb)30 nanorods prior to compaction (Tab. 2). Therefore, the cobalt core was preserved during cold compaction under 1.5 GPa and hot compaction at 180°C. The cobalt core sintering was avoided due to the thin CoSb shell. The compacted samples exhibited the properties of a permanent magnet, and figure 9 shows a sample strongly attached to a vertical steel plate. The energy product of the hot-compacted sample was equal to 10 kJ.m -3 . This value is lower than the energy product of aligned nanorods. An improvement in this value requires better alignment of the Co@CoSb rods to increase the Mr/Ms and the squareness of the magnetization curve. Co core agglomeration and preserves their shape anisotropy and magnetic properties. The consolidation studies demonstrated that macroscopic magnets can be prepared from the Co@CoSb nanorods. The magnetic measurements indicated that the integrity of the anisotropic cobalt core was preserved even after compaction at 1.5 GPa. The highest packing density was obtained for the cold-compacted samples where the highest pressure was applied.

Nevertheless, our results indicate that to achieve the best magnetic properties, hot compaction should be used on pre-aligned nanorods. A higher packing density and higher degree of alignment of the nanorods are required to further improve the magnet performance.

ACKNOWLEDGEMENT

L (nm) T (°C)

. Room temperature magnetization loop of a magnet made by the hot compaction of Co70@(Co0.5Sb0.5)30 nanorods (measurement with a pulse magnetometer). The magnetization curve was measured with the applied magnetic field parallel to the field direction that was applied to pre-align the rod before compaction.

Figure 1 .

 1 Figure 1. XRD pattern of powders prepared by reaction of an equimolar mixture of Co(acac)3 (5 mM) and Sb(CH3CO2)3 (5 mM) in oleylamine at 250°C for 30 min (a) in the absence of TDD and (b) in the presence of TDD (15 mM).

  the β-CoSb alloy at the surface of the Co rods was confirmed by XRD. Extending the reaction time to 2 h leads to the disappearance of Sb2O3 along with an increasing formation of the CoSb alloy (Fig.2d). The modification of the Co rod surface was observed in the TEM image (Fig.2c).These results suggest that the growth of the CoSb shell at the surface of the Co rods proceeded through a two-step process as follows: i) nucleation of Sb2O3 particles in solution followed by ii) their redissolution and reduction of Sb(III) species to form the CoSb alloy at the rod surface.

Figure 2 .

 2 Figure 2. (a-c) TEM images of the particles obtained by reaction of antimony(III) acetate with Co nanorods in oleylamine at (a) 150°C for 30 min, (b) 200°C for 30 min, and (c) 200°C for 2 h ( Sb/Co atomic ratio of 1/4). The scale bars represent 100 nm. (d) X-ray diffraction pattern of powders from (a), (b) and (c).

3 Figure 3 .

 33 Figure 3. (a-c) TEM images of the particles obtained by reaction of antimony(III) acetate with Co nanorods in oleylamine at 250°C for 30 min with various Sb/Co atomic ratios: (a)

1 ,

 1 and Fig.S2of supplementary materials). This observation suggests partial dissolution of the cobalt rods concomitantly with CoSb alloy growth. Local EDS analysis was performed using scanning transmission electron microscopy (STEM-EDS) to confirm the chemical composition in the core and shell regions of the Co@CoSb rods.

Figure 4

 4 Figure4shows the HAADF images of the Co/CoSb nanorods and the corresponding Co, Sb, and combined chemical mappings inferred from STEM-EDS analysis. A core-shell microstructure was confirmed by the maximum intensity of the Co content being located in the center of the rod and the Sb content being located on the edge. The shell appeared nearly continuous around the inner cobalt rod, and its thickness increased when the Sb amount in the reaction increased. The presence of an inner Co core and a shell consisting of a stoichiometric CoSb alloy was confirmed by local EDS analysis. Figure4mshows the emission spectra obtained from the center and edge of a Co/CoSb nanorod prepared with a Sb/Co ratio of 1/2.The corresponding Co-Sb compositions were determined to be Co75Sb25 at the center and Co55Sb45 at the edge, showing that the edge composition was very close to the stoichiometry of the intermetallic compound expected from the XRD pattern. As the core-shell texture was established, the chemical composition of the Co/CoSb samples is given as Cox@(Co0.5Sb0.5)y in table 1. For the same parent Co NRs, we followed the variation in the internal Co rod diameter (dCo) and the CoSb shell thickness (eCoSb) as a function of the Sb/Co ratio. When the Sb/Co ratio varied from 1/8 to 1/2, dCo decreased from 22 to 14 nm, and eCoSb increased from 5 to 15 nm (Tab. 1).

Figure 4 .

 4 Figure 4. STEM-HAADF images and EDS chemical mapping of the Co@CoSb particles prepared by reaction of Sb III acetate with Co NRs: (a)-(d) Sb/Co ratio = 1/8, (e)-(h) Sb/Co ratio = 1/4, and (i)-(l) Sb/Co ratio = 1/2. The scale bar represents 20 nm. (m) EDS spectra recorded at the center and on the edge of a single Co@CoSb rod (Sb/Co ratio = 1/2).

Figure 6

 6 Figure6shows a high-resolution electron microscopy image of a Co@CoSb NR prepared with a Sb/Co ratio of 1/4. A lattice fringe spacing that corresponds to the CoSb {hkil} planes was observed. The CoSb shell was polycrystalline with two different crystallographic orientations based on the numerical diffraction patterns. FigureS3(see supplementary materials) shows two additional examples of HRTEM images for Co@CoSb NRs prepared under the same conditions. The lattice fringes corresponding to the CoSb {10-11} planes were observed in both cases that spread across the entire area. However, their orientations with respect to the rod axis were different, confirming the polycrystallinity of the CoSb shell.The analysis of HRTEM images of Co@CoSb with a thicker shell, which was prepared with a Sb/Co ratio of 1/2, was difficult due to the superposition of the CoSb crystals in a different zone axis.

Figure 5 .Figure 6 .

 56 Figure 5. (a) Line analysis of the XRD pattern of the Co70@(Co0,5Sb0.5)30 nanorods in a 2θ range of 45-60°. (b) Evolution of the (0002) and (10-10) crystallite sizes of the hcp Co and (10-11), (10-12) and (11-20) crystallite sizes of the β-CoSb as a function of the Sb content.

  most likely the onset temperature of sintering of the CoSb alloy, leading to the coalescence of nanorods.

Figure 7 .

 7 Figure 7. Crystallite size of the Co50@(Co0.5Sb0.5)50 particles measured after annealing under forming gas at different temperature for the Co hcp phase perpendicular and parallel to the c axis calculated from the (10-10) and (0002) line broadening, respectively, and for the(10-11),(10-12) and(11-20) reflections of the β-CoSb phase. The fit of the corresponding XRD patterns is provides in the supplementary materials (Fig.S6).

Figure 8 .

 8 Figure 8. Room temperature magnetization loop of the Co@CoSb powders annealed under forming gas at 300°C: (a) Co70@(Co0.5Sb0.5)30, (b) Co50@(Co0.5Sb0.5)50, and (c) Co14@(Co0.5Sb0.5)86.

Figure 9 .Table 3 . 1 CONCLUSION

 931 Figure 9. Bulk magnet obtained by hot compaction of Co70@(Co0.5Sb0.5)30 nanorods (150 MPa, 180°C).

  This work was supported by the European Commission for the REFREEPERMAG FP7 project (EU NMP3-SL-2012-280670).ASSOCIATED CONTENTSupporting Information for Publication in file cm-2016-01196c SI.pdf, including TEM images of CoSb NPs, EDX analysis results on Co@CoSb rods, complementary HRTEM images, TEM and XRD of Co@CoSb rods after annealing at different temperatures, M(H) loop of consolidated Co@CoSb magnet.

Figure S1 .

 S1 Figure S1. TEM images of CoSb NPs prepared by the reduction of a mixture of antimony acetate and cobalt acetylacetonate in a solution of oleylamine containg tetradecanediol.

Figure S2 . 5 Figure S3 .Figure S7 .Figure S8 .

 S25S3S7S8 Figure S2. Sb/Co atomic ratio measured in the powders prepared by reaction of antimony(III) acetate with Co nanorods vs the Sb/Co ratio in the starting mixtures.

Table 1 .

 1 Chemical composition and mean diameter (dtotal) of the Co/CoSb samples prepared by reaction of antimony(III) acetate with Co nanorods in oleylamine at 250°C for 30 min with various Sb/Co atomic ratios. The diameter of the inner core (dCo) and the thickness of the CoSb shell (eCoSb), which were determined from STEM-EDS analysis, are also listed.

	Samples	Global compo. (at. %)	Core-Shell compo. (at. %)	dCo	eCoSb	dtotal
		Targeted	Measured	Cox@(Co0.5Sb0.5)y	(nm)	(nm)	(nm)
	Sb/Co = 1/8	Co89Sb11	Co85Sb15	Co70@(Co0.5Sb0.5)30	22	5	32
	Sb/Co = 1/4	Co80Sb20	Co75Sb25	Co50@(Co0.5Sb0.5)50	18	8	34
	Sb/Co = 1/2	Co67Sb33	Co57Sb43	Co14@(Co0.5Sb0.5)86	14	15	44

Table 2 .

 2 Room temperature coercivity and spontaneous magnetization of Co@CoSb powders after annealing at 300°C for 1 h under forming gas. The theoretical Ms was calculated as the product of the weight percent of hcp Co and the bulk Co magnetization.

	Co@CoSb (at. %)	Co70@(CoSb)30	Co50@(CoSb)50	Co14@(CoSb)86
	Co@CoSb (weight %)	Co60.3@(CoSb)39.7	Co39.5@(CoSb)60.5	Co9.6@(CoSb)90.4
	Hc (kOe)	3.1	3.4	3.4
	Ms(emu.g -1 ) exp. / theor.	75 / 96.5	53 / 63	8.5 / 15

AUTHORS INFORMATION

Corresponding author *E-mail: guillaume.viau@insa-toulouse.fr

Supplementary Information

Co@CoSb core-shell nanorods: from chemical coating at the nanoscale to macroscopic consolidation CoSb (11-20)


Martin Hoesli

Richard Malle

Commercial Real Estate Prices and Covid-19

Keywords: Commercial real estate prices, Covid-19, Pandemic, Office, Retail, Hospitality JEL Codes: R33, G12, G2

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Introduction

Commercial real estate is an attractive asset class for institutional investors. It offers stable income returns, its returns are weakly correlated with the returns of financial assets and the empirical evidence also points to its inflation-hedging effectiveness [START_REF] Falkenbach | Real estate investing: Opportunities and challenges[END_REF]. Against this background, several studies have documented the benefits of holding real estate assets in mixed-asset portfolios [START_REF] Hoesli | International evidence on real estate as a portfolio diversifier[END_REF][START_REF] Mackinnon | Real estate for the long term: The effect of return predictability on long-horizon allocations[END_REF][START_REF] Delfim | Real estate in mixed-asset portfolios for various investment horizons[END_REF].

The Covid-19 pandemic has affected some of the major factors influencing commercial real estate pricing. Rental streams have been significantly impacted. According to the World Tourism Barometer, for instance, international tourist arrivals declined by 65% during the first half-year of 2020 [START_REF] Unwto | World Tourism Barometer[END_REF]. This, together with a sharp decline in business travel, has led to much depressed hotel occupancy levels and often hotel closures. Retail incomes have also been severely hit by the pandemic. Due to lockdowns, in-store shopping was not possible in many locations, which led to the further increase in online retailing which had been growing fast even prior to the pandemic. The work from home policies that have been implemented in many regions have proved the effectiveness of such work organization, leading to concerns regarding the future of office space demand and hence of rental levels. The uncertainties on cash flows are likely to have led to an increase in risk premia and a decrease in growth expectations. These effects were mitigated by decreases in interest rates, leading to quite stable yields so far, at least in prime locations.

Several studies have analyzed the early-stage effects of the pandemic on commercial real estate prices. As such, the results cannot be extrapolated easily to gauge the long-term effects of Covid-19 on real estate prices. [START_REF] Ling | A first look at the impact of Covid-19 on commercial real estate prices: Asset-level evidence[END_REF] examine how U.S. Real Estate Investment Trust (REIT) returns are related to a geographically weighted exposure of their underlying assets to Covid-19 growth. They report a negative reaction of returns to such exposure. Firms focused on retail and residential properties react more negatively among all sectors, while healthcare and technology sectors are positively correlated with exposure to Covid-19 growth. [START_REF] Xie | Commercial Real Estate Prices in France and Italy (Desmoothed) Sources: MSCI and authors' calculations[END_REF] find negative effects of proximity to Covid-19 cases on the returns of Hong Kong real estate firms. Markets also perceive the risk to be higher in commercial buildings than in residential properties. [START_REF] Milcheva | Volatility and the cross-section of real estate equity returns during Covid-19[END_REF] reports that the effect of Covid-19 is associated with steep declines in international real estate security returns and an increase in risk. Retail is found to have the highest sensitivity to Covid-19, whereas healthcare has the lowest sensitivity. Finally, van Dijk et al. (2020) use liquidity impacts at the onset of the pandemic to infer future price changes on direct markets. They predict that the retail sector will be most badly hurt with price declines in the 14-19% range. The industrial sector is predicted to be slightly more resistant with price drops in the 10-15% range. [START_REF] Duca | The resilience and realignment of house prices in the era of Covid-19[END_REF] focus on the effects of Covid-19 on housing markets. They report variance in the evolution of house prices across countries, with locations depending heavily on tourism showing declining house prices while prices elsewhere have generally continued to increase. They argue that the lack of a negative impact on house prices largely owes to the low interest rate environment and the smaller relative effect of the pandemic on upper income households, but also to behavioral factors. The latter relate to beliefs about the duration of the economic crisis that has been triggered by the pandemic and the prospects for recovery, the sentiment that housing is a good investment in the long run, and declines in the number of assets for sale due to loss aversion behavior.

In this article, we seek to provide a better understanding of the reactions of commercial real estate prices during the Covid-19 crisis. We use direct real estate data for the U.S. and three European countries. We also use data for listed real estate in Europe. Given the greater efficiency of the listed market, such indices should make it possible to uncover more rapidly any changes in the pricing of commercial real estate assets. We focus on differences across property types. Caveats concerning direct real estate price indices that should be borne in mind are discussed. We also provide a discussion of the likely path of commercial real estate prices in the future, with again a focus on differences across property types.

Our analyses reveal that the hospitality and retail sectors have been affected the most by the crisis. Structural changes that are taking place in the retail market are also visible.

Although the office market has not been affected as badly as retail properties and hotels, price decreases remain significant and are likely indicative of shifts in work patterns, in particular the prospects for the development of work from home policies. Property prices in other sectors, in particular in the residential and logistics sectors, have been less affected, if at all, by the crisis. Using the current economic forecasts, we maintain that prices for commercial real estate assets are likely to increase in some market segments, in particular prime offices, for the years to come. However, as far as non-prime assets are concerned, decreases in values could occur in the short-to medium-term. The prospects for logistics and residential real estate are usually good, whereas the picture is more nuanced for retail properties and hotels.

In the future, we believe that the characteristics of assets should play a stronger role in their valuation.

The remainder of the paper is structured as follows. The next section highlights some caveats to bear in mind when using direct real estate indices. The following section discusses changes in commercial real estate prices and their driving factors since the onset of the Covid-19 crisis. We then turn to providing an outlook for the economy and commercial real estate markets. Some concluding remarks are provided in a final section.

Caveats Concerning Direct Real Estate Price Indices

A customary way of producing commercial real estate indices is to rely on the regular appraisal of a set of representative properties. The capital change component of the index is calculated on the basis of the change in the estimated property values, taking into account any capital expenditures incurred during the period. Much research has documented the smoothing and lagging of those types of indices [START_REF] Delfim | Robust desmoothed real estate returns[END_REF]. If a proper adjustment is not undertaken, real estate risk will be understated and turning points assessed incorrectly. The MSCI indices that we use below for the U.K., France and Italy are appraisalbased indices.

Another increasingly popular way of tracking price changes on commercial real estate markets is to rely on the repeat sales method [START_REF] Bailey | A regression method for real estate price index construction[END_REF]. This approach relies on transactions data, rather than appraisal data, and focuses on the price changes of properties that have been sold at least twice during a given period. A regression framework is used and the estimated coefficients on the time variables make it possible to construct the index.

Potential biases with this approach include the facts that the quality of properties can change between two sales (for instance, if there is a refurbishment) and the number of repeat sales on a given market can be limited. This latter concern is exacerbated in a crisis period given that transaction volumes tend to decline markedly. The CoStar indices that we use below for the U.S. market are constructed using this approach.

Direct real estate indices suffer also from the so-called escrow lag, i.e., the fact that prices recorded at a given point in time are likely to have been agreed upon several months before. This interval is largely related to the time that is needed for the due diligence process to take place. [START_REF] Hoesli | Do public real estate returns really lead private returns?[END_REF], for instance, use a 90-day escrow lag for their analyses of U.S. commercial real estate markets. Quarterly index values as of June 2020, and in some cases even September 2020, are affected by prices which had been agreed upon prior to the start of the pandemic. Also, given the crisis, index values are based on the evidence provided by limited volumes of transactions. Hence, caution has to be exercised as to not over interpret direct real estate price changes. This is compounded by the short history of commercial real estate price changes since the beginning of the pandemic.

As mentioned above, we use CoStar indices for the U.S. The indices are price indices and are available at the quarterly frequency for the various sectors. For the U.K., France and Italy, we use the capital return indices produced by MSCI. The U.K. indices are at the monthly frequency, whereas the indices for the other two countries are annual. As a result of being calculated on the basis of appraisal-based indices, capital returns suffer from smoothing and hence exhibit high levels of serial correlation. For the various property types, the serial correlation of U.K. commercial real estate capital returns is in the range from 0.511 (hotels) to 0.883 (industrial). For France, the figures are in the range from 0.336 (office) to 0.575 (retail).

For Italy, the lowest serial correlation is 0.544 (retail) and the highest correlation is 0.672 (industrial). Returns are desmoothed using a reverse filter [START_REF] Geltner | Estimating market values from appraised values without assuming an efficient market[END_REF]. The aim is to reduce the level of serial correlation to a level that is comparable to that observed for returns calculated by means of transaction-based indices. For U.K. returns, we use a desmoothing parameter of 0.3 for hotels and 0.7 for the other types of properties. This results in desmoothed capital return series with serial correlations between 0.167 (hotels) and 0.265 (offices). We use a desmoothing parameter of 0.4 for France and 0.3 for Italy. The desmoothed capital returns have a serial correlation from 0.073 (offices in Italy) to 0.365 (industrial in Italy).

Real Estate Prices and Covid-19

Although much alarming news concerning Covid-19 was emerging from China during January 2020, most people in Europe and the U.S. started realizing in February only that the disease was likely to affect their regions too. By the second half of February, there were a number of confirmed cases in several European countries. On March 11, the World Health Organization declared the crisis a pandemic. These developments led to many countries enforcing restrictions to the movement of people across countries and sometimes also within countries. Some countries introduced strict lockdowns; France and Italy being good examples. This had immediate effects on the income generated by many types of properties, in particular retail and hospitality real estate. In-store sales were often abruptly stopped and much retailing activity switched to online, leading to a jump in rent non-payments and an acceleration of the trend towards online retailing that had started several years ago. The increased demand from e-commerce companies in search of hubs to dispatch goods to customers benefited logistics properties. The effects on prices were exacerbated by the low completed and under construction supply of properties in main locations. As for hotels, both leisure and business travel were significantly affected, leading to low occupancy rates or hotel closures. It is also likely that risk premia were affected, as they were at the onset of the global financial crisis [START_REF] Duca | The other (commercial) real estate boom and bust: The effects of risk premia and regulatory capital arbitrage[END_REF].

Focusing first on U.S. commercial real estate prices (Figure 1), we observe some variance in price developments at the onset of the Covid-19 crisis. Whereas hospitality and retail prices declined at the start of the pandemic, no effect can be seen for the other sectors, even when data up to the first quarter of 2021 are taken into consideration. While hospitality prices have been declining for a full year now, retail prices are now higher than their levels prior to the pandemic, suggesting that in the U.S. the hospitality sector has been the hardest hit by the crisis. Figure 2 Industrial values briefly declined at the onset of the pandemic and then started rising again, suggesting that this sector benefited from the structural changes that have been taking place since the start of the pandemic. For France and Italy (Figure 3), both retail and office values were negatively affected by the crisis, whereas industrial values were stable. Caution should be exercised, however, as the indices for those two countries are annual and hence only one data point is available since the pandemic started (that for year 2020).

Price variations are generally consistent with changes in pricing fundamentals for the various market segments. Office values have been so far quite resistant, with limited decreases in rental incomes and pretty stable yields. In Paris, for instance, prime rents have increased slightly, but so have vacancy rates (BNP Paribas Real Estate, 2021b). Average rents, however, have declined. Despite increasing risk and lower investment activity, yields for prime and core assets decreased slightly as a result of lower risk-free interest rates and flight to quality (BNP Paribas Real Estate, 2021a). As of 2020Q4, net prime office yields in Paris were at 2.70%. For London, yields and prime rents have been stable; however, values declined somewhat due to higher vacancy rates.

The effects of the lockdowns were felt most acutely in the retail and hotel sectors, with large decreases in rental incomes. Increases in the risk premia more than offset any benefits from declining risk-free interest rates. This led to those two sectors being most affected by the pandemic. Industrial and logistics values were more resistant and sometimes even increased in the last few months. Rental incomes were not affected severely by the pandemic, whereas yields decreased slightly or were stable. This is consistent with a pattern of retailing activity shifting more significantly to e-commerce and the demand for logistics space to supply the goods.

Those conclusions hold by and large when the various sectors of the securitized real estate market are analyzed. Such analysis is useful as much research has shown that, given its greater information efficiency, the listed real estate market reacts more quickly to changes in fundamentals than does the direct market [START_REF] Hoesli | Are REITs real estate: Evidence from international sector level data[END_REF][START_REF] Ling | Returns and information transmission dynamics in public and private real estate markets[END_REF][START_REF] Hoesli | Does listed real estate behave like direct real estate? Updated and broader evidence[END_REF]. Hence, the listed real estate market should uncover any price developments before the direct market.

We use the EPRA Developed Europe price indices for six sectors (Figure 4). The indices are set at 100 as of February 21, 2020. This is the last trading day before the first lockdowns were enforced in some Northern Italy municipalities on February 23 and it was getting quite clear by then that Europe was headed for a crisis. Figure 4 shows that there are marked differences across sectors. The price of lodging/resort properties dropped the most at the onset of the crisis (the drop was almost 80%). The loss in value stabilized thereafter at about 50% and then was reduced in November 2020 with the positive announcements concerning the development of a vaccine. As of mid-June 2021, the loss in value relative to the value on February 21, 2020 is about 30%. The pricing reflects the uncertainties about the future of the travel industry, in particular whether business travel will ever revert to its pre-crisis levels. The retail sector was not affected quite as badly as the hotel sector, but drops in value continued for several months, reflecting the structural changes that are occurring in the sector. As is the case for hotels, the encouraging news regarding the development of a vaccine led to significant price gains in November.

The office sector was not as affected as the hotel and retail sectors, but decreases in values still amounted to more than 40% at the onset of the pandemic. This is likely due to the expectation that there will be less demand for office space even after the pandemic as a significant share of work from home is likely to remain. As in any crisis, there is also a fear of rising unemployment levels. It could also be due to some extent to the securitized real estate market overestimating the post Covid-19 shifts in demand. The healthcare sector was slightly less affected by the crisis, but prices still dropped by 35% at the onset on the crisis. Price losses had stabilized at about 10% by the end of the time period. The losses in value are likely a reflection of the classical medical activity being significantly affected as many non-essential surgeries did not take place during the pandemic. There were also high mortality rates in retirement homes. Many families whose elderly members were on a waiting list to enter such facilities opted not to accept an offer to move into such homes as rooms became available, leading to lower occupancy rates. Although prices dropped significantly at the onset of the crisis in the residential and industrial sectors, they had more than regained their losses by mid-June 2021. Demand for residential space is strong, with signs of some households seeking larger units as a result of the crisis [START_REF] Duca | The resilience and realignment of house prices in the era of Covid-19[END_REF]. As discussed above, the demand for logistics space has often increased as a consequence of the shift from physical retailing to online shopping, leading to logistics prices being 15% higher in mid-June 2021 than at the start of the crisis.

Economic and Property Outlook

This section analyzes trends in Gross Domestic Product (GDP) and interest rates as well as forecasts for commercial real estate markets. Our timeframe is from 2021 to 2025 to simulate a medium-term trend in the wake of the Covid-19 crisis, in line with the forecasts available to us. For GDP and interest rate forecasts, we use Consensus Forecasts published by Consensus Economics Inc. ( 2021), which provides an average of forecasts from the main international economic institutions. In April and October of each year, five-year forecasts are published for the main economic components. For real estate, we use BNP Paribas Real Estate sources, which generate forecasts from the economic scenarios issued by Consensus Forecasts.

GDP affects the profitability of real estate markets, mainly by influencing the demand for office space [START_REF] Benjamin | Returns and risk on real estate and other investments[END_REF]. For most countries, GDP contracted very sharply during 2020. From 2021 onwards, assuming a better control of the pandemic, increased immunity of the population through vaccination and the easing of health restrictions, economic growth is expected to be positive. However, most European countries will only return to their pre-crisis (2019) wealth generation levels in 2022-2023, while for the U.S. this could be as soon as 2021 thanks to a faster restart in activity. As such, after the major shock to the economy in 2020, this base case scenario points to a robust trend in terms of employment, investment and consumption from 2021 onwards. Of course, this consensus scenario entails uncertainty and could be adjusted either upward to reflect higher levels of consumer and company confidence, or downward in case of a resurgence of the pandemic.

Our property forecasts below are built from the base case economic scenario.

Interest rates play a fundamental role in the valuation of investment properties [START_REF] Johnson | Monetary policy and real estate returns[END_REF]. Indeed, the initial yield can be calculated as the sum of the risk-free yield, generally reflected by the 10-year government bond yield, and a risk premium. Moreover, investment properties are valued customarily using the income approach, with a discount rate that also depends on the risk-free rate (see, e.g., [START_REF] Brueggeman | Real Estate Finance and Investments[END_REF]. Ten-year bond yields hit a historical low at the end of 2020 (-0.3% in France, 0.2% in the U.K., 0.5% in Italy and 0.9% in the U.S.). Countries became very heavily indebted during 2020 to help finance the impact of health measures and support economic activity (International Monetary Fund, 2020). These government-issued debts were largely absorbed by Quantitative Easing policies, which can be defined as an expansionary monetary policy aimed at buying financial instruments, such as government bonds, to stimulate the economy [START_REF] Joyce | Quantitative easing and unconventional monetary policy -an introduction[END_REF]. From 2021, Consensus Forecasts sees government bond yields rising, albeit still only to historically low levels.

Like bond yields, initial prime office yields changed little in Europe from 2019 to 2020 in countries such as the U.K., France and Italy (Figure 5). The crisis could have led to a sharp increase in prime office yields, as occurred during the 2009 financial crisis, but the resilience can be explained by several factors. First, demand for prime office assets has been fueled by the abundance of liquidity and the quest for guaranteed assets. Another consideration is that the yield gap, calculated as the difference between initial real estate yields and the risk-free rate, reached sufficient levels in 2020 to compensate for the additional risk following the Covid-19 crisis. As of the end of 2020, the yield gap stood at 3.3%, 3.0% and 2.7% in London, Paris and Milan, respectively, compared to averages of 1.9%, 2.3% and 1.1% over the 2010-2019 period. This is why, according to BNP Paribas Real Estate data, initial prime office yields over the 2021-2025 period should contract in Paris (-20 basis points), Milan (-30 basis points), and even London (-35 basis points) thanks to a clearer overall situation (including less uncertainty around Brexit). However, the yields for riskier office assets (which may have shortcomings in terms of location, quality of the premises, or rental status) are set to increase, although this is hard to quantify due to both the lack of recorded transactions and the heterogeneous nature of these assets.

Figure 6 shows the prime office rent trend for London, Paris and Milan. The robust economic growth expected from 2021 as well as controlled supply levels in the main European business districts should lead to resiliency in prime rents, despite the economic and health context. From 2020 to 2025, prime rents are expected to remain pretty stable in Paris and Milan (+3% and +0% respectively, after increasing by +13% in Paris and +25% in Milan over the 2015-2020 period), while they are forecast to increase by 12% in London. Applying a simple direct capitalization valuation method, i.e., calculating the ratio between the expected change in rents and the change in yields for prime office assets from 2020 to 2025, gives us an estimate of the possible trajectory of asset values. Prices could record a surge in London (+24%), while increasing more moderately in Paris (+12%) and Milan (+10%).

These outlooks may seem counterintuitive given the steep decline in rental demand and the rise in teleworking that has reduced the need for office space since the Covid-19 crisis.

Nevertheless, the rigidity of leases is a factor that limits supply and rental variations as companies must wait for their leases to end before relocating and possibly reducing their floor areas. Furthermore, it is exceedingly hard to gauge the degree to which teleworking will be used once the health crisis is over, and this will depend on each company in terms of its location, size, business sector and corporate culture. Rents and prices in non-prime locations are likely to see a more downward trend over the next five years, with some outlying areas less sought after or even shunned by companies.

For retail, investors may therefore demand higher risk premiums, implying higher initial yields and lower prices until the pandemic is fully under control. The fall in the value of prime retail assets could be reversed when the health measures come to an end and once domestic and international demand is restored close to pre-crisis levels. This could be in 2022 or 2023, considering the delayed and uncertain effect between the lifting of travel constraints and the return of distant consumers. We note that the initial prime yields of street-level stores are showing a historical anomaly insofar as they are equal to or greater than those of offices, with differences of 0 basis points in the U.K., +20 basis points in Italy and +45 basis points in France at the end of 2020, compared to average differences of -43, -19 and -29 basis points, respectively, over the 2010-2019 period. As yields are expected to be very low for 10-year bonds from 2021 to 2025 and with further declines for initial prime office yields, the initial yields for prime street-level stores may diminish considerably, which would boost the capital values of these assets. On the other hand, an increase in the capital values of shopping centers and out-of-town retail looks more doubtful following the health crisis. In contrast to high streets, the stock of shopping centers and out-of-town retail has been rising continuously, with growth estimated at an annual average of 1% in the U.K., 1.7% in Italy and 1.8% in France over the 2010-2019 period (Source: BNP Paribas Real Estate, PMA).

The outlook for the hotel market depends on many of the same factors as retail. The continued health measures together with their immediate and delayed effects on domestic and international travel, both professional and private, will dampen hotel performances.

Hotels with the best locations and the most stars should be revived following the health crisis.

At the other end of the scale, some facilities are likely to close given the length of the crisis. Also, much doubt remains concerning the extent to which domestic and international professional travel will recover, as many trips may be replaced by remote meetings, to save time and travel costs for companies. As such, many hotels may never revert to their pre-crisis occupancy rates.

The capital value trend for industrial assets may well be upward over the 2021-2025 period, after having been resistant in 2020. This situation observed during the Covid-19 crisis differs greatly from that during the financial crisis of 2009, when prices fell sharply as in the U.K. (-41% between July 2007 and July 2009, Figure 2). There will be two lasting differences for logistics after 2020, namely controlled levels of supply in most markets and continued strong demand from retail and particularly e-commerce players. Prime rents are therefore expected to rise in Europe from 2021 to 2025 (annual average of +1.5% per year), after having significantly increased already from 2015 to 2020 (+2.5%). Initial prime yields in logistics may narrow further in the coming years throughout Europe (-35 basis points expected between 2020 and 2025). This is all the more remarkable in that these yields were already at historically low levels at the end of 2020 (-148 basis points compared to their 2010-2019 average, vs. -112 and -27 basis points for offices and retail, respectively). These assumptions suggest that the price of prime logistics assets in Europe may rise by +16% from 2020 to 2025.

Finally, residential real estate prices have been stable, in both Europe and the U.S., despite a fall in sales volumes due to the repeated health constraints throughout 2020. The main pre-crisis fundamentals remain unaffected and should underpin demand in most cities, namely rising revenues and demographics, as well as very favorable borrowing conditions with interest rates low over the long term. Furthermore, as people have been spending longer at home since the outbreak of Covid-19, their wellbeing there has become more important.

Households may therefore assign greater value to properties according to their characteristics (location, nearby services and retail, sunshine, size, number of rooms, etc.), even earmarking more of their budget to spending on the home, which will underpin price rises.

Conclusions

Our analyses reveal that the hospitality and retail markets and to a lesser extent the office sector have been affected the most by the Covid-19 pandemic. Prices have been more resistant in other sectors. Although the pandemic has clearly affected commercial real estate prices, it is important to bear in mind that the available data since the outburst of the pandemic cover a short period only and hence caution has to be exercised not to overinterpret the price changes.

The future of commercial real estate prices will largely depend on the state of the macroeconomy and whether the vaccines and drugs prove effective in eradicating the pandemic. So far, aided by strong fiscal and monetary policy counter measures, macroeconomies have generally performed better than the dire economic forecasts made in the spring of 2020. However, it is unclear how much longer governments will be able to borrow to support businesses and households through the downturn. It is also unclear how much more and how fast shopping patterns, work from home policies and business travel will evolve in the years ahead. Stated differently, it is hard to disentangle the permanent effects of the pandemic on the real estate sector from the transitory ones.

Bearing those uncertainties in mind, we maintain that valuations of real estate assets will take varying trajectories in the future. Overall, prospects are better for industrial and residential real estate and to a lesser extent offices than for retail and hotel properties. Prices are likely to depend more heavily and more narrowly on the type and location of the assets, while current and future rental conditions should be taken into account to a greater extent in the risk premium. Consequently, financial markets may struggle to value listed property companies, and such valuations may become more volatile over the next few years. The many uncertainties concerning the long-term effects of the pandemic on commercial real estate values certainly leave researchers and the real estate industry with many important and interesting issues to grapple with in the years ahead.

  depicts the desmoothed capital return indices for the U.K. Values in all sectors except the industrial sector have been significantly affected by the crisis. Retail values have been declining since the beginning of 2018, with the crisis accelerating the drop.

Figure

  Figure 1: Commercial Real Estate Prices in the U.S.